Related papers: Effective uniform bounding in partial differential…

We prove analogs of the Bezout and the Bernstein-Kushnirenko-Khovanskii theorems for systems of algebraic differential conditions over differentially closed fields. Namely, given a system of algebraic conditions on the first $l$ derivatives…

We study upper bounds, approximations, and limits for functions of motivic exponential class, uniformly in non-Archimedean local fields whose characteristic is $0$ or sufficiently large. Our results together form a flexible framework for…

This work concerns about stochastic Burgers type equations with reflection. First of all, by means of the equicontinuous uniform Laplace principle, we prove the Freidlin-Wentzell uniform large deviation principle for these equations…

Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…

We consider a semilinear elliptic equation with Dirichlet boundary conditions in a smooth, possibly unbounded, domain. Under suitable assumptions, we deduce a condition on the size of the domain that implies the existence of a positive…

For a class of systems of semi-linear elliptic equations, including \[ -\Delta u_i=f_i(x,u_i) - \beta u_i\sum_{j\neq i}a_{ij}u_j^p,\qquad i=1,\dots,k, \] for $p=2$ (variational-type interaction) or $p = 1$ (symmetric-type interaction), we…

We explore systems of polynomial equations where we seek complex solutions with absolute value 1. Geometrically, this amounts to understanding intersections of algebraic varieties with tori -- Cartesian powers of the unit circle. We study…

We consider bivariate piecewise polynomial finite element spaces for curved domains bounded by piecewise conics satisfying homogeneous boundary conditions, construct stable local bases for them using Bernstein-B\'ezier techniques, prove…

We establish a majorization-based theory for bounding observables of waves with varied coherence. For any measurement, exact bounds are attained by the maximal and minimal elements in the set of input coherence spectra. The set's supremum…

In this paper we study upper bounds for the density of solution of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/3. We show that under some geometric conditions, in the regular case H >…

Let $f \colon X \to B$ be a complex elliptic surface and let $\DD \subset X$ be an integral divisor dominating $B$. It is well-known that the Parshin-Arakelov theorem implies the Mordell conjecture over complex function fields by a…

Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of…

Let $\Omega \subset \RR^d$, $d \geqslant 1$, be a bounded domain with piecewise smooth boundary $\partial \Omega $ and let $U$ be an open subset of a Banach space $Y$. Motivated by questions in "Uncertainty Quantification," we consider a…

We provide the first known upper bounds for the packing dimension of weighted singular and weighted $\omega$-singular matrices. We also prove upper bounds for these sets when intersected with fractal subsets. The latter results, even in the…

We estimate the distribution of relatively $r$-prime lattice points in number fields $K$ with their components having a norm less than $x$. In the previous paper we obtained uniform upper bounds as $K$ runs through all number fields under…

We develop the theory of difference algebraic groups in the case where we have finitely many pairwise commuting difference operators. We show that the defining ideal of a difference algebraic group is finitely generated as a difference…

The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of…

The aim of this paper is to establish convergence, properties and error bounds for the fully discrete solutions of a class of nonlinear systems of reaction-diffusion nonlocal type with moving boundaries, using the finite element method with…

In this paper estimates for the uniform norm of solutions of parabolic SPDEs are derived. The result is obtained through iteration techniques, motivated by the work of Moser in deterministic settings. As an application of the main result,…

We introduce the notion of \delta-viscosity solutions for fully nonlinear uniformly parabolic PDE on bounded domains. We prove that \delta-viscosity solutions are uniformly close to the actual viscosity solution. As a consequence we obtain…