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eigenvectors</title> <meta name="description" content="Search results for: eigenvectors"> <meta name="keywords" content="eigenvectors"> <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 d-lg-none navbar-toggler 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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="eigenvectors"> <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> 16</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: eigenvectors</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">16</span> Using Eigenvalues and Eigenvectors in Population Growth and Stability Obtaining</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abubakar%20Sadiq%20Mensah">Abubakar Sadiq Mensah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Knowledge of the population growth of a nation is paramount to national planning. The population of a place is studied and a model developed over a period of time, Matrices is used to form model for population growth. The eigenvalue ƛ of the matrix A and its corresponding eigenvector X is such that AX = ƛX is calculated. The stable age distribution of the population is obtained using the eigenvalue and the characteristic polynomial. Hence, estimation could be made using eigenvalues and eigenvectors. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=eigenvalues" title="eigenvalues">eigenvalues</a>, <a href="https://publications.waset.org/abstracts/search?q=eigenvectors" title=" eigenvectors"> eigenvectors</a>, <a href="https://publications.waset.org/abstracts/search?q=population" title=" population"> population</a>, <a href="https://publications.waset.org/abstracts/search?q=growth%2Fstability" title=" growth/stability"> growth/stability</a> </p> <a href="https://publications.waset.org/abstracts/49175/using-eigenvalues-and-eigenvectors-in-population-growth-and-stability-obtaining" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/49175.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">521</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">15</span> Power Iteration Clustering Based on Deflation Technique on Large Scale Graphs </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Taysir%20Soliman">Taysir Soliman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> One of the current popular clustering techniques is Spectral Clustering (SC) because of its advantages over conventional approaches such as hierarchical clustering, k-means, etc. and other techniques as well. However, one of the disadvantages of SC is the time consuming process because it requires computing the eigenvectors. In the past to overcome this disadvantage, a number of attempts have been proposed such as the Power Iteration Clustering (PIC) technique, which is one of versions from SC; some of PIC advantages are: 1) its scalability and efficiency, 2) finding one pseudo-eigenvectors instead of computing eigenvectors, and 3) linear combination of the eigenvectors in linear time. However, its worst disadvantage is an inter-class collision problem because it used only one pseudo-eigenvectors which is not enough. Previous researchers developed Deflation-based Power Iteration Clustering (DPIC) to overcome problems of PIC technique on inter-class collision with the same efficiency of PIC. In this paper, we developed Parallel DPIC (PDPIC) to improve the time and memory complexity which is run on apache spark framework using sparse matrix. To test the performance of PDPIC, we compared it to SC, ESCG, ESCALG algorithms on four small graph benchmark datasets and nine large graph benchmark datasets, where PDPIC proved higher accuracy and better time consuming than other compared algorithms. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=spectral%20clustering" title="spectral clustering">spectral clustering</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20iteration%20clustering" title=" power iteration clustering"> power iteration clustering</a>, <a href="https://publications.waset.org/abstracts/search?q=deflation-based%20power%20iteration%20clustering" title=" deflation-based power iteration clustering"> deflation-based power iteration clustering</a>, <a href="https://publications.waset.org/abstracts/search?q=Apache%20spark" title=" Apache spark"> Apache spark</a>, <a href="https://publications.waset.org/abstracts/search?q=large%20graph" title=" large graph"> large graph</a> </p> <a href="https://publications.waset.org/abstracts/120360/power-iteration-clustering-based-on-deflation-technique-on-large-scale-graphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/120360.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">189</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">14</span> A Contribution to the Polynomial Eigen Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Malika%20Yaici">Malika Yaici</a>, <a href="https://publications.waset.org/abstracts/search?q=Kamel%20Hariche"> Kamel Hariche</a>, <a href="https://publications.waset.org/abstracts/search?q=Tim%20Clarke"> Tim Clarke</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The relationship between eigenstructure (eigenvalues and eigenvectors) and latent structure (latent roots and latent vectors) is established. In control theory eigenstructure is associated with the state space description of a dynamic multi-variable system and a latent structure is associated with its matrix fraction description. Beginning with block controller and block observer state space forms and moving on to any general state space form, we develop the identities that relate eigenvectors and latent vectors in either direction. Numerical examples illustrate this result. A brief discussion of the potential of these identities in linear control system design follows. Additionally, we present a consequent result: a quick and easy method to solve the polynomial eigenvalue problem for regular matrix polynomials. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=eigenvalues%2Feigenvectors" title="eigenvalues/eigenvectors">eigenvalues/eigenvectors</a>, <a href="https://publications.waset.org/abstracts/search?q=latent%20values%2Fvectors" title=" latent values/vectors"> latent values/vectors</a>, <a href="https://publications.waset.org/abstracts/search?q=matrix%20fraction%20description" title=" matrix fraction description"> matrix fraction description</a>, <a href="https://publications.waset.org/abstracts/search?q=state%20space%20description" title=" state space description "> state space description </a> </p> <a href="https://publications.waset.org/abstracts/14247/a-contribution-to-the-polynomial-eigen-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14247.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">470</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">13</span> Symmetry Properties of Linear Algebraic Systems with Non-Canonical Scalar Multiplication</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Krish%20Jhurani">Krish Jhurani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The research paper presents an in-depth analysis of symmetry properties in linear algebraic systems under the operation of non-canonical scalar multiplication structures, specifically semirings, and near-rings. The objective is to unveil the profound alterations that occur in traditional linear algebraic structures when we replace conventional field multiplication with these non-canonical operations. In the methodology, we first establish the theoretical foundations of non-canonical scalar multiplication, followed by a meticulous investigation into the resulting symmetry properties, focusing on eigenvectors, eigenspaces, and invariant subspaces. The methodology involves a combination of rigorous mathematical proofs and derivations, supplemented by illustrative examples that exhibit these discovered symmetry properties in tangible mathematical scenarios. The core findings uncover unique symmetry attributes. For linear algebraic systems with semiring scalar multiplication, we reveal eigenvectors and eigenvalues. Systems operating under near-ring scalar multiplication disclose unique invariant subspaces. These discoveries drastically broaden the traditional landscape of symmetry properties in linear algebraic systems. With the application of these findings, potential practical implications span across various fields such as physics, coding theory, and cryptography. They could enhance error detection and correction codes, devise more secure cryptographic algorithms, and even influence theoretical physics. This expansion of applicability accentuates the significance of the presented research. The research paper thus contributes to the mathematical community by bringing forth perspectives on linear algebraic systems and their symmetry properties through the lens of non-canonical scalar multiplication, coupled with an exploration of practical applications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=eigenspaces" title="eigenspaces">eigenspaces</a>, <a href="https://publications.waset.org/abstracts/search?q=eigenvectors" title=" eigenvectors"> eigenvectors</a>, <a href="https://publications.waset.org/abstracts/search?q=invariant%20subspaces" title=" invariant subspaces"> invariant subspaces</a>, <a href="https://publications.waset.org/abstracts/search?q=near-rings" title=" near-rings"> near-rings</a>, <a href="https://publications.waset.org/abstracts/search?q=non-canonical%20scalar%20multiplication" title=" non-canonical scalar multiplication"> non-canonical scalar multiplication</a>, <a href="https://publications.waset.org/abstracts/search?q=semirings" title=" semirings"> semirings</a>, <a href="https://publications.waset.org/abstracts/search?q=symmetry%20properties" title=" symmetry properties"> symmetry properties</a> </p> <a href="https://publications.waset.org/abstracts/167875/symmetry-properties-of-linear-algebraic-systems-with-non-canonical-scalar-multiplication" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/167875.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">123</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">12</span> Random Matrix Theory Analysis of Cross-Correlation in the Nigerian Stock Exchange</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chimezie%20P.%20Nnanwa">Chimezie P. Nnanwa</a>, <a href="https://publications.waset.org/abstracts/search?q=Thomas%20C.%20Urama"> Thomas C. Urama</a>, <a href="https://publications.waset.org/abstracts/search?q=Patrick%20O.%20Ezepue"> Patrick O. Ezepue</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we use Random Matrix Theory to analyze the eigen-structure of the empirical correlations of 82 stocks which are consistently traded in the Nigerian Stock Exchange (NSE) over a 4-year study period 3 August 2009 to 26 August 2013. We apply the Marchenko-Pastur distribution of eigenvalues of a purely random matrix to investigate the presence of investment-pertinent information contained in the empirical correlation matrix of the selected stocks. We use hypothesised standard normal distribution of eigenvector components from RMT to assess deviations of the empirical eigenvectors to this distribution for different eigenvalues. We also use the Inverse Participation Ratio to measure the deviation of eigenvectors of the empirical correlation matrix from RMT results. These preliminary results on the dynamics of asset price correlations in the NSE are important for improving risk-return trade-offs associated with Markowitz’s portfolio optimization in the stock exchange, which is pursued in future work. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=correlation%20matrix" title="correlation matrix">correlation matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=eigenvalue%20and%20eigenvector" title=" eigenvalue and eigenvector"> eigenvalue and eigenvector</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20participation%20ratio" title=" inverse participation ratio"> inverse participation ratio</a>, <a href="https://publications.waset.org/abstracts/search?q=portfolio%20optimization" title=" portfolio optimization"> portfolio optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=random%20matrix%20theory" title=" random matrix theory"> random matrix theory</a> </p> <a href="https://publications.waset.org/abstracts/68007/random-matrix-theory-analysis-of-cross-correlation-in-the-nigerian-stock-exchange" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/68007.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">344</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">11</span> Construction of Graph Signal Modulations via Graph Fourier Transform and Its Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xianwei%20Zheng">Xianwei Zheng</a>, <a href="https://publications.waset.org/abstracts/search?q=Yuan%20Yan%20Tang"> Yuan Yan Tang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Classical window Fourier transform has been widely used in signal processing, image processing, machine learning and pattern recognition. The related Gabor transform is powerful enough to capture the texture information of any given dataset. Recently, in the emerging field of graph signal processing, researchers devoting themselves to develop a graph signal processing theory to handle the so-called graph signals. Among the new developing theory, windowed graph Fourier transform has been constructed to establish a time-frequency analysis framework of graph signals. The windowed graph Fourier transform is defined by using the translation and modulation operators of graph signals, following the similar calculations in classical windowed Fourier transform. Specifically, the translation and modulation operators of graph signals are defined by using the Laplacian eigenvectors as follows. For a given graph signal, its translation is defined by a similar manner as its definition in classical signal processing. Specifically, the translation operator can be defined by using the Fourier atoms; the graph signal translation is defined similarly by using the Laplacian eigenvectors. The modulation of the graph can also be established by using the Laplacian eigenvectors. The windowed graph Fourier transform based on these two operators has been applied to obtain time-frequency representations of graph signals. Fundamentally, the modulation operator is defined similarly to the classical modulation by multiplying a graph signal with the entries in each Fourier atom. However, a single Laplacian eigenvector entry cannot play a similar role as the Fourier atom. This definition ignored the relationship between the translation and modulation operators. In this paper, a new definition of the modulation operator is proposed and thus another time-frequency framework for graph signal is constructed. Specifically, the relationship between the translation and modulation operations can be established by the Fourier transform. Specifically, for any signal, the Fourier transform of its translation is the modulation of its Fourier transform. Thus, the modulation of any signal can be defined as the inverse Fourier transform of the translation of its Fourier transform. Therefore, similarly, the graph modulation of any graph signal can be defined as the inverse graph Fourier transform of the translation of its graph Fourier. The novel definition of the graph modulation operator established a relationship of the translation and modulation operations. The new modulation operation and the original translation operation are applied to construct a new framework of graph signal time-frequency analysis. Furthermore, a windowed graph Fourier frame theory is developed. Necessary and sufficient conditions for constructing windowed graph Fourier frames, tight frames and dual frames are presented in this paper. The novel graph signal time-frequency analysis framework is applied to signals defined on well-known graphs, e.g. Minnesota road graph and random graphs. Experimental results show that the novel framework captures new features of graph signals. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=graph%20signals" title="graph signals">graph signals</a>, <a href="https://publications.waset.org/abstracts/search?q=windowed%20graph%20Fourier%20transform" title=" windowed graph Fourier transform"> windowed graph Fourier transform</a>, <a href="https://publications.waset.org/abstracts/search?q=windowed%20graph%20Fourier%20frames" title=" windowed graph Fourier frames"> windowed graph Fourier frames</a>, <a href="https://publications.waset.org/abstracts/search?q=vertex%20frequency%20analysis" title=" vertex frequency analysis"> vertex frequency analysis</a> </p> <a href="https://publications.waset.org/abstracts/63133/construction-of-graph-signal-modulations-via-graph-fourier-transform-and-its-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/63133.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">341</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">10</span> Signs-Only Compressed Row Storage Format for Exact Diagonalization Study of Quantum Fermionic Models</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Michael%20Danilov">Michael Danilov</a>, <a href="https://publications.waset.org/abstracts/search?q=Sergei%20Iskakov"> Sergei Iskakov</a>, <a href="https://publications.waset.org/abstracts/search?q=Vladimir%20Mazurenko"> Vladimir Mazurenko</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The present paper describes a high-performance parallel realization of an exact diagonalization solver for quantum-electron models in a shared memory computing system. The proposed algorithm contains a storage format for efficient computing eigenvalues and eigenvectors of a quantum electron Hamiltonian matrix. The results of the test calculations carried out for 15 sites Hubbard model demonstrate reduction in the required memory and good multiprocessor scalability, while maintaining performance of the same order as compressed row storage. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=sparse%20matrix" title="sparse matrix">sparse matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=compressed%20format" title=" compressed format"> compressed format</a>, <a href="https://publications.waset.org/abstracts/search?q=Hubbard%20model" title=" Hubbard model"> Hubbard model</a>, <a href="https://publications.waset.org/abstracts/search?q=Anderson%20model" title=" Anderson model"> Anderson model</a> </p> <a href="https://publications.waset.org/abstracts/48308/signs-only-compressed-row-storage-format-for-exact-diagonalization-study-of-quantum-fermionic-models" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48308.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">402</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">9</span> An Eigen-Approach for Estimating the Direction-of Arrival of Unknown Number of Signals</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dia%20I.%20Abu-Al-Nadi">Dia I. Abu-Al-Nadi</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20J.%20Mismar"> M. J. Mismar</a>, <a href="https://publications.waset.org/abstracts/search?q=T.%20H.%20Ismail"> T. H. Ismail</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A technique for estimating the direction-of-arrival (DOA) of unknown number of source signals is presented using the eigen-approach. The eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix yields the minimum output power of the array. Also, the array polynomial with this eigenvector possesses roots on the unit circle. Therefore, the pseudo-spectrum is found by perturbing the phases of the roots one by one and calculating the corresponding array output power. The results indicate that the DOAs and the number of source signals are estimated accurately in the presence of a wide range of input noise levels. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=array%20signal%20processing" title="array signal processing">array signal processing</a>, <a href="https://publications.waset.org/abstracts/search?q=direction-of-arrival" title=" direction-of-arrival"> direction-of-arrival</a>, <a href="https://publications.waset.org/abstracts/search?q=antenna%20arrays" title=" antenna arrays"> antenna arrays</a>, <a href="https://publications.waset.org/abstracts/search?q=Eigenvalues" title=" Eigenvalues"> Eigenvalues</a>, <a href="https://publications.waset.org/abstracts/search?q=Eigenvectors" title=" Eigenvectors"> Eigenvectors</a>, <a href="https://publications.waset.org/abstracts/search?q=Lagrange%20multiplier" title=" Lagrange multiplier"> Lagrange multiplier</a> </p> <a href="https://publications.waset.org/abstracts/50693/an-eigen-approach-for-estimating-the-direction-of-arrival-of-unknown-number-of-signals" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/50693.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">334</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">8</span> Principal Component Analysis Applied to the Electric Power Systems – Practical Guide; Practical Guide for Algorithms</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=John%20Morales">John Morales</a>, <a href="https://publications.waset.org/abstracts/search?q=Eduardo%20Ordu%C3%B1a"> Eduardo Orduña</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Currently the Principal Component Analysis (PCA) theory has been used to develop algorithms regarding to Electric Power Systems (EPS). In this context, this paper presents a practical tutorial of this technique detailed their concept, on-line and off-line mathematical foundations, which are necessary and desirables in EPS algorithms. Thus, features of their eigenvectors which are very useful to real-time process are explained, showing how it is possible to select these parameters through a direct optimization. On the other hand, in this work in order to show the application of PCA to off-line and on-line signals, an example step to step using Matlab commands is presented. Finally, a list of different approaches using PCA is presented, and some works which could be analyzed using this tutorial are presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=practical%20guide%3B%20on-line%3B%20off-line" title="practical guide; on-line; off-line">practical guide; on-line; off-line</a>, <a href="https://publications.waset.org/abstracts/search?q=algorithms" title=" algorithms"> algorithms</a>, <a href="https://publications.waset.org/abstracts/search?q=faults" title=" faults"> faults</a> </p> <a href="https://publications.waset.org/abstracts/34859/principal-component-analysis-applied-to-the-electric-power-systems-practical-guide-practical-guide-for-algorithms" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/34859.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">563</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">7</span> Analysis of Cross-Correlations in Emerging Markets Using Random Matrix Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Thomas%20Chinwe%20Urama">Thomas Chinwe Urama</a>, <a href="https://publications.waset.org/abstracts/search?q=Patrick%20Oseloka%20Ezepue"> Patrick Oseloka Ezepue</a>, <a href="https://publications.waset.org/abstracts/search?q=Peters%20Chimezie%20Nnanwa"> Peters Chimezie Nnanwa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper investigates the universal financial dynamics in two dominant stock markets in Sub-Saharan Africa, through an in-depth analysis of the cross-correlation matrix of price returns in Nigerian Stock Market (NSM) and Johannesburg Stock Exchange (JSE), for the period 2009 to 2013. The strength of correlations between stocks is known to be higher in JSE than that of the NSM. Particularly important for modelling Nigerian derivatives in the future, the interactions of other stocks with the oil sector are weak, whereas the banking sector has strong positive interactions with the other sectors in the stock exchange. For the JSE, it is the oil sector and beverages that have greater sectorial correlations, instead of the banks which have the weaker correlation with other sectors in the stock exchange. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=random%20matrix%20theory" title="random matrix theory">random matrix theory</a>, <a href="https://publications.waset.org/abstracts/search?q=cross-correlations" title=" cross-correlations"> cross-correlations</a>, <a href="https://publications.waset.org/abstracts/search?q=emerging%20markets" title=" emerging markets"> emerging markets</a>, <a href="https://publications.waset.org/abstracts/search?q=option%20pricing" title=" option pricing"> option pricing</a>, <a href="https://publications.waset.org/abstracts/search?q=eigenvalues%20eigenvectors" title=" eigenvalues eigenvectors"> eigenvalues eigenvectors</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20participation%20ratios%20and%20implied%20volatility" title=" inverse participation ratios and implied volatility"> inverse participation ratios and implied volatility</a> </p> <a href="https://publications.waset.org/abstracts/65711/analysis-of-cross-correlations-in-emerging-markets-using-random-matrix-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/65711.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">299</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">6</span> Analysis Rotor Bearing System Dynamic Interaction with Bearing Supports</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=V.%20T.%20Ngo">V. T. Ngo</a>, <a href="https://publications.waset.org/abstracts/search?q=D.%20M.%20Xie"> D. M. Xie</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Frequently, in the design of machines, some of parameters that directly affect the rotor dynamics of the machines are not accurately known. In particular, bearing stiffness support is one such parameter. One of the most basic principles to grasp in rotor dynamics is the influence of the bearing stiffness on the critical speeds and mode shapes associated with a rotor-bearing system. Taking a rig shafting as an example, this paper studies the lateral vibration of the rotor with multi-degree-of-freedom by using Finite Element Method (FEM). The FEM model is created and the eigenvalues and eigenvectors are calculated and analyzed to find natural frequencies, critical speeds, mode shapes. Then critical speeds and mode shapes are analyzed by set bearing stiffness changes. The model permitted to identify the critical speeds and bearings that have an important influence on the vibration behavior. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=lateral%20vibration" title="lateral vibration">lateral vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20method" title=" finite element method"> finite element method</a>, <a href="https://publications.waset.org/abstracts/search?q=rig%20shafting" title=" rig shafting"> rig shafting</a>, <a href="https://publications.waset.org/abstracts/search?q=critical%20speed" title=" critical speed"> critical speed</a> </p> <a href="https://publications.waset.org/abstracts/7560/analysis-rotor-bearing-system-dynamic-interaction-with-bearing-supports" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7560.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">340</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">5</span> Data-Driven Analysis of Velocity Gradient Dynamics Using Neural Network</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nishant%20Parashar">Nishant Parashar</a>, <a href="https://publications.waset.org/abstracts/search?q=Sawan%20S.%20Sinha"> Sawan S. Sinha</a>, <a href="https://publications.waset.org/abstracts/search?q=Balaji%20Srinivasan"> Balaji Srinivasan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We perform an investigation of the unclosed terms in the evolution equation of the velocity gradient tensor (VGT) in compressible decaying turbulent flow. Velocity gradients in a compressible turbulent flow field influence several important nonlinear turbulent processes like cascading and intermittency. In an attempt to understand the dynamics of the velocity gradients various researchers have tried to model the unclosed terms in the evolution equation of the VGT. The existing models proposed for these unclosed terms have limited applicability. This is mainly attributable to the complex structure of the higher order gradient terms appearing in the evolution equation of VGT. We investigate these higher order gradients using the data from direct numerical simulation (DNS) of compressible decaying isotropic turbulent flow. The gas kinetic method aided with weighted essentially non-oscillatory scheme (WENO) based flow- reconstruction is employed to generate DNS data. By applying neural-network to the DNS data, we map the structure of the unclosed higher order gradient terms in the evolution of the equation of the VGT with VGT itself. We validate our findings by performing alignment based study of the unclosed higher order gradient terms obtained using the neural network with the strain rate eigenvectors. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=compressible%20turbulence" title="compressible turbulence">compressible turbulence</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20network" title=" neural network"> neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=velocity%20gradient%20tensor" title=" velocity gradient tensor"> velocity gradient tensor</a>, <a href="https://publications.waset.org/abstracts/search?q=direct%20numerical%20simulation" title=" direct numerical simulation"> direct numerical simulation</a> </p> <a href="https://publications.waset.org/abstracts/101552/data-driven-analysis-of-velocity-gradient-dynamics-using-neural-network" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/101552.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">168</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">4</span> Feedback Matrix Approach for Relativistic Runaway Electron Avalanches Dynamics in Complex Electric Field Structures</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Egor%20Stadnichuk">Egor Stadnichuk</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Relativistic runaway electron avalanches (RREA) are a widely accepted source of thunderstorm gamma-radiation. In regions with huge electric field strength, RREA can multiply via relativistic feedback. The relativistic feedback is caused both by positron production and by runaway electron bremsstrahlung gamma-rays reversal. In complex multilayer thunderstorm electric field structures, an additional reactor feedback mechanism appears due to gamma-ray exchange between separate strong electric field regions with different electric field directions. The study of this reactor mechanism in conjunction with the relativistic feedback with Monte Carlo simulations or by direct solution of the kinetic Boltzmann equation requires a significant amount of computational time. In this work, a theoretical approach to study feedback mechanisms in RREA physics is developed. It is based on the matrix of feedback operators construction. With the feedback matrix, the problem of the dynamics of avalanches in complex electric structures is reduced to the problem of finding eigenvectors and eigenvalues. A method of matrix elements calculation is proposed. The proposed concept was used to study the dynamics of RREAs in multilayer thunderclouds. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=terrestrial%20Gamma-ray%20flashes" title="terrestrial Gamma-ray flashes">terrestrial Gamma-ray flashes</a>, <a href="https://publications.waset.org/abstracts/search?q=thunderstorm%20ground%20enhancement" title=" thunderstorm ground enhancement"> thunderstorm ground enhancement</a>, <a href="https://publications.waset.org/abstracts/search?q=relativistic%20runaway%20electron%20avalanches" title=" relativistic runaway electron avalanches"> relativistic runaway electron avalanches</a>, <a href="https://publications.waset.org/abstracts/search?q=gamma-rays" title=" gamma-rays"> gamma-rays</a>, <a href="https://publications.waset.org/abstracts/search?q=high-energy%20atmospheric%20physics" title=" high-energy atmospheric physics"> high-energy atmospheric physics</a>, <a href="https://publications.waset.org/abstracts/search?q=TGF" title=" TGF"> TGF</a>, <a href="https://publications.waset.org/abstracts/search?q=TGE" title=" TGE"> TGE</a>, <a href="https://publications.waset.org/abstracts/search?q=thunderstorm" title=" thunderstorm"> thunderstorm</a>, <a href="https://publications.waset.org/abstracts/search?q=relativistic%20feedback" title=" relativistic feedback"> relativistic feedback</a>, <a href="https://publications.waset.org/abstracts/search?q=reactor%20feedback" title=" reactor feedback"> reactor feedback</a>, <a href="https://publications.waset.org/abstracts/search?q=reactor%20model" title=" reactor model"> reactor model</a> </p> <a href="https://publications.waset.org/abstracts/142458/feedback-matrix-approach-for-relativistic-runaway-electron-avalanches-dynamics-in-complex-electric-field-structures" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/142458.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">172</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">3</span> Halogenated Methoxy- and Methyl-benzoic Acids: Joint Experimental and DFT Study For Molecular Structure, Vibrational Analysis, and Other Molecular Properties</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Boda%20Sreenivas">Boda Sreenivas</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyathakula%20Ravindranath"> Lyathakula Ravindranath</a>, <a href="https://publications.waset.org/abstracts/search?q=Kanugula%20Srishailam"> Kanugula Srishailam</a>, <a href="https://publications.waset.org/abstracts/search?q=Byru%20Venkatram%20Reddy"> Byru Venkatram Reddy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Extensive research into the optimized structure and molecular properties of 3-Flouro-2-methylbenzoicacid(FMB), 3-Chloro-2-methoxybenzoicacid (CMB), and 3-Bromo-2-methylbenzoicacid (BMB) was carried out using FT-IR, FT-Raman and UV-Visible spectra, as well as theoretically using the DFT approach with B3LYPfunctional in conjunction with 6-311++G(d,p) basis set. The optimized structure was determined by evaluating torsional scans about free rotation bonds. Structure parameters, harmonic vibrational frequencies, potential energy distribution(PED), and infrared and Raman intensities were computed. The computational results from the DFT approach, such asFT-IR, FT-Raman, and UV-Visible spectra, were compared with the experimental results and found good agreement. Observed and calculated frequencies agreed with an rms error of 8.42, 6.60, and 6.95 cm-1 for FMB, CMB, and BMB, respectively. Unambiguous vibrational assignments were made for all fundamentals using PED and eigenvectors. The electronic HOMO-LUMO, H-bonding, and strong conjugative interactions across different molecular entities are discussed using experimental and simulated Ultraviolet-Visible spectra. The title molecules' molecular properties such as dipole moment, mean polarizability, and first-order hyperpolarizability, were calculated to study their non-linear optical (NLO) behavior. The chemical reactivity descriptors and mapped electrostatic surface potential (MESP) were also evaluated. Natural bond orbital (NBO) analysis was used to examine the stability of molecules resulting from hyperconjugative interactions and charge delocalization. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=ftir%2Framan%20spectra" title="ftir/raman spectra">ftir/raman spectra</a>, <a href="https://publications.waset.org/abstracts/search?q=DFT" title=" DFT"> DFT</a>, <a href="https://publications.waset.org/abstracts/search?q=NLO" title=" NLO"> NLO</a>, <a href="https://publications.waset.org/abstracts/search?q=homo-lumo" title=" homo-lumo"> homo-lumo</a>, <a href="https://publications.waset.org/abstracts/search?q=NBO" title=" NBO"> NBO</a>, <a href="https://publications.waset.org/abstracts/search?q=halogenated%20benzoic%20acids" title=" halogenated benzoic acids"> halogenated benzoic acids</a> </p> <a href="https://publications.waset.org/abstracts/162874/halogenated-methoxy-and-methyl-benzoic-acids-joint-experimental-and-dft-study-for-molecular-structure-vibrational-analysis-and-other-molecular-properties" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/162874.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">76</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">2</span> Combining Diffusion Maps and Diffusion Models for Enhanced Data Analysis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Meng%20Su">Meng Su</a> </p> <p class="card-text"><strong>Abstract:</strong></p> High-dimensional data analysis often presents challenges in capturing the complex, nonlinear relationships and manifold structures inherent to the data. This article presents a novel approach that leverages the strengths of two powerful techniques, Diffusion Maps and Diffusion Probabilistic Models (DPMs), to address these challenges. By integrating the dimensionality reduction capability of Diffusion Maps with the data modeling ability of DPMs, the proposed method aims to provide a comprehensive solution for analyzing and generating high-dimensional data. The Diffusion Map technique preserves the nonlinear relationships and manifold structure of the data by mapping it to a lower-dimensional space using the eigenvectors of the graph Laplacian matrix. Meanwhile, DPMs capture the dependencies within the data, enabling effective modeling and generation of new data points in the low-dimensional space. The generated data points can then be mapped back to the original high-dimensional space, ensuring consistency with the underlying manifold structure. Through a detailed example implementation, the article demonstrates the potential of the proposed hybrid approach to achieve more accurate and effective modeling and generation of complex, high-dimensional data. Furthermore, it discusses possible applications in various domains, such as image synthesis, time-series forecasting, and anomaly detection, and outlines future research directions for enhancing the scalability, performance, and integration with other machine learning techniques. By combining the strengths of Diffusion Maps and DPMs, this work paves the way for more advanced and robust data analysis methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=diffusion%20maps" title="diffusion maps">diffusion maps</a>, <a href="https://publications.waset.org/abstracts/search?q=diffusion%20probabilistic%20models%20%28DPMs%29" title=" diffusion probabilistic models (DPMs)"> diffusion probabilistic models (DPMs)</a>, <a href="https://publications.waset.org/abstracts/search?q=manifold%20learning" title=" manifold learning"> manifold learning</a>, <a href="https://publications.waset.org/abstracts/search?q=high-dimensional%20data%20analysis" title=" high-dimensional data analysis"> high-dimensional data analysis</a> </p> <a href="https://publications.waset.org/abstracts/165159/combining-diffusion-maps-and-diffusion-models-for-enhanced-data-analysis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/165159.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">108</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">1</span> Active Vibration Reduction for a Flexible Structure Bonded with Sensor/Actuator Pairs on Efficient Locations Using a Developed Methodology</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ali%20H.%20Daraji">Ali H. Daraji</a>, <a href="https://publications.waset.org/abstracts/search?q=Jack%20M.%20Hale"> Jack M. Hale</a>, <a href="https://publications.waset.org/abstracts/search?q=Ye%20Jianqiao"> Ye Jianqiao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> With the extensive use of high specific strength structures to optimise the loading capacity and material cost in aerospace and most engineering applications, much effort has been expended to develop intelligent structures for active vibration reduction and structural health monitoring. These structures are highly flexible, inherently low internal damping and associated with large vibration and long decay time. The modification of such structures by adding lightweight piezoelectric sensors and actuators at efficient locations integrated with an optimal control scheme is considered an effective solution for structural vibration monitoring and controlling. The size and location of sensor and actuator are important research topics to investigate their effects on the level of vibration detection and reduction and the amount of energy provided by a controller. Several methodologies have been presented to determine the optimal location of a limited number of sensors and actuators for small-scale structures. However, these studies have tackled this problem directly, measuring the fitness function based on eigenvalues and eigenvectors achieved with numerous combinations of sensor/actuator pair locations and converging on an optimal set using heuristic optimisation techniques such as the genetic algorithms. This is computationally expensive for small- and large-scale structures subject to optimise a number of s/a pairs to suppress multiple vibration modes. This paper proposes an efficient method to determine optimal locations for a limited number of sensor/actuator pairs for active vibration reduction of a flexible structure based on finite element method and Hamilton’s principle. The current work takes the simplified approach of modelling a structure with sensors at all locations, subjecting it to an external force to excite the various modes of interest and noting the locations of sensors giving the largest average percentage sensors effectiveness measured by dividing all sensor output voltage over the maximum for each mode. The methodology was implemented for a cantilever plate under external force excitation to find the optimal distribution of six sensor/actuator pairs to suppress the first six modes of vibration. It is shown that the results of the optimal sensor locations give good agreement with published optimal locations, but with very much reduced computational effort and higher effectiveness. Furthermore, it is shown that collocated sensor/actuator pairs placed in these locations give very effective active vibration reduction using optimal linear quadratic control scheme. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=optimisation" title="optimisation">optimisation</a>, <a href="https://publications.waset.org/abstracts/search?q=plate" title=" plate"> plate</a>, <a href="https://publications.waset.org/abstracts/search?q=sensor%20effectiveness" title=" sensor effectiveness"> sensor effectiveness</a>, <a href="https://publications.waset.org/abstracts/search?q=vibration%20control" title=" vibration control "> vibration control </a> </p> <a href="https://publications.waset.org/abstracts/62737/active-vibration-reduction-for-a-flexible-structure-bonded-with-sensoractuator-pairs-on-efficient-locations-using-a-developed-methodology" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/62737.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">232</span> </span> </div> </div> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Account <li><a href="https://waset.org/profile">My Account</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Explore <li><a href="https://waset.org/disciplines">Disciplines</a></li> <li><a href="https://waset.org/conferences">Conferences</a></li> <li><a href="https://waset.org/conference-programs">Conference Program</a></li> <li><a href="https://waset.org/committees">Committees</a></li> <li><a href="https://publications.waset.org">Publications</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Research <li><a href="https://publications.waset.org/abstracts">Abstracts</a></li> <li><a href="https://publications.waset.org">Periodicals</a></li> <li><a href="https://publications.waset.org/archive">Archive</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Open Science <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Philosophy.pdf">Open Science Philosophy</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Award.pdf">Open Science Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Society-Open-Science-and-Open-Innovation.pdf">Open Innovation</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Postdoctoral-Fellowship-Award.pdf">Postdoctoral Fellowship Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Scholarly-Research-Review.pdf">Scholarly Research Review</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Support <li><a href="https://waset.org/page/support">Support</a></li> <li><a href="https://waset.org/profile/messages/create">Contact Us</a></li> <li><a href="https://waset.org/profile/messages/create">Report Abuse</a></li> </ul> </div> </div> </div> </div> </div> <div class="container text-center"> <hr style="margin-top:0;margin-bottom:.3rem;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" class="text-muted small">Creative Commons Attribution 4.0 International License</a> <div id="copy" class="mt-2">© 2024 World Academy of Science, Engineering and Technology</div> </div> </footer> <a href="javascript:" id="return-to-top"><i class="fas fa-arrow-up"></i></a> <div class="modal" id="modal-template"> <div class="modal-dialog"> <div class="modal-content"> <div class="row m-0 mt-1"> <div class="col-md-12"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> </div> </div> <div class="modal-body"></div> </div> </div> </div> <script src="https://cdn.waset.org/static/plugins/jquery-3.3.1.min.js"></script> <script src="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.waset.org/static/js/site.js?v=150220211556"></script> <script> jQuery(document).ready(function() { /*jQuery.get("https://publications.waset.org/xhr/user-menu", function (response) { jQuery('#mainNavMenu').append(response); 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