相关论文: Local approximation of the solutions of algebraic …

Let F be a holomorphic map whose components satisfy some polynomial relations. We present an algorithm for constructing Nash maps locally approximating F, whose components satisfy the same relations.

A continuous solution of an algebraic equation with holomorphic almost periodic coefficients is also almost periodic.

We show that any function can be locally approximated by solutions of prescribed linear equations of nonlocal type. In particular, we show that every function is locally $s$-caloric, up to a small error. The case of non-elliptic and…

Let {X_n} be a sequence of analytic sets converging to some analytic set X in the sense of holomorphic chains. We introduce a condition which implies that every irreducible component of X is the limit of a sequence of irreducible components…

A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…

An existing solvability result for relaxed one-sided Lipschitz algebraic inclusions is substantially improved. This enhanced solvability result allows the design of a very robust numerical method for the approximation of a solution of the…

We derive efficient algorithms for coarse approximation of algebraic hypersurfaces, useful for estimating the distance between an input polynomial zero set and a given query point. Our methods work best on sparse polynomials of high degree…

This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…

A method for converting the geometrical problem of rectangle packing to an algebraic problem of solving a system of polynomial equations is described.

In this paper, an algorithm to compute a certified $G^1$ rational parametric approximation for algebraic space curves is given by extending the local generic position method for solving zero dimensional polynomial equation systems to the…

We study local existence for the Boltzmann equation near a global Maxwellian.

A computation method of algebraic local cohomology with parameters, associated with zero-dimensional ideal with parameter, is introduced. This computation method gives us in particular a decomposition of the parameter space depending on the…

We provide a local approximation result of non-holomorphic discs with small d-bar by pseudoholomorphic ones. As an application, we provide a certain gluing construction.

Local Fourier analysis is a strong and well-established tool for analyzing the convergence of numerical methods for partial differential equations. The key idea of local Fourier analysis is to represent the occurring functions in terms of a…

A review of the Hodge and Hopf-algebraic approach to QFT.

We study local equivalence of bounded complexes over a polynomial ring $R[w]$, where $R$ is a noetherian ring. We provide a homological algebra approach to the results, the variants of which have been proved in many places in the…

Solutions to hyperbolic conservation laws can be approximated in many different ways: by vanishing viscosity, relaxations, discrete or semi-discrete numerical schemes, approximation with a nonlocal flux, etc$\ldots$ For some of these…

A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…

We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…

It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper we generalize this property to finite-dimensional commutative algebras. We prove that if some basis of a…