相关论文: Formal and convergent solutions of analytic equati…

We present two possible generalisations of Roth's approximation theorem on proper adelic curves, assuming some technical conditions on the behavior of the logarithmic absolute values. We illustrate how tightening such assumptions makes our…

In this paper the double-sided Taylor's approximations are studied. A short proof of a well-known theorem on the double-sided Taylor's approximations is introduced. Also, two new theorems are proved regarding the monotonicity of such…

The classical Artin approximation (AP) reads: any formal solution of a system of (analytic, resp. algebraic) equations of implicit function type is approximated by ``ordinary" solutions (i.e. analytic, resp. algebraic). Morphisms of…

We prove convergence results for `increasing' sequences of sectorial forms. We treat both the case of closed forms and the case of non-closable forms.

We propose a numerical analysis of a simplified version of the previous paper "Multiplicity hunting and approximating multiple roots of polynomial systems" written by the two authors.

In this paper, we use the idempotent decomposition to give an explicit isomorphism from an arbitrary semisimple Artinian ring to an external direct sum of finitely many full matrix rings over division rings.

An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…

An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut

Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new correctness proofs of abstract completion, both for finite and infinite runs. For the…

Let H:(M,p)->(M',p') be a formal mapping between two germs of real-analytic generic submanifolds in C^N with nonvanishing Jacobian. Assuming M to be minimal at p and M' holomorphically nondegenerate at p', we prove the convergence of the…

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…

We suggest a new approach to Artin's constant that leads to its representation as an infinite sum divided by another infinite sum. The same approach works well for Stephens' constant and higher rank Artin's constants. The main results are…

In this paper, we give a form of refined Roth's theorem. As an application, we prove a special case of the $abc$-conjecture.

We show, that under natural assumptions, solutions of Dirichlet problems for uniformly elliptic divergence form operator can be approximated pointwise by solutions of some versions of Robin problems. The proof is based on stochastic…

We show a new, elementary and geometric proof of the classical Alexandrov theorem about the second order differentiability of convex functions. We also show new proofs of recent results about Lusin approximation of convex functions and…

We give a new proof of a classical theorem on approximation of continuous functions on totally real sets

In this paper we give conditions on a homogeneous polynomial for which the associated graded Artin algebra is a complete intersection.

Assuming that a formal approximation of multiple waves has been obtained by matched asymptotic methods, we derive a {\em Spatial Shadowing lemma} to construct exact solutions near the formal approximation. In Part I, we consider a general…

We prove an analogue of the classical Bernstein theorem concerning the rate of polynomial approximation of piecewise analytic functions on a compact subset of the real line.

The purpose of this article is twofold. On the one hand, we prove asymptotic formulas for the quantitative distribution of rational points on any smooth non-split projective quadratic surface. We obtain the optimal error term for the real…