Related papers: General position theorem and its applications
We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way…
Zalcman's Lemma makes significant applications in normal families, complex dynamics and related problems in complex analysis. In the present paper, we are devoted to generalizing the classical Zalcman's lemma to complex Lie groups by means…
This expository paper presents some applications of the parameterized Picard-Vessiot theory for ordinary differential equations, mainly related to monodromy.
Fractal geometry and analysis constitute a growing field, with numerous applications, based on the principles of fractional calculus. Fractals sets are highly effective in improving convex inequalities and their generalisations. In this…
For a given partially ordered set (poset) and a given family of mappings of the poset into itself, we study the problem of the description of joint fixed points of this family. Well-known Tarski's theorem gives the structure of the set of…
A generalization of G-sets, called partial G-sets, are the sets that admit an action of partial maps on their subsets. Partial actions are a powerful tool to generalize many results of group actions. These generalizations are obtained by…
In this article, after recalling and discussing the conventional extremality, local extremality, stationarity and approximate stationarity properties of collections of sets and the corresponding (extended) extremal principle, we focus on…
We consider some applications of the theory of generalized Ore supplement conditions in the study of finite groups.
We introduce an equivalence relation on the global class of morphisms of a category that extends several classical notions of equivalence in mathematics. We show that the standard group-action equivalence is a special case of our framework.…
We prove a parametric generalization of the classical Poincare-Perron theorem on stabilizing recurrence relations where we assume that the varying coefficients of a recurrence depend on auxiliary parameters and converge uniformly in these…
We study the geometry of forces in some simple models for granular stackings. The information contained in geometry is complementary to that in the distribution of forces in a single inter-particle contact, which is more widely studied. We…
There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…
We establish coupled fixed point theorems for contraction involving rational expressions in partially ordered metric spaces.
Partially ordered sets (posets) play a universal role as an abstract structure in many areas of mathematics. For finite posets, an explicit enumeration of distinct partial orders on a set of unlabelled elements is known only up to a…
In this article, we provide a simple and systematic way to represent general (inhomogeneous) fractals that may look different at different scales and places. By using set-valued compression maps, we express these general fractals as…
We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]
Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.
A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated…
We present a detailed synthetic overview of the utilisation of categorical techniques in the study of order structures together with their applications in operational quantum theory. First, after reviewing the notion of residuation and its…
We prove a myriad of results related to the stabilizer in an algebraic group $G$ of a generic vector in a representation $V$ of $G$ over an algebraically closed field $k$. Our results are on the level of group schemes, which carries more…