Related papers: Bases of Solutions for Linear Congruences
In case the stability relation is a congruence, a necessary and also a sufficient condition for its equality with the center congruence is given.
A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable…
We make some remarks on the linear wave equation concerning the existence and uniqueness of weak solutions, satisfaction of the energy equation, growth properties of solutions, the passage from bounded to unbounded domains, and…
We develop the basic properties of the higher commutator for congruence modular varieties.
Using Eulerian and Euler numbers, we establish congruences concerning sums involving harmonic numbers, tangent numbers and Genocchi numbers.
The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous…
We prove that several results of lineability/spaceability in the framework of sequence spaces are valid in a stricter sense.
It is shown that every scalar linear quadrilateral lattice equation lies within a family of similar equations, members of which are compatible between one another on a higher dimensional lattice. There turn out to be two such families, a…
This article considers the minimal non-zero (= indecomposable) solutions of the linear congruence $1\cdot x_1 + \cdots + (m-1)\cdot x_{m-1} \equiv 0 \pmod m$ for unknown non-negative integers $x_1, \ldots, x_n$, and characterizes the…
In this article, we study about the solutions of second order linear differential equations by considering several conditions on the coefficients of homogenous linear differential equation and its associated non-homogenous linear…
Linear systems are the bedrock of virtually all numerical computation. Machine learning poses specific challenges for the solution of such systems due to their scale, characteristic structure, stochasticity and the central role of…
We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
This paper shows the complementary roles of mathematical and engineering points of view when dealing with truss analysis problems involving systems of linear equations and inequalities. After the compatibility condition and the mathematical…
We consider the problem of describing all non-negative integer solutions to a linear congruence in many variables. This question may be reduced to solving the congruence $x_1 + 2x_2 + 3x_3 + ... + (n-1)x_{n-1} \equiv 0 \pmod n$ where values…
In this article we study congruences of lines in $\mathbb{P}^n$, and in particular of order one. After giving general results, we obtain a complete classification in the case of $\mathbb{P}^4$ in which the fundamental surface $F$ is in fact…
In this paper, we propose a generalization of a congruence due to Carlitz.
This is an introduction to the theory of disconjugacy for a second order linear differential equation. We give new proofs of some of basic results and obtain new sufficient conditions for disconjugacy (in particular, on the whole real…
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…
An approach is proposed for bounding the number of zeros that solutions of linear differential systems with polynomial coefficients may have. A bound is obtained in a special case which improves upon currently existing.