Mathematical and Computational Applications | An Open Access Journal from MDPI

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<option value="brainsci" > Brain Sciences </option> <option value="buildings" > Buildings </option> <option value="businesses" > Businesses </option> <option value="carbon" > C </option> <option value="cancers" > Cancers </option> <option value="cardiogenetics" > Cardiogenetics </option> <option value="catalysts" > Catalysts </option> <option value="cells" > Cells </option> <option value="ceramics" > Ceramics </option> <option value="challenges" > Challenges </option> <option value="ChemEngineering" > ChemEngineering </option> <option value="chemistry" > Chemistry </option> <option value="chemproc" > Chemistry Proceedings </option> <option value="chemosensors" > Chemosensors </option> <option value="children" > Children </option> <option value="chips" > Chips </option> <option value="civileng" > CivilEng </option> <option value="cleantechnol" > Clean Technologies (Clean Technol.) </option> <option value="climate" > Climate </option> <option value="ctn" > Clinical and Translational Neuroscience (CTN) </option> <option value="clinbioenerg" > Clinical Bioenergetics </option> <option value="clinpract" > Clinics and Practice </option> <option value="clockssleep" > Clocks & Sleep </option> <option value="coasts" > Coasts </option> <option value="coatings" > Coatings </option> <option value="colloids" > Colloids and Interfaces </option> <option value="colorants" > Colorants </option> <option value="commodities" > Commodities </option> <option value="complications" > Complications </option> <option value="compounds" > Compounds </option> <option value="computation" > Computation </option> <option value="csmf" > Computer Sciences & Mathematics Forum </option> <option value="computers" > Computers </option> <option value="condensedmatter" > Condensed Matter </option> <option value="conservation" > Conservation </option> <option value="constrmater" > Construction Materials </option> <option value="cmd" > Corrosion and Materials Degradation (CMD) </option> <option value="cosmetics" > Cosmetics </option> <option value="covid" > COVID </option> <option value="crops" > Crops </option> <option value="cryo" > Cryo </option> <option value="cryptography" > Cryptography </option> <option value="crystals" > Crystals </option> <option value="cimb" > Current Issues in Molecular Biology (CIMB) </option> <option value="curroncol" > Current Oncology </option> <option value="dairy" > Dairy </option> <option value="data" > Data </option> <option value="dentistry" > Dentistry Journal </option> <option value="dermato" > Dermato </option> <option value="dermatopathology" > Dermatopathology </option> <option value="designs" > Designs </option> <option value="diabetology" > Diabetology </option> <option value="diagnostics" > Diagnostics </option> <option value="dietetics" > Dietetics </option> <option value="digital" > Digital </option> <option value="disabilities" > Disabilities </option> <option value="diseases" > Diseases </option> <option value="diversity" > 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value="engproc" > Engineering Proceedings </option> <option value="entropy" > Entropy </option> <option value="environsciproc" > Environmental Sciences Proceedings </option> <option value="environments" > Environments </option> <option value="epidemiologia" > Epidemiologia </option> <option value="epigenomes" > Epigenomes </option> <option value="ebj" > European Burn Journal (EBJ) </option> <option value="ejihpe" > European Journal of Investigation in Health, Psychology and Education (EJIHPE) </option> <option value="fermentation" > Fermentation </option> <option value="fibers" > Fibers </option> <option value="fintech" > FinTech </option> <option value="fire" > Fire </option> <option value="fishes" > Fishes </option> <option value="fluids" > Fluids </option> <option value="foods" > Foods </option> <option value="forecasting" > Forecasting </option> <option value="forensicsci" > Forensic Sciences </option> <option value="forests" > Forests </option> <option value="fossstud" > Fossil 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</option> <option value="geometry" > Geometry </option> <option value="geosciences" > Geosciences </option> <option value="geotechnics" > Geotechnics </option> <option value="geriatrics" > Geriatrics </option> <option value="glacies" > Glacies </option> <option value="gucdd" > Gout, Urate, and Crystal Deposition Disease (GUCDD) </option> <option value="grasses" > Grasses </option> <option value="hardware" > Hardware </option> <option value="healthcare" > Healthcare </option> <option value="hearts" > Hearts </option> <option value="hemato" > Hemato </option> <option value="hematolrep" > Hematology Reports </option> <option value="heritage" > Heritage </option> <option value="histories" > Histories </option> <option value="horticulturae" > Horticulturae </option> <option value="hospitals" > Hospitals </option> <option value="humanities" > Humanities </option> <option value="humans" > Humans </option> <option value="hydrobiology" > Hydrobiology </option> <option value="hydrogen" > Hydrogen </option> <option value="hydrology" > Hydrology </option> <option value="hygiene" > Hygiene </option> <option value="immuno" > Immuno </option> <option value="idr" > Infectious Disease Reports </option> <option value="informatics" > Informatics </option> <option value="information" > Information </option> <option value="infrastructures" > Infrastructures </option> <option value="inorganics" > Inorganics </option> <option value="insects" > Insects </option> <option value="instruments" > Instruments </option> <option value="iic" > Intelligent Infrastructure and Construction </option> <option value="ijerph" > International Journal of Environmental Research and Public Health (IJERPH) </option> <option value="ijfs" > International Journal of Financial Studies (IJFS) </option> <option value="ijms" > International Journal of Molecular Sciences (IJMS) </option> <option value="IJNS" > International Journal of Neonatal Screening (IJNS) </option> <option value="ijpb" > International Journal of Plant Biology (IJPB) </option> <option value="ijt" > International Journal of Topology </option> <option value="ijtm" > International Journal of Translational Medicine (IJTM) </option> <option value="ijtpp" > International Journal of Turbomachinery, Propulsion and Power (IJTPP) </option> <option value="ime" > International Medical Education (IME) </option> <option value="inventions" > Inventions </option> <option value="IoT" > IoT </option> <option value="ijgi" > ISPRS International Journal of Geo-Information (IJGI) </option> <option value="J" > J </option> <option value="jal" > Journal of Ageing and Longevity (JAL) </option> <option value="jcdd" > Journal of Cardiovascular Development and Disease (JCDD) </option> <option value="jcto" > Journal of Clinical & Translational Ophthalmology (JCTO) </option> <option value="jcm" > Journal of Clinical Medicine (JCM) </option> <option value="jcs" > Journal of Composites Science (J. Compos. Sci.) </option> <option value="jcp" > Journal of Cybersecurity and Privacy (JCP) </option> <option value="jdad" > Journal of Dementia and Alzheimer's Disease (JDAD) </option> <option value="jdb" > Journal of Developmental Biology (JDB) </option> <option value="jeta" > Journal of Experimental and Theoretical Analyses (JETA) </option> <option value="jfb" > Journal of Functional Biomaterials (JFB) </option> <option value="jfmk" > Journal of Functional Morphology and Kinesiology (JFMK) </option> <option value="jof" > Journal of Fungi (JoF) </option> <option value="jimaging" > Journal of Imaging (J. Imaging) </option> <option value="jintelligence" > Journal of Intelligence (J. Intell.) </option> <option value="jlpea" > Journal of Low Power Electronics and Applications (JLPEA) </option> <option value="jmmp" > Journal of Manufacturing and Materials Processing (JMMP) </option> <option value="jmse" > Journal of Marine Science and Engineering (JMSE) </option> <option value="jmahp" > Journal of Market Access & Health Policy (JMAHP) </option> <option value="jmp" > Journal of Molecular Pathology (JMP) </option> <option value="jnt" > Journal of Nanotheranostics (JNT) </option> <option value="jne" > Journal of Nuclear Engineering (JNE) </option> <option value="ohbm" > Journal of Otorhinolaryngology, Hearing and Balance Medicine (JOHBM) </option> <option value="jop" > Journal of Parks </option> <option value="jpm" > Journal of Personalized Medicine (JPM) </option> <option value="jpbi" > Journal of Pharmaceutical and BioTech Industry (JPBI) </option> <option value="jor" > Journal of Respiration (JoR) </option> <option value="jrfm" > Journal of Risk and Financial Management (JRFM) </option> <option value="jsan" > Journal of Sensor and Actuator Networks (JSAN) </option> <option value="joma" > Journal of the Oman Medical Association (JOMA) </option> <option value="jtaer" > Journal of Theoretical and Applied Electronic Commerce Research (JTAER) </option> <option value="jvd" > Journal of Vascular Diseases (JVD) </option> <option value="jox" > Journal of Xenobiotics (JoX) </option> <option value="jzbg" > Journal of Zoological and Botanical Gardens (JZBG) </option> <option value="journalmedia" > Journalism and Media </option> <option value="kidneydial" > Kidney and Dialysis </option> <option value="kinasesphosphatases" > Kinases and Phosphatases </option> <option value="knowledge" > Knowledge </option> <option value="labmed" > LabMed </option> <option value="laboratories" > Laboratories </option> <option value="land" > Land </option> <option value="languages" > Languages </option> <option value="laws" > Laws </option> <option value="life" > Life </option> <option value="limnolrev" > Limnological Review </option> <option value="lipidology" > Lipidology </option> <option value="liquids" > Liquids </option> <option value="literature" > Literature </option> <option value="livers" > Livers </option> <option value="logics" > Logics </option> <option value="logistics" > Logistics </option> <option value="lubricants" > Lubricants </option> <option value="lymphatics" > Lymphatics </option> <option value="make" > Machine Learning and Knowledge Extraction (MAKE) </option> <option value="machines" > Machines </option> <option value="macromol" > Macromol </option> <option value="magnetism" > Magnetism </option> <option value="magnetochemistry" > Magnetochemistry </option> <option value="marinedrugs" > Marine Drugs </option> <option value="materials" > Materials </option> <option value="materproc" > Materials Proceedings </option> <option value="mca" selected='selected'> Mathematical and Computational Applications (MCA) </option> <option value="mathematics" > Mathematics </option> <option value="medsci" > Medical Sciences </option> <option value="msf" > Medical Sciences Forum </option> <option value="medicina" > Medicina </option> <option value="medicines" > Medicines </option> <option value="membranes" > Membranes </option> <option value="merits" > Merits </option> <option value="metabolites" > Metabolites </option> <option value="metals" > Metals </option> <option value="meteorology" > Meteorology </option> <option value="methane" > Methane </option> <option value="mps" > Methods and Protocols (MPs) </option> <option value="metrics" > Metrics </option> <option value="metrology" > Metrology </option> <option value="micro" > Micro </option> <option value="microbiolres" > Microbiology Research </option> <option value="micromachines" > Micromachines </option> <option value="microorganisms" > Microorganisms </option> <option value="microplastics" > Microplastics </option> <option value="minerals" > Minerals </option> <option value="mining" > Mining </option> <option value="modelling" > Modelling </option> <option value="mmphys" > Modern Mathematical Physics </option> <option value="molbank" > Molbank </option> <option value="molecules" > Molecules </option> <option value="mti" > Multimodal Technologies and Interaction (MTI) </option> <option value="muscles" > Muscles </option> <option value="nanoenergyadv" > Nanoenergy Advances </option> <option value="nanomanufacturing" > Nanomanufacturing </option> <option value="nanomaterials" > Nanomaterials </option> <option value="ndt" > NDT </option> <option value="network" > Network </option> <option value="neuroglia" > Neuroglia </option> <option value="neurolint" > Neurology International </option> <option value="neurosci" > NeuroSci </option> <option value="nitrogen" > Nitrogen </option> <option value="ncrna" > Non-Coding RNA (ncRNA) </option> <option value="nursrep" > Nursing Reports </option> <option value="nutraceuticals" > Nutraceuticals </option> <option value="nutrients" > Nutrients </option> <option value="obesities" > Obesities </option> <option value="oceans" > Oceans </option> <option value="onco" > Onco </option> <option value="optics" > Optics </option> <option value="oral" > Oral </option> <option value="organics" > Organics </option> <option value="organoids" > Organoids </option> <option value="osteology" > Osteology </option> <option value="oxygen" > Oxygen </option> <option value="parasitologia" > Parasitologia </option> <option value="particles" > Particles </option> <option value="pathogens" > Pathogens </option> <option value="pathophysiology" > Pathophysiology </option> <option value="pediatrrep" > Pediatric Reports </option> <option value="pets" > Pets </option> <option value="pharmaceuticals" > Pharmaceuticals </option> <option value="pharmaceutics" > Pharmaceutics </option> <option value="pharmacoepidemiology" > Pharmacoepidemiology </option> <option value="pharmacy" > Pharmacy </option> <option value="philosophies" > Philosophies </option> <option value="photochem" > Photochem </option> <option value="photonics" > Photonics </option> <option value="phycology" > Phycology </option> <option value="physchem" > Physchem </option> <option value="psf" > Physical Sciences Forum </option> <option value="physics" > Physics </option> <option value="physiologia" > Physiologia </option> <option value="plants" > Plants </option> <option value="plasma" > Plasma </option> <option value="platforms" > Platforms </option> <option value="pollutants" > Pollutants </option> <option value="polymers" > Polymers </option> <option value="polysaccharides" > Polysaccharides </option> <option value="populations" > Populations </option> <option value="poultry" > Poultry </option> <option value="powders" > Powders </option> <option value="proceedings" > Proceedings </option> <option value="processes" > Processes </option> <option value="prosthesis" > Prosthesis </option> <option value="proteomes" > Proteomes </option> <option value="psychiatryint" > Psychiatry International </option> <option value="psychoactives" > Psychoactives </option> <option value="psycholint" > Psychology International </option> <option value="publications" > Publications </option> <option value="qubs" > Quantum Beam Science (QuBS) </option> <option value="quantumrep" > Quantum Reports </option> <option value="quaternary" > Quaternary </option> <option value="radiation" > Radiation </option> <option value="reactions" > Reactions </option> <option value="realestate" > Real Estate </option> <option value="receptors" > Receptors </option> <option value="recycling" > Recycling </option> <option value="rsee" > Regional Science and Environmental Economics (RSEE) </option> <option value="religions" > Religions </option> <option value="remotesensing" > Remote Sensing </option> <option value="reports" > Reports </option> <option value="reprodmed" > Reproductive Medicine (Reprod. Med.) </option> <option value="resources" > Resources </option> <option value="rheumato" > Rheumato </option> <option value="risks" > Risks </option> <option value="robotics" > Robotics </option> <option value="ruminants" > Ruminants </option> <option value="safety" > Safety </option> <option value="sci" > Sci </option> <option value="scipharm" > Scientia Pharmaceutica (Sci. Pharm.) </option> <option value="sclerosis" > Sclerosis </option> <option value="seeds" > Seeds </option> <option value="sensors" > Sensors </option> <option value="separations" > Separations </option> <option value="sexes" > Sexes </option> <option value="signals" > Signals </option> <option value="sinusitis" > Sinusitis </option> <option value="smartcities" > Smart Cities </option> <option value="socsci" > Social Sciences </option> <option value="siuj" > Société Internationale d’Urologie Journal (SIUJ) </option> <option value="societies" > Societies </option> <option value="software" > Software </option> <option value="soilsystems" > Soil Systems </option> <option value="solar" > Solar </option> <option value="solids" > Solids </option> <option value="spectroscj" > Spectroscopy Journal </option> <option value="sports" > Sports </option> <option value="standards" > Standards </option> <option value="stats" > Stats </option> <option value="stresses" > Stresses </option> <option value="surfaces" > Surfaces </option> <option value="surgeries" > Surgeries </option> <option value="std" > Surgical Techniques Development </option> <option value="sustainability" > Sustainability </option> <option value="suschem" > Sustainable Chemistry </option> <option value="symmetry" > Symmetry </option> <option value="synbio" > SynBio </option> <option value="systems" > Systems </option> <option value="targets" > Targets </option> <option value="taxonomy" > Taxonomy </option> <option value="technologies" > Technologies </option> <option value="telecom" > Telecom </option> <option value="textiles" > Textiles </option> <option value="thalassrep" > Thalassemia Reports </option> <option value="therapeutics" > Therapeutics </option> <option value="thermo" > Thermo </option> <option value="timespace" > Time and Space </option> <option value="tomography" > Tomography </option> <option value="tourismhosp" > Tourism and Hospitality </option> <option value="toxics" > Toxics </option> <option value="toxins" > Toxins </option> <option value="transplantology" > Transplantology </option> <option value="traumacare" > Trauma Care </option> <option value="higheredu" > Trends in Higher Education </option> <option value="tropicalmed" > Tropical Medicine and Infectious Disease (TropicalMed) </option> <option value="universe" > Universe </option> <option value="urbansci" > Urban Science </option> <option value="uro" > Uro </option> <option value="vaccines" > Vaccines </option> <option value="vehicles" > Vehicles </option> <option value="venereology" > Venereology </option> <option value="vetsci" > Veterinary Sciences </option> <option value="vibration" > Vibration </option> <option value="virtualworlds" > Virtual Worlds </option> <option value="viruses" > Viruses </option> <option value="vision" > Vision </option> <option value="waste" > Waste </option> <option value="water" > Water </option> <option value="wild" > Wild </option> <option value="wind" > Wind </option> <option 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Mahtabi</strong>, </span><span class="inlineblock "><strong>Arash Ghasemi</strong>, </span><span class="inlineblock "><strong>Amirehsan Ghasemi</strong> and </span><span class="inlineblock "><strong>James C. Newman III</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(6), 110; <a href="https://doi.org/10.3390/mca29060110">https://doi.org/10.3390/mca29060110</a> - 25 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> In spectral/finite element methods, a robust and stable high-order polynomial approximation method for the solution can significantly reduce the required number of degrees of freedom (DOFs) to achieve a certain level of accuracy. In this work, a closed-form relation is proposed to approximate <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/110/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> In spectral/finite element methods, a robust and stable high-order polynomial approximation method for the solution can significantly reduce the required number of degrees of freedom (DOFs) to achieve a certain level of accuracy. In this work, a closed-form relation is proposed to approximate the Fekete points (AFPs) on arbitrary shape domains based on the singular value decomposition (SVD) of the Vandermonde matrix. In addition, a novel method is derived to compute the moments on highly complex domains, which may include discontinuities. Then, AFPs are used to generate compatible basis functions using SVD. Equations are derived and presented to determine orthogonal/orthonormal modal basis functions, as well as the Lagrange basis. Furthermore, theorems are proved to show the convergence and accuracy of the proposed method, together with an explicit form of the Weierstrass theorem for polynomial approximation. The method was implemented and some classical cases were analyzed. The results show the superior performance of the proposed method in terms of convergence and accuracy using many fewer DOFs and, thus, a much lower computational cost. It was shown that the orthogonal modal basis is the best choice to decrease the DOFs while maintaining a small Lebesgue constant when very high degree of polynomial is employed. <a href="/2297-8747/29/6/110">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/mca/special_issues/JN_Reddy ">Mathematical and Computational Approaches in Applied Mechanics: A Themed Issue Dedicated to Professor J.N. Reddy</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/110/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1528851"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1528851"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1528851" data-cycle-prev="#prev1528851" data-cycle-progressive="#images1528851" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1528851-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g001-550.jpg?1732531745" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1528851" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1528851-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g002-550.jpg?1732531746'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1528851-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g003-550.jpg?1732531748'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1528851-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g004-550.jpg?1732531749'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1528851-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g005-550.jpg?1732531750'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1528851-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g006-550.jpg?1732531752'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1528851-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g007-550.jpg?1732531754'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1528851-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g008-550.jpg?1732531756'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1528851-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g009-550.jpg?1732531756'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1528851-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g010-550.jpg?1732531757'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1528851-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g011-550.jpg?1732531758'><p>Figure 11</p></div></script></div></div><div id="article-1528851-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g001-550.jpg?1732531745" title=" <strong>Figure 1</strong><br/> <p>Application of the SVD-based approach of Equation (<a href="#FD10-mca-29-00110" class="html-disp-formula">10</a>) to candidate points (<b>a</b>) and selecting AFPs (<b>b</b>) on a concave domain.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/110'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g002-550.jpg?1732531746" title=" <strong>Figure 2</strong><br/> <p>The decay of the Generalized Fourier Coefficients (GFCs): dashed bars correspond to the orthogonal basis <math display="inline"><semantics> <mover accent="true"> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </semantics></math> and the solid bars correspond to the orthonormal basis <math display="inline"><semantics> <mover accent="true"> <mi>ψ</mi> <mo stretchy="false">˜</mo> </mover> </semantics></math>, which, according to Theorem 7, monotonically decrease.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/110'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g003-550.jpg?1732531748" title=" <strong>Figure 3</strong><br/> <p>The transformation of <math display="inline"><semantics> <mi mathvariant="sans-serif">Ω</mi> </semantics></math> to a bounded area near the origin. Here, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo form="prefix">tanh</mo> <mo>(</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> <mo>)</mo> <mo>=</mo> <mn>0.4621</mn> <mo>…</mo> <mo>.</mo> </mrow> </semantics></math> (<b>a</b>) Two-dimensional; (<b>b</b>) three-dimensional.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/110'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g004-550.jpg?1732531749" title=" <strong>Figure 4</strong><br/> <p>Comparison between SVD and QR (one iteration) approaches for finding AFPs: (<b>left</b>) the interpolation error versus polynomial degree and (<b>right</b>) various measures.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/110'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g005-550.jpg?1732531750" title=" <strong>Figure 5</strong><br/> <p>The <span class="html-italic">orthogonal</span> modal basis functions of Equation (<a href="#FD22-mca-29-00110" class="html-disp-formula">22</a>), evaluated on Chebyshev points. (<b>a</b>) <math display="inline"><semantics> <msub> <mover accent="true"> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> <mn>1</mn> </msub> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <msub> <mover accent="true"> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> <mn>2</mn> </msub> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <msub> <mover accent="true"> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> <mn>60</mn> </msub> </semantics></math>; (<b>d</b>) last mode, i.e., <math display="inline"><semantics> <msub> <mover accent="true"> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> <mn>400</mn> </msub> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/110'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g006-550.jpg?1732531752" title=" <strong>Figure 6</strong><br/> <p>The spectral filtering of <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>=</mo> <mo form="prefix">cos</mo> <mfenced separators="" open="(" close=")"> <mn>4</mn> <mi>π</mi> <msqrt> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> </msqrt> </mfenced> </mrow> </semantics></math> in <span class="html-italic">Q</span>-space by eliminating the higher-frequency orthogonal basis Equation (<a href="#FD26-mca-29-00110" class="html-disp-formula">26</a>). (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>400</mn> </mrow> </semantics></math>, i.e., <span class="html-italic">full rank</span>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>200</mn> </mrow> </semantics></math>, i.e., <span class="html-italic">half rank</span>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>360</mn> </mrow> </semantics></math>, i.e., <span class="html-italic">ninety percent rank</span>; (<b>d</b>) exact.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/110'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g007-550.jpg?1732531754" title=" <strong>Figure 7</strong><br/> <p>The first and the 200th basis functions of the <span class="html-italic">nodal</span> (<b>left column</b>) and <span class="html-italic">modal</span> (<b>right column</b>) approximate Fekete basis. <b>Top-left</b>: <math display="inline"><semantics> <msub> <mi>ψ</mi> <mn>1</mn> </msub> </semantics></math>, <b>bottom-left</b>: <math display="inline"><semantics> <msub> <mi>ψ</mi> <mn>200</mn> </msub> </semantics></math>, <b>top-right</b>: <math display="inline"><semantics> <msub> <mover accent="true"> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> <mn>1</mn> </msub> </semantics></math>, and <b>bottom-right</b>: <math display="inline"><semantics> <msub> <mover accent="true"> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> <mn>200</mn> </msub> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/110'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g008-550.jpg?1732531756" title=" <strong>Figure 8</strong><br/> <p>Comparison of the orthogonal modal basis functions (<math display="inline"><semantics> <mover accent="true"> <mi mathvariant="sans-serif">Ψ</mi> <mo stretchy="false">¯</mo> </mover> </semantics></math>) and RBFs in reconstructing the solution on two domains. (<b>Top</b> row) With the same DOF. (<b>Bottom</b> row) With same <math display="inline"><semantics> <msub> <mi>L</mi> <mn>2</mn> </msub> </semantics></math> error. <b>Left</b> column shows the RBFs; <b>right</b> column corresponds to the orthogonal modal basis functions <math display="inline"><semantics> <mover accent="true"> <mi mathvariant="sans-serif">Ψ</mi> <mo stretchy="false">¯</mo> </mover> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/110'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g009-550.jpg?1732531756" title=" <strong>Figure 9</strong><br/> <p>Sub-elemental resolution of six wavelengths of <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>=</mo> <mo form="prefix">sin</mo> <mo>(</mo> <mn>2</mn> <mi>π</mi> <mi>x</mi> <mo>)</mo> <mo form="prefix">sin</mo> <mo>(</mo> <mn>2</mn> <mi>π</mi> <mi>y</mi> <mo>)</mo> </mrow> </semantics></math> on a highly concave domain. As shown in the middle, the spectral accuracy corresponding to the optimal resolution is demonstrated.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/110'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g010-550.jpg?1732531757" title=" <strong>Figure 10</strong><br/> <p>Superlinear convergence of the modal basis on the concave T-shape domain. (<b>Left</b>) Reconstructed function using the 16th-order modal basis constructed on the AFPs. (<b>Right</b>) <math display="inline"><semantics> <msub> <mi>L</mi> <mn>2</mn> </msub> </semantics></math> error compared with the exact reconstruction.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/110'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00110/article_deploy/html/images/mca-29-00110-g011-550.jpg?1732531758" title=" <strong>Figure 11</strong><br/> <p>The spectra of <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>=</mo> <mo form="prefix">sin</mo> <mo>(</mo> <mi>π</mi> <mi>x</mi> <mo>)</mo> <mo form="prefix">sin</mo> <mo>(</mo> <mi>π</mi> <mi>y</mi> <mo>)</mo> </mrow> </semantics></math> on different convex/concave elements. (<b>Left</b>) Using the 7th-order orthogonal modal basis <math display="inline"><semantics> <mover accent="true"> <mi mathvariant="sans-serif">Ψ</mi> <mo stretchy="false">¯</mo> </mover> </semantics></math> on a quadrilateral element. (<b>Middle</b>) Using the 11th <math display="inline"><semantics> <mover accent="true"> <mi mathvariant="sans-serif">Ψ</mi> <mo stretchy="false">¯</mo> </mover> </semantics></math> on a hexagonal element. (<b>Right</b>) Using the 16th <math display="inline"><semantics> <mover accent="true"> <mi mathvariant="sans-serif">Ψ</mi> <mo stretchy="false">¯</mo> </mover> </semantics></math> on a T-shape element.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/110'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="extending-content content-ready"> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 3 pages, 194 KiB   </span> <a href="/2297-8747/29/6/109/pdf?version=1732513551" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Mathematical and Computational Modelling in Mechanics of Materials and Structures" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Editorial</span></div> <a class="title-link" href="/2297-8747/29/6/109">Mathematical and Computational Modelling in Mechanics of Materials and Structures</a> <div class="authors"> by <span class="inlineblock "><strong>Nicholas Fantuzzi</strong>, </span><span class="inlineblock "><strong>Francesco Fabbrocino</strong>, </span><span class="inlineblock "><strong>Marco Montemurro</strong>, </span><span class="inlineblock "><strong>Francesca Nanni</strong>, </span><span class="inlineblock "><strong>Qun Huang</strong>, </span><span class="inlineblock "><strong>José António Correia</strong>, </span><span class="inlineblock "><strong>Leonardo Dassatti</strong> and </span><span class="inlineblock "><strong>Michele Bacciocchi</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(6), 109; <a href="https://doi.org/10.3390/mca29060109">https://doi.org/10.3390/mca29060109</a> - 25 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-full inline"> The intersection of mathematics and computational modeling with the mechanics of materials and structural engineering continues to yield substantial advancements in both theoretical and applied domains [...] <a href="/2297-8747/29/6/109">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/mca/special_issues/Mech_Mater_Struct ">Mathematical and Computational Modelling in Mechanics of Materials and Structures</a>)<br/> </div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 25 pages, 1578 KiB   </span> <a href="/2297-8747/29/6/108/pdf?version=1732442566" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Optimizing Power Flow and Stability in Hybrid AC/DC Microgrids: AC, DC, and Combined Analysis" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Review</span></div> <a class="title-link" href="/2297-8747/29/6/108">Optimizing Power Flow and Stability in Hybrid AC/DC Microgrids: AC, DC, and Combined Analysis</a> <div class="authors"> by <span class="inlineblock "><strong>Ghanshyam Meena</strong>, </span><span class="inlineblock "><strong>Veerpratap Meena</strong>, </span><span class="inlineblock "><strong>Akhilesh Mathur</strong>, </span><span class="inlineblock "><strong>Vinay Pratap Singh</strong>, </span><span class="inlineblock "><strong>Ahmad Taher Azar</strong> and </span><span class="inlineblock "><strong>Ibrahim A. Hameed</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(6), 108; <a href="https://doi.org/10.3390/mca29060108">https://doi.org/10.3390/mca29060108</a> - 24 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> A microgrid (MG) is a unique area of a power distribution network that combines distributed generators (conventional as well as renewable power sources) and energy storage systems. Due to the integration of renewable generation sources, microgrids have become more unpredictable. MGs can operate <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/108/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> A microgrid (MG) is a unique area of a power distribution network that combines distributed generators (conventional as well as renewable power sources) and energy storage systems. Due to the integration of renewable generation sources, microgrids have become more unpredictable. MGs can operate in two different modes, namely, grid-connected and islanded modes. MGs face various challenges of voltage variations, frequency deviations, harmonics, unbalances, etc., due to the uncertain behavior of renewable sources. To study the impact of these issues, it is necessary to analyze the behavior of the MG system under normal and abnormal operating conditions. Two different tools are used for the analysis of microgrids under normal and abnormal conditions, namely, power flow and short-circuit analysis, respectively. Power flow analysis is used to determine the voltages, currents, and real and reactive power flow in the MG system under normal operating conditions. Short-circuit analysis is carried out to analyze the behavior of MGs under faulty conditions. In this paper, a review of power flow and short-circuit analysis algorithms for MG systems under two different modes of operation, grid-connected and islanded, is presented. This paper also presents a comparison of various power flow as well as short-circuit analysis techniques for MGs in tabular form. The modeling of different components of MGs is also discussed in this paper. <a href="/2297-8747/29/6/108">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/mca/special_issues/O70J996J9R ">Applied Optimization in Automatic Control and Systems Engineering</a>)<br/> </div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 18 pages, 2638 KiB   </span> <a href="/2297-8747/29/6/107/pdf?version=1732192107" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/6/107">Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation</a> <div class="authors"> by <span class="inlineblock "><strong>Youssri Hassan Youssri</strong> and </span><span class="inlineblock "><strong>Ahmed Gamal Atta</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(6), 107; <a href="https://doi.org/10.3390/mca29060107">https://doi.org/10.3390/mca29060107</a> - 21 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> This paper presents a novel numerical spectral scheme to handle the time-fractional KdV–Burgers’ equation, which is very important in both physics and engineering. The scheme basically uses the tau approach combined with Gegenbauer polynomials to provide accurate and stable numerical solutions. Instead of <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/107/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> This paper presents a novel numerical spectral scheme to handle the time-fractional KdV–Burgers’ equation, which is very important in both physics and engineering. The scheme basically uses the tau approach combined with Gegenbauer polynomials to provide accurate and stable numerical solutions. Instead of solving the differential problem together with the conditions, we solve a system of algebraic equations. The method can handle complex boundary conditions. Some numerical experiments are exhibited to demonstrate that this approach is highly efficient and produces results that are better than some existing numerical methods in the literature. This technique offers more advanced solutions for time-fractional problems in various fields. <a href="/2297-8747/29/6/107">Full article</a> </div> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/107/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1526233"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1526233"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1526233" data-cycle-prev="#prev1526233" data-cycle-progressive="#images1526233" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1526233-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/mca/mca-29-00107/article_deploy/html/images/mca-29-00107-g001-550.jpg?1732192238" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1526233" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1526233-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00107/article_deploy/html/images/mca-29-00107-g002-550.jpg?1732192240'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1526233-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00107/article_deploy/html/images/mca-29-00107-g003-550.jpg?1732192242'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1526233-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00107/article_deploy/html/images/mca-29-00107-g004-550.jpg?1732192243'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1526233-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00107/article_deploy/html/images/mca-29-00107-g005-550.jpg?1732192244'><p>Figure 5</p></div></script></div></div><div id="article-1526233-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00107/article_deploy/html/images/mca-29-00107-g001-550.jpg?1732192238" title=" <strong>Figure 1</strong><br/> <p>The absolute errors (<b>left</b>) and spectral solution (<b>right</b>) of Example 1 at <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>1.8</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/107'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00107/article_deploy/html/images/mca-29-00107-g002-550.jpg?1732192240" title=" <strong>Figure 2</strong><br/> <p>The absolute errors of Example 1 at different values of <math display="inline"><semantics> <mi>μ</mi> </semantics></math> when <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/107'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00107/article_deploy/html/images/mca-29-00107-g003-550.jpg?1732192242" title=" <strong>Figure 3</strong><br/> <p>The absolute errors of Example 2 at different values of <span class="html-italic">M</span> when <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/107'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00107/article_deploy/html/images/mca-29-00107-g004-550.jpg?1732192243" title=" <strong>Figure 4</strong><br/> <p>The absolute errors of Example 3 at different values of <span class="html-italic">M</span> when <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/107'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00107/article_deploy/html/images/mca-29-00107-g005-550.jpg?1732192244" title=" <strong>Figure 5</strong><br/> <p>The absolute errors (<b>left</b>) and spectral solution (<b>right</b>) of Example 3 at <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/107'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 23 pages, 463 KiB   </span> <a href="/2297-8747/29/6/106/pdf?version=1731922458" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Semantic Categories: Uncertainty and Similarity" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/6/106">Semantic Categories: Uncertainty and Similarity</a> <div class="authors"> by <span class="inlineblock "><strong>Ares Fabregat-Hernández</strong>, </span><span class="inlineblock "><strong>Javier Palanca</strong> and </span><span class="inlineblock "><strong>Vicent Botti</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(6), 106; <a href="https://doi.org/10.3390/mca29060106">https://doi.org/10.3390/mca29060106</a> - 16 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> This paper addresses understanding and categorizing language by using Markov categories to establish a mathematical framework for semantic concepts. This framework enables us to measure the semantic similarity between linguistic expressions within a given text. Furthermore, this approach enables the measurement and control <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/106/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> This paper addresses understanding and categorizing language by using Markov categories to establish a mathematical framework for semantic concepts. This framework enables us to measure the semantic similarity between linguistic expressions within a given text. Furthermore, this approach enables the measurement and control of uncertainty in language categorization and the creation of metrics for evaluating semantic similarity. We provide use cases to demonstrate how the proposed methods can be applied and computed, focusing on their interpretability and the universality of categorical constructions. This work contributes to the field by offering a novel perspective on semantic similarity and uncertainty metrics in language processing, generating criteria to automate their computation. <a href="/2297-8747/29/6/106">Full article</a> </div> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/106/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1522477"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1522477"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1522477" data-cycle-prev="#prev1522477" data-cycle-progressive="#images1522477" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1522477-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/mca/mca-29-00106/article_deploy/html/images/mca-29-00106-g001-550.jpg?1731922548" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1522477" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1522477-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00106/article_deploy/html/images/mca-29-00106-g002-550.jpg?1731922549'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1522477-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00106/article_deploy/html/images/mca-29-00106-g003-550.jpg?1731922550'><p>Figure 3</p></div></script></div></div><div id="article-1522477-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00106/article_deploy/html/images/mca-29-00106-g001-550.jpg?1731922548" title=" <strong>Figure 1</strong><br/> <p>Cone representing <math display="inline"><semantics> <msub> <mi mathvariant="script">L</mi> <mi>T</mi> </msub> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/106'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00106/article_deploy/html/images/mca-29-00106-g002-550.jpg?1731922549" title=" <strong>Figure 2</strong><br/> <p>Representation of <math display="inline"><semantics> <msub> <mi mathvariant="script">P</mi> <mi>T</mi> </msub> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/106'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00106/article_deploy/html/images/mca-29-00106-g003-550.jpg?1731922550" title=" <strong>Figure 3</strong><br/> <p>Depiction of <math display="inline"><semantics> <msub> <mi>F</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/106'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 13 pages, 436 KiB   </span> <a href="/2297-8747/29/6/105/pdf?version=1731892711" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Structural Stability of Pseudo-Parabolic Equations for Basic Data" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/6/105">Structural Stability of Pseudo-Parabolic Equations for Basic Data</a> <div class="authors"> by <span class="inlineblock "><strong>Yanping Wang</strong> and </span><span class="inlineblock "><strong>Yuanfei Li</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(6), 105; <a href="https://doi.org/10.3390/mca29060105">https://doi.org/10.3390/mca29060105</a> - 15 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> This article investigates the spatial decay properties and continuous dependence on the basic geometric structure. Assuming that the total potential energy is bounded and the homogeneous Dirichlet condition is satisfied on the side of the solution within the cylindrical domain, we establish an <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/105/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> This article investigates the spatial decay properties and continuous dependence on the basic geometric structure. Assuming that the total potential energy is bounded and the homogeneous Dirichlet condition is satisfied on the side of the solution within the cylindrical domain, we establish an auxiliary function related to the solution. By extending the data at the finite end forward, we can establish the continuous dependence on the perturbation of base data. <a href="/2297-8747/29/6/105">Full article</a> </div> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/105/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1521761"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1521761"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1521761" data-cycle-prev="#prev1521761" data-cycle-progressive="#images1521761" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1521761-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/mca/mca-29-00105/article_deploy/html/images/mca-29-00105-g001-550.jpg?1731892929" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1521761" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1521761-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00105/article_deploy/html/images/mca-29-00105-g002-550.jpg?1731892930'><p>Figure 2</p></div></script></div></div><div id="article-1521761-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00105/article_deploy/html/images/mca-29-00105-g001-550.jpg?1731892929" title=" <strong>Figure 1</strong><br/> <p>Cylindrical pipe R.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/105'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00105/article_deploy/html/images/mca-29-00105-g002-550.jpg?1731892930" title=" <strong>Figure 2</strong><br/> <p>Cylindrical pipe <math display="inline"><semantics> <msub> <mi>R</mi> <mi>f</mi> </msub> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/105'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 22 pages, 56577 KiB   </span> <a href="/2297-8747/29/6/104/pdf?version=1731391556" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Resolving Contrast and Detail Trade-Offs in Image Processing with Multi-Objective Optimization" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/6/104">Resolving Contrast and Detail Trade-Offs in Image Processing with Multi-Objective Optimization</a> <div class="authors"> by <span class="inlineblock "><strong>Daniel Molina-Pérez</strong> and </span><span class="inlineblock "><strong>Alam Gabriel Rojas-López</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(6), 104; <a href="https://doi.org/10.3390/mca29060104">https://doi.org/10.3390/mca29060104</a> - 11 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> This article addresses the complex challenge of simultaneously enhancing contrast and detail in an image, where improving one property often compromises the other. This trade-off is tackled using a multi-objective optimization approach. Specifically, the proposal’s model integrates the sigmoid transformation function and unsharp <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/104/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> This article addresses the complex challenge of simultaneously enhancing contrast and detail in an image, where improving one property often compromises the other. This trade-off is tackled using a multi-objective optimization approach. Specifically, the proposal’s model integrates the sigmoid transformation function and unsharp masking highboost filtering with the NSGA-II algorithm. Additionally, a posterior preference articulation is introduced to select three key solutions from the Pareto front: the maximum contrast solution, the maximum detail solution, and the knee point solution. The proposed technique is evaluated on a range of image types, including medical and natural scenes. The final solutions demonstrated significant superiority in terms of contrast and detail compared to the original images. The three selected solutions, although all are optimal, captured distinct characteristics within the images, offering different solutions according to field preferences. This highlights the method’s effectiveness across different types and enhancement requirements and emphasizes the importance of the proposed preferences in different contexts. <a href="/2297-8747/29/6/104">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/mca/special_issues/JNB5544SAC ">Numerical and Evolutionary Optimization 2024</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/104/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1518387"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1518387"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1518387" data-cycle-prev="#prev1518387" data-cycle-progressive="#images1518387" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1518387-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/mca/mca-29-00104/article_deploy/html/images/mca-29-00104-g001-550.jpg?1731391682" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1518387" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1518387-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00104/article_deploy/html/images/mca-29-00104-g002-550.jpg?1731391686'><p>Figure 2</p></div></script></div></div><div id="article-1518387-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00104/article_deploy/html/images/mca-29-00104-g001-550.jpg?1731391682" title=" <strong>Figure 1</strong><br/> <p>Comparison of sigmoid correction curves demonstrating the impact of varying parameters on image enhancement. (<b>a</b>) Effect of different <math display="inline"><semantics> <mi>α</mi> </semantics></math> values on the gradient of the sigmoid curve, influencing the contrast adjustment. (<b>b</b>) Impact of different (<math display="inline"><semantics> <mo>∆</mo> </semantics></math>) values on the midpoint of the sigmoid curve, affecting the balance between light and dark regions.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/104'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00104/article_deploy/html/images/mca-29-00104-g002-550.jpg?1731391686" title=" <strong>Figure 2</strong><br/> <p>The flowchart depicts the multi-objective optimization process for image enhancement, starting with the initialization of a random population of decision vectors <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">ϕ</mi> <mo>=</mo> <msup> <mrow> <mo>[</mo> <mi>α</mi> <mo>,</mo> <mo>∆</mo> <mo>]</mo> </mrow> <mi>T</mi> </msup> </mrow> </semantics></math> that control the sigmoid transformation for contrast adjustment. Balloon 1 denotes the evaluation procedure, which includes image enhancement via sigmoid correction and highboost filtering, followed by evaluating individuals based on contrast and detail objectives. Non-dominated sorting ranks the individuals and tournament selection generates offspring, iterating until stop criteria are met. Finally, the algorithm returns three solutions that present opposing balances between contrast and detail.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/104'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 16 pages, 504 KiB   </span> <a href="/2297-8747/29/6/103/pdf?version=1731316194" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="An Experimental Comparison of Self-Adaptive Differential Evolution Algorithms to Induce Oblique Decision Trees" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/6/103">An Experimental Comparison of Self-Adaptive Differential Evolution Algorithms to Induce Oblique Decision Trees</a> <div class="authors"> by <span class="inlineblock "><strong>Rafael Rivera-López</strong>, </span><span class="inlineblock "><strong>Efrén Mezura-Montes</strong>, </span><span class="inlineblock "><strong>Juana Canul-Reich</strong> and </span><span class="inlineblock "><strong>Marco-Antonio Cruz-Chávez</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(6), 103; <a href="https://doi.org/10.3390/mca29060103">https://doi.org/10.3390/mca29060103</a> - 9 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> This study addresses the challenge of generating accurate and compact oblique decision trees using self-adaptive differential evolution algorithms. Although traditional decision tree induction methods create explainable models, they often fail to achieve optimal classification accuracy. To overcome these limitations, other strategies, such as <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/103/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> This study addresses the challenge of generating accurate and compact oblique decision trees using self-adaptive differential evolution algorithms. Although traditional decision tree induction methods create explainable models, they often fail to achieve optimal classification accuracy. To overcome these limitations, other strategies, such as those based on evolutionary computation, have been proposed in the literature. In particular, we evaluate the use of self-adaptive differential evolution variants to evolve a population of oblique decision trees encoded as real-valued vectors. Our proposal includes (1) an alternative initialization strategy that reduces redundant nodes and (2) a fitness function that penalizes excessive leaf nodes, promoting smaller and more accurate decision trees. We perform a comparative performance analysis of these differential evolution variants, showing that while they exhibit similar statistical behavior, the Single-Objective real-parameter optimization (jSO) method produces the most accurate oblique decision trees and is second best in compactness. The findings highlight the potential of self-adaptive differential evolution algorithms to improve the effectiveness of oblique decision trees in machine learning applications. <a href="/2297-8747/29/6/103">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Collection <a href=" /journal/mca/topical_collections/M6509N770O ">Feature Papers in Mathematical and Computational Applications 2024</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/103/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1517549"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1517549"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1517549" data-cycle-prev="#prev1517549" data-cycle-progressive="#images1517549" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1517549-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/mca/mca-29-00103/article_deploy/html/images/mca-29-00103-g001-550.jpg?1731316279" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1517549" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1517549-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00103/article_deploy/html/images/mca-29-00103-g002-550.jpg?1731316280'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1517549-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00103/article_deploy/html/images/mca-29-00103-g003-550.jpg?1731316281'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1517549-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00103/article_deploy/html/images/mca-29-00103-g004-550.jpg?1731316281'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1517549-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00103/article_deploy/html/images/mca-29-00103-g005-550.jpg?1731316283'><p>Figure 5</p></div></script></div></div><div id="article-1517549-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00103/article_deploy/html/images/mca-29-00103-g001-550.jpg?1731316279" title=" <strong>Figure 1</strong><br/> <p>An example of an oblique decision tree. The black lines represent oblique hyperplanes, the red circles represent instances of class C1, the blue squares represent instances of class C2, and the green triangles represent instances of class C3.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/103'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00103/article_deploy/html/images/mca-29-00103-g002-550.jpg?1731316280" title=" <strong>Figure 2</strong><br/> <p>The linear encoding scheme for the internal nodes of a complete binary oblique tree.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/103'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00103/article_deploy/html/images/mca-29-00103-g003-550.jpg?1731316281" title=" <strong>Figure 3</strong><br/> <p>DTs for the Iris dataset using J48 (<b>Left</b>) and LSHADE (<b>Right</b>).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/103'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00103/article_deploy/html/images/mca-29-00103-g004-550.jpg?1731316281" title=" <strong>Figure 4</strong><br/> <p>The ranking plot with the BH test for the results shown in <a href="#mca-29-00103-t003" class="html-table">Table 3</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/103'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00103/article_deploy/html/images/mca-29-00103-g005-550.jpg?1731316283" title=" <strong>Figure 5</strong><br/> <p>The ranking plot with the BH test for the results shown in <a href="#mca-29-00103-t004" class="html-table">Table 4</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/103'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 21 pages, 3240 KiB   </span> <a href="/2297-8747/29/6/102/pdf?version=1730970841" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="A Mathematical Lens on the Zoonotic Transmission of Lassa Virus Infections Leading to Disabilities in Severe Cases" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/6/102">A Mathematical Lens on the Zoonotic Transmission of Lassa Virus Infections Leading to Disabilities in Severe Cases</a> <div class="authors"> by <span class="inlineblock "><strong>Yasir Ramzan</strong>, </span><span class="inlineblock "><strong>Hanadi Alzubadi</strong>, </span><span class="inlineblock "><strong>Aziz Ullah Awan</strong>, </span><span class="inlineblock "><strong>Kamel Guedri</strong>, </span><span class="inlineblock "><strong>Mohammed Alharthi</strong> and </span><span class="inlineblock "><strong>Bandar M. Fadhl</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(6), 102; <a href="https://doi.org/10.3390/mca29060102">https://doi.org/10.3390/mca29060102</a> - 7 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> This study aims to analyze the dynamics of Lassa fever transmission and its impact on the brain and spinal cord then devise and analyze preventive actions. The stability of the infection-free equilibrium point is evaluated; the model’s precision is examined using empirical data; <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/102/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> This study aims to analyze the dynamics of Lassa fever transmission and its impact on the brain and spinal cord then devise and analyze preventive actions. The stability of the infection-free equilibrium point is evaluated; the model’s precision is examined using empirical data; and all parameters are estimated and fitted. Subsequently, the basic reproductive number is determined, and subpopulation trends are observed over time. Sensitivity analysis is conducted to identify critical drivers influencing transmission dynamics. Two-dimensional plots visualize the impact of crucial parameters on the reproductive number. Through a comprehensive literature review and case analysis, an association between Lassa fever and various disabilities is established, including conditions such as encephalitis, hearing loss, ataxia, neuropsychiatric manifestations, meningitis, seizures, and coma. Solutions are devised and analyzed to enhance early detection, treatment, and mitigation of disease. <a href="/2297-8747/29/6/102">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/mca/special_issues/I91AN829PK ">New Trends in Biomathematics</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/102/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1515896"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1515896"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1515896" data-cycle-prev="#prev1515896" data-cycle-progressive="#images1515896" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1515896-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g001-550.jpg?1730970983" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1515896" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1515896-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g002-550.jpg?1730970983'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1515896-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g003-550.jpg?1730970985'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1515896-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g004-550.jpg?1730970987'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1515896-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g005-550.jpg?1730970988'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1515896-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g006-550.jpg?1730970989'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1515896-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g007-550.jpg?1730970991'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1515896-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g008a-550.jpg?1730970993'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1515896-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g008b-550.jpg?1730970995'><p>Figure 8 Cont.</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1515896-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g009a-550.jpg?1730970997'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1515896-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g009b-550.jpg?1730971001'><p>Figure 9 Cont.</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1515896-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g009c-550.jpg?1730971004'><p>Figure 9 Cont.</p></div></script></div></div><div id="article-1515896-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g001-550.jpg?1730970983" title=" <strong>Figure 1</strong><br/> <p>Transmission of Lassa virus.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/102'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g002-550.jpg?1730970983" title=" <strong>Figure 2</strong><br/> <p>Schematic diagram of Model (<a href="#FD1-mca-29-00102" class="html-disp-formula">1</a>).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/102'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g003-550.jpg?1730970985" title=" <strong>Figure 3</strong><br/> <p>Visualization depicting the tally of confirmed cases in Nigeria—comparing actual versus estimated numbers. The various marker shapes denote actual cases per week, while the line represents estimated data. Data are categorized as (<b>a</b>) mild and (<b>b</b>) severe cases, spanning four weeks from 2 January to 30 January 2022 [<a href="#B4-mca-29-00102" class="html-bibr">4</a>]. The estimated data exhibit a close resemblance to the actual data.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/102'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g004-550.jpg?1730970987" title=" <strong>Figure 4</strong><br/> <p>Illustration depicting the population dynamics using estimated values of the parameters for <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>&lt;</mo> <mn>1</mn> </mrow> </semantics></math>, where <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>m</mi> </msub> <mo>=</mo> <mn>0.8940</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.9110</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>0.7812</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/102'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g005-550.jpg?1730970988" title=" <strong>Figure 5</strong><br/> <p>Illustration depicting the population dynamics using estimated values of the parameters for <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </semantics></math>, where <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>m</mi> </msub> <mo>=</mo> <mn>2.3148</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>2.42288</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>3.1250</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/102'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g006-550.jpg?1730970989" title=" <strong>Figure 6</strong><br/> <p>Visual illustration of sensitivity indices using mildly infected population.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/102'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g007-550.jpg?1730970991" title=" <strong>Figure 7</strong><br/> <p>Visual illustration of sensitivity indices using severely infected population.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/102'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g008a-550.jpg?1730970993" title=" <strong>Figure 8</strong><br/> <p>Contour plot depicting the influence of parameters on <math display="inline"><semantics> <msub> <mi>R</mi> <mn>0</mn> </msub> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/102'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g008b-550.jpg?1730970995" title=" <strong>Figure 8 Cont.</strong><br/> <p>Contour plot depicting the influence of parameters on <math display="inline"><semantics> <msub> <mi>R</mi> <mn>0</mn> </msub> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/102'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g009a-550.jpg?1730970997" title=" <strong>Figure 9</strong><br/> <p>Implementation of controls <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="double-struck">C</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi mathvariant="double-struck">C</mi> <mn>2</mn> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <msub> <mi mathvariant="double-struck">C</mi> <mn>3</mn> </msub> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/102'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g009b-550.jpg?1730971001" title=" <strong>Figure 9 Cont.</strong><br/> <p>Implementation of controls <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="double-struck">C</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi mathvariant="double-struck">C</mi> <mn>2</mn> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <msub> <mi mathvariant="double-struck">C</mi> <mn>3</mn> </msub> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/102'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00102/article_deploy/html/images/mca-29-00102-g009c-550.jpg?1730971004" title=" <strong>Figure 9 Cont.</strong><br/> <p>Implementation of controls <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="double-struck">C</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi mathvariant="double-struck">C</mi> <mn>2</mn> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <msub> <mi mathvariant="double-struck">C</mi> <mn>3</mn> </msub> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/102'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <a data-dropdown="drop-supplementary-1513483" aria-controls="drop-supplementary-1513483" aria-expanded="false" title="Supplementary Material"> <i class="material-icons">attachment</i> </a> <div id="drop-supplementary-1513483" class="f-dropdown label__btn__dropdown label__btn__dropdown--wide" data-dropdown-content aria-hidden="true" tabindex="-1"> Supplementary material: <br/> <a href="/2297-8747/29/6/101/s1?version=1730710522"> Supplementary File 1 (ZIP, 1148 KiB) </a><br/> </div> </div> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 19 pages, 5947 KiB   </span> <a href="/2297-8747/29/6/101/pdf?version=1730710522" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Analytical Solutions of PBTK Models for Evaluating the Impact of Surface Diffusion Characteristics on the Leaching Profile of Implant Bioproducts" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/6/101">Analytical Solutions of PBTK Models for Evaluating the Impact of Surface Diffusion Characteristics on the Leaching Profile of Implant Bioproducts</a> <div class="authors"> by <span class="inlineblock "><strong>Matheos Giakoumi</strong>, </span><span class="inlineblock "><strong>Konstantinos Kapnisis</strong>, </span><span class="inlineblock "><strong>Andreas Anayiotos</strong> and </span><span class="inlineblock "><strong>Pavlos S. Stephanou</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(6), 101; <a href="https://doi.org/10.3390/mca29060101">https://doi.org/10.3390/mca29060101</a> - 4 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Toxicokinetic or pharmacokinetic models, physiologically based or not, offer a unique avenue to understand the transport of toxins or pharmaceuticals in living organisms. The availability of analytical solutions to such models offers the means to engage in a plethora of applications. In the <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/101/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Toxicokinetic or pharmacokinetic models, physiologically based or not, offer a unique avenue to understand the transport of toxins or pharmaceuticals in living organisms. The availability of analytical solutions to such models offers the means to engage in a plethora of applications. In the present work, we provide the framework to solve analytically such models using the matrix exponential, and we then apply this method to derive an explicit solution to four-to-five-compartment physiologically based toxicokinetic (PBTK) models considering a single- and an infinite-exponential expression for the amount of mass released from an implantable device. We also offer the conditions that need to be met for analytical solutions to be obtained when the kinetic rates are time-dependent functions. Our analysis compares the computation time between analytical and numerical solutions and characterizes the dependency of the maximum substance mass value and the time it occurs in the various tissue compartments from the material surface diffusion characteristics. Our analytical solutions, which have several advantages over the solutions obtained using numerical solvers, can be incorporated into <i>in silico</i> tools and provide valuable information for human health risk assessment. <a href="/2297-8747/29/6/101">Full article</a> </div> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/101/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1513483"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1513483"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1513483" data-cycle-prev="#prev1513483" data-cycle-progressive="#images1513483" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1513483-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-ag-550.jpg?1730710684" alt="" style="border: 0;"><p>Graphical abstract</p></div><script id="images1513483" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1513483-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g001-550.jpg?1730710666'><p>Figure 1</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1513483-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g002-550.jpg?1730710670'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1513483-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g003-550.jpg?1730710672'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1513483-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g004-550.jpg?1730710674'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1513483-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g005-550.jpg?1730710675'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1513483-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g006-550.jpg?1730710677'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1513483-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g007-550.jpg?1730710678'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1513483-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g008-550.jpg?1730710680'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1513483-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g009-550.jpg?1730710681'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1513483-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g010-550.jpg?1730710683'><p>Figure 10</p></div></script></div></div><div id="article-1513483-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-ag-550.jpg?1730710684" title=" <strong>Graphical abstract</strong><br/><strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/101'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g001-550.jpg?1730710666" title=" <strong>Figure 1</strong><br/> <p>SM model derived-predictions of the nickel concentration–time profiles in the tissue and body fluid compartments for varying values of the model parameters. The parameters <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>u</mi> </msub> <mo>,</mo> <mo> </mo> <msub> <mi>k</mi> <mi>g</mi> </msub> <mo>,</mo> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mrow> <mi>surf</mi> </mrow> </msub> <mo>,</mo> <mo> </mo> <mi>a</mi> <mo>,</mo> <mo> </mo> <mi>τ</mi> <mo>,</mo> <mo> </mo> <msub> <mi>V</mi> <mi>s</mi> </msub> <mo>,</mo> <mo> </mo> <msub> <mi>Q</mi> <mi>u</mi> </msub> </mrow> </semantics></math> are kept constant and equal to the values provided in <a href="#mca-29-00101-t001" class="html-table">Table 1</a>. Note that the local tissue profile only depends on <math display="inline"><semantics> <mrow> <mi>F</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>l</mi> </msub> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/101'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g002-550.jpg?1730710670" title=" <strong>Figure 2</strong><br/> <p>SMK model derived predictions of the nickel concentration–time profiles in the tissue and body fluid compartments for varying values of the model parameters. The parameters <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>u</mi> </msub> <mo>,</mo> <mo> </mo> <msub> <mi>k</mi> <mi>g</mi> </msub> <mo>,</mo> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mrow> <mi>surf</mi> </mrow> </msub> <mo>,</mo> <mo> </mo> <mi>a</mi> <mo>,</mo> <mo> </mo> <mi>τ</mi> <mo>,</mo> <mo> </mo> <msub> <mi>V</mi> <mi>s</mi> </msub> <mo>,</mo> <mo> </mo> <msub> <mi>Q</mi> <mi>u</mi> </msub> </mrow> </semantics></math> are kept constant and equal to the values provided in <a href="#mca-29-00101-t001" class="html-table">Table 1</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/101'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g003-550.jpg?1730710672" title=" <strong>Figure 3</strong><br/> <p>(<b>a</b>) The maximum Ni mass value and (<b>b</b>) the time it occurs in the local tissue compartment for both the SM and SMK model when using Equation (15). The corresponding contour plots are also depicted in parts (<b>c</b>) and (<b>d</b>), respectively.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/101'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g004-550.jpg?1730710674" title=" <strong>Figure 4</strong><br/> <p>(<b>a</b>) The maximum Ni mass value and (<b>b</b>) the time it occurs in the serum compartment for the SM model when using Equation (15). The corresponding contour plots are also depicted in parts (<b>c</b>) and (<b>d</b>), respectively.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/101'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g005-550.jpg?1730710675" title=" <strong>Figure 5</strong><br/> <p>(<b>a</b>) The maximum Ni mass value and (<b>b</b>) the time it occurs in the urine compartment for the SM model when using Equation (15). The corresponding contour plots are also depicted in parts (<b>c</b>) and (<b>d</b>), respectively.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/101'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g006-550.jpg?1730710677" title=" <strong>Figure 6</strong><br/> <p>(<b>a</b>) The maximum Ni mass value and (<b>b</b>) the time it occurs in the other tissues compartment for the SM model when using Equation (15). The corresponding contour plots are also depicted in parts (<b>c</b>) and (<b>d</b>), respectively.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/101'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g007-550.jpg?1730710678" title=" <strong>Figure 7</strong><br/> <p>(<b>a</b>) The maximum Ni mass value and (<b>b</b>) the time it occurs in the serum compartment for the SMK model when using Equation (15). The corresponding contour plots are also depicted in parts (<b>c</b>) and (<b>d</b>), respectively.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/101'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g008-550.jpg?1730710680" title=" <strong>Figure 8</strong><br/> <p>(<b>a</b>) The maximum Ni mass value and (<b>b</b>) the time it occurs in the urine compartment for the SMK model when using Equation (15). The corresponding contour plots are also depicted in parts (<b>c</b>) and (<b>d</b>), respectively.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/101'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g009-550.jpg?1730710681" title=" <strong>Figure 9</strong><br/> <p>(<b>a</b>) The maximum Ni mass value and (<b>b</b>) the time it occurs in the other tissues compartment for the SMK model when using Equation (15). The corresponding contour plots are also depicted in parts (<b>c</b>) and (<b>d</b>), respectively.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/101'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00101/article_deploy/html/images/mca-29-00101-g010-550.jpg?1730710683" title=" <strong>Figure 10</strong><br/> <p>(<b>a</b>) The maximum Ni mass value and (<b>b</b>) the time it occurs in the kidneys compartment for the SMK model when using Equation (15). The corresponding contour plots are also depicted in parts (<b>c</b>) and (<b>d</b>), respectively.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/101'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 17 pages, 532 KiB   </span> <a href="/2297-8747/29/6/100/pdf?version=1730693796" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Numerical Study of Multi-Term Time-Fractional Sub-Diffusion Equation Using Hybrid L1 Scheme with Quintic Hermite Splines" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/6/100">Numerical Study of Multi-Term Time-Fractional Sub-Diffusion Equation Using Hybrid L1 Scheme with Quintic Hermite Splines</a> <div class="authors"> by <span class="inlineblock "><strong>Priyanka Priyanka</strong>, </span><span class="inlineblock "><strong>Shelly Arora</strong>, </span><span class="inlineblock "><strong>Saroj Sahani</strong> and </span><span class="inlineblock "><strong>Sharandeep Singh</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(6), 100; <a href="https://doi.org/10.3390/mca29060100">https://doi.org/10.3390/mca29060100</a> - 2 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Anomalous diffusion of particles has been described by the time-fractional reaction–diffusion equation. A hybrid formulation of numerical technique is proposed to solve the time-fractional-order reaction–diffusion (FRD) equation numerically. The technique comprises the semi-discretization of the time variable using an L1 finite-difference scheme and <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/100/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Anomalous diffusion of particles has been described by the time-fractional reaction–diffusion equation. A hybrid formulation of numerical technique is proposed to solve the time-fractional-order reaction–diffusion (FRD) equation numerically. The technique comprises the semi-discretization of the time variable using an L1 finite-difference scheme and space discretization using the quintic Hermite spline collocation method. The hybrid technique reduces the problem to an iterative scheme of an algebraic system of equations. The stability analysis of the proposed numerical scheme and the optimal error bounds for the approximate solution are also studied. A comparative study of the obtained results and an error analysis of approximation show the efficiency, accuracy, and effectiveness of the technique. <a href="/2297-8747/29/6/100">Full article</a> </div> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/100/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1512866"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1512866"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1512866" data-cycle-prev="#prev1512866" data-cycle-progressive="#images1512866" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1512866-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/mca/mca-29-00100/article_deploy/html/images/mca-29-00100-g001-550.jpg?1730693991" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1512866" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1512866-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00100/article_deploy/html/images/mca-29-00100-g002-550.jpg?1730693992'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1512866-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00100/article_deploy/html/images/mca-29-00100-g003-550.jpg?1730693993'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1512866-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00100/article_deploy/html/images/mca-29-00100-g004-550.jpg?1730693994'><p>Figure 4</p></div></script></div></div><div id="article-1512866-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00100/article_deploy/html/images/mca-29-00100-g001-550.jpg?1730693991" title=" <strong>Figure 1</strong><br/> <p>The arrangement of collocation points over the spatial domain.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/100'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00100/article_deploy/html/images/mca-29-00100-g002-550.jpg?1730693992" title=" <strong>Figure 2</strong><br/> <p>The behaviour of approximate solution, exact solution, absolute error and <math display="inline"><semantics> <msub> <mi>L</mi> <mn>2</mn> </msub> </semantics></math>-norm at the node points for Example 1.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/100'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00100/article_deploy/html/images/mca-29-00100-g003-550.jpg?1730693993" title=" <strong>Figure 3</strong><br/> <p>The behaviour of computed approximate solution, exact solution and absolute error at the node points for Example 2.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/100'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00100/article_deploy/html/images/mca-29-00100-g004-550.jpg?1730693994" title=" <strong>Figure 4</strong><br/> <p>The behaviour of approximate and exact solution with the comparison by absolute error for Example 3.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/100'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 3 pages, 154 KiB   </span> <a href="/2297-8747/29/6/99/pdf?version=1730449859" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Feature Paper Collection of Mathematical and Computational Applications—2023" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Editorial</span></div> <a class="title-link" href="/2297-8747/29/6/99">Feature Paper Collection of <i>Mathematical and Computational Applications</i>—2023</a> <div class="authors"> by <span class="inlineblock "><strong>Gianluigi Rozza</strong>, </span><span class="inlineblock "><strong>Oliver Schütze</strong> and </span><span class="inlineblock "><strong>Nicholas Fantuzzi</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(6), 99; <a href="https://doi.org/10.3390/mca29060099">https://doi.org/10.3390/mca29060099</a> - 1 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-full inline"> This Special Issue comprises the second collection of papers submitted by both the Editorial Board Members (EBMs) of the journal <i>Mathematical and Computational Applications</i> (<i>MCA</i>) and the outstanding scholars working in the core research fields of <i>MCA</i> [...] <a href="/2297-8747/29/6/99">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Collection <a href=" /journal/mca/topical_collections/ZGRQX7CNGE ">Feature Papers in Mathematical and Computational Applications 2023</a>)<br/> </div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 24 pages, 6455 KiB   </span> <a href="/2297-8747/29/6/98/pdf?version=1730381555" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Using Artificial Neural Network Analysis to Study Jeffrey Nanofluid Flow in Cone–Disk Systems" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/6/98">Using Artificial Neural Network Analysis to Study Jeffrey Nanofluid Flow in Cone–Disk Systems</a> <div class="authors"> by <span class="inlineblock "><strong>Nasser Nammas Albaqami</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(6), 98; <a href="https://doi.org/10.3390/mca29060098">https://doi.org/10.3390/mca29060098</a> - 31 Oct 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Artificial intelligence (AI) is employed in fluid flow models to enhance the simulation’s accuracy, to more effectively optimize the fluid flow models, and to realize reliable fluid flow systems with improved performance. Jeffery fluid flow through the interstice of a cone-and-disk system is <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/98/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Artificial intelligence (AI) is employed in fluid flow models to enhance the simulation’s accuracy, to more effectively optimize the fluid flow models, and to realize reliable fluid flow systems with improved performance. Jeffery fluid flow through the interstice of a cone-and-disk system is considered in this study. The mathematical description of this flow involves converting a partial differential system into a nonlinear ordinary differential system and solving it using a neurocomputational technique. The fluid streaming through the disk–cone gap is investigated under four contrasting frameworks, i.e., (i) passive cone and spinning disk, (ii) spinning cone and passive disk, (iii) cone and disk rotating in the same direction, and (iv) cone and disk rotating in opposite directions. Employing the recently developed technique of artificial neural networks (ANNs) can be effective for handling and optimizing fluid flow exploits. The proposed approach integrates training, testing and analysis, and authentication based on a locus dataset to address various aspects of fluid problems. The mean square error, regression plots, curve-fitting graphs, and error histograms are used to evaluate the performance of the least mean square neural network algorithm (LMS-NNA). The results show that these equations are consistently aligned, and agreement is, on average, in the order of 10<sup>−8</sup>. While the resting parameters were kept static, the transverse velocity distribution, in all four cases, exhibited an incremental decreasing behavior in the estimates of magnetic and Jeffery fluid factors. Furthermore, the results obtained were compared with those in the literature, and the close agreement confirms our results. To train the model, 80% of the data were used for LMS-NNA, with 10% used for testing and the remaining 10% for validation. The quantitative and qualitative outputs obtained from the neural network strategy and parameter variation were thoroughly examined and discussed. <a href="/2297-8747/29/6/98">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/mca/special_issues/8V8TL020L4 ">Symmetry Methods for Solving Differential Equations</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/98/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1511399"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1511399"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1511399" data-cycle-prev="#prev1511399" 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src='https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g018-550.jpg?1730381661'><p>Figure 18</p></div> --- <div class='openpopupgallery' data-imgindex='18' data-target='article-1511399-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g019-550.jpg?1730381663'><p>Figure 19</p></div></script></div></div><div id="article-1511399-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g001-550.jpg?1730381619" title=" <strong>Figure 1</strong><br/> <p>Physical interpretation of cone–disk geometry.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g002-550.jpg?1730381621" title=" <strong>Figure 2</strong><br/> <p>(<b>a</b>) ANN structure for model problem. (<b>b</b>) ANN design for proposed LMS-NNA.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g003-550.jpg?1730381624" title=" <strong>Figure 3</strong><br/> <p>(<b>a</b>–<b>e</b>) The proposed fluid model <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Re</mi> </mrow> <mi>w</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>Re</mi> </mrow> <mi mathvariant="sans-serif">Ω</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> where <math display="inline"><semantics> <mrow> <mi>g</mi> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math> is plotted using the LMS-NNA for <math display="inline"><semantics> <mi>λ</mi> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g004-550.jpg?1730381628" title=" <strong>Figure 4</strong><br/> <p>(<b>a</b>–<b>e</b>) The proposed fluid model <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Re</mi> </mrow> <mi>w</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>Re</mi> </mrow> <mi mathvariant="sans-serif">Ω</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <mi>g</mi> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math> is plotted using the LMS-NNA for <math display="inline"><semantics> <mi>M</mi> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g005-550.jpg?1730381632" title=" <strong>Figure 5</strong><br/> <p>(<b>a</b>–<b>e</b>) The proposed fluid model <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Re</mi> </mrow> <mi>w</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>Re</mi> </mrow> <mi mathvariant="sans-serif">Ω</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <mi>g</mi> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math> is plotted using the LMS-NNA for <math display="inline"><semantics> <mi>λ</mi> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g006-550.jpg?1730381635" title=" <strong>Figure 6</strong><br/> <p>(<b>a</b>–<b>e</b>) The proposed fluid model <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Re</mi> </mrow> <mi>w</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>Re</mi> </mrow> <mi mathvariant="sans-serif">Ω</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <mi>g</mi> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math> is plotted using the LMS-NNA for <math display="inline"><semantics> <mi>M</mi> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g007-550.jpg?1730381639" title=" <strong>Figure 7</strong><br/> <p>(<b>a</b>–<b>e</b>) The proposed fluid model <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Re</mi> </mrow> <mi>w</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>Re</mi> </mrow> <mi mathvariant="sans-serif">Ω</mi> </msub> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <mi>g</mi> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math> is plotted using the LMS-NNA for <math display="inline"><semantics> <mi>λ</mi> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g008-550.jpg?1730381642" title=" <strong>Figure 8</strong><br/> <p>(<b>a</b>–<b>e</b>) The proposed fluid model <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Re</mi> </mrow> <mi>w</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>Re</mi> </mrow> <mi mathvariant="sans-serif">Ω</mi> </msub> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> where <math display="inline"><semantics> <mrow> <mi>g</mi> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math> is plotted using the LMS-NNA for <math display="inline"><semantics> <mi>M</mi> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g009-550.jpg?1730381646" title=" <strong>Figure 9</strong><br/> <p>(<b>a</b>–<b>e</b>) The proposed fluid model <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Re</mi> </mrow> <mi>w</mi> </msub> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>Re</mi> </mrow> <mi mathvariant="sans-serif">Ω</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> where <math display="inline"><semantics> <mrow> <mi>g</mi> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math> is plotted using the LMS-NNA for <math display="inline"><semantics> <mrow> <mi>g</mi> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g010-550.jpg?1730381650" title=" <strong>Figure 10</strong><br/> <p>(<b>a</b>–<b>e</b>) The proposed fluid model <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Re</mi> </mrow> <mi>w</mi> </msub> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>Re</mi> </mrow> <mi mathvariant="sans-serif">Ω</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> where <math display="inline"><semantics> <mrow> <mi>g</mi> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math> is plotted using the LMS-NNA for <math display="inline"><semantics> <mi>M</mi> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g011-550.jpg?1730381651" title=" <strong>Figure 11</strong><br/> <p>The variation in the heat transfer rate using <math display="inline"><semantics> <mrow> <mi>N</mi> <mi>t</mi> <mo>,</mo> <mi>N</mi> <mi>b</mi> <mo>,</mo> <mi>λ</mi> <mn>1</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g012-550.jpg?1730381653" title=" <strong>Figure 12</strong><br/> <p>(<b>a</b>) Disparity in <span class="html-italic">λ</span> vs. <span class="html-italic">g</span>(<span class="html-italic">η</span>); (<b>b</b>) <span class="html-italic">λ</span> vs. AE.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g013-550.jpg?1730381654" title=" <strong>Figure 13</strong><br/> <p>(<b>a</b>) Disparity in <span class="html-italic">λ</span> &amp; <span class="html-italic">g</span>(<span class="html-italic">η</span>); (<b>b</b>) <span class="html-italic">λ</span> vs. AE.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g014-550.jpg?1730381656" title=" <strong>Figure 14</strong><br/> <p>(<b>a</b>) Disparity in <span class="html-italic">λ</span> &amp; <span class="html-italic">g</span>(<span class="html-italic">η</span>); (<b>b</b>) <span class="html-italic">λ</span> vs. AE.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g015-550.jpg?1730381657" title=" <strong>Figure 15</strong><br/> <p>(<b>a</b>) Disparity in <span class="html-italic">λ</span> &amp; <span class="html-italic">g</span>(<span class="html-italic">η</span>); (<b>b</b>) <span class="html-italic">λ</span> vs. AE.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g016-550.jpg?1730381659" title=" <strong>Figure 16</strong><br/> <p>(<b>a</b>) Disparity in <span class="html-italic">M</span> &amp; <span class="html-italic">g</span>(<span class="html-italic">η</span>); (<b>b</b>) <span class="html-italic">M</span> vs. AE.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g017-550.jpg?1730381660" title=" <strong>Figure 17</strong><br/> <p>(<b>a</b>) Disparity in <span class="html-italic">M</span> &amp; <span class="html-italic">g</span>(<span class="html-italic">η</span>); (<b>b</b>) <span class="html-italic">M</span> vs. AE.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g018-550.jpg?1730381661" title=" <strong>Figure 18</strong><br/> <p>(<b>a</b>) Disparity in <span class="html-italic">M</span> &amp; <span class="html-italic">g</span>(<span class="html-italic">η</span>); (<b>b</b>) <span class="html-italic">M</span> vs. AE.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00098/article_deploy/html/images/mca-29-00098-g019-550.jpg?1730381663" title=" <strong>Figure 19</strong><br/> <p>(<b>a</b>) Disparity in <span class="html-italic">M</span> &amp; <span class="html-italic">g</span>(<span class="html-italic">η</span>); (<b>b</b>) <span class="html-italic">M</span> vs. AE.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/98'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 13 pages, 7092 KiB   </span> <a href="/2297-8747/29/6/97/pdf?version=1730303186" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Design and Optimization of Microfluidic Vortex Diode" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/6/97">Design and Optimization of Microfluidic Vortex Diode</a> <div class="authors"> by <span class="inlineblock "><strong>Krzysztof Tadyszak</strong>, </span><span class="inlineblock "><strong>Alessandro Jäger</strong>, </span><span class="inlineblock "><strong>Jiří Pánek</strong> and </span><span class="inlineblock "><strong>Martin Hrubý</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(6), 97; <a href="https://doi.org/10.3390/mca29060097">https://doi.org/10.3390/mca29060097</a> - 30 Oct 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> The performed research presents modeling results for designing microfluidic vortex diodes. These devices rectify fluid flow and can be used in many applications on micro and macro scales. The modeling, utilizing computational fluid dynamics (CFD) with the turbulence model RANS <i>k-ε</i> in COMSOL <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/97/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> The performed research presents modeling results for designing microfluidic vortex diodes. These devices rectify fluid flow and can be used in many applications on micro and macro scales. The modeling, utilizing computational fluid dynamics (CFD) with the turbulence model RANS <i>k-ε</i> in COMSOL Multiphysics, has led to optimizing diodicity—the reversed-to-forward flow pressure drop ratio. The goal was to find the best flow-rectifying geometry within the 2D vortex-type design by changing the wall geometry, diode shape, and inflow velocities, identifying significant parameters and dependencies. Improving diodicity can be achieved by increasing the radius r<sub>1</sub> of the central channel, increasing the entire diode radius r<sub>2</sub>, decreasing the width <i>w</i> of the rectangular channel, and reducing its length <i>L</i>. Additionally, changing the circular shape of the diode to an elliptical one can improve diodicity. The significance of this research is evident in the potential applications of these devices in microfluidic setups where fixed-geometry unidirectional flow is required, e.g., mixing, filtration, cell separation, and drug delivery, or on industrial scales, e.g., energy harvesting, wastewater treatment, and water sterilization. <a href="/2297-8747/29/6/97">Full article</a> </div> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/97/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1510577"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1510577"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1510577" data-cycle-prev="#prev1510577" data-cycle-progressive="#images1510577" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1510577-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-ag-550.jpg?1730524342" alt="" style="border: 0;"><p>Graphical abstract</p></div><script id="images1510577" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1510577-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-g001-550.jpg?1730303278'><p>Figure 1</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1510577-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-g002-550.jpg?1730303281'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1510577-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-g003-550.jpg?1730303284'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1510577-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-g004-550.jpg?1730303288'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1510577-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-g005-550.jpg?1730303291'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1510577-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-g006-550.jpg?1730303292'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1510577-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-g007-550.jpg?1730303295'><p>Figure 7</p></div></script></div></div><div id="article-1510577-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-ag-550.jpg?1730524342" title=" <strong>Graphical abstract</strong><br/><strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/97'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-g001-550.jpg?1730303278" title=" <strong>Figure 1</strong><br/> <p>(<b>a</b>) Plain 2D model of the diode. The diode radius <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> is 100 μm, the circular channel radius <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> is 5 μm, the rectangular channel width <span class="html-italic">w</span> is 1 μm, and the length <span class="html-italic">L</span> is 100 μm; (<b>b</b>) magnification of the connection of rectangular channel with the diode; (<b>c</b>) the same magnification showing ignored edges; (<b>d</b>) diodicity <span class="html-italic">D</span> vs. the number of mesh elements. Mesh with 60,745 elements was used with <span class="html-italic">D</span> = 1231.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/97'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-g002-550.jpg?1730303281" title=" <strong>Figure 2</strong><br/> <p>Two-dimensional models of vortex diodes; maps of velocity magnitude with streamlines (<span class="html-italic">w</span>—width of the rectangular channel (default vale 1 μm), <span class="html-italic">L</span>—length of rectangular channel (default value 100 μm), <span class="html-italic">r</span><sub>1</sub>—radius of the central channel (default value 5 μm), <span class="html-italic">r</span><sub>2</sub>—radius of the diode (default value 100 μm): (<b>a</b>) forward flow direction—inflow from side channel outflow in the center; (<b>b</b>) reversed flow direction—inflow from center circle outflow by the side channel.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/97'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-g003-550.jpg?1730303284" title=" <strong>Figure 3</strong><br/> <p>(<b>a</b>) Parametric sweep through 3D space, diodicity <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mi>f</mi> <mo>(</mo> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo> </mo> <mi>w</mi> <mo>,</mo> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math>. The color overlay shows diodicity <math display="inline"><semantics> <mrow> <mi>D</mi> </mrow> </semantics></math> (red—highest, and blue—lowest value); (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>D</mi> </mrow> </semantics></math> vs. velocity for fixed radius <span class="html-italic">r</span><sub>1</sub> = 20 μm for multiple channel widths <span class="html-italic">w</span>. The inset shows <math display="inline"><semantics> <mrow> <mi>D</mi> </mrow> </semantics></math> vs. velocity for fixed channel width w = 1 μm and multiple radiuses <span class="html-italic">r</span><sub>1</sub>; (<b>c</b>) Max. <span class="html-italic">D</span> vs. channel width <span class="html-italic">w</span> for <span class="html-italic">r</span><sub>1</sub> = 20 μm, inset shows maximal velocity <math display="inline"><semantics> <mrow> <mi>v</mi> </mrow> </semantics></math> taken from function’s maximum in <a href="#mca-29-00097-f003" class="html-fig">Figure 3</a>b vs. its channel width <span class="html-italic">w</span>; (<b>d</b>) <span class="html-italic">D</span> vs. channel radius <span class="html-italic">r</span><sub>1</sub> for fixed channel width <span class="html-italic">w</span> = 1 μm and multiple velocities <span class="html-italic">ν<sub>in</sub></span>. Inset shows images of the diodes with radius <span class="html-italic">r</span><sub>1</sub> = 5 μm, <span class="html-italic">r</span><sub>1</sub> = 30 μm, <span class="html-italic">r</span><sub>1</sub> = 95 μm.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/97'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-g004-550.jpg?1730303288" title=" <strong>Figure 4</strong><br/> <p>(<b>a</b>) Diodicity <span class="html-italic">D</span> vs. length <span class="html-italic">L</span> of the rectangular channel and (<b>b</b>) <span class="html-italic">D</span> vs. <span class="html-italic">r</span><sub>2</sub> radius for <span class="html-italic">L</span> = 100 μm; (<b>c</b>) <span class="html-italic">D</span> vs. area of the diode for increased eccentricity (ellipse shape), where inset is the magnification of the main plot and additionally on top are the main ellipse shapes (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>); (<b>d</b>) <span class="html-italic">D</span> vs. horizontal radius <span class="html-italic">a</span> for central and focal placement of circular channel (left and right), for fixed vertical radius <span class="html-italic">b</span> = 100 μm, and fixed and varying <span class="html-italic">L</span> <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> <mo>)</mo> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/97'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-g005-550.jpg?1730303291" title=" <strong>Figure 5</strong><br/> <p>(<b>a</b>) Vortex diode with single triangle-shaped wall modification: height <span class="html-italic">h</span> = 20 μm, <span class="html-italic">a</span> = 20 μm, α—rotation angle, <span class="html-italic">w</span> = 1, <span class="html-italic">r</span><sub>1</sub> = 5 μm; (<b>b</b>) <span class="html-italic">D</span> vs. <span class="html-italic">h</span> and α for single triangle rotation; (<b>c</b>) model with multiple triangles separated by the same angle; (<b>d</b>) <span class="html-italic">D</span> vs. <span class="html-italic">N</span>—number of repetitions <span class="html-italic">N</span> in range of 0 to 13.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/97'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-g006-550.jpg?1730303292" title=" <strong>Figure 6</strong><br/> <p>Diodicity <span class="html-italic">D</span> vs. height (<span class="html-italic">h</span>) of the elliptically shaped tooth (base width <span class="html-italic">a</span> = 10 μm) for single tooth <span class="html-italic">N</span> = 1 (black squares) and <span class="html-italic">N</span> = 13 (open circles). Images of two models are shown for <span class="html-italic">N</span> = 1 and <span class="html-italic">N</span> = 13 teeth. The inset plot shows diodicity vs. rotation angle α for a single tooth (<span class="html-italic">N</span> = 1).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/97'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00097/article_deploy/html/images/mca-29-00097-g007-550.jpg?1730303295" title=" <strong>Figure 7</strong><br/> <p>(<b>a</b>) Vortex diode design cases: (<b>a1</b>)—internal channel (width 2 μm) symmetrically reduced with the increase in α; (<b>b1</b>)—internal channel (width 2 μm) reduced with the increase in α in one direction, (<b>c1</b>)—internal channel (width 1 μm, continuation of external rectangular channel); (<b>d1</b>)—external channel change from 0 (tangential) to 90° (perpendicular direction); (<b>e1</b>)—single airfoil profile—internal wall; (<b>f1</b>)—13 airfoil profiles; (<b>b</b>) <span class="html-italic">D</span> vs. <span class="html-italic">N</span>—number of airfoil profiles (black squares) and <span class="html-italic">D</span> vs. 13 with profile angle α (open red circles); (<b>c</b>) angular diodicity dependence for all cases from <a href="#mca-29-00097-f007" class="html-fig">Figure 7</a>a; (<b>d</b>) airfoil profile drawn in the range 15–95 μm used as blades in cases (<b>e1</b>,<b>f1</b>).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/97'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 30 pages, 858 KiB   </span> <a href="/2297-8747/29/6/96/pdf?version=1729910771" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Sliding Mode Fault-Tolerant Control for Nonlinear LPV Systems with Variable Time-Delay" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/6/96">Sliding Mode Fault-Tolerant Control for Nonlinear LPV Systems with Variable Time-Delay</a> <div class="authors"> by <span class="inlineblock "><strong>Omayma Mansouri</strong>, </span><span class="inlineblock "><strong>Ali Ben Brahim</strong>, </span><span class="inlineblock "><strong>Fayçal Ben Hmida</strong> and </span><span class="inlineblock "><strong>Anis Sellami</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(6), 96; <a href="https://doi.org/10.3390/mca29060096">https://doi.org/10.3390/mca29060096</a> - 26 Oct 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> This paper presents a robust sliding mode fault-tolerant control (FTC) strategy for a class of linear parameter variant (LPV) systems with variable time-delays and uncertainties. First fault estimation (FE) is conducted using a robust sliding mode observer, synthesized to simultaneously estimate the states <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/96/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> This paper presents a robust sliding mode fault-tolerant control (FTC) strategy for a class of linear parameter variant (LPV) systems with variable time-delays and uncertainties. First fault estimation (FE) is conducted using a robust sliding mode observer, synthesized to simultaneously estimate the states and actuator faults of LPV polytopic delayed systems. Second, a sliding mode FTC is developed, ensuring all states of the closed-loop system converge to the origin. This paper presents an integrated sliding mode FTC strategy to achieve optimal robustness between the observer and controller models. The integrated design approach offers several advantages over traditional separated FTC methods. Our novel approach is based on incorporating adaptive law into the design of the Lyapunov–Krasovskii functional to improve both robustness and performance. This is achieved by combining the concept of sliding mode control (SMC) with the Lyapunov–Krasovskii function under the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> criteria, which plays a key role in guaranteeing the stability of this class of system. The effectiveness of the proposed method is demonstrated through a diesel engine example, which highlights the validity and benefits of the integrated and separated FTC strategy for uncertain nonlinear systems with time delays and the sliding mode control. <a href="/2297-8747/29/6/96">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/mca/special_issues/O70J996J9R ">Applied Optimization in Automatic Control and Systems Engineering</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/6/96/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1507018"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1507018"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1507018" data-cycle-prev="#prev1507018" data-cycle-progressive="#images1507018" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1507018-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g001-550.jpg?1729910930" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1507018" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1507018-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g002-550.jpg?1729910931'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1507018-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g003-550.jpg?1729910931'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1507018-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g004-550.jpg?1729910932'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1507018-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g005-550.jpg?1729910934'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1507018-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g006-550.jpg?1729910934'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1507018-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g007-550.jpg?1729910935'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1507018-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g008-550.jpg?1729910936'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1507018-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g009-550.jpg?1729910937'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1507018-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g010-550.jpg?1729910938'><p>Figure 10</p></div></script></div></div><div id="article-1507018-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g001-550.jpg?1729910930" title=" <strong>Figure 1</strong><br/> <p>Separated Design FTC.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/96'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g002-550.jpg?1729910931" title=" <strong>Figure 2</strong><br/> <p>Integrated design of FTC.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/96'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g003-550.jpg?1729910931" title=" <strong>Figure 3</strong><br/> <p>The air path system of diesel engines.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/96'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g004-550.jpg?1729910932" title=" <strong>Figure 4</strong><br/> <p>Estimation of actuator fault: Actuator fault estimation without FTC (blue line), actuator fault estimation with the separated FTC (red line), and actuator fault estimation with the integrated FTC (green line).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/96'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g005-550.jpg?1729910934" title=" <strong>Figure 5</strong><br/> <p>First closed-loop system output response: output response with the separated FTC (red line) and output response with the integrated FTC (green line).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/96'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g006-550.jpg?1729910934" title=" <strong>Figure 6</strong><br/> <p>Second closed-loop system output response: output response with the separated FTC (red line) and output response with the integrated FTC (green line).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/96'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g007-550.jpg?1729910935" title=" <strong>Figure 7</strong><br/> <p>First output estimation error: First output estimation error with the separated FTC (red line) and the first output estimation error with the integrated FTC (green line).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/96'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g008-550.jpg?1729910936" title=" <strong>Figure 8</strong><br/> <p>Second output estimation error: Second output estimation error with the separated FTC (red line) and second output estimation error with the integrated FTC (green line).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/96'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g009-550.jpg?1729910937" title=" <strong>Figure 9</strong><br/> <p>Effect of increasing constant <math display="inline"><semantics> <mi>τ</mi> </semantics></math> on actuator fault reconstruction (<math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math> red line), (<math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> green line), (<math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math> brown line).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/96'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00096/article_deploy/html/images/mca-29-00096-g010-550.jpg?1729910938" title=" <strong>Figure 10</strong><br/> <p>Actuator fault estimation without FTC (blue line), actuator fault estimation with state feedback in [<a href="#B26-mca-29-00096" class="html-bibr">26</a>] (red line), and actuator fault estimation with the integrated FTC (green line).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/6/96'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 16 pages, 2663 KiB   </span> <a href="/2297-8747/29/5/95/pdf?version=1729415965" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Bag of Feature-Based Ensemble Subspace KNN Classifier in Muscle Ultrasound Diagnosis of Diabetic Peripheral Neuropathy" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/5/95">Bag of Feature-Based Ensemble Subspace KNN Classifier in Muscle Ultrasound Diagnosis of Diabetic Peripheral Neuropathy</a> <div class="authors"> by <span class="inlineblock "><strong>Kadhim K. Al-Barazanchi</strong>, </span><span class="inlineblock "><strong>Ali H. Al-Timemy</strong> and </span><span class="inlineblock "><strong>Zahid M. Kadhim</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(5), 95; <a href="https://doi.org/10.3390/mca29050095">https://doi.org/10.3390/mca29050095</a> - 20 Oct 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Muscle ultrasound quantification is a valuable complementary diagnostic tool for diabetic peripheral neuropathy (DPN), enhancing physicians’ diagnostic capabilities. Quantitative assessment is generally regarded as more reliable and sensitive than visual evaluation, which often necessitates specialized expertise. This work develops a computer-aided diagnostic (CAD) <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/5/95/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Muscle ultrasound quantification is a valuable complementary diagnostic tool for diabetic peripheral neuropathy (DPN), enhancing physicians’ diagnostic capabilities. Quantitative assessment is generally regarded as more reliable and sensitive than visual evaluation, which often necessitates specialized expertise. This work develops a computer-aided diagnostic (CAD) system based on muscle ultrasound that integrates the bag of features (BOF) and an ensemble subspace k-nearest neighbor (KNN) algorithm for DPN detection. The BOF creates a histogram of visual word occurrences to represent the muscle ultrasound images and trains an ensemble classifier through cross-validation, determining optimal parameters to improve classification accuracy for the ensemble diagnosis system. The dataset includes ultrasound images of six muscles from 53 subjects, consisting of 27 control and 26 patient cases. An empirical analysis was conducted for each binary classifier based on muscle type to select the best vocabulary tree properties or K values for BOF. The result indicates that ensemble subspace KNN classification, based on the bag of features, achieved an accuracy of 97.23%. CAD systems can effectively diagnose muscle pathology, thereby addressing limitations and identifying issues in individuals with diabetes. This research underscores muscle ultrasound as a promising diagnostic tool to aid physicians in making accurate diagnoses, streamlining workflow, and uncovering muscle-related complications in DPN patients. <a href="/2297-8747/29/5/95">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/mca/sections/Engineering">Engineering</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/5/95/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1502761"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1502761"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1502761" data-cycle-prev="#prev1502761" data-cycle-progressive="#images1502761" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1502761-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/mca/mca-29-00095/article_deploy/html/images/mca-29-00095-g001-550.jpg?1729416052" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1502761" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1502761-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00095/article_deploy/html/images/mca-29-00095-g002-550.jpg?1729416053'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1502761-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00095/article_deploy/html/images/mca-29-00095-g003-550.jpg?1729416054'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1502761-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00095/article_deploy/html/images/mca-29-00095-g004-550.jpg?1729416055'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1502761-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00095/article_deploy/html/images/mca-29-00095-g005-550.jpg?1729416057'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1502761-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00095/article_deploy/html/images/mca-29-00095-g006-550.jpg?1729416058'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1502761-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00095/article_deploy/html/images/mca-29-00095-g007-550.jpg?1729416060'><p>Figure 7</p></div></script></div></div><div id="article-1502761-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00095/article_deploy/html/images/mca-29-00095-g001-550.jpg?1729416052" title=" <strong>Figure 1</strong><br/> <p>Proposed BOF-based ensemble subspace KNN classification system for DPN diagnosis.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/95'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00095/article_deploy/html/images/mca-29-00095-g002-550.jpg?1729416053" title=" <strong>Figure 2</strong><br/> <p>Illustration of BOF steps.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/95'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00095/article_deploy/html/images/mca-29-00095-g003-550.jpg?1729416054" title=" <strong>Figure 3</strong><br/> <p>Ensemble subspace KNN algorithm architecture.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/95'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00095/article_deploy/html/images/mca-29-00095-g004-550.jpg?1729416055" title=" <strong>Figure 4</strong><br/> <p>The t-SNE display for the upper limb muscles (BB, BR, and ADM) BOF dataset with 400 visual words.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/95'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00095/article_deploy/html/images/mca-29-00095-g005-550.jpg?1729416057" title=" <strong>Figure 5</strong><br/> <p>The t-SNE display for the lower limb muscles (RF, TA, and AHB) BOF dataset with 400 visual words.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/95'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00095/article_deploy/html/images/mca-29-00095-g006-550.jpg?1729416058" title=" <strong>Figure 6</strong><br/> <p>Confusion matrix of the ensemble-BOF-based classifier with 400 visual words.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/95'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00095/article_deploy/html/images/mca-29-00095-g007-550.jpg?1729416060" title=" <strong>Figure 7</strong><br/> <p>ROC curve of the ensemble-BOF-based classifier with 400 visual words for ADM.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/95'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 16 pages, 1037 KiB   </span> <a href="/2297-8747/29/5/94/pdf?version=1728955828" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Mathematical Modeling and Analysis of Ebola Virus Disease Dynamics: Implications for Intervention Strategies and Healthcare Resource Optimization" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/5/94">Mathematical Modeling and Analysis of Ebola Virus Disease Dynamics: Implications for Intervention Strategies and Healthcare Resource Optimization</a> <div class="authors"> by <span class="inlineblock "><strong>Ikram Ullah</strong>, </span><span class="inlineblock "><strong>Imtiaz Ahmad</strong>, </span><span class="inlineblock "><strong>Nigar Ali</strong>, </span><span class="inlineblock "><strong>Ihtisham Ul Haq</strong>, </span><span class="inlineblock "><strong>Mohammad Idrees</strong>, </span><span class="inlineblock "><strong>Mohammed Daher Albalwi</strong> and </span><span class="inlineblock "><strong>Mehmet Yavuz</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(5), 94; <a href="https://doi.org/10.3390/mca29050094">https://doi.org/10.3390/mca29050094</a> - 12 Oct 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> This study implements a minded approach to studying Ebola virus disease (EVD) by dividing the infected population into aware and unaware groups and including a hospitalized compartment. This offers a more detailed understanding of illness distribution, potential analyses, and the influence of public <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/5/94/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> This study implements a minded approach to studying Ebola virus disease (EVD) by dividing the infected population into aware and unaware groups and including a hospitalized compartment. This offers a more detailed understanding of illness distribution, potential analyses, and the influence of public knowledge. The findings might improve healthcare budget apportionment, public health policy, and contest Ebola and related infections. In this study, we fully observe the new model <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>E</mi><mi>I</mi><mi>H</mi><mi>R</mi></mrow></semantics></math></inline-formula> that we have constructed. We start by outlining the essential concepts of the model and confirming its mathematical reliability. Next, we calculate the fundamental reproductive number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>R</mi><mn>0</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula>, which is critical for appreciating how the infection spreads and how effective treatments might be. We also study stability analysis, which looks at when the disease may decline or become chronic. Furthermore, we exhibit the occurrence of bifurcation in the EVD Epidemic Model and perform a sensitivity analysis of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>R</mi><mn>0</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula>. The main findings of this study show that for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>, the disease-free equilibrium, is globally stable, meaning the disease will die out, whereas for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>, the endemic equilibrium is stable, meaning the disease persists. Additionally, the sensitivity analysis reveals that the most influential parameters in controlling <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula> are the transmission rate and the recovery rate, which could guide effective intervention strategies. Finally, we use numerical simulations so that out outcomes are more significant. <a href="/2297-8747/29/5/94">Full article</a> </div> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/5/94/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1497597"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1497597"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1497597" data-cycle-prev="#prev1497597" data-cycle-progressive="#images1497597" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1497597-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/mca/mca-29-00094/article_deploy/html/images/mca-29-00094-g001-550.jpg?1728955909" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1497597" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1497597-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00094/article_deploy/html/images/mca-29-00094-g002-550.jpg?1728955911'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1497597-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00094/article_deploy/html/images/mca-29-00094-g003-550.jpg?1728955912'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1497597-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00094/article_deploy/html/images/mca-29-00094-g004-550.jpg?1728955914'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1497597-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00094/article_deploy/html/images/mca-29-00094-g005-550.jpg?1728955914'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1497597-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00094/article_deploy/html/images/mca-29-00094-g006-550.jpg?1728955916'><p>Figure 6</p></div></script></div></div><div id="article-1497597-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00094/article_deploy/html/images/mca-29-00094-g001-550.jpg?1728955909" title=" <strong>Figure 1</strong><br/> <p>Flowchart of the Ebola virus.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/94'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00094/article_deploy/html/images/mca-29-00094-g002-550.jpg?1728955911" title=" <strong>Figure 2</strong><br/> <p>(<b>a</b>) The effect of <math display="inline"><semantics> <mo>Λ</mo> </semantics></math>, <math display="inline"><semantics> <msub> <mi>η</mi> <mn>1</mn> </msub> </semantics></math> on <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>.</mo> </mrow> </semantics></math> (<b>b</b>) The influence of <math display="inline"><semantics> <msub> <mi>α</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>σ</mi> <mn>1</mn> </msub> </semantics></math> on <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>.</mo> </mrow> </semantics></math> (<b>c</b>) The effect of <math display="inline"><semantics> <mi>μ</mi> </semantics></math> and <math display="inline"><semantics> <msub> <mi>δ</mi> <mn>1</mn> </msub> </semantics></math> on <math display="inline"><semantics> <msub> <mi>R</mi> <mn>0</mn> </msub> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/94'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00094/article_deploy/html/images/mca-29-00094-g003-550.jpg?1728955912" title=" <strong>Figure 3</strong><br/> <p>Sensitivity index of <math display="inline"><semantics> <msub> <mi>R</mi> <mn>0</mn> </msub> </semantics></math> for the model parameters.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/94'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00094/article_deploy/html/images/mca-29-00094-g004-550.jpg?1728955914" title=" <strong>Figure 4</strong><br/> <p>Variation of the total number of individuals over time for: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.01234</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.02877</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.04000</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <msub> <mi>R</mi> <mn>0</mn> </msub> </semantics></math> = 0.1837 (&lt;1); (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.1234</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>2877</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.4000</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <msub> <mi>R</mi> <mn>0</mn> </msub> </semantics></math> = 1.8372 (&gt;1).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/94'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00094/article_deploy/html/images/mca-29-00094-g005-550.jpg?1728955914" title=" <strong>Figure 5</strong><br/> <p>Variation of the total number of infectious individuals over time with different initial values for <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </semantics></math>. Subfigure (<b>a</b>) shows the variation for <math display="inline"><semantics> <msub> <mi>I</mi> <mi>u</mi> </msub> </semantics></math>, representing untreated infections, while subfigure (<b>b</b>) illustrates the variation for <math display="inline"><semantics> <msub> <mi>I</mi> <mi>a</mi> </msub> </semantics></math>, representing AIDS cases.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/94'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00094/article_deploy/html/images/mca-29-00094-g006-550.jpg?1728955916" title=" <strong>Figure 6</strong><br/> <p>Effects of Parameters <math display="inline"><semantics> <msub> <mi>α</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>η</mi> <mn>1</mn> </msub> </semantics></math>, and <math display="inline"><semantics> <msub> <mi>σ</mi> <mn>1</mn> </msub> </semantics></math> on the Infected Population (<math display="inline"><semantics> <msub> <mi>I</mi> <mi>u</mi> </msub> </semantics></math>). (<b>a</b>) Effects of <math display="inline"><semantics> <msub> <mi>α</mi> <mn>1</mn> </msub> </semantics></math> on <math display="inline"><semantics> <msub> <mi>I</mi> <mi>u</mi> </msub> </semantics></math>. (<b>b</b>) Effects of <math display="inline"><semantics> <msub> <mi>η</mi> <mn>1</mn> </msub> </semantics></math> on <math display="inline"><semantics> <msub> <mi>I</mi> <mi>u</mi> </msub> </semantics></math>. (<b>c</b>) Effects of <math display="inline"><semantics> <msub> <mi>σ</mi> <mn>1</mn> </msub> </semantics></math> on <math display="inline"><semantics> <msub> <mi>I</mi> <mi>u</mi> </msub> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/94'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 13 pages, 4030 KiB   </span> <a href="/2297-8747/29/5/93/pdf?version=1728651789" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Application of Bispectral Analysis to Assess the Effect of Drought on the Photosynthetic Activity of Lettuce Plants Lactuca sativa L." data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/5/93">Application of Bispectral Analysis to Assess the Effect of Drought on the Photosynthetic Activity of Lettuce Plants <i>Lactuca sativa</i> L.</a> <div class="authors"> by <span class="inlineblock "><strong>Maxim E. Astashev</strong>, </span><span class="inlineblock "><strong>Dmitriy E. Burmistrov</strong>, </span><span class="inlineblock "><strong>Denis V. Yanykin</strong>, </span><span class="inlineblock "><strong>Andrey A. Grishin</strong>, </span><span class="inlineblock "><strong>Inna V. Knyazeva</strong>, </span><span class="inlineblock "><strong>Alexey S. Dorokhov</strong> and </span><span class="inlineblock "><strong>Sergey V. Gudkov</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(5), 93; <a href="https://doi.org/10.3390/mca29050093">https://doi.org/10.3390/mca29050093</a> - 11 Oct 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> This article proposes a new method for determining the pathological state of a plant, based on a combination of the method for measuring the dynamics of photosystem II pigment fluorescence in the leaves of <i>L. sativa</i> plants and analyzing the resulting time series <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/5/93/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> This article proposes a new method for determining the pathological state of a plant, based on a combination of the method for measuring the dynamics of photosystem II pigment fluorescence in the leaves of <i>L. sativa</i> plants and analyzing the resulting time series using bispectral analysis based on the wavelet transform. The article theoretically shows a possible mechanism for the appearance of a peak on the map of bispectrum indexes during nonlinear analog conversion of a physiological signal in a biological object. The phenomenon of increasing the degree of nonlinearity in the transmission of an external periodic signal in plant signaling systems has been experimentally demonstrated. <a href="/2297-8747/29/5/93">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/mca/sections/natural_sciences">Natural Sciences</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/5/93/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1496701"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1496701"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1496701" data-cycle-prev="#prev1496701" data-cycle-progressive="#images1496701" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1496701-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g001-550.jpg?1728651862" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1496701" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1496701-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g002-550.jpg?1728651863'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1496701-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g003-550.jpg?1728651866'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1496701-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g004-550.jpg?1728651867'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1496701-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g005-550.jpg?1728651869'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1496701-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g006-550.jpg?1728651870'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1496701-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g007-550.jpg?1728651872'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1496701-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g008-550.jpg?1728651873'><p>Figure 8</p></div></script></div></div><div id="article-1496701-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g001-550.jpg?1728651862" title=" <strong>Figure 1</strong><br/> <p>Photography of <span class="html-italic">Lactuca sativa</span> L. plants before drought modeling (<b>a</b>) and after (<b>b</b>).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/93'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g002-550.jpg?1728651863" title=" <strong>Figure 2</strong><br/> <p>Experimental design.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/93'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g003-550.jpg?1728651866" title=" <strong>Figure 3</strong><br/> <p>Dependence of the wavelet coefficient modulus on time and frequency for model signals. Harmonic sinusoidal signal without nonlinear transformation (<b>a</b>). Harmonic sinusoidal signal with nonlinearity level A/B = 0.1 (<b>b</b>). Harmonic sinusoidal signal with nonlinearity level A/B = 0.3 (<b>c</b>). Harmonic sinusoidal signal with nonlinearity level A/B = 1 (<b>d</b>).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/93'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g004-550.jpg?1728651867" title=" <strong>Figure 4</strong><br/> <p>Frequency dependences of the modulus of wavelet coefficients (<b>a</b>) and diagonal elements of the bispectrum (<b>b</b>). Dependences are given for the degrees of nonlinearity of 0, 0.1, 0.3 and 1.0 (the color coding is indicated in the legend, and is the same for (<b>a</b>,<b>b</b>)).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/93'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g005-550.jpg?1728651869" title=" <strong>Figure 5</strong><br/> <p>Dependences of the bispectrum index on the frequencies ω<sub>1</sub> and ω<sub>2</sub> for nonlinearity degrees of 0 (<b>a</b>), 0.1 (<b>b</b>), 0.3 (<b>c</b>), and 1.0 (<b>d</b>). The color scale for all graphs is the same and is normalized to the maximum of the inset (<b>d</b>).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/93'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g006-550.jpg?1728651870" title=" <strong>Figure 6</strong><br/> <p>Examples of records of the baseline fluorescence level in the 24 h mode without growth lighting. Green: record of fluorescence of a plant with normal watering. Red: record of a plant under drought conditions. The insets show 7 consecutive reactions to the saturating pulse aligned at the beginning of the saturating illumination pulse. The black line in the insets is the average value.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/93'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g007-550.jpg?1728651872" title=" <strong>Figure 7</strong><br/> <p>Wavelet coefficients of the baseline fluorescence level records in the 24 h mode without growth lighting. Recording of fluorescence of a plant with normal watering (<b>a</b>), recording of fluorescence of a plant under drought conditions (<b>b</b>), map of the values of bispectral coefficients of oscillations of the baseline fluorescence level of control plants (<b>c</b>), map of the values of bispectral coefficients of oscillations of the baseline fluorescence level of plants with drought modeling (<b>d</b>); the dashed line in the fields (<b>a</b>,<b>b</b>) is the oscillation period corresponding to 1 h.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/93'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00093/article_deploy/html/images/mca-29-00093-g008-550.jpg?1728651873" title=" <strong>Figure 8</strong><br/> <p>Plot of bispectral coefficients versus frequency (<b>a</b>) and comparison of bispectral coefficients for a period of 3600 s in healthy plants and plants under stress (<b>b</b>). Green color indicates data obtained for healthy plants, red color indicates data for plants under drought conditions.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/93'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 17 pages, 293 KiB   </span> <a href="/2297-8747/29/5/92/pdf?version=1728571265" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Lie Symmetry Analysis, Closed-Form Solutions, and Conservation Laws for the Camassa–Holm Type Equation" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/5/92">Lie Symmetry Analysis, Closed-Form Solutions, and Conservation Laws for the Camassa–Holm Type Equation</a> <div class="authors"> by <span class="inlineblock "><strong>Jonathan Lebogang Bodibe</strong> and </span><span class="inlineblock "><strong>Chaudry Masood Khalique</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(5), 92; <a href="https://doi.org/10.3390/mca29050092">https://doi.org/10.3390/mca29050092</a> - 10 Oct 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> In this paper, we study the Camassa–Holm type equation, which has applications in mathematical physics and engineering. Its applications extend across disciplines, contributing to our understanding of complex systems and helping to develop innovative solutions in diverse areas of research. Our main aim <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/5/92/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> In this paper, we study the Camassa–Holm type equation, which has applications in mathematical physics and engineering. Its applications extend across disciplines, contributing to our understanding of complex systems and helping to develop innovative solutions in diverse areas of research. Our main aim is to construct closed-form solutions of the equation using a powerful technique, namely the Lie group analysis method. Firstly, we derive the Lie point symmetries of the equation. Thereafter, the equation is reduced to non-linear ordinary differential equations using symmetry reductions. Furthermore, the solutions of the equation are derived using the extended Jacobi elliptic function technique, the simplest equation method, and the power series method. In conclusion, we construct conservation laws for the equation using Noether’s theorem and the multiplier approach, which plays a crucial role in understanding the behavior of non-linear equations, especially in physics and engineering, and these laws are derived from fundamental principles such as the conservation of mass, energy, momentum, and angular momentum. <a href="/2297-8747/29/5/92">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/mca/special_issues/8V8TL020L4 ">Symmetry Methods for Solving Differential Equations</a>)<br/> </div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 35 pages, 970 KiB   </span> <a href="/2297-8747/29/5/91/pdf?version=1728625870" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Using Symmetries to Investigate the Complete Integrability, Solitary Wave Solutions and Solitons of the Gardner Equation" data-journal="mca"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2297-8747/29/5/91">Using Symmetries to Investigate the Complete Integrability, Solitary Wave Solutions and Solitons of the Gardner Equation</a> <div class="authors"> by <span class="inlineblock "><strong>Willy Hereman</strong> and </span><span class="inlineblock "><strong>Ünal Göktaş</strong></span> </div> <div class="color-grey-dark"> <em>Math. Comput. Appl.</em> <b>2024</b>, <em>29</em>(5), 91; <a href="https://doi.org/10.3390/mca29050091">https://doi.org/10.3390/mca29050091</a> - 3 Oct 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> In this paper, using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations, thereby establishing their complete integrability. The Gardner equation is chosen as the <a href="#" data-counterslink = "https://www.mdpi.com/2297-8747/29/5/91/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> In this paper, using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations, thereby establishing their complete integrability. The Gardner equation is chosen as the key example, as it comprises both the Korteweg–de Vries and modified Korteweg–de Vries equations. The Gardner and Miura transformations, which connect these equations, are also computed using the concept of scaling homogeneity. Exact solitary wave solutions and solitons of the Gardner equation are derived using Hirota’s method and other direct methods. The nature of these solutions depends on the sign of the cubic term in the Gardner equation and the underlying mKdV equation. It is shown that flat (table-top) waves of large amplitude only occur when the sign of the cubic nonlinearity is negative (defocusing case), whereas the focusing Gardner equation has standard elastically colliding solitons. This paper’s aim is to provide a review of the integrability properties and solutions of the Gardner equation and to illustrate the applicability of the scaling symmetry approach. The methods and algorithms used in this paper have been implemented in <i>Mathematica</i>, but can be adapted for major computer algebra systems. <a href="/2297-8747/29/5/91">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/mca/special_issues/8V8TL020L4 ">Symmetry Methods for Solving Differential Equations</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2297-8747/29/5/91/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1491711"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1491711"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1491711" data-cycle-prev="#prev1491711" data-cycle-progressive="#images1491711" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1491711-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g001-550.jpg?1728625946" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1491711" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1491711-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g002-550.jpg?1728625947'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1491711-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g003-550.jpg?1728625947'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1491711-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g004-550.jpg?1728625949'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1491711-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g005-550.jpg?1728625950'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1491711-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g006-550.jpg?1728625951'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1491711-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g007-550.jpg?1728625951'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1491711-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g008-550.jpg?1728625952'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1491711-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g009-550.jpg?1728625953'><p>Figure 9</p></div></script></div></div><div id="article-1491711-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g001-550.jpg?1728625946" title=" <strong>Figure 1</strong><br/> <p>Graphs of the solitary wave (solid line) and cnoidal wave (dashed line) solutions for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>6</mn> <mo>,</mo> <mi>k</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mspace width="0.166667em"/> <mi>m</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="false"> <mfrac> <mn>9</mn> <mn>10</mn> </mfrac> </mstyle> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/91'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g002-550.jpg?1728625947" title=" <strong>Figure 2</strong><br/> <p>Graphs of (<a href="#FD145-mca-29-00091" class="html-disp-formula">145</a>) (<b>left</b>) and (<a href="#FD146-mca-29-00091" class="html-disp-formula">146</a>) (<b>right</b>) both with the minus signs in front of the square roots, and both for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>. The curves on the right correspond to <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0.25</mn> </mrow> </semantics></math> (dashed line) and <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math> (solid line).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/91'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g003-550.jpg?1728625947" title=" <strong>Figure 3</strong><br/> <p>Graphs of (<a href="#FD149-mca-29-00091" class="html-disp-formula">149</a>) (<b>left</b>) and (<a href="#FD150-mca-29-00091" class="html-disp-formula">150</a>) (<b>right</b>), both for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mo>−</mo> <mn>6</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>. The curves on the right correspond to <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0.25</mn> </mrow> </semantics></math> (dashed line) and <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math> (solid line).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/91'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g004-550.jpg?1728625949" title=" <strong>Figure 4</strong><br/> <p>Graphs of (<a href="#FD151-mca-29-00091" class="html-disp-formula">151</a>) for <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>0.625</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>0.75</mn> </mrow> </semantics></math> (<b>left</b>), and <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>0.9999</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>0.999995</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>0.9999995</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (<b>right</b>). The solitary wave becomes taller and narrower as the value of <span class="html-italic">k</span> increases.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/91'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g005-550.jpg?1728625950" title=" <strong>Figure 5</strong><br/> <p>Graphs of (<a href="#FD151-mca-29-00091" class="html-disp-formula">151</a>) (full line) and (<a href="#FD153-mca-29-00091" class="html-disp-formula">153</a>) (dashed line) for four different values of <span class="html-italic">k</span>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/91'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g006-550.jpg?1728625951" title=" <strong>Figure 6</strong><br/> <p>Graph of the two-soliton solution (<a href="#FD155-mca-29-00091" class="html-disp-formula">155</a>) of the focusing Gardner equation at three different moments in time.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/91'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g007-550.jpg?1728625951" title=" <strong>Figure 7</strong><br/> <p>Bird’s eye view of a two-soliton collision for the focusing Gardner equation. Notice the phase shift after collision: the taller (faster) soliton is shifted forward and the shorter (slower) soliton backward relative to where they would have been if they had not collided.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/91'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g008-550.jpg?1728625952" title=" <strong>Figure 8</strong><br/> <p>2D and 3D graphs of solution (<a href="#FD156-mca-29-00091" class="html-disp-formula">156</a>) for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mo>−</mo> <mn>6</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0.65</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2297-8747/29/5/91'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/mca/mca-29-00091/article_deploy/html/images/mca-29-00091-g009-550.jpg?1728625953" title=" <strong>Figure 9</strong><br/> <p>2D and 3D graphs of solution (<a href="#FD156-mca-29-00091" class="html-disp-formula">156</a>) for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mo>−</mo> <mn>6</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 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