Related papers: The Hadamard product and recursively defined seque…
In this paper we give efficient algorithms for computing second-, third-, and fourth-order linear recurrences. We also present an algorithm scheme for computing terms with the indices $N,\ldots,N+n-1$ of an $n$th-order linear recurrence.…
In this short note we are presenting a method of finding particular solutions of nonhomegeneous linear equations. This approach is different from methods of undetermined coefficients or variation of parameters presented in virtually every…
We provide a recursive construction of all the semi-Heyting algebras that can be defined on a chain with $n$ elements. This construction allows us to count them easily. We also compare the formula for the number of semi-Heyting chains thus…
This article begins the study of irreducible maps involving finite-dimensional uniserial modules over finite-dimensional associative algebras. We work on the classification of irreducible maps between two uniserials over triangular…
This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary,…
We present a conspicuous number of indefinite integrals involving Heun functions and their products obtained by means of the Lagrangian formulation of a general homogeneous linear ordinary differential equation. As a by-product we also…
Consider a sequence of real-valued functions of a real variable given by a homogeneous linear recursion with differentiable coefficients. We show that if the functions in the sequence are differentiable, then the sequence of derivatives…
Number sequences defined by a linear recursion relation are studied by means of generating functions. Indices of the terms in the recursion relation have arbitrary differenses. In addition to formulas for the nth term an algorithm is…
In this paper, we present formula solutions of a family of difference equations of higher order. We discuss the periodic nature of the solutions and we investigate the stability character of the equilibrium points. We utilize Lie symmetry…
In this article, we explain the link between Pohlen's extended Hadamard product and the holomorphic cohomological convolution on $\mathbb{C}^*$. For this purpose, we introduce a generalized Hadamard product, which is defined even if the…
We study the termination problem for nondeterministic recursive probabilistic programs. First, we show that a ranking-supermartingales-based approach is both sound and complete for bounded terminiation (i.e., bounded expected termination…
A new recursion procedure for deriving renormalized perturbation expansions for the one-dimensional anharmonic oscillator is offered. Based upon the $\hbar$-expansions and suitable quantization conditions, the recursion formulae obtained…
Determinants of structured matrices play a fundamental role in both pure and applied mathematics, with wide-ranging applications in linear algebra, combinatorics, coding theory, and numerical analysis. In this work, the enumeration of…
The aim of this article is to introduce an iterative algorithm for finding a common solution from the set of an equilibrium point for a bifunction and the set of a singularity of an inclusion problem on an Hadamard manifold. We also discuss…
We provide a simple method to recognize classical orthogonal polynomials on lattices defined only by their coefficients of the three term recurrence relation.
We derive a concise closed-form solution for a linear three-term recurrence relation. Such recurrence relations are very common in the quantitative sciences, and describe finite difference schemes, solutions to problems in Markov processes…
In this paper we obtain new estimates of the Hadamard fractional derivatives of a function at its extreme points. The extremum principle is then applied to show that the initial-boundary-value problem for linear and nonlinear…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
In this work we propose a generalization of the Hadamard product between two matrices to a tensor-valued, multi-linear product between k matrices for any $k \ge 1$. A multi-linear dual operator to the generalized Hadamard product is…
This work establishes a quenched (trajectory-wise) linear response formula for random intermittent dynamical systems, consisting of Liverani-Saussol-Vaienti maps with varying parameters. This result complements recent annealed (averaged)…