Related papers: Approximate Axiomatization for Differentially-Defi…
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…
The Dirichlet forms methods, in order to represent errors and their propagation, are particularly powerful in infinite dimensional problems such as models involving stochastic analysis encountered in finance or physics, cf. [5]. Now, coming…
By studying $\mathbb{A}^1$-curves on varieties, we propose a geometric approach to strong approximation problem over function fields of complex curves. We prove that strong approximation holds for smooth, low degree affine complete…
We introduce an axiomatization for the notion of computation. Based on the idea of Brouwer choice sequences, we construct a model, denoted by $E$, which satisfies our axioms and $E \models \mathrm{ P \neq NP}$. In other words, regarding…
In this paper we define "a continued fraction expansion of the exponential integral $E_{1}(x)$ at infinity", which is analogous to the regular continued fraction expansion of real numbers, and prove that this expansion gives the same…
In this article we give strong versions for preparation theorems for $\mathbb{R}_{an,exp}$-definable functions outgoing from methods of Lion and Rolin ($\mathbb{R}_{an,exp}$ is the o-minimal structure generated by all restricted analytic…
The perimeter and area generating functions of exactly solvable polygon models satisfy q-functional equations, where q is the area variable. The behaviour in the vicinity of the point where the perimeter generating function diverges can…
We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result…
We introduce an asymmetric operator of generalised translation, define the generalised modulus of smoothness by its means, and obtain the direct and inverse theorems in approximation theory for it.
We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
It is known that a subharmonic function of finite order $\rho$ can be approximated by the logarithm of the modulus of an entire function at the point $z$ outside an exceptional set up to $C\log|z|$. In this article we prove that if such an…
An equational axiomatisation of probability functions for one-dimensional event spaces in the language of signed meadows is expanded with conditional values. Conditional values constitute a so-called signed vector meadow. In the presence of…
We explain how to compute in the algebraic closure of a valued field. These computations heavily rely on the \NPAz. They are made in the same spirit as the dynamic algebraic closure of a field. They give a concrete content to the theorem…
In this article we develop a theory of exact linear penalty functions that generalizes and unifies most of the results on exact penalization existing in the literature. We discuss several approaches to the study of both locally and globally…
By taking the viewpoint of Brownian additive functionals, we extend an existing approximation theorem of the two-dimensional Laplacian singularly perturbed at the origin. The approximate operators are defined by adding a rescaled function…
In earlier work, the second author showed that a closed subset of a polynomial functor can always be defined by finitely many polynomial equations. In follow-up work on $\operatorname{GL}\nolimits_{\infty}$-varieties,…
We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in the whole space or in any cylindrical smooth domain with smooth boundary data one can find an…
In logic programming, negation can be interpreted in various ways. Probably best known is the concept of "negation as failure", where "$\mathit{not}\, p$" is true if we have no evidence for $p$. On the other hand, strong negation requires…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…