scholarly journals A note on the eigenvalue free intervals of some classes of signed threshold graphs

2019 ◽  
Vol 7 (1) ◽  
pp. 218-225
Author(s):  
Milica Anđelić ◽  
Tamara Koledin ◽  
Zoran Stanić
Keyword(s):  
Tridiagonal Matrix ◽  
Constant Sign ◽  
Equitable Partition ◽  
Elementary Matrix ◽  
Matrix Operations ◽  
Threshold Graphs ◽  
The Matrix ◽  
Threshold Graph

Abstract We consider a particular class of signed threshold graphs and their eigenvalues. If Ġ is such a threshold graph and Q(Ġ ) is a quotient matrix that arises from the equitable partition of Ġ , then we use a sequence of elementary matrix operations to prove that the matrix Q(Ġ ) – xI (x ∈ ℝ) is row equivalent to a tridiagonal matrix whose determinant is, under certain conditions, of the constant sign. In this way we determine certain intervals in which Ġ has no eigenvalues.

Configuration Based Improved Synthesis of Metamorphic Mechanisms

2009 ◽  
Author(s):  
Duanling Li ◽  
Zhonghai Zhang ◽  
Jian S. Dai ◽  
J. Michael McCarthy
Keyword(s):  
Adjacency Matrix ◽  
Matrix Transformations ◽  
Mechanism Synthesis ◽  
Matrix Operation ◽  
Elementary Matrix ◽  
Matrix Operations ◽  
The Matrix ◽  
Potential Applications ◽  
Synthesis Procedure ◽  
Metamorphic Mechanisms

Metamorphic mechanisms are a class of mechanisms that change their mobility during motions. The deployable and retractable characteristics of these unique mechanisms generate much interest in further investigating their behaviors and potential applications. This paper investigates the resultant configuration variation based on adjacency matrix operation and an improved approach to mechanism synthesis is proposed by adopting elementary matrix operations on the configuration states so as to avoid some omissions caused by existing methods. The synthesis procedure begins with a final configuration of the mechanism, then enumerates possible combinations of different links and associates added links with the binary inverse operations in the matrix transformations of the configuration states, and finally obtains a synthesis result. An algorithm is presented and the topological symmetry of links is used to reduce the number of mechanisms in the synthesis. Some mechanisms of this kind are illustrated as examples.

Application of Fuzzy Petri Nets in Hydraulic Pump Fault Diagnosis

2014 ◽  
Vol 1008-1009 ◽  
pp. 1176-1179
Author(s):  
Hai Dong ◽  
Heng Bao Xin
Keyword(s):  
Fault Diagnosis ◽  
Petri Nets ◽  
Hydraulic Pump ◽  
Modeling And Analysis ◽  
Matrix Operations ◽  
Knowledge Reasoning ◽  
Fuzzy Production Rules ◽  
The Matrix ◽  
Fuzzy Petri Nets ◽  
Definition Of

In this paper, an approach of fuzzy Petri nets (FPN) is proposed to simulate the fault spreading and diagnosis of hydraulic pump. First, the fuzzy production rules and the definition of FPN were briefly introduced. Then, its knowledge reasoning process and the matrix operations based on an algorithm were conducted, which makes full use of its parallel reasoning ability and makes it simpler and easier to implement. Finally, a case of hydraulic pump fault diagnosis with FPN was presented in detail, for illustrating the interest of the proposed modeling and analysis algorithm.

On the Matrix With Elements 1/(r+s-1)

1974 ◽  
Vol 17 (2) ◽  
pp. 297-298 ◽  
Author(s):  
W. W. Sawyer
Keyword(s):  
Tridiagonal Matrix ◽  
The Matrix ◽  
Eigenvectors And Eigenvalues

A standard example of a matrix for which the computation of eigenvectors and eigenvalues is very awkward is the matrix A with ars=1/(r+s—1), 1≤r≤n, 1 ≤s≤n. It is therefore of interest that A commutes with a tridiagonal matrix.

scholarly journals Generating a Cancellable Fingerprint using Matrices Operations and Its Fingerprint Processing Requirements

2018 ◽  
Vol 14 (6) ◽  
pp. 1 ◽  
Author(s):  
Riki Mukhaiyar
Keyword(s):  
Region Of Interest ◽  
Original Form ◽  
Biometric Data ◽  
Matrix Operations ◽  
The Matrix ◽  
Robust Image ◽  
Reciprocal Matrix ◽  
Processing Steps ◽  
Fingerprint Feature

Cancellable fingerprint uses transformed or intentionally distorted biometric data instead of the original biometric data for identifying person. When a set of biometric data is found to be compromised, they can be discarded, and a new set of biometric data can be regenerated. This initial principal is identical with a non-invertible concept in matrices operations. In matrix domain, a matrix cannot be transformed into its original form if it meets several requirements such as non-square form matrix, consist of one zero row/column, and no row as multiple of another row. These conditions can be acquired by implementing three matrix operations using Kronecker Product (KP) operation, Elementary Row Operation (ERO), and Inverse Matrix (INV) operation. KP is useful to produce a non-square form matrix, to enlarge the size of matrix, to distinguish and disguise the element of matrix by multiplying each of elements of the matrix with a particular matrix. ERO can be defined as multiplication and addition force to matrix rows. INV is utilized to transform one matrix to another one with a different element or form as a reciprocal matrix of the original. These three matrix operations should be implemented together in generating the cancellable feature to robust image. So, if once three conditions are met by imposter, it is impossible to find the original image of the fingerprint. The initial aim of these operations is to camouflage the original look of the fingerprint feature into an abstract-look to deceive an un-authorized personal using the fingerprint irresponsibly. In this research, several fingerprint processing steps such as fingerprint pre-processing, core-point identification, region of interest, minutiae extration, etc; are determined to improve the quality of the cancellable feature. Three different databases i.e. FVC2002, FVC2004, and BRC are utilized in this work.

scholarly journals Bidiagonalization of (k, k + 1)-tridiagonal matrices

2019 ◽  
Vol 7 (1) ◽  
pp. 20-26 ◽  
Author(s):  
S. Takahira ◽  
T. Sogabe ◽  
T.S. Usuda
Keyword(s):  
Tridiagonal Matrix ◽  
Permutation Matrix ◽  
Block Diagonalization ◽  
Tridiagonal Matrices ◽  
The Matrix ◽  
Appl Math ◽  
Diagonalization Algorithm

Abstract In this paper,we present the bidiagonalization of n-by-n (k, k+1)-tridiagonal matriceswhen n < 2k. Moreover,we show that the determinant of an n-by-n (k, k+1)-tridiagonal matrix is the product of the diagonal elements and the eigenvalues of the matrix are the diagonal elements. This paper is related to the fast block diagonalization algorithm using the permutation matrix from [T. Sogabe and M. El-Mikkawy, Appl. Math. Comput., 218, (2011), 2740-2743] and [A. Ohashi, T. Sogabe, and T. S. Usuda, Int. J. Pure and App. Math., 106, (2016), 513-523].

Performance Analysis of the PISO-Based CFD Simulation

2014 ◽  
Vol 607 ◽  
pp. 872-876 ◽  
Author(s):  
Xiao Guang Ren
Keyword(s):  
Performance Optimization ◽  
Execution Time ◽  
Cfd Simulation ◽  
Fluid Flows ◽  
Total Execution Time ◽  
Simulation Performance ◽  
Simulation Efficiency ◽  
Matrix Operations ◽  
The Matrix ◽  
Computational Fluid Dynamics Cfd

Computational Fluid Dynamics (CFD) is widely applied for the simulation of fluid flows, and the performance of the simulation process is critical for the simulation efficiency. In this paper, we analyze the performance of CFD simulation application with profiling technology, which gets the portions of the main parts’ execution time. Through the experiment, we find that the PISO algorithm has a significant impact on the CFD simulation performance, which account for more than 90% of the total execution time. The matrix operations are also account for more than 60% of the total execution time, which provides opportunity for performance optimization.

A Trust Evaluation of Networks Utilizing Matrix Operations Based on t-norms and t-conorms

2012 ◽  
Vol 16 (1) ◽  
pp. 154-161
Author(s):  
Masaya Nohmi ◽  
◽  
Aoi Honda ◽  
Yoshiaki Okazaki
Keyword(s):  
Trust Evaluation ◽  
Matrix Operations ◽  
Fuzzy Graphs ◽  
Algebraic Properties ◽  
The Matrix ◽  
Membership Value

A new scheme for numerical trust evaluation of networks is proposed. Matrix operations based on t-norms and t-conorms are used for the evaluation. The algebraic properties of the matrix operations are studied. Fuzzy graphs, in which nodes are linked with some membership value, are proposed, using the matrices as adjacent matrices. Furthermore, the fuzzinesses of the trustability distribution are calculated.

scholarly journals Algebraic Characteristics of the Matrix Conversions Class and Its Hardware Implementation

2021 ◽  
Vol 4 (2) ◽  
Author(s):  
Stanislav V. Kudlai
Keyword(s):  
Algebraic System ◽  
Hardware Implementation ◽  
Matrix Transformations ◽  
Matrix Functions ◽  
Hardware Support ◽  
Algebra Isomorphism ◽  
Program Algebra ◽  
Matrix Operations ◽  
The Matrix ◽  
Recursive Matrix

This paper derives the algebraic characteristic of the matrix transformations class by the method of isomorphic mappings on the algebraic characteristic of the class of vector transformations using the primitive program algebras. The paper also describes the hardware implementation of the matrix operations accelerator based on the obtained results. The urgency of the work is caused by the fact that today there is a rapid integration of computer technology in all spheres of society and, as a consequence, the amount of data that needs to be processed per unit time is constantly increasing. Many problems involving large amounts of complex computation are solved by methods based on matrix operations. Therefore, the study of matrix calculations and their acceleration is a very important task. In this paper, as a contribution in this direction, we propose a study of the matrix transformations class using signature operations of primitive program algebra such as multi place superposition, branching, cycling, which are refinements of the most common control structures in most high-level programming languages, and also isomorphic mapping. Signature operations of primitive program algebra in combination with basic partial-recursive matrix functions and predicates allow to realize the set of all partial-recursive matrix functions and predicates. Obtained the result on the basis of matrix primitive program algebra. Isomorphism provides the reproduction of partially recursive functions and predicates for matrix transformations as a map of partially recursive vector functions and predicates. The completeness of the algebraic system of matrix transformations is ensured due to the available results on the derivation of the algebraic system completeness for vector transformations. A name model of matrix data has been created and optimized for the development of hardware implementation. The hardware implementation provides support for signature operations of primitive software algebra and for isomorphic mapping. Hardware support for the functions of sum, multiplication and transposition of matrices, as well as the predicate of equality of two matrices is implemented. Support for signature operations of primitive software algebra is provided by the design of the control part of the matrix computer based on the RISC architecture. The hardware support of isomorphism is based on counters, they allow to intuitively implement cycling in the functions of isomorphic mappings. Fast execution of vector operations is provided by the principle of computer calculations SIMD.

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