Admissible multivalued hybrid $\mathcal{Z}$-contractions with applications
AIMS Mathematics, 2021 In this paper, we introduce new concepts, admissible multivalued hybrid $\mathcal{Z}$-contractions and multivalued hybrid $\mathcal{Z}$-contractions in the framework of $b$-metric spaces and establish sufficient conditions for existence of fixed points ...
Monairah Alansari +3 more
doaj +1 more source
Green's Matrix for a Second Order Self-Adjoint Matrix Differential Operator [PDF]
, 2009 A systematic construction of the Green's matrix for a second order, self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out.
Bayram Tekin +12 more
core +2 more sources
A simple method for solving matrix equations $ AXB = D $ and $ GXH = C $
AIMS Mathematics, 2021 A simple method to solve the common solution to the pair of linear matrix equations $ AXB = D $ and $ GXH = C $ is introduced. Some necessary and sufficient conditions for the existence of a common solution, and two expressions for the general common ...
Huiting Zhang +3 more
doaj +1 more source
Non-commutative NLS-type hierarchies: dressing & solutions [PDF]
, 2019 We consider the generalized matrix non-linear Schrodinger (NLS) hierarchy. By employing the universal Darboux-dressing scheme we derive solutions for the hierarchy of integrable PDEs via solutions of the matrix Gelfand-Levitan-Marchenko equation, and we ...
Doikou, Anastasia +2 more
core +2 more sources
Prime decomposition of quadratic matrix polynomials
AIMS Mathematics, 2021 We study the prime decomposition of a quadratic monic matrix polynomial. From the prime decomposition of a quadratic matrix polynomial, we obtain a formula of the general solution to the corresponding second-order differential equation.
Yunbo Tian, Sheng Chen
doaj +1 more source
Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions [PDF]
, 2010 We express AKNS hierarchies, admitting reductions to matrix NLS and matrix mKdV hierarchies, in terms of a bidifferential graded algebra. Application of a universal result in this framework quickly generates an infinite family of exact solutions ...
Dimakis, Aristophanes +1 more
core +4 more sources
Algebraic Characterizations of Relationships between Different Linear Matrix Functions
Mathematics, 2023 Let f(X1,X2,…,Xk) be a matrix function over the field of complex numbers, where X1,X2,…,Xk are a family of matrices with variable entries. The purpose of this paper is to propose and investigate the relationships between certain linear matrix functions ...
Yongge Tian, Ruixia Yuan
doaj +1 more source
A Diagrammatic Equation for Oriented Planar Graphs [PDF]
, 2010 In this paper we introduce a diagrammatic equation for the planar sector of square non hermitian random matrix models strongly reminiscent of Polchinski's equation in quantum field theory.
Ambjorn +27 more
core +1 more source
A general method for solving linear matrix equations of elliptic biquaternions with applications
AIMS Mathematics, 2020 In this study, we obtain the real representations of elliptic biquaternion matrices. Afterwards, with the aid of these representations, we develop a general method to solve the linear matrix equations over the elliptic biquaternion algebra. Also we apply
Kahraman Esen Özen
doaj +1 more source
Field Equations of Massless Fields in the New Interpretation of the Matrix Model [PDF]
, 2006 Recently, some of the authors have introduced a new interpretation of matrix models in which covariant derivatives on any curved space can be expressed by large-N matrices.
Aoyama +19 more
core +3 more sources