Related papers: Implicit Linear Difference Equation over Residue C…
The transformation of the Nth- order linear difference equation into a system of the first order difference equations is presented. The proposed transformation gives possibility to get new forms of the N-dimensional system of the first…
On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.
For a division ring $\mathbb F$, the polynomials $f\in\mathbb F$ can be evaluated "on the left" and "on the right" giving rise to left and right Lagrange interpolation problems. The problems containig interpolation conditions of the same…
In this paper we shall establish some regularity results of solutions of a class of fully nonlinear equations, with a first order term which is sub-linear. We prove local H\"older regularity of the gradient both in the interior and up to…
We study first order linear partial differential equations that appear, for example, in the analysis of dimishing urn models with the help of the method of characteristics and formulate sufficient conditions for a central limit theorem.
In this short paper we identify special systems of (an arbitrary number) N of first-order Difference Equations with nonlinear homogeneous polynomials of arbitrary degree M in their right-hand sides, which feature very simple explicit…
An algebraic criterion that is sufficient to establish the existence of certain a priori estimates for the solution of first-order homogeneous linear characteristic problems is derived. Estimates of such kind ensure the stability of the…
In this paper, we study existence results for initial value problems for hybrid fractional integro-differential equations. Our investigation is based on the Dhage hybrid fixed point theorem. Some fundamental fractional differential…
Using an adaptation of Qin Jiushao's method from the 13th century, it is possible to prove that a system of linear modular equations a(i,1) x(i) + ... + a(i,n) x(n) = b(i) mod m(i), i=1, ..., n has integer solutions if m(i)>1 are pairwise…
Local existence properties of initial boundary value problems associated with a new type of systems of differential equations with "maxima" are investigated.
In this article we give, for the fist time the solution of the general difference equation of 2-degree. We also give as application the expansion of a continued fraction into series, which was first proved, found in the past by the author.
We demonstrate that an equivalence of categories using $\varepsilon$-interleavings as a fundamental component exists between the model of persistence modules as graded modules over a polynomial ring and the model of persistence modules as…
Firstly, we give a partial solution to the isomorphism problem for uniserial modules of finite length with the help of the morphisms between these modules over an arbitrary ring. Later, under suitable assumptions on the lattice of the…
We consider polynomial equations, or systems of polynomial equations, with integer coefficients, modulo prime numbers $p$. We offer an elementary approach based on a counting method. The outcome is a weak form of the Lang-Weil lower bound…
This paper presents an a priori error analysis of the Deep Mixed Residual method (MIM) for solving high-order elliptic equations with non-homogeneous boundary conditions, including Dirichlet, Neumann, and Robin conditions. We examine MIM…
We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…
In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…
We propose a proof of the Lagrange Interpolation Formula based on the Chinese Remainder Theorem for arbitrary rings. Even such relationships are known, we think that our viewpoint is worth being published.
We consider a long but finite (ladder) circuit with alternating connections of resistors in series and parallel and derive an explicit expression for its equivalent resistance as a function of the number of repeating blocks, $R_{\rm…
Schemes defined by residual intersections have been extensively studied in the case when they are Cohen-Macaulay, but this is a very restrictive condition. In this paper we make the first study of a class of natural examples far from…