Related papers: Solutions for Underdetermined Generalized Absolute…

We give a sufficient condition on totally disconnected topological graphs such that their associated topological graph algebras are purely infinite.

We investigate existence and uniqueness of solutions to a class of fractional parabolic equations satisfying prescribed pointwise conditions at infinity (in space), which can be time- dependent. Moreover, we study the asymptotic behaviour…

A general formula is presented for any order derivative of Chebyshev polynomials instead of the existing recursive relationship. Hence, the Chebyshev finite difference method is made applicable not only to second order problems but also to…

We obtain a new bound for incomplete Gauss sums modulo primes. Our argument falls under the framework of Vinogradov's method which we use to reduce the problem under consideration to bounding the number of solutions to two distinct systems…

We provide a sufficient condition for solvability of a system of real quadratic equations $p_i(x)=y_i$, $i=1, \ldots, m$, where $p_i: {\mathbb R}^n \longrightarrow {\mathbb R}$ are quadratic forms. By solving a positive semidefinite…

In the paper a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems the constraints depend both on the parameter as well as on the decision variable itself and they…

Let Q be a non-singular quadratic form with integer coefficients. When Q is indefinite we provide new upper bounds for the least non-trivial integral solution to the equation Q=0. When Q is positive definite we provide improved upper bounds…

A special class of solutions to the generalised WDVV equations related to a finite set of covectors is considered. We describe the geometric conditions ($\vee$-conditions) on such a set which are necessary and sufficient for the…

For an arbitrary ordinary second order differential equation a test is constructed that checks if this equation is equivalent to Painleve I, II or Painleve III with three zero parameters equations under the substitutions of variables. If it…

In this paper, we develop a Bayesian multiscale approach based on a multiscale finite element method. Because of scale disparity in many multiscale applications, computational models can not resolve all scales. Various subgrid models are…

We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…

Geodesics deviation equation (GDE) is itroduced. In "adiabatic" approximation exact solution of the GDE if found. Perturbation theory in general case is formulated. Geometrical criterion of local instability which may lead to chaos is…

Infinitely many explicit solutions of certain second-order differential equations with an apparent singularity of characteristic exponent -2 are constructed by adjusting the parameter of the multi-indexed Laguerre polynomials.

First, we consider the equation $ax^2 - by^2 + c = 0$, with $a,b \in N*$ and $c \in Z*$, which is a generalization of Pell's equation. Here, we show that: if this equation has an integer solution and $ab$ is not a perfect square, then it…

The main purpose of this paper is to determine the solution of generalized convex set-valued mappings satisfying certain functional equation. Some conclusions of stability of set-valued functional equations are obtained.

Short nonstandard proofs are given for some results about infinite systems of equations in infinitely many variables.

The existence of EFX allocations is a major open problem in fair division, even for additive valuations. The current state of the art is that no setting where EFX allocations are impossible is known, and EFX is known to exist for ($i$)…

Equation $(-\Delta+k^2)u+f(u)=0$ in $D$, $u\mid_{\partial D}=0$, where $k=\const>0$ and $D\subset\R^3$ is a bounded domain, has a solution if $f:\R\to\R$ is a continuous function in the region $|u|\geq a$, piecewise-continuous in the region…

A vacuum solution of the Einstein gravitational field equation is given that follows from a general ansatz but fails to follow from it if a certain symmetric matrix is assumed to be in diagonal form from the beginning.

The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are…