scholarly journals The determinants of the block matrices in the 3D Fourier equation

2012 ◽  
Vol 11 (4) ◽  
pp. 5-10
Author(s):  
Grzegorz Biernat ◽  
◽  
Sylwia Lara-Dziembek ◽  
Edyta Pawlak ◽  
◽  
...  
Keyword(s):  
Block Matrices ◽  
Fourier Equation

Representations for the image-kernel (p,q)-inverses of block matrices in rings

2020 ◽  
Vol 27 (2) ◽  
pp. 297-305
Author(s):  
Dijana Mosić
Keyword(s):  
Block Matrix ◽  
Block Matrices ◽  
Schur Form

AbstractWe present the conditions for a block matrix of a ring to have the image-kernel{(p,q)}-inverse in the generalized Banachiewicz–Schur form. We give representations for the image-kernel inverses of the sum and the product of two block matrices. Some characterizations of the image-kernel{(p,q)}-inverse in a ring with involution are investigated too.

Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Leonid L. Frumin
Keyword(s):  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Numerical Algorithms ◽  
Scattering Problems ◽  
Block Matrices ◽  
Nonlinear Schrödinger ◽  
Direct Scattering ◽  
Vector Case ◽  
Manakov Model ◽  
Vector Variant

AbstractWe introduce numerical algorithms for solving the inverse and direct scattering problems for the Manakov model of vector nonlinear Schrödinger equation. We have found an algebraic group of 4-block matrices with off-diagonal blocks consisting of special vector-like matrices for generalizing the scalar problem’s efficient numerical algorithms to the vector case. The inversion of block matrices of the discretized system of Gelfand–Levitan–Marchenko integral equations solves the inverse scattering problem using the vector variant the Toeplitz Inner Bordering algorithm of Levinson’s type. The reversal of steps of the inverse problem algorithm gives the solution of the direct scattering problem. Numerical tests confirm the proposed vector algorithms’ efficiency and stability. We also present an example of the algorithms’ application to simulate the Manakov vector solitons’ collision.

Euclidean norm estimates of the inverse of some special block matrices

2016 ◽  
Vol 284 ◽  
pp. 12-23 ◽  
Author(s):  
Ljiljana Cvetković ◽  
Vladimir Kostić ◽  
Ksenija Doroslovački ◽  
Dragana Lj. Cvetković
Keyword(s):  
Euclidean Norm ◽  
Block Matrices ◽  
Norm Estimates

scholarly journals Structure of positive block-matrices and nonstationary prediction

1987 ◽  
Vol 70 (2) ◽  
pp. 402-425 ◽  
Author(s):  
Gr Arsene ◽  
T Constantinescu
Keyword(s):  
Block Matrices

Neutrosophic Soft Block Matrices And Some Of Its Properties

2020 ◽  
pp. 39-49
Author(s):  
admin admin ◽  
Keyword(s):  
Decision Making ◽  
Crucial Role ◽  
Real Life ◽  
Decision Making Process ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Neutrosophic Sets ◽  
Block Matrices ◽  
Inconsistent Information

In real life situations, there are many issues in which there are uncertainties, vagueness, complexities and unpredictability. Neutrosophic sets are a mathematical tool to address some issues which cannot be met using the existing methods. Neutrosophic soft matrices play a crucial role in handling indeterminant and inconsistent information during decision making process. The main focus of this article is to discuss the concept of neutrosophic sets, neutrosophic soft sets, neutrosophic soft matrices theory and finally to discuss about neutrosophic soft block matrics which are very useful and applicable in various situations involving uncertainties and imprecisions. In this article, neutrosophic soft block matrices, various types of neutrosophic soft block matrices, some operations on it along with some properties associated with it are discussed in details.

Spreadsheet Tool for Quick-Turn 3D Numerical Modeling of Package Thermal Performance With Non-Uniform Die Heating

2001 ◽  
Author(s):  
Abhay A. Watwe ◽  
Ravi S. Prasher
Keyword(s):  
Finite Element ◽  
Numerical Modeling ◽  
Finite Volume ◽  
Thermal Performance ◽  
Three Dimensional ◽  
3D Numerical Modeling ◽  
Conventional Analysis ◽  
Time Required ◽  
The Impact ◽  
Fourier Equation

Abstract Traditional methods of estimating package thermal performance employ numerical modeling using commercially available finite-volume or finite-element tools. Use of these tools requires training and experience in thermal modeling. This methodology restricts the ability of die designers to quickly evaluate the thermal impact of their die architecture due to the added throughput time required to enlist the services of a thermal analyst. This paper describes the development of an easy to use spreadsheet tool, which performs quick-turn numerical evaluations of the impact of non-uniform die heating. The tool employs well-established finite-volume numerical techniques to solve the steady-state, three-dimensional Fourier equation of conduction in the package geometry. Minimal input data is required and the inputs are customized using visual basic pull-down menus to assist die designers who may not be thermal experts. Data showing comparison of the estimates from the spreadsheet tool with that obtained from a conventional analysis using the commercially available finite element code ANSYS™ is also presented.

scholarly journals Block matrices and Guo's index for block circulant matrices with circulant blocks

2018 ◽  
Vol 556 ◽  
pp. 301-322 ◽  
Author(s):  
Enide Andrade ◽  
Cristina Manzaneda ◽  
Hans Nina ◽  
María Robbiano
Keyword(s):  
Circulant Matrices ◽  
Block Matrices
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