Results 251 to 260 of about 7,086 (290)

Matrix Kadomtsev Petviashvili equation: matrix identities and explicit non-singular solutions

Journal of Physics A: Mathematical and General, 2003
Summary: A new version of the Bäcklund--Darboux transformation for the matrix Kadomtsev-Petviashvili (KP) equation is used to construct and study explicit multi-parameter solutions and wavefunctions (in terms of the matrix exponents). A class of the self-adjoint non-singular solutions of KP I is introduced using the controllability notion from system ...
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On identities associated with generalized Fibonacci and Tribonacci numbers using matrices

Journal of difference equations and applications (Print)
A relationship between a square matrix X satisfying the equation $ X^3-(r+p)X^2+(rp-q)X+qrI=\mathbf{0} $ X3−(r+p)X2+(rp−q)X+qrI=0 and the generalized Fibonacci sequence $ \{U_n\} $ {Un} is first obtained.
Sinan Karakaya, Halim Özdemir
semanticscholar   +1 more source

One-dimensional integral equations for a system of three identical particles in the boundary condition model and the possibility of changing the off-shell behaviour of the two-particle T-matrix

Nuclear Physics A, 1976
Abstract It is shown that in the framework of the boundary condition model (BCM) for the two-particle interaction the Schrodinger equation for the system of three identical bosons can be reduced to the one-dimensional integral equation in an exact way.
V.N. Efimov, H. Schulz
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Equations of motion with the identity mass matrix for holonomic systems

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2004
Some consequences concerning holonomic systems described in terms of the inertial quasi-velocities (IQV) are discussed in this note. Introducing the IQV vector into Lagrange's formulation leads to first-order equations with the identity mass matrix of the system.
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The Matrix Form of the k-Pell Hyperbolic Functions

Journal of Engineering Technology and Applied Sciences
In the present paper, we introduce the matrix form of the k-Pell hyperbolic sine and cosine functions, along with their symmetrical forms. We examine their recurrence and hyperbolic properties, including Pythagorean, de Moivre, Catalan, Cassini, and d ...
Efruz Özlem Mersin
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Equation for Density Matrix Systems of Identical Particles

2020
The equations for the statistical operator and the density matrix are considered here for a single particle and a system of identical particles when dissipative forces act on them. From the equation for the density matrix, a kinetic equation can be obtained when the density matrix is diagonal. These equations are the basis for the study of the simplest
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(w; β)-BELL POLYNOMIALS ∀w ∈ C, β > 0, THEIR APPLICATIONS IN IDENTITIES EVALUATION AND MATRIX EQUATION REPRESENTATION

jnanabha
In the present paper on application of (w; β)-Bell polynomials ∀w ∈ C, β > 0, authors obtain identities of Kummer confluent hypergeometric function and Srivastava - Daoust function of two variables. Next they derive that the differentiation of these polynomials is connected with Stirling numbers of second kind.
R. C. Singh Chandel, Hemant Kumar, null J. L´opez-Bonilla   +2 more
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Canonical Equation K 32 for Normalized Spectral Functions of Random Gram Matrices with Identically Distributed Independent Blocks. Block Matrix Density

2001
The Chapter extends the “One quarter Law” \( {(2\pi )^{ - 1}}\sqrt {(4 - x)} \;{x^{ - 1/2}},\;{\rm{0}}\;{\rm{ < }}\;x {\rm{ < }}\;{\rm{4}} \) to Gram random matrices with independent random blocks obeying a Lindeberg-type condition and allowing arbitrary dependence of entries within each block.
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Canonical Equation K 28 for Normalized Spectral Functions of Random Symmetric Matrices with Identically Distributed Independent Blocks. Block Matrix Density. SS-Laws

2001
The first asymptotics of normalized spectral functions of random matrices were obtained for the matrices with independent entries. As we have seen in the previous chapter, it is possible to find the general form of possible limit normalized spectral functions of random symmetric matrices with asymptotically independent random blocks.
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A direct method in noncommutative integrable systems

Journal of Mathematics and Physics
We present a constructive framework for deriving noncommutative (NC) integrable equations directly from quasi-determinant solutions. Building upon the quasi-Wronskian structure, we extend the classical direct method to the NC setting, where standard ...
Shi‐Hao Li, Shou-Feng Shen, Guowei Yu, Jun-Yang Zhang   +3 more
semanticscholar   +1 more source