On Rank Invariance of Schwarz-Pick-Potapov Block Matrices of Matrix-Valued Carathéodory Functions

2002 ◽  
pp. 161-181 ◽  
Author(s):  
Bernd Fritzsche ◽  
Bernd Kirstein ◽  
Andreas Lasarow
Keyword(s):  
Block Matrices ◽  
Carathéodory Functions

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.

The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*

2020 ◽  
Vol 70 (4) ◽  
pp. 849-862
Author(s):  
Shagun Banga ◽  
S. Sivaprasad Kumar
Keyword(s):  
Triangle Inequality ◽  
Starlike Functions ◽  
Sharp Bound ◽  
The Novel ◽  
Sharp Bounds ◽  
Hankel Determinants ◽  
Lemniscate Of Bernoulli ◽  
Carathéodory Functions ◽  
The Right

AbstractIn this paper, we use the novel idea of incorporating the recently derived formula for the fourth coefficient of Carathéodory functions, in place of the routine triangle inequality to achieve the sharp bounds of the Hankel determinants H3(1) and H2(3) for the well known class 𝓢𝓛* of starlike functions associated with the right lemniscate of Bernoulli. Apart from that the sharp bound of the Zalcman functional: $\begin{array}{} |a_3^2-a_5| \end{array}$ for the class 𝓢𝓛* is also estimated. Further, a couple of interesting results of 𝓢𝓛* are also discussed.

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.

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

scholarly journals A note on the representations for the Drazin inverse of 2×2 block matrices

2007 ◽  
Vol 423 (2-3) ◽  
pp. 332-338 ◽  
Author(s):  
Xiezhang Li ◽  
Yimin Wei
Keyword(s):  
Drazin Inverse ◽  
Block Matrices
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