Related papers: Effective inseparability and some applications in …
This paper is aimed to prove the strong duality theorem for continuous-time linear programming problems in which the coefficients are assumed to be piecewise continuous functions. The previous paper proved the strong duality theorem for the…
In the object reallocation problem, achieving Pareto-efficiency is desirable, but may be too demanding for implementation purposes. In contrast, pair-efficiency, which is the minimal efficiency requirement, is more suitable. Despite being a…
Using a standard definition of fractional powers on the universal cover $\exp:S\to \mathbb{C}^*$ seen as an infinite helicoid embedded in $\mathbb{R}^3$, we study the statistics of pairs from the countable family $\{n^\alpha \, : \, n \in…
The effective conductivity of the infinite checkerboard (chessboard) and analogous higher-dimensional checkered structures, are considered. An algebraic expression is derived by accounting for the symmetries of the structures.
Given two relations containing multiple measurements - possibly with uncertainties - our objective is to find which sets of attributes from the first have a corresponding set on the second, using exclusively a sample of the data. This…
We study the interpolation group whose elements are suitable pairs of formal power series. This group has a faithful representation into infinite lower triangular matrices and carries thus a natural structure as a Lie group. The matrix…
Rosser theories play an important role in the study of the incompleteness phenomenon and meta-mathematics of arithmetic. In this paper, we first define the notions of $n$-Rosser theories, exact $n$-Rosser theories, effectively $n$-Rosser…
In the framework of Asplund spaces, we use two equivalent instruments - rich families and suitable models from logic - for performing separable reductions of various statements on Frechet subdifferentiability of functions. This way,…
Effective field theories (EFTs) are widely considered by physicists to be explanatory and to be the appropriate frameworks for modelling various phenomena at different scales. At the same time, they are known to be approximate, restricted,…
Let $a,b$ be elements in a unital C$^*$-algebra with $0\leq a,b\leq 1$. The element $a$ is absolutely compatible with $b$ if $$\vert a - b \vert + \vert 1 - a - b \vert = 1.$$ In this note, we describe a complete list of absolutely…
We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite…
To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and…
Effective field theory provides a way of parameterizing strong-field deviations from General Relativity that might be observable in the gravitational waves emitted in a black hole merger. To perform numerical simulations of mergers in such…
Separability for groups refers to the question which subsets of a group can be detected in its finite quotients. Classically, separability is studied in terms of which classes have a certain separability property, and this question is…
As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently…
The rigorous description of correlated quantum many-body systems constitutes one of the most challenging tasks in contemporary physics and related disciplines. In this context, a particularly useful tool is the concept of effective pair…
After highlighting the cases in which the semantics of a language cannot be mechanically reproduced (in which case it is called inherent), the main epistemological consequences of the first incompleteness Theorem for the two fundamental…
Complementarity is a phenomenon explaining several core features of quantum theory, such as the well-known uncertainty principle. Roughly speaking, two objects are said to be complementary if being certain about one of them necessarily…
Mathematicians occasionally discover interesting truths even when they are playing with mathematical ideas with no thoughts about possible consequences of their actions. This paper describes two specific instances of this phenomenon. The…
In this paper, we study the notion of a separability idempotent in the C*-algebra framework. This is analogous to the notion in the purely algebraic setting, typically considered in the case of (finite-dimensional) algebras with identity,…