Related papers: Using digraphs to compute determinant, permanent a…
Let $R$ be an associative ring with an identity and suppose that $a,b,c,d \in R$ satisfy $bdb = bac,dbd = acd$. If $ac$ has generalized Drazin ( respectively, pseudo Drazin, Drazin) inverse, we prove that $bd$ has generalized Drazin…
The Alvarez-Macovski method [Alvarez, R. E and Macovski, A., "Energy-selective reconstructions in X-ray computerized tomography", Phys. Med. Biol. (1976), 733--44] requires the inversion of the transformation from the line integrals of the…
We obtain some new formulae to compute the first derivative of confluent and biconfluent Heun functions under the minimal assumption of fixing only one parameter. These results together with the Lagrangian formulation of a general…
A fundamental problem in computational algebraic geometry is the computation of the resultant. A central question is when and how to compute it as the determinant of a matrix. whose elements are the coefficients of the input polynomials…
We create an algorithm to determine whether any two graphical representations (adinkras) of equations possessing the property of supersymmetry in one or two dimensions are isomorphic in shape. The algorithm is based on the determinant of…
The problem of determining whether a diagonally dominant matrix is singular or nonsingular is a classical topic in matrix theory. This paper develops necessary and sufficient conditions for the singularity or nonsingularity of diagonally…
We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of theoretical problems, such as the continuity of…
Counting integral binary quadratic forms with certain restrictions is a classical problem. In this paper, we count binary quadratic forms of fixed discriminant given restrictions on the size of their coefficients. We accomplish this by…
The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…
One of the most significant challenges in Computing Determinant of Rectangular Matrices is high time complexity of its algorithm. Among all definitions of determinant of rectangular matrices, used definition has special features which make…
We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on…
A well-known problem in Malliavin calculus concerns the relation between the determinant of the Malliavin matrix of a random vector and the determinant of its covariance matrix. We give an explicit relation between these two determinants…
This work further develops the properties of fractional differential forms. In particular, finite dimensional subspaces of fractional form spaces are considered. An inner product, Hodge dual, and covariant derivative are defined. Coordinate…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
We present a matrix-based algorithm for deciding if the parametrization of a curve or a surface is invertible or not, and for computing the inverse of the parametrization if it exists.
We give the first exact determinantal formula for the resultant of an unmixed sparse system of four Laurent polynomials in three variables with arbitrary support. This follows earlier work by the author on exact formulas for bivariate…
For both continuous-time and discrete-time Markov Chains, we provide criteria for inverse problems of classical types of ergodicity: (ordinary) erogodicity, algebraic ergodicity, exponential ergodicity and strong ergodicity. Our criteria…
In this work derivations of definite integrals listed in Prudnikov volume I, Gradshteyn and Ryzhik and a few other tables are produced. Special cases of these integrals in terms of fundamental constants are also evaluated. The method used…
This paper is dedicated to compute Pfaffian and determinant of one type of skew centrosymmetric matrices in terms of general number sequence of second order.
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…