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method posting</title> <meta name="description" content="Search results for: matrix method posting"> <meta name="keywords" content="matrix method posting"> <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="matrix method posting"> <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> 20444</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: matrix method posting</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">20444</span> Matrix Method Posting</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Varong%20Pongsai">Varong Pongsai</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The objective of this paper is introducing a new method of accounting posting which is called Matrix Method Posting. This method is based on the Matrix operation of pure Mathematics. Although, accounting field is classified as one of the social-science knowledge, many of accounting operations are placed by Mathematics sign and operation. Through the operation applying, it seems to be that the operations of Mathematics should be applied to accounting possibly. So, this paper tries to over-lap Mathematics logic to accounting logic smoothly. According to the context of discovery, deductive approach is employed to prove a simultaneously logical concept of both Mathematics and Accounting. The result proves that the Matrix can be placed to operate accounting perfectly, because Matrix and accounting logic also have a similarity concept which is balancing 2 sides during operations. Moreover, the Matrix posting also has a lot of benefit. It can help financial analyst calculating financial ratios comfortably. Furthermore, the matrix determinant which is a signature operation itself also helps auditors checking out the correction of clients’ recording. If the determinant is not equaled to 0, it will point out that the recording process of clients getting into the problem. Finally, the Matrix should be easily determining a concept of merger and consolidation far beyond the present day concept. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=matrix%20method%20posting" title="matrix method posting">matrix method posting</a>, <a href="https://publications.waset.org/abstracts/search?q=deductive%20approach" title=" deductive approach"> deductive approach</a>, <a href="https://publications.waset.org/abstracts/search?q=determinant" title=" determinant"> determinant</a>, <a href="https://publications.waset.org/abstracts/search?q=accounting%20application" title=" accounting application"> accounting application</a> </p> <a href="https://publications.waset.org/abstracts/31039/matrix-method-posting" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/31039.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">367</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">20443</span> Understanding How Posting and Replying Behaviors in Social Media Differentiate the Social Capital Cultivation Capabilities of Users</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jung%20Lee">Jung Lee</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study identifies how the cultivation capabilities of social capital influence the overall attitudes of social media users and how these influences differ across user groups. First, the cultivation capabilities of social capital are identified from three aspects, namely, social capital accessibility, potentiality and sensitivity. These three types of social capital acquisition capabilities collectively represent how the social media users perceive the social media environment in terms of possibilities for social capital creation. These three capabilities are hypothesized to influence social media satisfaction and continuing use intention. Next, two essential activities in social media are identified, namely, posting and replying, to categorise social media users based on behavioral patterns. Various social media activities consist of the combinations of these two basic activities. Posting represents the broadcasting aspect of social media, whereas replying represents the communicative aspect of social media. We categorize users into four from communicators to observers by using these two behaviors to develop usage pattern matrix. By applying the usage pattern matrix to the capability model, we argue that posting behavior generally has a positive moderating effect on the attitudes of social media users, whereas replying behavior occasionally exhibits the negative moderating effect. These different moderating effects of posting and replying behavior are explained based on the different levels of social capital sensitivity and expectation of individuals. When a person is highly expecting social capital from social media, he or she would post actively. However, when one is highly sensitive to social capital, he or she would actively respond and reply to postings of other people because such an act would create a longer and more interactive relationship. A total of 512 social media users are invited to answer the survey. They were asked about their attitudes toward the social media and how they expect social capital through this practice. They were asked to check their general social media usage pattern for user categorization. Result confirmed that most of the hypotheses were supported. Three types of social capital cultivation capabilities are significant determinants of social media attitudes, and two social media activities (i.e., posting and replying) exhibited different moderating effects on attitudes. This study provides following discussions. First, three types of social capital cultivation capabilities were identified. Despite the numerous concerns about social media, such as whether it is a decent and real environment that produces social capital, this study confirms that people explicitly expect and experience social capital values from social media. Second, posting and replying activities are two building blocks of social media activities. These two activities are useful in explaining different the attitudes of social media users and predict future usage. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=social%20media" title="social media">social media</a>, <a href="https://publications.waset.org/abstracts/search?q=social%20capital" title=" social capital"> social capital</a>, <a href="https://publications.waset.org/abstracts/search?q=social%20media%20satisfaction" title=" social media satisfaction"> social media satisfaction</a>, <a href="https://publications.waset.org/abstracts/search?q=social%20media%20use%20intention" title=" social media use intention"> social media use intention</a> </p> <a href="https://publications.waset.org/abstracts/89112/understanding-how-posting-and-replying-behaviors-in-social-media-differentiate-the-social-capital-cultivation-capabilities-of-users" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/89112.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">191</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">20442</span> On a Generalization of the Spectral Dichotomy Method of a Matrix With Respect to Parabolas</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mouhamadou%20Dosso">Mouhamadou Dosso</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents methods of spectral dichotomy of a matrix which compute spectral projectors on the subspace associated with the eigenvalues external to the parabolas described by a general equation. These methods are modifications of the one proposed in [A. N. Malyshev and M. Sadkane, SIAM J. MATRIX ANAL. APPL. 18 (2), 265-278, 1997] which uses the spectral dichotomy method of a matrix with respect to the imaginary axis. Theoretical and algorithmic aspects of the methods are developed. Numerical results obtained by applying methods presented on matrices are reported. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=spectral%20dichotomy%20method" title="spectral dichotomy method">spectral dichotomy method</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20projector" title=" spectral projector"> spectral projector</a>, <a href="https://publications.waset.org/abstracts/search?q=eigensubspaces" title=" eigensubspaces"> eigensubspaces</a>, <a href="https://publications.waset.org/abstracts/search?q=eigenvalue" title=" eigenvalue"> eigenvalue</a> </p> <a href="https://publications.waset.org/abstracts/159807/on-a-generalization-of-the-spectral-dichotomy-method-of-a-matrix-with-respect-to-parabolas" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/159807.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">94</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">20441</span> On Direct Matrix Factored Inversion via Broyden's Updates</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Adel%20Mohsen">Adel Mohsen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A direct method based on the good Broyden's updates for evaluating the inverse of a nonsingular square matrix of full rank and solving related system of linear algebraic equations is studied. For a matrix A of order n whose LU-decomposition is A = LU, the multiplication count is O (n3). This includes the evaluation of the LU-decompositions of the inverse, the lower triangular decomposition of A as well as a “reduced matrix inverse”. If an explicit value of the inverse is not needed the order reduces to O (n3/2) to compute to compute inv(U) and the reduced inverse. For a symmetric matrix only O (n3/3) operations are required to compute inv(L) and the reduced inverse. An example is presented to demonstrate the capability of using the reduced matrix inverse in treating ill-conditioned systems. Besides the simplicity of Broyden's update, the method provides a mean to exploit the possible sparsity in the matrix and to derive a suitable preconditioner. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Broyden%27s%20updates" title="Broyden's updates">Broyden's updates</a>, <a href="https://publications.waset.org/abstracts/search?q=matrix%20inverse" title=" matrix inverse"> matrix inverse</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20factorization" title=" inverse factorization"> inverse factorization</a>, <a href="https://publications.waset.org/abstracts/search?q=solution%20of%20linear%20algebraic%20equations" title=" solution of linear algebraic equations"> solution of linear algebraic equations</a>, <a href="https://publications.waset.org/abstracts/search?q=ill-conditioned%20matrices" title=" ill-conditioned matrices"> ill-conditioned matrices</a>, <a href="https://publications.waset.org/abstracts/search?q=preconditioning" title=" preconditioning"> preconditioning</a> </p> <a href="https://publications.waset.org/abstracts/22126/on-direct-matrix-factored-inversion-via-broydens-updates" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22126.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">479</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">20440</span> The Research on Association between Social Media and Audit Opinion</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Meiqun%20Yin">Meiqun Yin</a>, <a href="https://publications.waset.org/abstracts/search?q=Jidong%20Zhang"> Jidong Zhang</a>, <a href="https://publications.waset.org/abstracts/search?q=Fan%20Liu"> Fan Liu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper investigates the impact of social media on audit opinion. The numbers of posting and reposting negative reports from SINA Micro-blog are collected to measure the influence of social media. The research collected the samples from Chinese public firms from 2012 to 2014. It is found that the numbers of posting and reposting negative reports in SINA Micro-Blog would significantly relate to the qualified opinion while controlling firm size. Another finding is that the numbers of posting and reposting negative reports would be much more significantly impact on audit opinion if the firm received a qualified opinion in the previous period. It is also found that the involvement of more independent directors has no relationship with the influence of social media on audit opinion. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=association" title="association">association</a>, <a href="https://publications.waset.org/abstracts/search?q=social%20media" title=" social media"> social media</a>, <a href="https://publications.waset.org/abstracts/search?q=audit%20opinion" title=" audit opinion"> audit opinion</a>, <a href="https://publications.waset.org/abstracts/search?q=SINA%20Micro-Blog" title=" SINA Micro-Blog"> SINA Micro-Blog</a> </p> <a href="https://publications.waset.org/abstracts/63914/the-research-on-association-between-social-media-and-audit-opinion" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/63914.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">266</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">20439</span> On the Application of Heuristics of the Traveling Salesman Problem for the Task of Restoring the DNA Matrix</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Boris%20Melnikov">Boris Melnikov</a>, <a href="https://publications.waset.org/abstracts/search?q=Dmitrii%20Chaikovskii"> Dmitrii Chaikovskii</a>, <a href="https://publications.waset.org/abstracts/search?q=Elena%20Melnikova"> Elena Melnikova</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The traveling salesman problem (TSP) is a well-known optimization problem that seeks to find the shortest possible route that visits a set of points and returns to the starting point. In this paper, we apply some heuristics of the TSP for the task of restoring the DNA matrix. This restoration problem is often considered in biocybernetics. For it, we must recover the matrix of distances between DNA sequences if not all the elements of the matrix under consideration are known at the input. We consider the possibility of using this method in the testing of distance calculation algorithms between a pair of DNAs to restore the partially filled matrix. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=optimization%20problems" title="optimization problems">optimization problems</a>, <a href="https://publications.waset.org/abstracts/search?q=DNA%20matrix" title=" DNA matrix"> DNA matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=partially%20filled%20matrix" title=" partially filled matrix"> partially filled matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=traveling%20salesman%20problem" title=" traveling salesman problem"> traveling salesman problem</a>, <a href="https://publications.waset.org/abstracts/search?q=heuristic%20algorithms" title=" heuristic algorithms"> heuristic algorithms</a> </p> <a href="https://publications.waset.org/abstracts/172868/on-the-application-of-heuristics-of-the-traveling-salesman-problem-for-the-task-of-restoring-the-dna-matrix" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/172868.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">150</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">20438</span> The Second Smallest Eigenvalue of Complete Tripartite Hypergraph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alfi%20Y.%20Zakiyyah">Alfi Y. Zakiyyah</a>, <a href="https://publications.waset.org/abstracts/search?q=Hanni%20Garminia"> Hanni Garminia</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Salman"> M. Salman</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20N.%20Irawati"> A. N. Irawati</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the terminology of the hypergraph, there is a relation with the terminology graph. In the theory of graph, the edges connected two vertices. In otherwise, in hypergraph, the edges can connect more than two vertices. There is representation matrix of a graph such as adjacency matrix, Laplacian matrix, and incidence matrix. The adjacency matrix is symmetry matrix so that all eigenvalues is real. This matrix is a nonnegative matrix. The all diagonal entry from adjacency matrix is zero so that the trace is zero. Another representation matrix of the graph is the Laplacian matrix. Laplacian matrix is symmetry matrix and semidefinite positive so that all eigenvalues are real and non-negative. According to the spectral study in the graph, some that result is generalized to hypergraph. A hypergraph can be represented by a matrix such as adjacency, incidence, and Laplacian matrix. Throughout for this term, we use Laplacian matrix to represent a complete tripartite hypergraph. The aim from this research is to determine second smallest eigenvalues from this matrix and find a relation this eigenvalue with the connectivity of that hypergraph. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=connectivity" title="connectivity">connectivity</a>, <a href="https://publications.waset.org/abstracts/search?q=graph" title=" graph"> graph</a>, <a href="https://publications.waset.org/abstracts/search?q=hypergraph" title=" hypergraph"> hypergraph</a>, <a href="https://publications.waset.org/abstracts/search?q=Laplacian%20matrix" title=" Laplacian matrix"> Laplacian matrix</a> </p> <a href="https://publications.waset.org/abstracts/34000/the-second-smallest-eigenvalue-of-complete-tripartite-hypergraph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/34000.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">488</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">20437</span> Computer Simulations of Stress Corrosion Studies of Quartz Particulate Reinforced ZA-27 Metal Matrix Composites</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=K.%20Vinutha">K. Vinutha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The stress corrosion resistance of ZA-27 / TiO2 metal matrix composites (MMC’s) in high temperature acidic media has been evaluated using an autoclave. The liquid melt metallurgy technique using vortex method was used to fabricate MMC’s. TiO2 particulates of 50-80 µm in size are added to the matrix. ZA-27 containing 2,4,6 weight percentage of TiO2 are prepared. Stress corrosion tests were conducted by weight loss method for different exposure time, normality and temperature of the acidic medium. The corrosion rates of composites were lower to that of matrix ZA-27 alloy under all conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=autoclave" title="autoclave">autoclave</a>, <a href="https://publications.waset.org/abstracts/search?q=MMC%E2%80%99s" title=" MMC’s"> MMC’s</a>, <a href="https://publications.waset.org/abstracts/search?q=stress%20corrosion" title=" stress corrosion"> stress corrosion</a>, <a href="https://publications.waset.org/abstracts/search?q=vortex%20method" title=" vortex method"> vortex method</a> </p> <a href="https://publications.waset.org/abstracts/28848/computer-simulations-of-stress-corrosion-studies-of-quartz-particulate-reinforced-za-27-metal-matrix-composites" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/28848.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">477</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">20436</span> Multiple Images Stitching Based on Gradually Changing Matrix</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shangdong%20Zhu">Shangdong Zhu</a>, <a href="https://publications.waset.org/abstracts/search?q=Yunzhou%20Zhang"> Yunzhou Zhang</a>, <a href="https://publications.waset.org/abstracts/search?q=Jie%20Zhang"> Jie Zhang</a>, <a href="https://publications.waset.org/abstracts/search?q=Hang%20Hu"> Hang Hu</a>, <a href="https://publications.waset.org/abstracts/search?q=Yazhou%20Zhang"> Yazhou Zhang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Image stitching is a very important branch in the field of computer vision, especially for panoramic map. In order to eliminate shape distortion, a novel stitching method is proposed based on gradually changing matrix when images are horizontal. For images captured horizontally, this paper assumes that there is only translational operation in image stitching. By analyzing each parameter of the homography matrix, the global homography matrix is gradually transferred to translation matrix so as to eliminate the effects of scaling, rotation, etc. in the image transformation. This paper adopts matrix approximation to get the minimum value of the energy function so that the shape distortion at those regions corresponding to the homography can be minimized. The proposed method can avoid multiple horizontal images stitching failure caused by accumulated shape distortion. At the same time, it can be combined with As-Projective-As-Possible algorithm to ensure precise alignment of overlapping area. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=image%20stitching" title="image stitching">image stitching</a>, <a href="https://publications.waset.org/abstracts/search?q=gradually%20changing%20matrix" title=" gradually changing matrix"> gradually changing matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=horizontal%20direction" title=" horizontal direction"> horizontal direction</a>, <a href="https://publications.waset.org/abstracts/search?q=matrix%20approximation" title=" matrix approximation"> matrix approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=homography%20matrix" title=" homography matrix"> homography matrix</a> </p> <a href="https://publications.waset.org/abstracts/85912/multiple-images-stitching-based-on-gradually-changing-matrix" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/85912.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">319</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">20435</span> On Block Vandermonde Matrix Constructed from Matrix Polynomial Solvents</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> </p> <p class="card-text"><strong>Abstract:</strong></p> In control engineering, systems described by matrix fractions are studied through properties of block roots, also called solvents. These solvents are usually dealt with in a block Vandermonde matrix form. Inverses and determinants of Vandermonde matrices and block Vandermonde matrices are used in solving problems of numerical analysis in many domains but require costly computations. Even though Vandermonde matrices are well known and method to compute inverse and determinants are many and, generally, based on interpolation techniques, methods to compute the inverse and determinant of a block Vandermonde matrix have not been well studied. In this paper, some properties of these matrices and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given. These methods are deducted from the partitioned matrix inversion and determinant computing methods. Due to their great size, parallelization may be a solution to reduce the computations cost, so a parallelization of these algorithms is proposed and validated by a comparison using algorithmic complexity. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=block%20vandermonde%20matrix" title="block vandermonde matrix">block vandermonde matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=solvents" title=" solvents"> solvents</a>, <a href="https://publications.waset.org/abstracts/search?q=matrix%20polynomial" title=" matrix polynomial"> matrix polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=matrix%20inverse" title=" matrix inverse"> matrix inverse</a>, <a href="https://publications.waset.org/abstracts/search?q=matrix%20determinant" title=" matrix determinant"> matrix determinant</a>, <a href="https://publications.waset.org/abstracts/search?q=parallelization" title=" parallelization"> parallelization</a> </p> <a href="https://publications.waset.org/abstracts/89115/on-block-vandermonde-matrix-constructed-from-matrix-polynomial-solvents" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/89115.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">20434</span> A Comprehensive Method of Fault Detection and Isolation based on Testability Modeling Data</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Junyou%20Shi">Junyou Shi</a>, <a href="https://publications.waset.org/abstracts/search?q=Weiwei%20Cui"> Weiwei Cui</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Testability modeling is a commonly used method in testability design and analysis of system. A dependency matrix will be obtained from testability modeling, and we will give a quantitative evaluation about fault detection and isolation. Based on the dependency matrix, we can obtain the diagnosis tree. The tree provides the procedures of the fault detection and isolation. But the dependency matrix usually includes built-in test (BIT) and manual test in fact. BIT runs the test automatically and is not limited by the procedures. The method above cannot give a more efficient diagnosis and use the advantages of the BIT. A Comprehensive method of fault detection and isolation is proposed. This method combines the advantages of the BIT and Manual test by splitting the matrix. The result of the case study shows that the method is effective. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fault%20detection" title="fault detection">fault detection</a>, <a href="https://publications.waset.org/abstracts/search?q=fault%20isolation" title=" fault isolation"> fault isolation</a>, <a href="https://publications.waset.org/abstracts/search?q=testability%20modeling" title=" testability modeling"> testability modeling</a>, <a href="https://publications.waset.org/abstracts/search?q=BIT" title=" BIT"> BIT</a> </p> <a href="https://publications.waset.org/abstracts/27181/a-comprehensive-method-of-fault-detection-and-isolation-based-on-testability-modeling-data" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27181.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">20433</span> Conditions on Expressing a Matrix as a Sum of α-Involutions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ric%20Joseph%20R.%20Murillo">Ric Joseph R. Murillo</a>, <a href="https://publications.waset.org/abstracts/search?q=Edna%20N.%20Gueco"> Edna N. Gueco</a>, <a href="https://publications.waset.org/abstracts/search?q=Dennis%20I.%20Merino"> Dennis I. Merino</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let F be C or R, where C and R are the set of complex numbers and real numbers, respectively, and n be a natural number. An n-by-n matrix A over the field F is called an α-involutory matrix or an α-involution if there exists an α in the field such that the square of the matrix is equal to αI, where I is the n-by-n identity matrix. If α is a complex number or a nonnegative real number, then an n-by-n matrix A over the field F can be written as a sum of n-by-n α-involutory matrices over the field F if and only if the trace of that matrix is an integral multiple of the square root of α. Meanwhile, if α is a negative real number, then a 2n-by-2n matrix A over R can be written as a sum of 2n-by-2n α-involutory matrices over R if and only the trace of the matrix is zero. Some other properties of α-involutory matrices are also determined <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%CE%B1-involutory%20Matrices" title="α-involutory Matrices">α-involutory Matrices</a>, <a href="https://publications.waset.org/abstracts/search?q=sum%20of%20%CE%B1-involutory%20Matrices" title=" sum of α-involutory Matrices"> sum of α-involutory Matrices</a>, <a href="https://publications.waset.org/abstracts/search?q=Trace" title=" Trace"> Trace</a>, <a href="https://publications.waset.org/abstracts/search?q=Matrix%20Theory" title=" Matrix Theory"> Matrix Theory</a> </p> <a href="https://publications.waset.org/abstracts/95131/conditions-on-expressing-a-matrix-as-a-sum-of-a-involutions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/95131.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">198</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">20432</span> Social Information Seeking: Studying the Effect of Question Type on Responses in Social Q&A Sites</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arshia%20Ayoub">Arshia Ayoub</a>, <a href="https://publications.waset.org/abstracts/search?q=Zahid%20Ashraf%20Wani"> Zahid Ashraf Wani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> With the introduction of online social Q&A sites, people are able to reach each other efficiently for information seeking and simultaneously creating social bonds. There prevails an issue of low or no response for some questions posed by an information seeker on these sites. So this study tries to understand the effect of question type on responses in Social Q & A sites. The study found that among the answered queries, majority of them were answered within 24 hours of posting the questions and surprisingly most replies were received within one hour of posting. It was observed that questions of general information type were most likely to be answered followed by verification type. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=community%E2%80%90based%20services" title="community‐based services">community‐based services</a>, <a href="https://publications.waset.org/abstracts/search?q=information%20seeking" title=" information seeking"> information seeking</a>, <a href="https://publications.waset.org/abstracts/search?q=social%20search" title=" social search"> social search</a>, <a href="https://publications.waset.org/abstracts/search?q=social%20Q%26A%20site" title=" social Q&A site"> social Q&A site</a> </p> <a href="https://publications.waset.org/abstracts/146095/social-information-seeking-studying-the-effect-of-question-type-on-responses-in-social-qa-sites" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/146095.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">176</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">20431</span> Corrosion Characterization of Al6061 Hybrid Metal Matrix Composites in Acid Medium</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=P.%20V.%20Krupakara">P. V. Krupakara</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with the high corrosion resistance developed by the hybrid metal matrix composites when compared with that of matrix alloy. Matrix selected is Al6061. Reinforcements selected are graphite and red mud particulates. The composites are prepared using liquid melt metallurgy technique using vortex method. Metal matrix composites containing 2 percent graphite and 2 percent red mud, 2 percent graphite and 4 percent red mud, 2 percent graphite and 6 percent of red mud are prepared. Bar castings are cut into cylindrical discs of 20mm diameter and 20mm thickness. Corrosion tests were conducted at room temperature (230 °C) using conventional weight loss method according to ASTM G69-80. The corrodents used for the test were hydrochloric acid solution of different concentrations. Specimens were tested for every 24 hours interval up to 96 hours. Four specimens for each condition and time were immersed in corrodent. In each case the corrosion rate decreases with increase in exposure time for matrix and metal matrix composites whatever may be the concentration of hydrochloric acid. This may be due to aluminium, which may induce passivation due to development of non-porous layer. As red mud content increases the composites become corrosion resistant due to insulating nature of ceramic material red mud and less exposure of matrix alloy in those metal matrix composites. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Al6061" title="Al6061">Al6061</a>, <a href="https://publications.waset.org/abstracts/search?q=graphite" title=" graphite"> graphite</a>, <a href="https://publications.waset.org/abstracts/search?q=passivation" title=" passivation"> passivation</a>, <a href="https://publications.waset.org/abstracts/search?q=red%20mud" title=" red mud"> red mud</a>, <a href="https://publications.waset.org/abstracts/search?q=vortex" title=" vortex"> vortex</a> </p> <a href="https://publications.waset.org/abstracts/24636/corrosion-characterization-of-al6061-hybrid-metal-matrix-composites-in-acid-medium" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24636.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">542</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">20430</span> A Method for Modeling Flexible Manipulators: Transfer Matrix Method with Finite Segments</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Haijie%20Li">Haijie Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Xuping%20Zhang"> Xuping Zhang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=flexible%20manipulator" title="flexible manipulator">flexible manipulator</a>, <a href="https://publications.waset.org/abstracts/search?q=transfer%20matrix%20method" title=" transfer matrix method"> transfer matrix method</a>, <a href="https://publications.waset.org/abstracts/search?q=linearization" title=" linearization"> linearization</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20segment%20method" title=" finite segment method"> finite segment method</a> </p> <a href="https://publications.waset.org/abstracts/51465/a-method-for-modeling-flexible-manipulators-transfer-matrix-method-with-finite-segments" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51465.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">430</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">20429</span> Plasticity in Matrix Dominated Metal-Matrix Composite with One Active Slip Based Dislocation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Temesgen%20Takele%20Kasa">Temesgen Takele Kasa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The main aim of this paper is to suggest one active slip based continuum dislocation approach to matrix dominated MMC plasticity analysis. The approach centered the free energy principles through the continuum behavior of dislocations combined with small strain continuum kinematics. The analytical derivation of this method includes the formulation of one active slip system, the thermodynamic approach of dislocations, determination of free energy, and evolution of dislocations. In addition zero and non-zero energy dissipation analysis of dislocation evolution is also formulated by using varational energy minimization method. In general, this work shows its capability to analyze the plasticity of matrix dominated MMC with inclusions. The proposed method is also found to be capable of handling plasticity of MMC. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=active%20slip" title="active slip">active slip</a>, <a href="https://publications.waset.org/abstracts/search?q=continuum%20dislocation" title=" continuum dislocation"> continuum dislocation</a>, <a href="https://publications.waset.org/abstracts/search?q=distortion" title=" distortion"> distortion</a>, <a href="https://publications.waset.org/abstracts/search?q=dominated" title=" dominated"> dominated</a>, <a href="https://publications.waset.org/abstracts/search?q=energy%20dissipation" title=" energy dissipation"> energy dissipation</a>, <a href="https://publications.waset.org/abstracts/search?q=matrix%20dominated" title=" matrix dominated"> matrix dominated</a>, <a href="https://publications.waset.org/abstracts/search?q=plasticity" title=" plasticity"> plasticity</a> </p> <a href="https://publications.waset.org/abstracts/66664/plasticity-in-matrix-dominated-metal-matrix-composite-with-one-active-slip-based-dislocation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/66664.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">388</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">20428</span> Investigation on the Properties of Particulate Reinforced AA2014 Metal Matrix Composite Materials Produced by Vacuum Infiltration Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Isil%20Kerti">Isil Kerti</a>, <a href="https://publications.waset.org/abstracts/search?q=Onur%20Okur"> Onur Okur</a>, <a href="https://publications.waset.org/abstracts/search?q=Sibel%20Daglilar"> Sibel Daglilar</a>, <a href="https://publications.waset.org/abstracts/search?q=Recep%20Calin"> Recep Calin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Particulate reinforced aluminium matrix composites have gained more importance in automotive, aeronautical and defense industries due to their specific properties like as low density, high strength and stiffness, good fatigue strength, dimensional stability at high temperature and acceptable tribological properties. In this study, 2014 Aluminium alloy used as a matrix material and B₄C and SiC were selected as reinforcements components. For production of composites materials, vacuum infiltration method was used. In the experimental studies, the reinforcement volume ratios were defined by mixing as totally 10% B₄C and SiC. Aging treatment (T6) was applied to the specimens. The effect of T6 treatment on hardness was determined by using Brinell hardness test method. The effects of the aging treatment on microstructure and chemical structure were analysed by making XRD, SEM and EDS analysis on the specimens. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=metal%20matrix%20composite" title="metal matrix composite">metal matrix composite</a>, <a href="https://publications.waset.org/abstracts/search?q=vacumm%20infiltration%20method" title=" vacumm infiltration method"> vacumm infiltration method</a>, <a href="https://publications.waset.org/abstracts/search?q=aluminum%20metal%20matrix" title=" aluminum metal matrix"> aluminum metal matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=mechanical%20feature" title=" mechanical feature"> mechanical feature</a> </p> <a href="https://publications.waset.org/abstracts/81221/investigation-on-the-properties-of-particulate-reinforced-aa2014-metal-matrix-composite-materials-produced-by-vacuum-infiltration-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/81221.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">315</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">20427</span> Redundancy Component Matrix and Structural Robustness</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xinjian%20Kou">Xinjian Kou</a>, <a href="https://publications.waset.org/abstracts/search?q=Linlin%20Li"> Linlin Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Yongju%20Zhou"> Yongju Zhou</a>, <a href="https://publications.waset.org/abstracts/search?q=Jimian%20Song"> Jimian Song</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We introduce the redundancy matrix that expresses clearly the geometrical/topological configuration of the structure. With the matrix, the redundancy of the structure is resolved into redundant components and assigned to each member or rigid joint. The values of the diagonal elements in the matrix indicates the importance of the corresponding members or rigid joints, and the geometrically correlations can be shown with the non-diagonal elements. If a member or rigid joint failures, reassignment of the redundant components can be calculated with the recursive method given in the paper. By combining the indexes of reliability and redundancy components, we define an index concerning the structural robustness. To further explain the properties of the redundancy matrix, we cited several examples of statically indeterminate structures, including two trusses and a rigid frame. With the examples, some simple results and the properties of the matrix are discussed. The examples also illustrate that the redundancy matrix and the relevant concepts are valuable in structural safety analysis. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Structural%20Robustness" title="Structural Robustness">Structural Robustness</a>, <a href="https://publications.waset.org/abstracts/search?q=Structural%20Reliability" title=" Structural Reliability"> Structural Reliability</a>, <a href="https://publications.waset.org/abstracts/search?q=Redundancy%20Component" title=" Redundancy Component"> Redundancy Component</a>, <a href="https://publications.waset.org/abstracts/search?q=Redundancy%20Matrix" title=" Redundancy Matrix"> Redundancy Matrix</a> </p> <a href="https://publications.waset.org/abstracts/66420/redundancy-component-matrix-and-structural-robustness" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/66420.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">272</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">20426</span> Bridging Stress Modeling of Composite Materials Reinforced by Fiber Using Discrete Element Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chong%20Wang">Chong Wang</a>, <a href="https://publications.waset.org/abstracts/search?q=Kellem%20M.%20Soares"> Kellem M. Soares</a>, <a href="https://publications.waset.org/abstracts/search?q=Luis%20E.%20Kosteski"> Luis E. Kosteski</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The problem of toughening in brittle materials reinforced by fibers is complex, involving all the mechanical properties of fibers, matrix, the fiber/matrix interface, as well as the geometry of the fiber. An appropriate method applicable to the simulation and analysis of toughening is essential. In this work, we performed simulations and analysis of toughening in brittle matrix reinforced by randomly distributed fibers by means of the discrete elements method. At first, we put forward a mechanical model of the contribution of random fibers to the toughening of composite. Then with numerical programming, we investigated the stress, damage and bridging force in the composite material when a crack appeared in the brittle matrix. From the results obtained, we conclude that: (i) fibers with high strength and low elasticity modulus benefit toughening; (ii) fibers with relatively high elastic modulus compared to the matrix may result in considerable matrix damage (spalling effect); (iii) employment of high-strength synthetic fiber is a good option. The present work makes it possible to optimize the parameters in order to produce advanced ceramic with desired performance. We believe combination of the discrete element method (DEM) with the finite element method (FEM) can increase the versatility and efficiency of the software developed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bridging%20stress" title="bridging stress">bridging stress</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20element%20method" title=" discrete element method"> discrete element method</a>, <a href="https://publications.waset.org/abstracts/search?q=fiber%20reinforced%20composites" title=" fiber reinforced composites"> fiber reinforced composites</a>, <a href="https://publications.waset.org/abstracts/search?q=toughening" title=" toughening"> toughening</a> </p> <a href="https://publications.waset.org/abstracts/15719/bridging-stress-modeling-of-composite-materials-reinforced-by-fiber-using-discrete-element-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15719.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">445</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">20425</span> Manufacturing and Characterization of Ni-Matrix Composite Reinforced with Ti3SiC2 and Ti2AlC; and Al-Matrix with Ti2SiC</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Hadji">M. Hadji</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Chiker"> N. Chiker</a>, <a href="https://publications.waset.org/abstracts/search?q=Y.%20Hadji"> Y. Hadji</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Haddad"> A. Haddad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we report for the first time on the synthesis and characterization of novel MAX phases (Ti3SiC2, Ti2AlC) reinforced Ni-matrix and Ti2AlC reinforced Al-matrix. The stability of MAX phases in Al-matrix and Ni-matrix at a temperature of 985°C has been investigated. All the composites were cold pressed and sintered at a temperature of 985°C for 20min in H2 environment, except (Ni/Ti3SiC2) who was sintered at 1100°C for 1h.Microstructure analysis by scanning electron microscopy and phase analysis by X-Ray diffraction confirmed that there was minimal interfacial reaction between MAX particles and Ni, thus Al/MAX samples shown that MAX phases was totally decomposed at 985°C.The Addition of MAX enhanced the Al-matrix and Ni-matrix. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=MAX%20phase" title="MAX phase">MAX phase</a>, <a href="https://publications.waset.org/abstracts/search?q=microstructures" title=" microstructures"> microstructures</a>, <a href="https://publications.waset.org/abstracts/search?q=composites" title=" composites"> composites</a>, <a href="https://publications.waset.org/abstracts/search?q=hardness" title=" hardness"> hardness</a>, <a href="https://publications.waset.org/abstracts/search?q=SEM" title=" SEM"> SEM</a> </p> <a href="https://publications.waset.org/abstracts/40223/manufacturing-and-characterization-of-ni-matrix-composite-reinforced-with-ti3sic2-and-ti2alc-and-al-matrix-with-ti2sic" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/40223.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">347</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">20424</span> An Efficient Fundamental Matrix Estimation for Moving Object Detection</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yeongyu%20Choi">Yeongyu Choi</a>, <a href="https://publications.waset.org/abstracts/search?q=Ju%20H.%20Park"> Ju H. Park</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20M.%20Lee"> S. M. Lee</a>, <a href="https://publications.waset.org/abstracts/search?q=Ho-Youl%20Jung"> Ho-Youl Jung</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, an improved method for estimating fundamental matrix is proposed. The method is applied effectively to monocular camera based moving object detection. The method consists of corner points detection, moving object’s motion estimation and fundamental matrix calculation. The corner points are obtained by using Harris corner detector, motions of moving objects is calculated from pyramidal Lucas-Kanade optical flow algorithm. Through epipolar geometry analysis using RANSAC, the fundamental matrix is calculated. In this method, we have improved the performances of moving object detection by using two threshold values that determine inlier or outlier. Through the simulations, we compare the performances with varying the two threshold values. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=corner%20detection" title="corner detection">corner detection</a>, <a href="https://publications.waset.org/abstracts/search?q=optical%20flow" title=" optical flow"> optical flow</a>, <a href="https://publications.waset.org/abstracts/search?q=epipolar%20geometry" title=" epipolar geometry"> epipolar geometry</a>, <a href="https://publications.waset.org/abstracts/search?q=RANSAC" title=" RANSAC"> RANSAC</a> </p> <a href="https://publications.waset.org/abstracts/79103/an-efficient-fundamental-matrix-estimation-for-moving-object-detection" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/79103.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">409</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">20423</span> Inverse Matrix in the Theory of Dynamical Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Renata%20Masarova">Renata Masarova</a>, <a href="https://publications.waset.org/abstracts/search?q=Bohuslava%20Juhasova"> Bohuslava Juhasova</a>, <a href="https://publications.waset.org/abstracts/search?q=Martin%20Juhas"> Martin Juhas</a>, <a href="https://publications.waset.org/abstracts/search?q=Zuzana%20Sutova"> Zuzana Sutova</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamic%20system" title="dynamic system">dynamic system</a>, <a href="https://publications.waset.org/abstracts/search?q=transfer%20matrix" title=" transfer matrix"> transfer matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20matrix" title=" inverse matrix"> inverse matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=modeling" title=" modeling "> modeling </a> </p> <a href="https://publications.waset.org/abstracts/22680/inverse-matrix-in-the-theory-of-dynamical-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22680.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">516</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">20422</span> Membership Surface and Arithmetic Operations of Imprecise Matrix</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dhruba%20Das">Dhruba Das</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a method has been developed to construct the membership surfaces of row and column vectors and arithmetic operations of imprecise matrix. A matrix with imprecise elements would be called an imprecise matrix. The membership surface of imprecise vector has been already shown based on Randomness-Impreciseness Consistency Principle. The Randomness- Impreciseness Consistency Principle leads to defining a normal law of impreciseness using two different laws of randomness. In this paper, the author has shown row and column membership surfaces and arithmetic operations of imprecise matrix and demonstrated with the help of numerical example. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=imprecise%20number" title="imprecise number">imprecise number</a>, <a href="https://publications.waset.org/abstracts/search?q=imprecise%20vector" title=" imprecise vector"> imprecise vector</a>, <a href="https://publications.waset.org/abstracts/search?q=membership%20surface" title=" membership surface"> membership surface</a>, <a href="https://publications.waset.org/abstracts/search?q=imprecise%20matrix" title=" imprecise matrix"> imprecise matrix</a> </p> <a href="https://publications.waset.org/abstracts/33597/membership-surface-and-arithmetic-operations-of-imprecise-matrix" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33597.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">386</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">20421</span> Corrosion Characterization of Al6061, Quartz Metal Matrix Composites in Alkali Medium</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Radha%20H.%20R.">Radha H. R.</a>, <a href="https://publications.waset.org/abstracts/search?q=Krupakara%20P.%20V."> Krupakara P. V.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Metal matrix composites are attracting today's manufacturers of many automobile parts so that they lost longer and their properties can be tailored according to the requirement. In this paper an attempt has been made to study the corrosion characteristics of Aluminium 6061 / quartz metal matrix composites in alkali medium like sodium hydroxide solutions. Metal matrix composites are heterogeneous mixtures of a matrix and reinforcement. In this work the matrix selected is Aluminium 6061 alloy which is commercially available and the reinforcement selected is quartz particulates of 50-80 micron size which is available in plenty in and around Bangalore district, India. Composites containing Aluminium 6061 with 2, 4 and 6 weight percent of quartz are manufactured by liquid melt metallurgy technique using vortex method. Corrosion tests like static weight loss and open circuit potential tests are conducted in different concentrated solutions of sodium hydroxide. To compare the results the matrix Aluminium 6061 is also casted in the same way. Specimens for the test are prepared according to ASTM standards. In all the tests the metal matrix composites showed better corrosion resistance than matrix alloy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=aluminium%206061" title="aluminium 6061">aluminium 6061</a>, <a href="https://publications.waset.org/abstracts/search?q=corrosion" title=" corrosion"> corrosion</a>, <a href="https://publications.waset.org/abstracts/search?q=quartz" title=" quartz"> quartz</a>, <a href="https://publications.waset.org/abstracts/search?q=vortex" title=" vortex "> vortex </a> </p> <a href="https://publications.waset.org/abstracts/24586/corrosion-characterization-of-al6061-quartz-metal-matrix-composites-in-alkali-medium" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24586.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">409</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">20420</span> System Identification in Presence of Outliers </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chao%20Yu">Chao Yu</a>, <a href="https://publications.waset.org/abstracts/search?q=Qing-Guo%20Wang"> Qing-Guo Wang</a>, <a href="https://publications.waset.org/abstracts/search?q=Dan%20Zhang"> Dan Zhang </a> </p> <p class="card-text"><strong>Abstract:</strong></p> The outlier detection problem for dynamic systems is formulated as a matrix decomposition problem with low-rank, sparse matrices and further recast as a semidefinite programming (SDP) problem. A fast algorithm is presented to solve the resulting problem while keeping the solution matrix structure and it can greatly reduce the computational cost over the standard interior-point method. The computational burden is further reduced by proper construction of subsets of the raw data without violating low rank property of the involved matrix. The proposed method can make exact detection of outliers in case of no or little noise in output observations. In case of significant noise, a novel approach based on under-sampling with averaging is developed to denoise while retaining the saliency of outliers and so-filtered data enables successful outlier detection with the proposed method while the existing filtering methods fail. Use of recovered “clean” data from the proposed method can give much better parameter estimation compared with that based on the raw data. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=outlier%20detection" title="outlier detection">outlier detection</a>, <a href="https://publications.waset.org/abstracts/search?q=system%20identification" title=" system identification"> system identification</a>, <a href="https://publications.waset.org/abstracts/search?q=matrix%20decomposition" title=" matrix decomposition"> matrix decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=low-rank%20matrix" title=" low-rank matrix"> low-rank matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=sparsity" title=" sparsity"> sparsity</a>, <a href="https://publications.waset.org/abstracts/search?q=semidefinite%20programming" title=" semidefinite programming"> semidefinite programming</a>, <a href="https://publications.waset.org/abstracts/search?q=interior-point%20methods" title=" interior-point methods"> interior-point methods</a>, <a href="https://publications.waset.org/abstracts/search?q=denoising" title=" denoising"> denoising</a> </p> <a href="https://publications.waset.org/abstracts/13363/system-identification-in-presence-of-outliers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13363.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">307</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">20419</span> Out-of-Plane Free Vibrations of Circular Rods</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Faruk%20Firat%20%C3%87alim">Faruk Firat Çalim</a>, <a href="https://publications.waset.org/abstracts/search?q=Nurullah%20Karaca"> Nurullah Karaca</a>, <a href="https://publications.waset.org/abstracts/search?q=Hakan%20Tacettin%20T%C3%BCrker"> Hakan Tacettin Türker</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=circular%20rod" title="circular rod">circular rod</a>, <a href="https://publications.waset.org/abstracts/search?q=out-of-plane%20free%20vibration%20analysis" title=" out-of-plane free vibration analysis"> out-of-plane free vibration analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=transfer%20matrix%20method" title=" transfer matrix method"> transfer matrix method</a> </p> <a href="https://publications.waset.org/abstracts/29528/out-of-plane-free-vibrations-of-circular-rods" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/29528.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">309</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">20418</span> A Variant of a Double Structure-Preserving QR Algorithm for Symmetric and Hamiltonian Matrices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20Salam">Ahmed Salam</a>, <a href="https://publications.waset.org/abstracts/search?q=Haithem%20Benkahla"> Haithem Benkahla</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Recently, an efficient backward-stable algorithm for computing eigenvalues and vectors of a symmetric and Hamiltonian matrix has been proposed. The method preserves the symmetric and Hamiltonian structures of the original matrix, during the whole process. In this paper, we revisit the method. We derive a way for implementing the reduction of the matrix to the appropriate condensed form. Then, we construct a novel version of the implicit QR-algorithm for computing the eigenvalues and vectors. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=block%20implicit%20QR%20algorithm" title="block implicit QR algorithm">block implicit QR algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=preservation%20of%20a%20double%20structure" title=" preservation of a double structure"> preservation of a double structure</a>, <a href="https://publications.waset.org/abstracts/search?q=QR%20algorithm" title=" QR algorithm"> QR algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=symmetric%20and%20Hamiltonian%20structures" title=" symmetric and Hamiltonian structures"> symmetric and Hamiltonian structures</a> </p> <a href="https://publications.waset.org/abstracts/61018/a-variant-of-a-double-structure-preserving-qr-algorithm-for-symmetric-and-hamiltonian-matrices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/61018.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">409</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">20417</span> An Application of Graph Theory to The Electrical Circuit Using Matrix Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Samai%27la%20Abdullahi">Samai'la Abdullahi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A graph is a pair of two set and so that a graph is a pictorial representation of a system using two basic element nodes and edges. A node is represented by a circle (either hallo shade) and edge is represented by a line segment connecting two nodes together. In this paper, we present a circuit network in the concept of graph theory application and also circuit models of graph are represented in logical connection method were we formulate matrix method of adjacency and incidence of matrix and application of truth table. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=euler%20circuit%20and%20path" title="euler circuit and path">euler circuit and path</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20representation%20of%20circuit%20networks" title=" graph representation of circuit networks"> graph representation of circuit networks</a>, <a href="https://publications.waset.org/abstracts/search?q=representation%20of%20graph%20models" title=" representation of graph models"> representation of graph models</a>, <a href="https://publications.waset.org/abstracts/search?q=representation%20of%20circuit%20network%20using%20logical%20truth%20table" title=" representation of circuit network using logical truth table"> representation of circuit network using logical truth table</a> </p> <a href="https://publications.waset.org/abstracts/32358/an-application-of-graph-theory-to-the-electrical-circuit-using-matrix-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32358.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">561</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">20416</span> A Multistep Broyden’s-Type Method for Solving Systems of Nonlinear Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Y.%20Waziri">M. Y. Waziri</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20A.%20Aliyu"> M. A. Aliyu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=mulit-step%20Broyden" title="mulit-step Broyden">mulit-step Broyden</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20systems%20of%20equations" title=" nonlinear systems of equations"> nonlinear systems of equations</a>, <a href="https://publications.waset.org/abstracts/search?q=computational%20efficiency" title=" computational efficiency"> computational efficiency</a>, <a href="https://publications.waset.org/abstracts/search?q=iterate" title=" iterate"> iterate</a> </p> <a href="https://publications.waset.org/abstracts/13750/a-multistep-broydens-type-method-for-solving-systems-of-nonlinear-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13750.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">638</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">20415</span> Infinite Impulse Response Digital Filters Design</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Phuoc%20Si%20Nguyen">Phuoc Si Nguyen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Infinite impulse response (IIR) filters can be designed from an analogue low pass prototype by using frequency transformation in the s-domain and bilinear z-transformation with pre-warping frequency; this method is known as frequency transformation from the s-domain to the z-domain. This paper will introduce a new method to transform an IIR digital filter to another type of IIR digital filter (low pass, high pass, band pass, band stop or narrow band) using a technique based on inverse bilinear z-transformation and inverse matrices. First, a matrix equation is derived from inverse bilinear z-transformation and Pascal’s triangle. This Low Pass Digital to Digital Filter Pascal Matrix Equation is used to transform a low pass digital filter to other digital filter types. From this equation and the inverse matrix, a Digital to Digital Filter Pascal Matrix Equation can be derived that is able to transform any IIR digital filter. This paper will also introduce some specific matrices to replace the inverse matrix, which is difficult to determine due to the larger size of the matrix in the current method. This will make computing and hand calculation easier when transforming from one IIR digital filter to another in the digital domain. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bilinear%20z-transformation" title="bilinear z-transformation">bilinear z-transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=frequency%20transformation" title=" frequency transformation"> frequency transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20bilinear%20z-transformation" title=" inverse bilinear z-transformation"> inverse bilinear z-transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=IIR%20digital%20filters" title=" IIR digital filters"> IIR digital filters</a> </p> <a href="https://publications.waset.org/abstracts/48777/infinite-impulse-response-digital-filters-design" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48777.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">423</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=matrix%20method%20posting&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=matrix%20method%20posting&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=matrix%20method%20posting&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=matrix%20method%20posting&page=5">5</a></li> <li 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