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product state</title> <meta name="description" content="Search results for: matrix product state"> <meta name="keywords" content="matrix product state"> <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 product state"> <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> 12706</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: matrix product state</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">12706</span> Parallel Computation of the Covariance-Matrix</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Claude%20Tadonki">Claude Tadonki</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We address the issues related to the computation of the covariance matrix. This matrix is likely to be ill conditioned following its canonical expression, thus consequently raises serious numerical issues. The underlying linear system, which therefore should be solved by means of iterative approaches, becomes computationally challenging. A huge number of iterations is expected in order to reach an acceptable level of convergence, necessary to meet the required accuracy of the computation. In addition, this linear system needs to be solved at each iteration following the general form of the covariance matrix. Putting all together, its comes that we need to compute as fast as possible the associated matrix-vector product. This is our purpose in the work, where we consider and discuss skillful formulations of the problem, then propose a parallel implementation of the matrix-vector product involved. Numerical and performance oriented discussions are provided based on experimental evaluations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=covariance-matrix" title="covariance-matrix">covariance-matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=multicore" title=" multicore"> multicore</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20computing" title=" numerical computing"> numerical computing</a>, <a href="https://publications.waset.org/abstracts/search?q=parallel%20computing" title=" parallel computing"> parallel computing</a> </p> <a href="https://publications.waset.org/abstracts/59579/parallel-computation-of-the-covariance-matrix" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59579.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">312</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">12705</span> Application of Neural Network in Portfolio Product Companies: Integration of Boston Consulting Group Matrix and Ansoff Matrix</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Khajezadeh">M. Khajezadeh</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Saied%20Fallah%20Niasar"> M. Saied Fallah Niasar</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Ali%20Asli"> S. Ali Asli</a>, <a href="https://publications.waset.org/abstracts/search?q=D.%20Davani%20Davari"> D. Davani Davari</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Godarzi"> M. Godarzi</a>, <a href="https://publications.waset.org/abstracts/search?q=Y.%20Asgari"> Y. Asgari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study aims to explore the joint application of both Boston and Ansoff matrices in the operational development of the product. We conduct deep analysis, by utilizing the Artificial Neural Network, to predict the position of the product in the market while the company is interested in increasing its share. The data are gathered from two industries, called hygiene and detergent. In doing so, the effort is being made by investigating the behavior of top player companies and, recommend strategic orientations. In conclusion, this combination analysis is appropriate for operational development; as well, it plays an important role in providing the position of the product in the market for both hygiene and detergent industries. More importantly, it will elaborate on the company’s strategies to increase its market share related to a combination of the Boston Consulting Group (BCG) Matrix and Ansoff Matrix. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=artificial%20neural%20network" title="artificial neural network">artificial neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=portfolio%20analysis" title=" portfolio analysis"> portfolio analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=BCG%20matrix" title=" BCG matrix"> BCG matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=Ansoff%20matrix" title=" Ansoff matrix"> Ansoff matrix</a> </p> <a href="https://publications.waset.org/abstracts/103499/application-of-neural-network-in-portfolio-product-companies-integration-of-boston-consulting-group-matrix-and-ansoff-matrix" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/103499.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">143</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">12704</span> Implementing Quality Function Deployment Tool for a Customer Driven New Product Development in a Kuwait SME</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Asma%20AlQahtani">Asma AlQahtani</a>, <a href="https://publications.waset.org/abstracts/search?q=Jumana%20AlHadad"> Jumana AlHadad</a>, <a href="https://publications.waset.org/abstracts/search?q=Maryam%20AlQallaf"> Maryam AlQallaf</a>, <a href="https://publications.waset.org/abstracts/search?q=Shoug%20AlHasan"> Shoug AlHasan </a> </p> <p class="card-text"><strong>Abstract:</strong></p> New product development (NPD) is the complete process of bringing a new product to the customer by integrating the two broad divisions; one involving the idea generation, product design and detail engineering; and the other involving market research and marketing analysis. It is a common practice for companies to undertake some of these tasks simultaneously (concurrent engineering) and also consider them as an ongoing process (continuous development). The current study explores the framework and methodology for a new product development process utilizing the Quality Function Deployment (QFD) tool for bringing the customer opinion into the product development process. An elaborate customer survey with focus groups in the region was carried out to ensure that customer requirements are integrated into new products as early as the design stage including identifying the recognition of need for the new product. A QFD Matrix (House of Quality) was prepared that links customer requirements to product engineering requirements and a feasibility study and risk assessment exercise was carried out for a Small and Medium Enterprise (SME) in Kuwait for development of the new product. SMEs in Kuwait, particularly in manufacturing sector are mainly focused on serving the local demand, and often lack of product quality adversely affects the ability of the companies to compete on a regional/global basis. Further, lack of focus on identifying customer requirements often deters SMEs to envisage the idea of a New Product Development. The current study therefore focuses in utilizing QFD Matrix right from the conceptual design to detail design and to some extent, extending the link this to design of the manufacturing system. The outcome of the project resulted in a development of the prototype for a new molded product which can ensure consistency between the customer’s requirements and the measurable characteristics of the product. The Engineering Economics and Cost studies were also undertaken to analyse the viability of the new product, the results of which was also linked to the successful implementation of the initial QFD Matrix. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Quality%20Function%20Deployment" title="Quality Function Deployment">Quality Function Deployment</a>, <a href="https://publications.waset.org/abstracts/search?q=QFD%20Matrix" title=" QFD Matrix"> QFD Matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=new%20product%20development" title=" new product development"> new product development</a>, <a href="https://publications.waset.org/abstracts/search?q=NPD" title=" NPD"> NPD</a>, <a href="https://publications.waset.org/abstracts/search?q=Kuwait%20SMEs" title=" Kuwait SMEs"> Kuwait SMEs</a>, <a href="https://publications.waset.org/abstracts/search?q=prototype%20development" title=" prototype development "> prototype development </a> </p> <a href="https://publications.waset.org/abstracts/9348/implementing-quality-function-deployment-tool-for-a-customer-driven-new-product-development-in-a-kuwait-sme" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9348.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">414</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">12703</span> Encryption Image via Mutual Singular Value Decomposition</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Adil%20Al-Rammahi">Adil Al-Rammahi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Image or document encryption is needed through e- government data base. Really in this paper we introduce two matrices images, one is the public, and the second is the secret (original). The analyses of each matrix is achieved using the transformation of singular values decomposition. So each matrix is transformed or analyzed to three matrices say row orthogonal basis, column orthogonal basis, and spectral diagonal basis. Product of the two row basis is calculated. Similarly the product of the two column basis is achieved. Finally we transform or save the files of public, row product and column product. In decryption stage, the original image is deduced by mutual method of the three public files. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=image%20cryptography" title="image cryptography">image cryptography</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20values%20decomposition" title=" singular values decomposition"> singular values decomposition</a> </p> <a href="https://publications.waset.org/abstracts/13714/encryption-image-via-mutual-singular-value-decomposition" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13714.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">436</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">12702</span> A Framework for Designing Complex Product-Service Systems with a Multi-Domain Matrix</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yoonjung%20An">Yoonjung An</a>, <a href="https://publications.waset.org/abstracts/search?q=Yongtae%20Park"> Yongtae Park</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Offering a Product-Service System (PSS) is a well-accepted strategy that companies may adopt to provide a set of systemic solutions to customers. PSSs were initially provided in a simple form but now take diversified and complex forms involving multiple services, products and technologies. With the growing interest in the PSS, frameworks for the PSS development have been introduced by many researchers. However, most of the existing frameworks fail to examine various relations existing in a complex PSS. Since designing a complex PSS involves full integration of multiple products and services, it is essential to identify not only product-service relations but also product-product/ service-service relations. It is also equally important to specify how they are related for better understanding of the system. Moreover, as customers tend to view their purchase from a more holistic perspective, a PSS should be developed based on the whole system’s requirements, rather than focusing only on the product requirements or service requirements. Thus, we propose a framework to develop a complex PSS that is coordinated fully with the requirements of both worlds. Specifically, our approach adopts a multi-domain matrix (MDM). A MDM identifies not only inter-domain relations but also intra-domain relations so that it helps to design a PSS that includes highly desired and closely related core functions/ features. Also, various dependency types and rating schemes proposed in our approach would help the integration process. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=inter-domain%20relations" title="inter-domain relations">inter-domain relations</a>, <a href="https://publications.waset.org/abstracts/search?q=intra-domain%20relations" title=" intra-domain relations"> intra-domain relations</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-domain%20matrix" title=" multi-domain matrix"> multi-domain matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=product-service%20system%20design" title=" product-service system design"> product-service system design</a> </p> <a href="https://publications.waset.org/abstracts/26766/a-framework-for-designing-complex-product-service-systems-with-a-multi-domain-matrix" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/26766.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">641</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">12701</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">12700</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">12699</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">12698</span> Degree of Approximation of Functions Conjugate to Periodic Functions Belonging to Lipschitz Classes by Product Matrix Means</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Smita%20Sonker">Smita Sonker</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Various investigators have determined the degree of approximation of conjugate signals (functions) of functions belonging to different classes Lipα, Lip(α,p), Lip(ξ(t),p), W(Lr,ξ(t), (β ≥ 0)) by matrix summability means, lower triangular matrix operator, product means (i.e. (C,1)(E,1), (C,1)(E,q), (E,q)(C,1) (N,p,q)(E,1), and (E,q)(N,pn) of their conjugate trigonometric Fourier series. In this paper, we shall determine the degree of approximation of 2π-periodic function conjugate functions of f belonging to the function classes Lipα and W(Lr; ξ(t); (β ≥ 0)) by (C1.T) -means of their conjugate trigonometric Fourier series. On the other hand, we shall review above-mentioned work in the light of Lenski. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=signals" title="signals">signals</a>, <a href="https://publications.waset.org/abstracts/search?q=trigonometric%20fourier%20approximation" title=" trigonometric fourier approximation"> trigonometric fourier approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=class%20W%28L%5Er" title=" class W(L^r"> class W(L^r</a>, <a href="https://publications.waset.org/abstracts/search?q=%5Cxi%28t%29" title="\xi(t)">\xi(t)</a>, <a href="https://publications.waset.org/abstracts/search?q=conjugate%20fourier%20series" title=" conjugate fourier series"> conjugate fourier series</a> </p> <a href="https://publications.waset.org/abstracts/20996/degree-of-approximation-of-functions-conjugate-to-periodic-functions-belonging-to-lipschitz-classes-by-product-matrix-means" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20996.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">397</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">12697</span> Reliable Consensus Problem for Multi-Agent Systems with Sampled-Data </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20H.%20Lee">S. H. Lee</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20J.%20Park"> M. J. Park</a>, <a href="https://publications.waset.org/abstracts/search?q=O.%20M.%20Kwon"> O. M. Kwon</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, reliable consensus of multi-agent systems with sampled-data is investigated. By using a suitable Lyapunov-Krasovskii functional and some techniques such as Wirtinger Inequality, Schur Complement and Kronecker Product, the results of this systems are obtained by solving a set of Linear Matrix Inequalities(LMIs). One numerical example is included to show the effectiveness of the proposed criteria. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=multi-agent" title="multi-agent">multi-agent</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20matrix%20inequalities%20%28LMIs%29" title=" linear matrix inequalities (LMIs)"> linear matrix inequalities (LMIs)</a>, <a href="https://publications.waset.org/abstracts/search?q=kronecker%20product" title=" kronecker product"> kronecker product</a>, <a href="https://publications.waset.org/abstracts/search?q=sampled-data" title=" sampled-data"> sampled-data</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov%20method" title=" Lyapunov method"> Lyapunov method</a> </p> <a href="https://publications.waset.org/abstracts/25582/reliable-consensus-problem-for-multi-agent-systems-with-sampled-data" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25582.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">528</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">12696</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">12695</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">12694</span> Redesigning Malaysia Batik Sarong by Applying Quality Function Deployment</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Kamal">M. Kamal</a>, <a href="https://publications.waset.org/abstracts/search?q=Y.%20Wang"> Y. Wang</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Kennon"> R. Kennon</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Quality Function Deployment is a useful tool in product development with the application of voice of customer. In this paper, it aims to be applied as a product development tool in redesigning fashion and textile product. The purpose of these studies is to apply the effective use of Voice of Customer in redesigning cultural fashion product. The data collection from Voice of Customer or consumers’ feedback might help the producer to improve the quality of merchandise ahead. Voice of Customer could give a specific detailing for quality which needs to be redesigned according to customers’ requirements. Meanwhile, the next objective is to differentiate design specifications and characteristics using House of Quality. In product designing phase, it is very important to distinguish each specification and characteristic which translated from Voice of Customer to House of Quality matrix. This matrix would help designers to development according to qualities that customer wants for the better and successful product in the market. It is hope this research would indicate the customers’ requirements and production team idea might be measured and translated to a systematic data. The specific technical data could be planned ahead with specific design details as well. This could be a sustainable approach for a traditional product which could control the material that they use and sustain the quality as the past production. As a conclusion, this study would benefit the Small Medium Enterprises design team or the designers to style an item from customers view with organised projection of the product. The finding also could assist designers or batik producers’ to recognise specific details Batik sarong from consumers as well as in in advertising and marketing strategy plan. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=house%20of%20quality" title="house of quality">house of quality</a>, <a href="https://publications.waset.org/abstracts/search?q=Malaysia%20batik%20sarong" title=" Malaysia batik sarong"> Malaysia batik sarong</a>, <a href="https://publications.waset.org/abstracts/search?q=quality%20function%20deployment" title=" quality function deployment"> quality function deployment</a>, <a href="https://publications.waset.org/abstracts/search?q=voice%20of%20customer" title=" voice of customer "> voice of customer </a> </p> <a href="https://publications.waset.org/abstracts/29404/redesigning-malaysia-batik-sarong-by-applying-quality-function-deployment" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/29404.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">592</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">12693</span> Development of an Erodable Matrix Drug Delivery Platform for Controled Delivery of Non Steroidal Anti Inflamatory Drugs Using Melt Granulation Process</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Hilsana">A. Hilsana</a>, <a href="https://publications.waset.org/abstracts/search?q=Vinay%20U.%20Rao"> Vinay U. Rao</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Sudhakar"> M. Sudhakar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Even though a number of non-steroidal anti-inflammatory drugs (NSAIDS) are available with different chemistries, they share a common solubility characteristic that is they are relatively more soluble in alkaline environment and practically insoluble in acidic environment. This work deals with developing a wax matrix drug delivery platform for controlled delivery of three model NSAIDS, Diclofenac sodium (DNa), Mefenamic acid (MA) and Naproxen (NPX) using the melt granulation technique. The aim of developing the platform was to have a general understanding on how an erodible matrix system modulates drug delivery rate and extent and how it can be optimized to give a delivery system which shall release the drug as per a common target product profile (TPP). Commonly used waxes like Cetostearyl alcohol and stearic acid were used singly an in combination to achieve a TPP of not 15 to 35% in 1 hour and not less than 80% Q in 24 hours. Full factorial design of experiments was followed for optimization of the formulation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=NSAIDs" title="NSAIDs">NSAIDs</a>, <a href="https://publications.waset.org/abstracts/search?q=controlled%20delivery" title=" controlled delivery"> controlled delivery</a>, <a href="https://publications.waset.org/abstracts/search?q=target%20product%20profile" title=" target product profile"> target product profile</a>, <a href="https://publications.waset.org/abstracts/search?q=melt%20granulation" title=" melt granulation"> melt granulation</a> </p> <a href="https://publications.waset.org/abstracts/9021/development-of-an-erodable-matrix-drug-delivery-platform-for-controled-delivery-of-non-steroidal-anti-inflamatory-drugs-using-melt-granulation-process" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9021.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">12692</span> Modeling of Coupled Mechanical State and Diffusion in Composites with Impermeable Fibers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=D.%20Gueribiz">D. Gueribiz</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Jacquemin"> F. Jacquemin</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Fr%C3%A9our"> S. Fréour</a> </p> <p class="card-text"><strong>Abstract:</strong></p> During their service life, composite materials are submitted to humid environments. The moisture absorbed by their matrix polymer induced internal stresses which can lead to multi-scale damage and may reduce the lifetime of composite structures. The estimation of internal stresses is based at a first on realistic evaluation of the diffusive behavior of composite materials. Generally, the modeling and simulation of the diffusive behavior of composite materials are extensively investigated through decoupled models based on the assumption of Fickien behavior. For these approaches, the concentration and the deformation (or stresses), the two state variables of the problem considered are governed by independent equations which are solved separately. In this study, a model coupling diffusive behavior with stresses state for a polymer matrix composite reinforced with impermeable fibers is proposed, the investigation of diffusive behavior is based on a more general thermodynamic approach which introduces a dependence of diffusive behavior on internal stresses state. The coupled diffusive behavior modeling was established in first for homogeneous and isotropic matrix and it is, thereafter, extended to impermeable unidirectional composites. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=composites%20materials" title="composites materials">composites materials</a>, <a href="https://publications.waset.org/abstracts/search?q=moisture%20diffusion" title=" moisture diffusion"> moisture diffusion</a>, <a href="https://publications.waset.org/abstracts/search?q=effective%20moisture%20diffusivity" title=" effective moisture diffusivity"> effective moisture diffusivity</a>, <a href="https://publications.waset.org/abstracts/search?q=coupled%20moisture%20diffusion" title=" coupled moisture diffusion "> coupled moisture diffusion </a> </p> <a href="https://publications.waset.org/abstracts/48341/modeling-of-coupled-mechanical-state-and-diffusion-in-composites-with-impermeable-fibers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48341.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">308</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">12691</span> Robust H∞ State Feedback Control for Discrete Time T-S Fuzzy Systems Based on Fuzzy Lyapunov Function Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Walied%20Hanora">Walied Hanora</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents the problem of robust state feedback H∞ for discrete time nonlinear system represented by Takagi-Sugeno fuzzy systems. Based on fuzzy lyapunov function, the condition ,which is represented in the form of Liner Matrix Inequalities (LMI), guarantees the H∞ performance of the T-S fuzzy system with uncertainties. By comparison with recent literature, this approach will be more relaxed condition. Finally, an example is given to illustrate the proposed result. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20lyapunov%20function" title="fuzzy lyapunov function">fuzzy lyapunov function</a>, <a href="https://publications.waset.org/abstracts/search?q=H%E2%88%9E%20control" title=" H∞ control "> H∞ control </a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20matrix%20inequalities" title=" linear matrix inequalities"> linear matrix inequalities</a>, <a href="https://publications.waset.org/abstracts/search?q=state%20feedback" title=" state feedback"> state feedback</a>, <a href="https://publications.waset.org/abstracts/search?q=T-S%20fuzzy%20systems" title=" T-S fuzzy systems"> T-S fuzzy systems</a> </p> <a href="https://publications.waset.org/abstracts/58045/robust-h-state-feedback-control-for-discrete-time-t-s-fuzzy-systems-based-on-fuzzy-lyapunov-function-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/58045.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">288</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">12690</span> A New Nonlinear State-Space Model and Its Application</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdullah%20Eqal%20Al%20Mazrooei">Abdullah Eqal Al Mazrooei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, a new nonlinear model will be introduced. The model is in the state-space form. The nonlinearity of this model is in the state equation where the state vector is multiplied by its self. This technique makes our model generalizes many famous models as Lotka-Volterra model and Lorenz model which have many applications in the real life. We will apply our new model to estimate the wind speed by using a new nonlinear estimator which suitable to work with our model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20systems" title="nonlinear systems">nonlinear systems</a>, <a href="https://publications.waset.org/abstracts/search?q=state-space%20model" title=" state-space model"> state-space model</a>, <a href="https://publications.waset.org/abstracts/search?q=Kronecker%20product" title=" Kronecker product"> Kronecker product</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20estimator" title=" nonlinear estimator"> nonlinear estimator</a> </p> <a href="https://publications.waset.org/abstracts/34407/a-new-nonlinear-state-space-model-and-its-application" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/34407.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">691</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">12689</span> Robust Control of a Single-Phase Inverter Using Linear Matrix Inequality Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chivon%20Choeung">Chivon Choeung</a>, <a href="https://publications.waset.org/abstracts/search?q=Heng%20Tang"> Heng Tang</a>, <a href="https://publications.waset.org/abstracts/search?q=Panha%20Soth"> Panha Soth</a>, <a href="https://publications.waset.org/abstracts/search?q=Vichet%20Huy"> Vichet Huy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a robust control strategy for a single-phase DC-AC inverter with an output LC-filter. An all-pass filter is utilized to create an artificial β-signal so that the proposed controller can be simply used in dq-synchronous frame. The proposed robust controller utilizes a state feedback control with integral action in the dq-synchronous frame. A linear matrix inequality-based optimization scheme is used to determine stabilizing gains of the controllers to maximize the convergence rate to steady state in the presence of uncertainties. The uncertainties of the system are described as the potential variation range of the inductance and resistance in the LC-filter. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=single-phase%20inverter" title="single-phase inverter">single-phase inverter</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20matrix%20inequality" title=" linear matrix inequality"> linear matrix inequality</a>, <a href="https://publications.waset.org/abstracts/search?q=robust%20control" title=" robust control"> robust control</a>, <a href="https://publications.waset.org/abstracts/search?q=all-pass%20filter" title=" all-pass filter"> all-pass filter</a> </p> <a href="https://publications.waset.org/abstracts/127709/robust-control-of-a-single-phase-inverter-using-linear-matrix-inequality-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127709.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">142</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">12688</span> Approximation of Periodic Functions Belonging to Lipschitz Classes by Product Matrix Means of Fourier Series</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Smita%20Sonker">Smita Sonker</a>, <a href="https://publications.waset.org/abstracts/search?q=Uaday%20Singh"> Uaday Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Various investigators have determined the degree of approximation of functions belonging to the classes W(L r , ξ(t)), Lip(ξ(t), r), Lip(α, r), and Lipα using different summability methods with monotonocity conditions. Recently, Lal has determined the degree of approximation of the functions belonging to Lipα and W(L r , ξ(t)) classes by using Ces`aro-N¨orlund (C 1 .Np)- summability with non-increasing weights {pn}. In this paper, we shall determine the degree of approximation of 2π - periodic functions f belonging to the function classes Lipα and W(L r , ξ(t)) by C 1 .T - means of Fourier series of f. Our theorems generalize the results of Lal and we also improve these results in the light off. From our results, we also derive some corollaries. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lipschitz%20classes" title="Lipschitz classes">Lipschitz classes</a>, <a href="https://publications.waset.org/abstracts/search?q=product%20matrix%20operator" title=" product matrix operator"> product matrix operator</a>, <a href="https://publications.waset.org/abstracts/search?q=signals" title=" signals"> signals</a>, <a href="https://publications.waset.org/abstracts/search?q=trigonometric%20Fourier%20approximation" title=" trigonometric Fourier approximation"> trigonometric Fourier approximation</a> </p> <a href="https://publications.waset.org/abstracts/4757/approximation-of-periodic-functions-belonging-to-lipschitz-classes-by-product-matrix-means-of-fourier-series" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4757.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">12687</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">12686</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">12685</span> XANES Studies on the Oxidation States of Copper Ion in Silicate Glass </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=R.%20Buntem">R. Buntem</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20Samkongngam"> K. Samkongngam</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The silicate glass was prepared using rice husk as the source of silica. The base composition of glass sample is composed of SiO2 (from rice husk ash), Na2CO3, K2CO3, ZnO, H3BO3, CaO, Al2O3 or Al, and CuO. Aluminum is used in place of Al2O3 in order to reduce Cu2+ to Cu+. The red color of Cu2O in the glass matrix was observed when the Al was added into the glass mixture. The expansion coefficients of the copper doped glass are in the range of 1.2 x 10-5-1.4x10-5 (ºC -1) which is common for the silicate glass. The finger prints of the bond vibrations were studied using IR spectroscopy. While the oxidation state and the coordination information of the copper ion in the glass matrix were investigated using X-ray absorption spectroscopy. From the data, Cu+ and Cu2+ exist in the glass matrix. The red particles of Cu2O can be formed in the glass matrix when enough aluminum was added. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=copper%20in%20glass" title="copper in glass">copper in glass</a>, <a href="https://publications.waset.org/abstracts/search?q=coordination%20information" title=" coordination information"> coordination information</a>, <a href="https://publications.waset.org/abstracts/search?q=silicate%20glass" title=" silicate glass"> silicate glass</a>, <a href="https://publications.waset.org/abstracts/search?q=XANES%20spectrum" title=" XANES spectrum"> XANES spectrum</a> </p> <a href="https://publications.waset.org/abstracts/15673/xanes-studies-on-the-oxidation-states-of-copper-ion-in-silicate-glass" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15673.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">263</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">12684</span> Mechanism of Changing a Product Concept</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kiyohiro%20Yamazaki">Kiyohiro Yamazaki</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The purpose of this paper is to examine the hypothesis explaining the mechanism in the case, where the product is deleted or reduced the fundamental function of the product through the product concept changes in the digital camera industry. This paper points out not owning the fundamental technology might cause the change of the product concept. Casio could create new competitive factor so that this paper discusses a possibility of the mechanism of changing the product concept. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=firm%20without%20fundamental%20technology" title="firm without fundamental technology">firm without fundamental technology</a>, <a href="https://publications.waset.org/abstracts/search?q=product%20development" title=" product development"> product development</a>, <a href="https://publications.waset.org/abstracts/search?q=product%20concept" title=" product concept"> product concept</a>, <a href="https://publications.waset.org/abstracts/search?q=digital%20camera%20industry" title=" digital camera industry"> digital camera industry</a>, <a href="https://publications.waset.org/abstracts/search?q=Casio" title=" Casio"> Casio</a> </p> <a href="https://publications.waset.org/abstracts/16190/mechanism-of-changing-a-product-concept" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16190.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">562</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">12683</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">12682</span> A Review on Aluminium Metal Matric Composites</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=V.%20Singh">V. Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Singh"> S. Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20S.%20Garewal"> S. S. Garewal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Metal matrix composites with aluminum as the matrix material have been heralded as the next great development in advanced engineering materials. Aluminum metal matrix composites (AMMC) refer to the class of light weight high performance material systems. Properties of AMMCs can be tailored to the demands of different industrial applications by suitable combinations of matrix, reinforcement and processing route. AMMC finds its application in automotive, aerospace, defense, sports and structural areas. This paper presents an overview of AMMC material systems on aspects relating to processing, types and applications with case studies. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=aluminum%20metal%20matrix%20composites" title="aluminum metal matrix composites">aluminum metal matrix composites</a>, <a href="https://publications.waset.org/abstracts/search?q=applications%20of%20aluminum%20metal%20matrix%20composites" title=" applications of aluminum metal matrix composites"> applications of aluminum metal matrix composites</a>, <a href="https://publications.waset.org/abstracts/search?q=lighting%20material%20processing%20of%20aluminum%20metal%20matrix%20composites" title=" lighting material processing of aluminum metal matrix composites"> lighting material processing of aluminum metal matrix composites</a> </p> <a href="https://publications.waset.org/abstracts/62849/a-review-on-aluminium-metal-matric-composites" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/62849.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">465</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">12681</span> Anti-Phase Synchronization of Complex Delayed Networks with Output Coupling via Pinning Control</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chanyuan%20Gu">Chanyuan Gu</a>, <a href="https://publications.waset.org/abstracts/search?q=Shouming%20Zhong"> Shouming Zhong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Synchronization is a fundamental phenomenon that enables coherent behavior in networks as a result of interactions. The purpose of this research had been to investigate the problem of anti-phase synchronization for complex delayed dynamical networks with output coupling. The coupling configuration is general, with the coupling matrix not assumed to be symmetric or irreducible. The amount of the coupling variables between two connected nodes is flexible, the nodes in the drive and response systems need not to be identical and there is not any extra constraint on the coupling matrix. Some pinning controllers are designed to make the drive-response system achieve the anti-phase synchronization. For the convenience of description, we applied the matrix Kronecker product. Some new criteria are proposed based on the Lyapunov stability theory, linear matrix inequalities (LMI) and Schur complement. Lastly, some simulation examples are provided to illustrate the effectiveness of our proposed conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=anti-phase%20synchronization" title="anti-phase synchronization">anti-phase synchronization</a>, <a href="https://publications.waset.org/abstracts/search?q=complex%20networks" title=" complex networks"> complex networks</a>, <a href="https://publications.waset.org/abstracts/search?q=output%20coupling" title=" output coupling"> output coupling</a>, <a href="https://publications.waset.org/abstracts/search?q=pinning%20control" title=" pinning control"> pinning control</a> </p> <a href="https://publications.waset.org/abstracts/38055/anti-phase-synchronization-of-complex-delayed-networks-with-output-coupling-via-pinning-control" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/38055.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">394</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">12680</span> Numerical Simulation of Effect of Various Rib Configurations on Enhancing Heat Transfer of Matrix Cooling Channel</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Seok%20Min%20Choi">Seok Min Choi</a>, <a href="https://publications.waset.org/abstracts/search?q=Minho%20Bang"> Minho Bang</a>, <a href="https://publications.waset.org/abstracts/search?q=Seuong%20Yun%20Kim"> Seuong Yun Kim</a>, <a href="https://publications.waset.org/abstracts/search?q=Hyungmin%20Lee"> Hyungmin Lee</a>, <a href="https://publications.waset.org/abstracts/search?q=Won-Gu%20Joo"> Won-Gu Joo</a>, <a href="https://publications.waset.org/abstracts/search?q=Hyung%20Hee%20Cho"> Hyung Hee Cho</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The matrix cooling channel was used for gas turbine blade cooling passage. The matrix cooling structure is useful for the structure stability however the cooling performance of internal cooling channel was not enough for cooling. Therefore, we designed the rib configurations in the matrix cooling channel to enhance the cooling performance. The numerical simulation was conducted to analyze cooling performance of rib configured matrix cooling channel. Three different rib configurations were used which are vertical rib, angled rib and c-type rib. Three configurations were adopted in two positions of matrix cooling channel which is one fourth and three fourth of channel. The result shows that downstream rib has much higher cooling performance than upstream rib. Furthermore, the angled rib in the channel has much higher cooling performance than vertical rib. This is because; the angled rib improves the swirl effect of matrix cooling channel more effectively. The friction factor was increased with the installation of rib. However, the thermal performance was increased with the installation of rib in the matrix cooling channel. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=matrix%20cooling" title="matrix cooling">matrix cooling</a>, <a href="https://publications.waset.org/abstracts/search?q=rib" title=" rib"> rib</a>, <a href="https://publications.waset.org/abstracts/search?q=heat%20transfer" title=" heat transfer"> heat transfer</a>, <a href="https://publications.waset.org/abstracts/search?q=gas%20turbine" title=" gas turbine"> gas turbine</a> </p> <a href="https://publications.waset.org/abstracts/80524/numerical-simulation-of-effect-of-various-rib-configurations-on-enhancing-heat-transfer-of-matrix-cooling-channel" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/80524.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">460</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">12679</span> New Evaluation Methodology for Solidification Product Durability Assessment</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bozena%20Dohnalkova">Bozena Dohnalkova</a>, <a href="https://publications.waset.org/abstracts/search?q=Jakub%20Hodul"> Jakub Hodul</a>, <a href="https://publications.waset.org/abstracts/search?q=Rostislav%20Drochytka"> Rostislav Drochytka</a>, <a href="https://publications.waset.org/abstracts/search?q=Jana%20Kosikova"> Jana Kosikova</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with a proposal of a new methodology for durability assessment of solidification product for its safe further use. The new methodology is based on a review of the current state of assessment of treated waste in Czech Republic and abroad. The aim of the paper is to propose an optimal evaluation methodology for verifying properties of solidification product to ensure its safe further use in building industry. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=solidification" title="solidification">solidification</a>, <a href="https://publications.waset.org/abstracts/search?q=stabilization" title=" stabilization"> stabilization</a>, <a href="https://publications.waset.org/abstracts/search?q=durability" title=" durability"> durability</a>, <a href="https://publications.waset.org/abstracts/search?q=waste" title=" waste"> waste</a> </p> <a href="https://publications.waset.org/abstracts/10833/new-evaluation-methodology-for-solidification-product-durability-assessment" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/10833.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">429</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">12678</span> On the Optimality of Blocked Main Effects Plans</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rita%20SahaRay">Rita SahaRay</a>, <a href="https://publications.waset.org/abstracts/search?q=Ganesh%20Dutta"> Ganesh Dutta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article, experimental situations are considered where a main effects plan is to be used to study m two-level factors using n runs which are partitioned into b blocks, not necessarily of same size. Assuming the block sizes to be even for all blocks, for the case n &equiv; 2 (mod 4), optimal designs are obtained with respect to type 1 and type 2 optimality criteria in the class of designs providing estimation of all main effects orthogonal to the block effects. In practice, such orthogonal estimation of main effects is often a desirable condition. In the wider class of all available m two level even sized blocked main effects plans, where the factors do not occur at high and low levels equally often in each block, E-optimal designs are also characterized. Simple construction methods based on Hadamard matrices and Kronecker product for these optimal designs are presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=design%20matrix" title="design matrix">design matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=Hadamard%20matrix" title=" Hadamard matrix"> Hadamard matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=Kronecker%20product" title=" Kronecker product"> Kronecker product</a>, <a href="https://publications.waset.org/abstracts/search?q=type%201%20criteria" title=" type 1 criteria"> type 1 criteria</a>, <a href="https://publications.waset.org/abstracts/search?q=type%202%20criteria" title=" type 2 criteria"> type 2 criteria</a> </p> <a href="https://publications.waset.org/abstracts/55584/on-the-optimality-of-blocked-main-effects-plans" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55584.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">366</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">12677</span> Texture Analysis of Grayscale Co-Occurrence Matrix on Mammographic Indexed Image</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Sushma">S. Sushma</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Balasubramanian"> S. Balasubramanian</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20C.%20Latha"> K. C. Latha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The mammographic image of breast cancer compressed and synthesized to get co-efficient values which will be converted (5x5) matrix to get ROI image where we get the highest value of effected region and with the same ideology the technique has been extended to differentiate between Calcification and normal cell image using mean value derived from 5x5 matrix values <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=texture%20analysis" title="texture analysis">texture analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=mammographic%20image" title=" mammographic image"> mammographic image</a>, <a href="https://publications.waset.org/abstracts/search?q=partitioned%20gray%20scale%20co-oocurance%20matrix" title=" partitioned gray scale co-oocurance matrix"> partitioned gray scale co-oocurance matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=co-efficient" title=" co-efficient "> co-efficient </a> </p> <a href="https://publications.waset.org/abstracts/17516/texture-analysis-of-grayscale-co-occurrence-matrix-on-mammographic-indexed-image" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17516.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">533</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%20product%20state&page=2">2</a></li> <li class="page-item"><a class="page-link" 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