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Morse theory</title> <meta name="description" content="Search results for: Discrete Morse theory"> <meta name="keywords" content="Discrete Morse theory"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="Discrete Morse theory"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 5306</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Discrete Morse theory</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5306</span> A Look at the Quantum Theory of Atoms in Molecules from the Discrete Morse Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dairo%20Jose%20Hernandez%20Paez">Dairo Jose Hernandez Paez</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The quantum theory of atoms in molecules (QTAIM) allows us to obtain topological information on electronic density in quantum mechanical systems. The QTAIM starts by considering the electron density as a continuous mathematical object. On the other hand, the discretization of electron density is also a mathematical object, which, from discrete mathematics, would allow a new approach to its topological study. From this point of view, it is necessary to develop a series of steps that provide the theoretical support that guarantees its application. Some of the steps that we consider most important are mentioned below: (1) obtain good representations of the electron density through computational calculations, (2) design a methodology for the discretization of electron density, and construct the simplicial complex. (3) Make an analysis of the discrete vector field associating the simplicial complex. (4) Finally, in this research, we propose to use the discrete Morse theory as a mathematical tool to carry out studies of electron density topology. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=discrete%20mathematics" title="discrete mathematics">discrete mathematics</a>, <a href="https://publications.waset.org/abstracts/search?q=Discrete%20Morse%20theory" title=" Discrete Morse theory"> Discrete Morse theory</a>, <a href="https://publications.waset.org/abstracts/search?q=electronic%20density" title=" electronic density"> electronic density</a>, <a href="https://publications.waset.org/abstracts/search?q=computational%20calculations" title=" computational calculations"> computational calculations</a> </p> <a href="https://publications.waset.org/abstracts/163354/a-look-at-the-quantum-theory-of-atoms-in-molecules-from-the-discrete-morse-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/163354.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">104</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5305</span> A High Quality Factor Filter Based on Quasi- Periodic Photonic Structure</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hamed%20Alipour-Banaei">Hamed Alipour-Banaei</a>, <a href="https://publications.waset.org/abstracts/search?q=Farhad%20Mehdizadeh"> Farhad Mehdizadeh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We report the design and characterization of ultra high quality factor filter based on one-dimensional photonic-crystal Thue-Morse sequence structure. The behavior of aperiodic array of photonic crystal structure is numerically investigated and we show that by changing the angle of incident wave, desired wavelengths could be tuned and a tunable filter is realized. Also it is shown that high quality factor filter be achieved in the telecommunication window around 1550 nm, with a device based on Thue-Morse structure. Simulation results show that the proposed structure has a quality factor more than 100000 and it is suitable for DWDM communication applications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Thue-Morse" title="Thue-Morse">Thue-Morse</a>, <a href="https://publications.waset.org/abstracts/search?q=filter" title=" filter"> filter</a>, <a href="https://publications.waset.org/abstracts/search?q=quality%20factor" title=" quality factor"> quality factor</a>, <a href="https://publications.waset.org/abstracts/search?q=photonic" title=" photonic"> photonic</a> </p> <a href="https://publications.waset.org/abstracts/31621/a-high-quality-factor-filter-based-on-quasi-periodic-photonic-structure" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/31621.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">572</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5304</span> Discrete Sliding Modes Regulator with Exponential Holder for Non-Linear Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=G.%20Obregon-Pulido">G. Obregon-Pulido </a>, <a href="https://publications.waset.org/abstracts/search?q=G.%20C.%20Solis-Perales"> G. C. Solis-Perales</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20A.%20Meda-Campa%C3%B1a"> J. A. Meda-Campaña</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present a sliding mode controller in discrete time. The design of the controller is based on the theory of regulation for nonlinear systems. In the problem of disturbance rejection and/or output tracking, it is known that in discrete time, a controller that uses the zero-order holder only guarantees tracking at the sampling instances but not between instances. It is shown that using the so-called exponential holder, it is possible to guarantee asymptotic zero output tracking error, also between the sampling instant. For stabilizing the problem of close loop system we introduce the sliding mode approach relaxing the requirements of the existence of a linear stabilizing control law. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=regulation%20theory" title="regulation theory">regulation theory</a>, <a href="https://publications.waset.org/abstracts/search?q=sliding%20modes" title=" sliding modes"> sliding modes</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20controller" title=" discrete controller"> discrete controller</a>, <a href="https://publications.waset.org/abstracts/search?q=ripple-free%20tracking" title=" ripple-free tracking"> ripple-free tracking</a> </p> <a href="https://publications.waset.org/abstracts/178771/discrete-sliding-modes-regulator-with-exponential-holder-for-non-linear-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/178771.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">54</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5303</span> Application of the Micropolar Beam Theory for the Construction of the Discrete-Continual Model of Carbon Nanotubes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Samvel%20H.%20Sargsyan">Samvel H. Sargsyan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Together with the study of electron-optical properties of nanostructures and proceeding from experiment-based data, the study of the mechanical properties of nanostructures has become quite actual. For the study of the mechanical properties of fullerene, carbon nanotubes, graphene and other nanostructures one of the crucial issues is the construction of their adequate mathematical models. Among all mathematical models of graphene or carbon nano-tubes, this so-called discrete-continuous model is specifically important. It substitutes the interactions between atoms by elastic beams or springs. The present paper demonstrates the construction of the discrete-continual beam model for carbon nanotubes or graphene, where the micropolar beam model based on the theory of moment elasticity is accepted. With the account of the energy balance principle, the elastic moment constants for the beam model, expressed by the physical and geometrical parameters of carbon nanotube or graphene, are determined. By switching from discrete-continual beam model to the continual, the models of micropolar elastic cylindrical shell and micropolar elastic plate are confirmed as continual models for carbon nanotube and graphene respectively. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=carbon%20nanotube" title="carbon nanotube">carbon nanotube</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete-continual" title=" discrete-continual"> discrete-continual</a>, <a href="https://publications.waset.org/abstracts/search?q=elastic" title=" elastic"> elastic</a>, <a href="https://publications.waset.org/abstracts/search?q=graphene" title=" graphene"> graphene</a>, <a href="https://publications.waset.org/abstracts/search?q=micropolar" title=" micropolar"> micropolar</a>, <a href="https://publications.waset.org/abstracts/search?q=plate" title=" plate"> plate</a>, <a href="https://publications.waset.org/abstracts/search?q=shell" title=" shell"> shell</a> </p> <a href="https://publications.waset.org/abstracts/82214/application-of-the-micropolar-beam-theory-for-the-construction-of-the-discrete-continual-model-of-carbon-nanotubes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/82214.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">159</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5302</span> Optimization of Fourth Order Discrete-Approximation Inclusions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Elimhan%20N.%20Mahmudov">Elimhan N. Mahmudov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper concerns the necessary and sufficient conditions of optimality for Cauchy problem of fourth order discrete (PD) and discrete-approximate (PDA) inclusions. The main problem is formulation of the fourth order adjoint discrete and discrete-approximate inclusions and transversality conditions, which are peculiar to problems including fourth order derivatives and approximate derivatives. Thus the necessary and sufficient conditions of optimality are obtained incorporating the Euler-Lagrange and Hamiltonian forms of inclusions. Derivation of optimality conditions are based on the apparatus of locally adjoint mapping (LAM). Moreover in the application of these results we consider the fourth order linear discrete and discrete-approximate inclusions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=difference" title="difference">difference</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=fourth" title=" fourth"> fourth</a>, <a href="https://publications.waset.org/abstracts/search?q=approximation" title=" approximation"> approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=transversality" title=" transversality"> transversality</a> </p> <a href="https://publications.waset.org/abstracts/25199/optimization-of-fourth-order-discrete-approximation-inclusions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25199.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">374</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5301</span> Pure and Mixed Nash Equilibria Domain of a Discrete Game Model with Dichotomous Strategy Space</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20S.%20Mousa">A. S. Mousa</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Shoman"> F. Shoman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present a discrete game theoretical model with homogeneous individuals who make simultaneous decisions. In this model the strategy space of all individuals is a discrete and dichotomous set which consists of two strategies. We fully characterize the coherent, split and mixed strategies that form Nash equilibria and we determine the corresponding Nash domains for all individuals. We find all strategic thresholds in which individuals can change their mind if small perturbations in the parameters of the model occurs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=coherent%20strategy" title="coherent strategy">coherent strategy</a>, <a href="https://publications.waset.org/abstracts/search?q=split%20strategy" title=" split strategy"> split strategy</a>, <a href="https://publications.waset.org/abstracts/search?q=pure%20strategy" title=" pure strategy"> pure strategy</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed%20strategy" title=" mixed strategy"> mixed strategy</a>, <a href="https://publications.waset.org/abstracts/search?q=Nash%20equilibrium" title=" Nash equilibrium"> Nash equilibrium</a>, <a href="https://publications.waset.org/abstracts/search?q=game%20theory" title=" game theory"> game theory</a> </p> <a href="https://publications.waset.org/abstracts/128019/pure-and-mixed-nash-equilibria-domain-of-a-discrete-game-model-with-dichotomous-strategy-space" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/128019.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">148</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5300</span> A Review on the Problems of Constructing a Theory of Quantum Gravity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Amber%20Jamal">Amber Jamal</a>, <a href="https://publications.waset.org/abstracts/search?q=Imran%20Siddiqui"> Imran Siddiqui</a>, <a href="https://publications.waset.org/abstracts/search?q=Syed%20Tanveer%20Iqbal"> Syed Tanveer Iqbal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This review is aimed to shed some light on problems constructing a theory of spacetime and geometry in terms of all quantum degrees of freedom called ‘Quantum Gravity’. Such a theory, which is effective at all scales of distances and energies, describes the enigma of the beginning of the Universe, its possible end, and reducing to general relativity at large distances but in a semi-classical approximation. Furthermore, the theory of quantum gravity also describes the Universe as a whole and provides a description of most fundamental questions that have puzzled scientists for decades, such as: what is space, what is time, and what is the fundamental structure of the Universe, is the spacetime discrete, if it is, where does the continuum of spacetime come from at low energies and macroscopic scales and where does it emerge from its fundamentally discrete building blocks? Quantum Field Theory (QFT) is a framework which describes the microscopic properties and dynamics of the basic building blocks of any condensed matter system. In QFT, atoms are quanta of continuous fields. At smaller scales or higher energies, the continuum description of spacetime fails. Therefore, a new description is required in terms of microscopic constituents (atoms or molecules). The objective of this scientific endeavor is to discuss the above-mentioned problems rigorously and to discuss possible way-out of the problems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=QFT" title="QFT">QFT</a>, <a href="https://publications.waset.org/abstracts/search?q=quantum%20degrees%20of%20freedom" title=" quantum degrees of freedom"> quantum degrees of freedom</a>, <a href="https://publications.waset.org/abstracts/search?q=quantum%20gravity" title=" quantum gravity"> quantum gravity</a>, <a href="https://publications.waset.org/abstracts/search?q=semi-classical%20approximation" title=" semi-classical approximation"> semi-classical approximation</a> </p> <a href="https://publications.waset.org/abstracts/130610/a-review-on-the-problems-of-constructing-a-theory-of-quantum-gravity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/130610.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">119</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5299</span> Role of Discrete Event Simulation in the Assessment and Selection of the Potential Reconfigurable Manufacturing Solutions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohsin%20Raza">Mohsin Raza</a>, <a href="https://publications.waset.org/abstracts/search?q=Arne%20Bilberg"> Arne Bilberg</a>, <a href="https://publications.waset.org/abstracts/search?q=Thomas%20Ditlev%20Brun%C3%B8"> Thomas Ditlev Brunø</a>, <a href="https://publications.waset.org/abstracts/search?q=Ann-Louise%20Andersen"> Ann-Louise Andersen</a>, <a href="https://publications.waset.org/abstracts/search?q=Filip%20SK%C3%A4rin"> Filip SKärin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Shifting from a dedicated or flexible manufacturing system to a reconfigurable manufacturing system (RMS) requires a significant amount of time, money, and effort. Therefore, it is vital to verify beforehand that the potential reconfigurable solution will be able to achieve the organizational objectives. Discrete event simulation offers the opportunity of assessing several reconfigurable alternatives against the set objectives. This study signifies the importance of using discrete-event simulation as a tool to verify several reconfiguration options. Two different industrial cases have been presented in the study to elaborate on the role of discrete event simulation in the implementation methodology of RMSs. The study concluded that discrete event simulation is one of the important tools to consider in the RMS implementation methodology. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=reconfigurable%20manufacturing%20system" title="reconfigurable manufacturing system">reconfigurable manufacturing system</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20event%20simulation" title=" discrete event simulation"> discrete event simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=Tecnomatix%20plant%20simulation" title=" Tecnomatix plant simulation"> Tecnomatix plant simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=RMS" title=" RMS"> RMS</a> </p> <a href="https://publications.waset.org/abstracts/150254/role-of-discrete-event-simulation-in-the-assessment-and-selection-of-the-potential-reconfigurable-manufacturing-solutions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/150254.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">124</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5298</span> Simulation of Nonlinear Behavior of Reinforced Concrete Slabs Using Rigid Body-Spring Discrete Element Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Felix%20Jr.%20Garde">Felix Jr. Garde</a>, <a href="https://publications.waset.org/abstracts/search?q=Eric%20Augustus%20Tingatinga"> Eric Augustus Tingatinga</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Most analysis procedures of reinforced concrete (RC) slabs are based on elastic theory. When subjected to large forces, however, slabs deform beyond elastic range and the study of their behavior and performance require nonlinear analysis. This paper presents a numerical model to simulate nonlinear behavior of RC slabs using rigid body-spring discrete element method. The proposed slab model composed of rigid plate elements and nonlinear springs is based on the yield line theory which assumes that the nonlinear behavior of the RC slab subjected to transverse loads is contained in plastic or yield-lines. In this model, the displacement of the slab is completely described by the rigid elements and the deformation energy is concentrated in the flexural springs uniformly distributed at the potential yield lines. The spring parameters are determined from comparison of transverse displacements and stresses developed in the slab obtained using FEM and the proposed model with assumed homogeneous material. Numerical models of typical RC slabs with varying geometry, reinforcement, support conditions, and loading conditions, show reasonable agreement with available experimental data. The model was also shown to be useful in investigating dynamic behavior of slabs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=RC%20slab" title="RC slab">RC slab</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20behavior" title=" nonlinear behavior"> nonlinear behavior</a>, <a href="https://publications.waset.org/abstracts/search?q=yield%20line%20theory" title=" yield line theory"> yield line theory</a>, <a href="https://publications.waset.org/abstracts/search?q=rigid%20body-spring%20discrete%20element%20method" title=" rigid body-spring discrete element method"> rigid body-spring discrete element method</a> </p> <a href="https://publications.waset.org/abstracts/57601/simulation-of-nonlinear-behavior-of-reinforced-concrete-slabs-using-rigid-body-spring-discrete-element-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/57601.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">323</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5297</span> Multidimensional Integral and Discrete Opial–Type Inequalities</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Maja%20Andri%C4%87">Maja Andrić</a>, <a href="https://publications.waset.org/abstracts/search?q=Josip%20Pe%C4%8Dari%C4%87"> Josip Pečarić</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Over the last five decades, an enormous amount of work has been done on Opial’s integral inequality, dealing with new proofs, various generalizations, extensions and discrete analogs. The Opial inequality is recognized as a fundamental result in the analysis of qualitative properties of solution of differential equations. We use submultiplicative convex functions, appropriate representations of functions and inequalities involving means to obtain generalizations and extensions of certain known multidimensional integral and discrete Opial-type inequalities. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Opial%27s%20inequality" title="Opial's inequality">Opial's inequality</a>, <a href="https://publications.waset.org/abstracts/search?q=Jensen%27s%20inequality" title=" Jensen's inequality"> Jensen's inequality</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20inequality" title=" integral inequality"> integral inequality</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20inequality" title=" discrete inequality"> discrete inequality</a> </p> <a href="https://publications.waset.org/abstracts/41583/multidimensional-integral-and-discrete-opial-type-inequalities" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/41583.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">439</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5296</span> Numerical Modelling of Dry Stone Masonry Structures Based on Finite-Discrete Element Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=%C5%BD.%20Nikoli%C4%87">Ž. Nikolić</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20Smoljanovi%C4%87"> H. Smoljanović</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20%C5%BDivalji%C4%87"> N. Živaljić</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents numerical model based on finite-discrete element method for analysis of the structural response of dry stone masonry structures under static and dynamic loads. More precisely, each discrete stone block is discretized by finite elements. Material non-linearity including fracture and fragmentation of discrete elements as well as cyclic behavior during dynamic load are considered through contact elements which are implemented within a finite element mesh. The application of the model was conducted on several examples of these structures. The performed analysis shows high accuracy of the numerical results in comparison with the experimental ones and demonstrates the potential of the finite-discrete element method for modelling of the response of dry stone masonry structures. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dry%20stone%20masonry%20structures" title="dry stone masonry structures">dry stone masonry structures</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20load" title=" dynamic load"> dynamic load</a>, <a href="https://publications.waset.org/abstracts/search?q=finite-discrete%20element%20method" title=" finite-discrete element method"> finite-discrete element method</a>, <a href="https://publications.waset.org/abstracts/search?q=static%20load" title=" static load"> static load</a> </p> <a href="https://publications.waset.org/abstracts/47740/numerical-modelling-of-dry-stone-masonry-structures-based-on-finite-discrete-element-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/47740.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">414</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5295</span> Fundamental Solutions for Discrete Dynamical Systems Involving the Fractional Laplacian</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Gonzalez%20Camus">Jorge Gonzalez Camus</a>, <a href="https://publications.waset.org/abstracts/search?q=Valentin%20Keyantuo"> Valentin Keyantuo</a>, <a href="https://publications.waset.org/abstracts/search?q=Mahamadi%20Warma"> Mahamadi Warma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=discrete%20fractional%20Laplacian" title="discrete fractional Laplacian">discrete fractional Laplacian</a>, <a href="https://publications.waset.org/abstracts/search?q=explicit%20representation%20of%20solutions" title=" explicit representation of solutions"> explicit representation of solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20heat%20and%20wave%20equations" title=" fractional heat and wave equations"> fractional heat and wave equations</a>, <a href="https://publications.waset.org/abstracts/search?q=fundamental" title=" fundamental"> fundamental</a> </p> <a href="https://publications.waset.org/abstracts/99922/fundamental-solutions-for-discrete-dynamical-systems-involving-the-fractional-laplacian" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/99922.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">209</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5294</span> A Hybrid Watermarking Scheme Using Discrete and Discrete Stationary Wavelet Transformation For Color Images</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=B%C3%BClent%20Kantar">Bülent Kantar</a>, <a href="https://publications.waset.org/abstracts/search?q=Numan%20%C3%9Cnald%C4%B1"> Numan Ünaldı</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a new method which includes robust and invisible digital watermarking on images that is colored. Colored images are used as watermark. Frequency region is used for digital watermarking. Discrete wavelet transform and discrete stationary wavelet transform are used for frequency region transformation. Low, medium and high frequency coefficients are obtained by applying the two-level discrete wavelet transform to the original image. Low frequency coefficients are obtained by applying one level discrete stationary wavelet transform separately to all frequency coefficient of the two-level discrete wavelet transformation of the original image. For every low frequency coefficient obtained from one level discrete stationary wavelet transformation, watermarks are added. Watermarks are added to all frequency coefficients of two-level discrete wavelet transform. Totally, four watermarks are added to original image. In order to get back the watermark, the original and watermarked images are applied with two-level discrete wavelet transform and one level discrete stationary wavelet transform. The watermark is obtained from difference of the discrete stationary wavelet transform of the low frequency coefficients. A total of four watermarks are obtained from all frequency of two-level discrete wavelet transform. Obtained watermark results are compared with real watermark results, and a similarity result is obtained. A watermark is obtained from the highest similarity values. Proposed methods of watermarking are tested against attacks of the geometric and image processing. The results show that proposed watermarking method is robust and invisible. All features of frequencies of two level discrete wavelet transform watermarking are combined to get back the watermark from the watermarked image. Watermarks have been added to the image by converting the binary image. These operations provide us with better results in getting back the watermark from watermarked image by attacking of the geometric and image processing. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=watermarking" title="watermarking">watermarking</a>, <a href="https://publications.waset.org/abstracts/search?q=DWT" title=" DWT"> DWT</a>, <a href="https://publications.waset.org/abstracts/search?q=DSWT" title=" DSWT"> DSWT</a>, <a href="https://publications.waset.org/abstracts/search?q=copy%20right%20protection" title=" copy right protection"> copy right protection</a>, <a href="https://publications.waset.org/abstracts/search?q=RGB" title=" RGB "> RGB </a> </p> <a href="https://publications.waset.org/abstracts/16927/a-hybrid-watermarking-scheme-using-discrete-and-discrete-stationary-wavelet-transformation-for-color-images" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16927.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">535</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5293</span> Superconvergence of the Iterated Discrete Legendre Galerkin Method for Fredholm-Hammerstein Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Payel%20Das">Payel Das</a>, <a href="https://publications.waset.org/abstracts/search?q=Gnaneshwar%20Nelakanti"> Gnaneshwar Nelakanti</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we analyse the iterated discrete Legendre Galerkin method for Fredholm-Hammerstein integral equations with smooth kernel. Using sufficiently accurate numerical quadrature rule, we obtain superconvergence rates for the iterated discrete Legendre Galerkin solutions in both infinity and $L^2$-norm. Numerical examples are given to illustrate the theoretical results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hammerstein%20integral%20equations" title="hammerstein integral equations">hammerstein integral equations</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20method" title=" spectral method"> spectral method</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20galerkin" title=" discrete galerkin"> discrete galerkin</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%0D%0Aquadrature" title=" numerical quadrature"> numerical quadrature</a>, <a href="https://publications.waset.org/abstracts/search?q=superconvergence" title=" superconvergence"> superconvergence</a> </p> <a href="https://publications.waset.org/abstracts/22260/superconvergence-of-the-iterated-discrete-legendre-galerkin-method-for-fredholm-hammerstein-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22260.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">469</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5292</span> Characterizing the Geometry of Envy Human Behaviour Using Game Theory Model with Two Types of Homogeneous Players</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20S.%20Mousa">A. S. Mousa</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20I.%20Rajab"> R. I. Rajab</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20A.%20Pinto"> A. A. Pinto</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An envy behavioral game theoretical model with two types of homogeneous players is considered in this paper. The strategy space of each type of players is a discrete set with only two alternatives. The preferences of each type of players is given by a discrete utility function. All envy strategies that form Nash equilibria and the corresponding envy Nash domains for each type of players have been characterized. We use geometry to construct two dimensional envy tilings where the horizontal axis reflects the preference for players of type one, while the vertical axis reflects the preference for the players of type two. The influence of the envy behavior parameters on the Cartesian position of the equilibria has been studied, and in each envy tiling we determine the envy Nash equilibria. We observe that there are 1024 combinatorial classes of envy tilings generated from envy chromosomes: 256 of them are being structurally stable while 768 are with bifurcation. Finally, some conditions for the disparate envy Nash equilibria are stated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=game%20theory" title="game theory">game theory</a>, <a href="https://publications.waset.org/abstracts/search?q=Nash%20equilibrium" title=" Nash equilibrium"> Nash equilibrium</a>, <a href="https://publications.waset.org/abstracts/search?q=envy%20Nash%20behavior" title=" envy Nash behavior"> envy Nash behavior</a>, <a href="https://publications.waset.org/abstracts/search?q=geometric%20tilings" title=" geometric tilings"> geometric tilings</a>, <a href="https://publications.waset.org/abstracts/search?q=bifurcation%20thresholds" title=" bifurcation thresholds"> bifurcation thresholds</a> </p> <a href="https://publications.waset.org/abstracts/113577/characterizing-the-geometry-of-envy-human-behaviour-using-game-theory-model-with-two-types-of-homogeneous-players" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/113577.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">229</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5291</span> Discrete Tracking Control of Nonholonomic Mobile Robots: Backstepping Design Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alexander%20S.%20Andreev">Alexander S. Andreev</a>, <a href="https://publications.waset.org/abstracts/search?q=Olga%20A.%20Peregudova"> Olga A. Peregudova</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we propose a discrete tracking control of nonholonomic mobile robots with two degrees of freedom. The electro-mechanical model of a mobile robot moving on a horizontal surface without slipping, with two rear wheels controlled by two independent DC electric, and one front roal wheel is considered. We present back-stepping design based on the Euler approximate discrete-time model of a continuous-time plant. Theoretical considerations are verified by numerical simulation. The work was supported by RFFI (15-01-08482). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=actuator%20dynamics" title="actuator dynamics">actuator dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=back%20stepping" title=" back stepping"> back stepping</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete-time%20controller" title=" discrete-time controller"> discrete-time controller</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov%20function" title=" Lyapunov function"> Lyapunov function</a>, <a href="https://publications.waset.org/abstracts/search?q=wheeled%20mobile%20robot" title=" wheeled mobile robot "> wheeled mobile robot </a> </p> <a href="https://publications.waset.org/abstracts/15632/discrete-tracking-control-of-nonholonomic-mobile-robots-backstepping-design-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15632.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">415</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5290</span> Dynamical Systems and Fibonacci Numbers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Vandana%20N.%20Purav">Vandana N. Purav</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Dynamical systems concept is a mathematical formalization for any fixed rule that describes the time dependence of a points position in its ambient space. e.g. pendulum of a clock, the number of fish each spring in a lake, the number of rabbits spring in an enclosure, etc. The Dynamical system theory used to describe the complex nature that is dynamical systems with differential equations called continuous dynamical system or dynamical system with difference equations called discrete dynamical system. The concept of dynamical system has its origin in Newtonian mechanics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamical%20systems" title="dynamical systems">dynamical systems</a>, <a href="https://publications.waset.org/abstracts/search?q=Fibonacci%20numbers" title=" Fibonacci numbers"> Fibonacci numbers</a>, <a href="https://publications.waset.org/abstracts/search?q=Newtonian%20mechanics" title=" Newtonian mechanics"> Newtonian mechanics</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20dynamical%20system" title=" discrete dynamical system"> discrete dynamical system</a> </p> <a href="https://publications.waset.org/abstracts/25870/dynamical-systems-and-fibonacci-numbers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25870.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">492</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5289</span> Modeling Bessel Beams and Their Discrete Superpositions from the Generalized Lorenz-Mie Theory to Calculate Optical Forces over Spherical Dielectric Particles</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Leonardo%20A.%20Ambrosio">Leonardo A. Ambrosio</a>, <a href="https://publications.waset.org/abstracts/search?q=Carlos.%20H.%20Silva%20Santos"> Carlos. H. Silva Santos</a>, <a href="https://publications.waset.org/abstracts/search?q=Ivan%20E.%20L.%20Rodrigues"> Ivan E. L. Rodrigues</a>, <a href="https://publications.waset.org/abstracts/search?q=Ayumi%20K.%20de%20Campos"> Ayumi K. de Campos</a>, <a href="https://publications.waset.org/abstracts/search?q=Leandro%20A.%20Machado"> Leandro A. Machado</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we propose an algorithm developed under Python language for the modeling of ordinary scalar Bessel beams and their discrete superpositions and subsequent calculation of optical forces exerted over dielectric spherical particles. The mathematical formalism, based on the generalized Lorenz-Mie theory, is implemented in Python for its large number of free mathematical (as SciPy and NumPy), data visualization (Matplotlib and PyJamas) and multiprocessing libraries. We also propose an approach, provided by a synchronized Software as Service (SaaS) in cloud computing, to develop a user interface embedded on a mobile application, thus providing users with the necessary means to easily introduce desired unknowns and parameters and see the graphical outcomes of the simulations right at their mobile devices. Initially proposed as a free Android-based application, such an App enables data post-processing in cloud-based architectures and visualization of results, figures and numerical tables. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bessel%20Beams%20and%20Frozen%20Waves" title="Bessel Beams and Frozen Waves">Bessel Beams and Frozen Waves</a>, <a href="https://publications.waset.org/abstracts/search?q=Generalized%20Lorenz-Mie%20Theory" title=" Generalized Lorenz-Mie Theory"> Generalized Lorenz-Mie Theory</a>, <a href="https://publications.waset.org/abstracts/search?q=Numerical%20Methods" title=" Numerical Methods"> Numerical Methods</a>, <a href="https://publications.waset.org/abstracts/search?q=optical%20forces" title=" optical forces"> optical forces</a> </p> <a href="https://publications.waset.org/abstracts/43572/modeling-bessel-beams-and-their-discrete-superpositions-from-the-generalized-lorenz-mie-theory-to-calculate-optical-forces-over-spherical-dielectric-particles" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/43572.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">380</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5288</span> Analytical Solution of Non–Autonomous Discrete Non-Linear Schrodinger Equation With Saturable Non-Linearity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mishu%20Gupta">Mishu Gupta</a>, <a href="https://publications.waset.org/abstracts/search?q=Rama%20Gupta"> Rama Gupta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=B-E-Bose-Einstein" title="B-E-Bose-Einstein">B-E-Bose-Einstein</a>, <a href="https://publications.waset.org/abstracts/search?q=DNLSE-Discrete%20non%20linear%20schrodinger%20equation" title=" DNLSE-Discrete non linear schrodinger equation"> DNLSE-Discrete non linear schrodinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=NLSE-non%20linear%20schrodinger%20equation" title=" NLSE-non linear schrodinger equation"> NLSE-non linear schrodinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=SDNLSE%20-%20saturable%20discrete%20non%20linear%20Schrodinger%20equation" title=" SDNLSE - saturable discrete non linear Schrodinger equation"> SDNLSE - saturable discrete non linear Schrodinger equation</a> </p> <a href="https://publications.waset.org/abstracts/121074/analytical-solution-of-non-autonomous-discrete-non-linear-schrodinger-equation-with-saturable-non-linearity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/121074.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">155</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5287</span> A Particle Filter-Based Data Assimilation Method for Discrete Event Simulation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zhi%20Zhu">Zhi Zhu</a>, <a href="https://publications.waset.org/abstracts/search?q=Boquan%20Zhang"> Boquan Zhang</a>, <a href="https://publications.waset.org/abstracts/search?q=Tian%20Jing"> Tian Jing</a>, <a href="https://publications.waset.org/abstracts/search?q=Jingjing%20Li"> Jingjing Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Tao%20Wang"> Tao Wang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Data assimilation is a model and data hybrid-driven method that dynamically fuses new observation data with a numerical model to iteratively approach the real system state. It is widely used in state prediction and parameter inference of continuous systems. Because of the discrete event system’s non-linearity and non-Gaussianity, traditional Kalman Filter based on linear and Gaussian assumptions cannot perform data assimilation for such systems, so particle filter has gradually become a technical approach for discrete event simulation data assimilation. Hence, we proposed a particle filter-based discrete event simulation data assimilation method and took the unmanned aerial vehicle (UAV) maintenance service system as a proof of concept to conduct simulation experiments. The experimental results showed that the filtered state data is closer to the real state of the system, which verifies the effectiveness of the proposed method. This research can provide a reference framework for the data assimilation process of other complex nonlinear systems, such as discrete-time and agent simulation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=discrete%20event%20simulation" title="discrete event simulation">discrete event simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=data%20assimilation" title=" data assimilation"> data assimilation</a>, <a href="https://publications.waset.org/abstracts/search?q=particle%20filter" title=" particle filter"> particle filter</a>, <a href="https://publications.waset.org/abstracts/search?q=model%20and%20data-driven" title=" model and data-driven"> model and data-driven</a> </p> <a href="https://publications.waset.org/abstracts/192559/a-particle-filter-based-data-assimilation-method-for-discrete-event-simulation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/192559.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">13</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5286</span> Numerical Investigation of the Effect of Blast Pressure on Discrete Model in Shock Tube</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aldin%20Justin%20Sundararaj">Aldin Justin Sundararaj</a>, <a href="https://publications.waset.org/abstracts/search?q=Austin%20Lord%20Tennyson"> Austin Lord Tennyson</a>, <a href="https://publications.waset.org/abstracts/search?q=Divya%20Jose"> Divya Jose</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20N.%20Subash"> A. N. Subash</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Blast waves are generated due to the explosions of high energy materials. An explosion yielding a blast wave has the potential to cause severe damage to buildings and its personnel. In order to understand the physics of effects of blast pressure on buildings, studies in the shock tube on generic configurations are carried out at various pressures on discrete models. The strength of shock wave is systematically varied by using different driver gases and diaphragm thickness. The basic material of the diaphragm is Aluminum. To simulate the effect of shock waves on discrete models a shock tube was used. Generic models selected for this study are suitably scaled cylinder, cone and cubical blocks. The experiments were carried out with 2mm diaphragm with burst pressure ranging from 28 to 31 bar. Numerical analysis was carried out over these discrete models. A 3D model of shock-tube with different discrete models inside the tube was used for CFD computation. It was found that cone has dissipated most of the shock pressure compared to cylinder and cubical block. The robustness and the accuracy of the numerical model were validation with the analytical and experimental data. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=shock%20wave" title="shock wave">shock wave</a>, <a href="https://publications.waset.org/abstracts/search?q=blast%20wave" title=" blast wave"> blast wave</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20models" title=" discrete models"> discrete models</a>, <a href="https://publications.waset.org/abstracts/search?q=shock%20tube" title=" shock tube"> shock tube</a> </p> <a href="https://publications.waset.org/abstracts/58116/numerical-investigation-of-the-effect-of-blast-pressure-on-discrete-model-in-shock-tube" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/58116.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">330</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5285</span> A Generalization of Option Pricing with Discrete Dividends to Markets with Daily Price Limits</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jiahau%20Guo">Jiahau Guo</a>, <a href="https://publications.waset.org/abstracts/search?q=Yihe%20Zhang"> Yihe Zhang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper proposes solutions for pricing options on stocks paying discrete dividends in markets with daily price limits. We first extend the intraday density function of Guo and Chang (2020) to a multi-day one and use the framework of Haug et al. (2003) to value European options on stocks paying discrete dividends. Next, we adopt the fast Fourier transform (FFT) to derive accurate and efficient formulae for American options and further employ the three-point Richardson extrapolation to accelerate the computation. Finally, the accuracy of our proposed methods is verified by simulations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=daily%20price%20limit" title="daily price limit">daily price limit</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20dividend" title=" discrete dividend"> discrete dividend</a>, <a href="https://publications.waset.org/abstracts/search?q=early%20exercise" title=" early exercise"> early exercise</a>, <a href="https://publications.waset.org/abstracts/search?q=fast%20Fourier%20transform" title=" fast Fourier transform"> fast Fourier transform</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-day%20density%20function" title=" multi-day density function"> multi-day density function</a>, <a href="https://publications.waset.org/abstracts/search?q=Richardson%20extrapolation" title=" Richardson extrapolation"> Richardson extrapolation</a> </p> <a href="https://publications.waset.org/abstracts/129710/a-generalization-of-option-pricing-with-discrete-dividends-to-markets-with-daily-price-limits" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/129710.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">164</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5284</span> Number of Parametrization of Discrete-Time Systems without Unit-Delay Element: Single-Input Single-Output Case</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kazuyoshi%20Mori">Kazuyoshi Mori</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider the parametrization of the discrete-time systems without the unit-delay element within the framework of the factorization approach. In the parametrization, we investigate the number of required parameters. We consider single-input single-output systems in this paper. By the investigation, we find, on the discrete-time systems without the unit-delay element, three cases that are (1) there exist plants which require only one parameter and (2) two parameters, and (3) the number of parameters is at most three. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=factorization%20approach" title="factorization approach">factorization approach</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete-time%20system" title=" discrete-time system"> discrete-time system</a>, <a href="https://publications.waset.org/abstracts/search?q=parameterization%20of%20stabilizing%20controllers" title=" parameterization of stabilizing controllers"> parameterization of stabilizing controllers</a>, <a href="https://publications.waset.org/abstracts/search?q=system%20without%20unit-delay" title=" system without unit-delay"> system without unit-delay</a> </p> <a href="https://publications.waset.org/abstracts/74319/number-of-parametrization-of-discrete-time-systems-without-unit-delay-element-single-input-single-output-case" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/74319.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">240</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5283</span> Discrete-Time Bulk Queue with Service Capacity Depending on Previous Service Time</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yutae%20Lee">Yutae Lee</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper considers a discrete-time bulk-arrival bulkservice queueing system, where service capacity varies depending on the previous service time. By using the generating function technique and the supplementary variable method, we compute the distributions of the queue length at an arbitrary slot boundary and a departure time. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=discrete-time%20queue" title="discrete-time queue">discrete-time queue</a>, <a href="https://publications.waset.org/abstracts/search?q=bulk%20queue" title=" bulk queue"> bulk queue</a>, <a href="https://publications.waset.org/abstracts/search?q=variable%20service%20capacity" title=" variable service capacity"> variable service capacity</a>, <a href="https://publications.waset.org/abstracts/search?q=queue%20length%20distribution" title=" queue length distribution"> queue length distribution</a> </p> <a href="https://publications.waset.org/abstracts/4113/discrete-time-bulk-queue-with-service-capacity-depending-on-previous-service-time" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4113.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">476</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5282</span> 2.5D Face Recognition Using Gabor Discrete Cosine Transform</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ali%20Cheraghian">Ali Cheraghian</a>, <a href="https://publications.waset.org/abstracts/search?q=Farshid%20Hajati"> Farshid Hajati</a>, <a href="https://publications.waset.org/abstracts/search?q=Soheila%20Gheisari"> Soheila Gheisari</a>, <a href="https://publications.waset.org/abstracts/search?q=Yongsheng%20Gao"> Yongsheng Gao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present a novel 2.5D face recognition method based on Gabor Discrete Cosine Transform (GDCT). In the proposed method, the Gabor filter is applied to extract feature vectors from the texture and the depth information. Then, Discrete Cosine Transform (DCT) is used for dimensionality and redundancy reduction to improve computational efficiency. The system is combined texture and depth information in the decision level, which presents higher performance compared to methods, which use texture and depth information, separately. The proposed algorithm is examined on publically available Bosphorus database including models with pose variation. The experimental results show that the proposed method has a higher performance compared to the benchmark. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gabor%20filter" title="Gabor filter">Gabor filter</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20cosine%20transform" title=" discrete cosine transform"> discrete cosine transform</a>, <a href="https://publications.waset.org/abstracts/search?q=2.5d%20face%20recognition" title=" 2.5d face recognition"> 2.5d face recognition</a>, <a href="https://publications.waset.org/abstracts/search?q=pose" title=" pose"> pose</a> </p> <a href="https://publications.waset.org/abstracts/37341/25d-face-recognition-using-gabor-discrete-cosine-transform" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37341.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">328</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5281</span> Behavior Loss Aversion Experimental Laboratory of Financial Investments</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jihene%20Jebeniani">Jihene Jebeniani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We proposed an approach combining both the techniques of experimental economy and the flexibility of discrete choice models in order to test the loss aversion. Our main objective was to test the loss aversion of the Cumulative Prospect Theory (CPT). We developed an experimental laboratory in the context of the financial investments that aimed to analyze the attitude towards the risk of the investors. The study uses the lotteries and is basing on econometric modeling. The estimated model was the ordered probit. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=risk%20aversion" title="risk aversion">risk aversion</a>, <a href="https://publications.waset.org/abstracts/search?q=behavioral%20finance" title=" behavioral finance"> behavioral finance</a>, <a href="https://publications.waset.org/abstracts/search?q=experimental%20economic" title=" experimental economic"> experimental economic</a>, <a href="https://publications.waset.org/abstracts/search?q=lotteries" title=" lotteries"> lotteries</a>, <a href="https://publications.waset.org/abstracts/search?q=cumulative%20prospect%20theory" title=" cumulative prospect theory"> cumulative prospect theory</a> </p> <a href="https://publications.waset.org/abstracts/27084/behavior-loss-aversion-experimental-laboratory-of-financial-investments" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27084.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">471</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5280</span> Use of Six-sigma Concept in Discrete Manufacturing Industry</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ignatio%20Madanhire">Ignatio Madanhire</a>, <a href="https://publications.waset.org/abstracts/search?q=Charles%20Mbohwa"> Charles Mbohwa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Efficiency in manufacturing is critical in raising the value of exports so as to gainfully trade on the regional and international markets. There seems to be increasing popularity of continuous improvement strategies availed to manufacturing entities, but this research study established that there has not been a similar popularity accorded to the Six Sigma methodology. Thus this work was conducted to investigate the applicability, effectiveness, usefulness, application and suitability of the Six Sigma methodology as a competitiveness option for discrete manufacturing entity. Development of Six-sigma center in the country with continuous improvement information would go a long way in benefiting the entire industry <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=discrete%20manufacturing" title="discrete manufacturing">discrete manufacturing</a>, <a href="https://publications.waset.org/abstracts/search?q=six-sigma" title=" six-sigma"> six-sigma</a>, <a href="https://publications.waset.org/abstracts/search?q=continuous%20improvement" title=" continuous improvement"> continuous improvement</a>, <a href="https://publications.waset.org/abstracts/search?q=efficiency" title=" efficiency"> efficiency</a>, <a href="https://publications.waset.org/abstracts/search?q=competitiveness" title=" competitiveness"> competitiveness</a> </p> <a href="https://publications.waset.org/abstracts/13351/use-of-six-sigma-concept-in-discrete-manufacturing-industry" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13351.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">463</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5279</span> Stability of Hybrid Stochastic Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Manlika%20Ratchagit">Manlika Ratchagit</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=robust%20mean%20square%20stability" title="robust mean square stability">robust mean square stability</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete-time%20stochastic%20systems" title=" discrete-time stochastic systems"> discrete-time stochastic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20systems" title=" hybrid systems"> hybrid systems</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20time-varying%20delays" title=" interval time-varying delays"> interval time-varying delays</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov%20functional" title=" Lyapunov functional"> Lyapunov functional</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20matrix%20inequalities" title=" linear matrix inequalities"> linear matrix inequalities</a> </p> <a href="https://publications.waset.org/abstracts/20283/stability-of-hybrid-stochastic-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20283.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">485</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5278</span> New Results on Stability of Hybrid Stochastic Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Manlika%20Rajchakit">Manlika Rajchakit</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=robust%20mean%20square%20stability" title="robust mean square stability">robust mean square stability</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete-time%20stochastic%20systems" title=" discrete-time stochastic systems"> discrete-time stochastic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20systems" title=" hybrid systems"> hybrid systems</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20time-varying%20delays" title=" interval time-varying delays"> interval time-varying delays</a>, <a href="https://publications.waset.org/abstracts/search?q=lyapunov%20functional" title=" lyapunov functional"> lyapunov functional</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20matrix%20inequalities" title=" linear matrix inequalities"> linear matrix inequalities</a> </p> <a href="https://publications.waset.org/abstracts/19809/new-results-on-stability-of-hybrid-stochastic-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19809.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">429</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5277</span> Discretization of Cuckoo Optimization Algorithm for Solving Quadratic Assignment Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Elham%20Kazemi">Elham Kazemi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Quadratic Assignment Problem (QAP) is one the combinatorial optimization problems about which research has been done in many companies for allocating some facilities to some locations. The issue of particular importance in this process is the costs of this allocation and the attempt in this problem is to minimize this group of costs. Since the QAP’s are from NP-hard problem, they cannot be solved by exact solution methods. Cuckoo Optimization Algorithm is a Meta-heuristicmethod which has higher capability to find the global optimal points. It is an algorithm which is basically raised to search a continuous space. The Quadratic Assignment Problem is the issue which can be solved in the discrete space, thus the standard arithmetic operators of Cuckoo Optimization Algorithm need to be redefined on the discrete space in order to apply the Cuckoo Optimization Algorithm on the discrete searching space. This paper represents the way of discretizing the Cuckoo optimization algorithm for solving the quadratic assignment problem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Quadratic%20Assignment%20Problem%20%28QAP%29" title="Quadratic Assignment Problem (QAP)">Quadratic Assignment Problem (QAP)</a>, <a href="https://publications.waset.org/abstracts/search?q=Discrete%20Cuckoo%20Optimization%20Algorithm%20%28DCOA%29" title=" Discrete Cuckoo Optimization Algorithm (DCOA)"> Discrete Cuckoo Optimization Algorithm (DCOA)</a>, <a href="https://publications.waset.org/abstracts/search?q=meta-heuristic%20algorithms" title=" meta-heuristic algorithms"> meta-heuristic algorithms</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization%20algorithms" title=" optimization algorithms"> optimization algorithms</a> </p> <a href="https://publications.waset.org/abstracts/25249/discretization-of-cuckoo-optimization-algorithm-for-solving-quadratic-assignment-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25249.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">517</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Discrete%20Morse%20theory&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Discrete%20Morse%20theory&page=3">3</a></li> <li class="page-item"><a class="page-link" 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