Related papers: Classical theorems through convergence methods

Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This…

Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of…

This is a survey of old and new problems and results in additive number theory.

We introduce an object that has obvious similarity to the classical one - the algebra of supersymmetric polynomials. Despite the similarity, the known structure theorems on supersymmetric polynomials do not help in the study of the new…

The main purpose of the present article is to give some new Hilbert's sum type inequalities, which in special cases yield the classical Hilbert's inequalities. Our results provide some new estimates to these types of inequalities.

Approximation theory has long been concerned with the development of positive linear operators that effectively approximate classes of functions. Among the most well-known results in this area are Korovkin-type approximation theorems, which…

We present correspondences induced by some classical mappings between measures on an interval and measures on the unit circle. More precisely, we link their sequences of orthogonal polynomial and their recursion coefficients. We also deduce…

Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…

Argumentation theory is a powerful paradigm that formalizes a type of commonsense reasoning that aims to simulate the human ability to resolve a specific problem in an intelligent manner. A classical argumentation process takes into account…

In this paper, we prove well-posedness in $C^1(\mathbb{R})$ (a.k.a. classical solutions) of the Fornberg-Whitham equation. To achieve this objective, we study its weak formulation under a Lagrangian framework. Applying the fundamental…

This work proposes a complete algebraic model for classical information theory. As a precursor the essential probabilistic concepts have been defined and analyzed in the algebraic setting. Examples from probability and information theory…

We study several variants of Euler sums by using the methods of contour integration and residue theorem. These variants exhibit nice properties such as closed forms, reduction, etc., like classical Euler sums. In addition, we also define a…

The transition from the quantum to the classical world is not yet understood. Here we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except in some specific basis. But we have no…

Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the…

These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…

We analyze a supersymmetric system with four flat directions. We observe several interesting properties, such as the coexistence of the discrete and continuous spectrum in the same range of energies. We also solve numerically the classical…

Studying the reliability of complex systems using machine learning techniques involves facing a series of technical and practical challenges, ranging from the intrinsic nature of the system and data to the difficulties in modeling and…

Let F be a totally real field and p a rational prime unramified in F. We prove a partial classicality theorem for overconvergent Hilbert modular forms: when the slope is small compared to certain but not all weights, an overconvergent form…

Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.

In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…