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The main purpose of this paper is to study the existence of solutions for the following hybrid nonlinear fractional pantograph equation $$ \left\{\begin{aligned} &D_{0+}^\alpha…
We classify general systems of polynomial equations with a single solution, or, equivalently, collections of lattice polytopes of minimal positive mixed volume. As a byproduct, this classification provides an algorithm to evaluate the…
We study the monodromy representation of the generalized hypergeometric differential equation and that of Lauricella's $F_C$ system of hypergeometric differential equations. We use fundamental systems of solutions expressed by the…
We introduce some polynomial and analytic methods in the classification program for the complexity of planar graph homomorphisms. These methods allow us to handle infinitely many lattice conditions and isolate the new P-time tractable…
In exploratory factor analysis, rotation techniques are employed to derive interpretable factor loading matrices. Factor rotations deal with equality-constrained optimization problems aimed at determining a loading matrix based on measure…
We study a general class of recurrence relations that appear in the application of a matrix diagonalization procedure. We find general closed formula and determine analytical properties of the solutions. We finally apply these findings in…
To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…
The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so general that it requires an exponential number of oracle calls. Nevertheless, Lov\'asz (1980)…
This report is devoted to introduction in multichannel algorithm based on generalized numeration notations (GPN). The internal, external and mixed account are entered. The concept of the GPN and its classification as decomposition of an…
Necessary and sufficient conditions for the regularity of solutions of the functional equation appearing in the theory of classical orthogonal polynomials on lattices are stated. Moreover, the functional Rodrigues formula and a closed…
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
In this paper, we present a generic parametrization of generically zero-dimensional parametric polynomial systems. More specifically, we study the specialization properties of the Rational Univariate Representation and derive bounds on the…
In this letter we present a procedure for the calculation of the Casimir functions of finite-dimensional Poisson systems which avoids the burden of solving a set of partial differential equations, as it is usually suggested in the…
This paper proposes a unique optimization approach for estimating the minimax rational approximation and its application for evaluating matrix functions. Our method enables the extension to generalized rational approximations and has the…
This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical…
This article analyzes and develops a method to solve fractional ordinary differential equations using the Monte Carlo Method. A numerical simulation is performed for some differential equations, comparing the results with what exists in the…
In this note, we intend to produce all latin squares from one of them using suitable move which is defined by small trades and do the similar work on 4-cycle systems. These problems, reformulate as finding basis for the kernel of special…
In this research paper, we present an exact matrix form analytical solution of the multi-dimensional generalized Langevin equation with quadratic potentials. Our investigation provides detailed expressions for the two-dimensional…
A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones. Some new examples of linear Darboux matrices are discussed.
A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certain symmetry of the matrix and the choice of the voxel…