**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1020

# Search results for: adjacency matrix

##### 1020 Fuzzy Adjacency Matrix in Graphs

**Authors:**
Mahdi Taheri,
Mehrana Niroumand

**Abstract:**

**Keywords:**
Graph,
adjacency matrix,
fuzzy numbers

##### 1019 Bounds on the Second Stage Spectral Radius of Graphs

**Authors:**
S.K.Ayyaswamy,
S.Balachandran,
K.Kannan

**Abstract:**

Let G be a graph of order n. The second stage adjacency matrix of G is the symmetric n × n matrix for which the ijth entry is 1 if the vertices vi and vj are of distance two; otherwise 0. The sum of the absolute values of this second stage adjacency matrix is called the second stage energy of G. In this paper we investigate a few properties and determine some upper bounds for the largest eigenvalue.

**Keywords:**
Second stage spectral radius,
Irreducible matrix,
Derived graph

##### 1018 Bisymmetric, Persymmetric Matrices and Its Applications in Eigen-decomposition of Adjacency and Laplacian Matrices

**Authors:**
Mahdi Nouri

**Abstract:**

**Keywords:**
Graphs theory,
Eigensolution,
adjacency and
Laplacian matrix,
Canonical forms,
bisymmetric,
per symmetric.

##### 1017 A Deterministic Polynomial-time Algorithm for the Clique Problem and the Equality of P and NP Complexity Classes

**Authors:**
Zohreh O. Akbari

**Abstract:**

**Keywords:**
Clique problem,
Deterministic Polynomial-time
Algorithm,
Equality of P and NP Complexity Classes.

##### 1016 Reconstruction of Binary Matrices Satisfying Neighborhood Constraints by Simulated Annealing

**Authors:**
Divyesh Patel,
Tanuja Srivastava

**Abstract:**

This paper considers the NP-hard problem of reconstructing binary matrices satisfying exactly-1-4-adjacency constraint from its row and column projections. This problem is formulated into a maximization problem. The objective function gives a measure of adjacency constraint for the binary matrices. The maximization problem is solved by the simulated annealing algorithm and experimental results are presented.

**Keywords:**
Discrete Tomography,
exactly-1-4-adjacency,
simulated annealing.

##### 1015 Algebraic Riccati Matrix Equation for Eigen- Decomposition of Special Structured Matrices; Applications in Structural Mechanics

**Authors:**
Mahdi Nouri

**Abstract:**

In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.

**Keywords:**
Riccati,
matrix equation,
eigenvalue problem,
symmetric,
bisymmetric,
persymmetric,
decomposition,
canonical
forms,
Graphs theory,
adjacency and Laplacian matrices.

##### 1014 On Generalized New Class of Matrix Polynomial Set

**Authors:**
Ghazi S. Kahmmash

**Abstract:**

New generalization of the new class matrix polynomial set have been obtained. An explicit representation and an expansion of the matrix exponential in a series of these matrix are given for these matrix polynomials.

**Keywords:**
Generating functions,
Recurrences relation and Generalization of the new class matrix polynomial set.

##### 1013 The Partial Non-combinatorially Symmetric N10 -Matrix Completion Problem

**Authors:**
Gu-Fang Mou,
Ting-Zhu Huang

**Abstract:**

An n×n matrix is called an N1 0 -matrix if all principal minors are non-positive and each entry is non-positive. In this paper, we study the partial non-combinatorially symmetric N1 0 -matrix completion problems if the graph of its specified entries is a transitive tournament or a double cycle. In general, these digraphs do not have N1 0 -completion. Therefore, we have given sufficient conditions that guarantee the existence of the N1 0 -completion for these digraphs.

**Keywords:**
Matrix completion,
matrix completion,
N10 -matrix,
non-combinatorially symmetric,
cycle,
digraph.

##### 1012 An Adaptive Dimensionality Reduction Approach for Hyperspectral Imagery Semantic Interpretation

**Authors:**
Akrem Sellami,
Imed Riadh Farah,
Basel Solaiman

**Abstract:**

**Keywords:**
Band selection,
dimensionality reduction,
feature
extraction,
hyperspectral imagery,
semantic interpretation.

##### 1011 Inverse Matrix in the Theory of Dynamic Systems

**Authors:**
R. Masarova,
M. Juhas,
B. Juhasova,
Z. Sutova

**Abstract:**

**Keywords:**
Dynamic system,
transfer matrix,
inverse matrix,
modeling.

##### 1010 Numerical Treatment of Matrix Differential Models Using Matrix Splines

**Authors:**
Kholod M. Abualnaja

**Abstract:**

This paper consider the solution of the matrix differential models using quadratic, cubic, quartic, and quintic splines. Also using the Taylor’s and Picard’s matrix methods, one illustrative example is included.

**Keywords:**
Matrix Splines,
Cubic Splines,
Quartic Splines.

##### 1009 The Relationship of Eigenvalues between Backward MPSD and Jacobi Iterative Matrices

**Authors:**
Zhuan-de Wang,
Hou-biao Li,
Zhong-xi Gao

**Abstract:**

In this paper, the backward MPSD (Modified Preconditioned Simultaneous Displacement) iterative matrix is firstly proposed. The relationship of eigenvalues between the backward MPSD iterative matrix and backward Jacobi iterative matrix for block p-cyclic case is obtained, which improves and refines the results in the corresponding references.

**Keywords:**
Backward MPSD iterative matrix,
Jacobi iterative matrix,
eigenvalue,
p-cyclic matrix.

##### 1008 On Positive Definite Solutions of Quaternionic Matrix Equations

**Authors:**
Minghui Wang

**Abstract:**

**Keywords:**
Matrix equation,
Quaternionic matrix,
Real representation,
positive (semi)definite solutions.

##### 1007 Connectivity Estimation from the Inverse Coherence Matrix in a Complex Chaotic Oscillator Network

**Authors:**
Won Sup Kim,
Xue-Mei Cui,
Seung Kee Han

**Abstract:**

We present on the method of inverse coherence matrix for the estimation of network connectivity from multivariate time series of a complex system. In a model system of coupled chaotic oscillators, it is shown that the inverse coherence matrix defined as the inverse of cross coherence matrix is proportional to the network connectivity. Therefore the inverse coherence matrix could be used for the distinction between the directly connected links from indirectly connected links in a complex network. We compare the result of network estimation using the method of the inverse coherence matrix with the results obtained from the coherence matrix and the partial coherence matrix.

**Keywords:**
Chaotic oscillator,
complex network,
inverse coherence matrix,
network estimation.

##### 1006 Efficient Filtering of Graph Based Data Using Graph Partitioning

**Authors:**
Nileshkumar Vaishnav,
Aditya Tatu

**Abstract:**

**Keywords:**
Graph signal processing,
graph partitioning,
inverse
filtering on graphs,
algebraic signal processing.

##### 1005 Evolutionary Distance in the Yeast Genome

**Authors:**
Somayyeh Azizi,
Saeed Kaboli,
Atsushi Yagi

**Abstract:**

**Keywords:**
Whole-genome duplication,
Evolution,
Double-cutand-
join operation,
Yeast.

##### 1004 Solving Linear Matrix Equations by Matrix Decompositions

**Authors:**
Yongxin Yuan,
Kezheng Zuo

**Abstract:**

In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided.

**Keywords:**
Matrix equation,
Generalized inverse,
Generalized
singular-value decomposition.

##### 1003 The Convergence Results between Backward USSOR and Jacobi Iterative Matrices

**Authors:**
Zuan-De Wang,
Hou-biao Li,
Zhong-xi Gao

**Abstract:**

In this paper, the backward Ussor iterative matrix is proposed. The relationship of convergence between the backward Ussor iterative matrix and Jacobi iterative matrix is obtained, which makes the results in the corresponding references be improved and refined.Moreover,numerical examples also illustrate the effectiveness of these conclusions.

**Keywords:**
Backward USSOR iterative matrix,
Jacobi iterative matrix,
convergence,
spectral radius

##### 1002 An Algorithm of Ordered Schur Factorization For Real Nonsymmetric Matrix

**Authors:**
Lokendra K. Balyan

**Abstract:**

**Keywords:**
Schur Factorization,
Eigenvalues of nonsymmetric matrix,
Orthoganal matrix.

##### 1001 Tree Sign Patterns of Small Order that Allow an Eventually Positive Matrix

**Authors:**
Ber-Lin Yu,
Jie Cui,
Hong Cheng,
Zhengfeng Yu

**Abstract:**

**Keywords:**
Eventually positive matrix,
sign pattern,
tree.

##### 1000 Numerical Simulation of Effect of Various Rib Configurations on Enhancing Heat Transfer of Matrix Cooling Channel

**Authors:**
Seok Min Choi,
Minho Bang,
Seuong Yun Kim,
Hyungmin Lee,
Won-Gu Joo,
Hyung Hee Cho

**Abstract:**

**Keywords:**
Matrix cooling,
rib,
heat transfer,
gas turbine.

##### 999 Some New Subclasses of Nonsingular H-matrices

**Authors:**
Guangbin Wang,
Liangliang Li,
Fuping Tan

**Abstract:**

In this paper, we obtain some new subclasses of non¬singular H-matrices by using a diagonally dominant matrix

**Keywords:**
H-matrix,
diagonal dominance,
a diagonally dominant matrix.

##### 998 Effects of the Mass and Damping Matrix Model in the Nonlinear Seismic Response of Steel Frames

**Authors:**
A. Reyes-Salazar,
M. D. Llanes-Tizoc,
E. Bojorquez,
F. Valenzuela-Beltran,
J. Bojorquez,
J. R. Gaxiola-Camacho,
A. Haldar

**Abstract:**

Seismic analysis of steel buildings is usually based on the use of the concentrated mass (ML) matrix and the Rayleigh damping matrix (C). Similarly, the initial stiffness matrix (KO) and the first two modes associated to lateral vibrations are commonly used to develop the matrix C. The evaluation of the accuracy of these practices for the particular case of steel buildings with moment-resisting steel frames constitutes the main objective of this research. For this, the nonlinear seismic responses of three models of steel frames, representing low-, medium- and high-rise steel buildings, are considered. Results indicate that if the ML matrix is used, shears and bending moments in columns are underestimated by up to 30% and 65%, respectively, when compared to the corresponding results obtained with the consistent mass matrix (MC). It is also shown that if KO is used in C instead the tangent stiffness matrix (Kt), axial loads in columns are underestimated by up to 80%. It is concluded that the consistent mass matrix should be used in the structural modelling of moment resisting steel frames and the tangent stiffness matrix should be used to develop the Rayleigh damping matrix.

**Keywords:**
Moment-resisting steel frames,
consistent and concentrated mass matrices,
nonlinear seismic response,
Rayleigh damping.

##### 997 Redundancy Component Matrix and Structural Robustness

**Authors:**
Xinjian Kou,
Linlin Li,
Yongju Zhou,
Jimian Song

**Abstract:**

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.

**Keywords:**
Structural robustness,
structural reliability,
redundancy component,
redundancy matrix.

##### 996 Newton-Raphson State Estimation Solution Employing Systematically Constructed Jacobian Matrix

**Authors:**
Nursyarizal Mohd Nor,
Ramiah Jegatheesan,
Perumal Nallagownden

**Abstract:**

**Keywords:**
State Estimation (SE),
Weight Least Square (WLS),
Newton-Raphson State Estimation (NRSE),
Jacobian matrix H.

##### 995 Using Spectral Vectors and M-Tree for Graph Clustering and Searching in Graph Databases of Protein Structures

**Authors:**
Do Phuc,
Nguyen Thi Kim Phung

**Abstract:**

**Keywords:**
Eigenvalues,
m-tree,
graph database,
protein
structure,
spectra graph theory.

##### 994 Conjugate Gradient Algorithm for the Symmetric Arrowhead Solution of Matrix Equation AXB=C

**Authors:**
Minghui Wang,
Luping Xu,
Juntao Zhang

**Abstract:**

*AXB=C*and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.

**Keywords:**
Iterative method,
symmetric arrowhead matrix,
conjugate gradient algorithm.

##### 993 Membership Surface and Arithmetic Operations of Imprecise Matrix

**Authors:**
Dhruba Das

**Abstract:**

**Keywords:**
Imprecise number,
Imprecise vector,
Membership
surface,
Imprecise matrix.

##### 992 On the Positive Definite Solutions of Nonlinear Matrix Equation

**Authors:**
Tian Baoguang,
Liang Chunyan,
Chen Nan

**Abstract:**

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δ_{i} are discussed. An algorithm that avoids matrix inversion with the case -1<-δ_{i}<0 is proposed.

**Keywords:**
Nonlinear matrix equation,
Positive definite solution,
The maximal-minimal solution,
Iterative method,
Free-inversion

##### 991 An Iterative Method for the Symmetric Arrowhead Solution of Matrix Equation

**Authors:**
Minghui Wang,
Luping Xu,
Juntao Zhang

**Abstract:**

**Keywords:**
Symmetric arrowhead matrix,
iterative method,
like-minimum norm,
minimum norm,
Algorithm LSQR.