相关论文: Abstract Convexity and Cone-Vexing Abstractions

This paper is an introduction to soft cone metric spaces. We define the concept of soft cone metric via soft element, investigate soft converges in soft cone metric spaces and prove some fixed point theorems for contractive mappings on soft…

Convex geometries are closure systems satisfying the anti-exchange axiom. Every finite convex geometry can be embedded into a convex geometry of finitely many points in an n-dimensional space equipped with a convex hull operator, by the…

This work is a continuation of what was done in a previous paper and strongly connected to the recent work of U. Abel and I. Rasa [arXiv:1707.00127]

A self-contained introduction is presented of the notion of the (abstract) differentiable manifold and its tangent vector fields. The way in which elementary topological ideas stimulated the passage from Euclidean (vector) spaces and linear…

We introduce two notions of convexity for an infinite regular tree. For these two notions we show that given a continuous boundary datum there exists a unique convex envelope on the tree and characterize the equation that this envelope…

Methods for measuring convexity defects of compacts in R^n abound. However, none of the those measures seems to take into account continuity. Continuity in convexity measure is essential for optimization, stability analysis, global…

In this study, after given the definition of soft sets and their basic operations we define convex soft sets which is an important concept for operation research, optimization and related problems. Then, we define concave soft sets and give…

We establish an embedding from the Hecke algebra associated with the edge contraction of a Coxeter system along an edge to the Hecke algebra associated with the original Coxeter system.

In this paper we have introduced arithmetic ff-continuity and arithmetic fb-continuity utilizing the concept of forward and backward arithmetic convergence in quasi cone metric spaces. These concepts are used to prove some fascinating…

In search of a meaningful 2-dimensional analog to mono- tonicity, we introduce two new definitions and give examples of and dis- cuss the relationship between these definitions and others that we found in the literature. Note: After we…

The notion of an abstract convex geometry offers an abstraction of the standard notion of convexity in a linear space. Kashiwabara, Nakamura and Okamoto introduce the notion of a generalized convex shelling into $\mathbb{R}$ and prove that…

The tight span, or injective envelope, is an elegant and useful construction that takes a metric space and returns the smallest hyperconvex space into which it can be embedded. The concept has stimulated a large body of theory and has…

We consider the gravitational correction to the running of gauge coupling. Weak gravity conjecture implies that the gauge theories break down when the gravitational correction becomes greater than the contribution from gauge theories. This…

Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous spaces. In this survey we trace a few connections between different manifestations of…

In this paper the concept of a partial cone metric space is investigated, some continuity type theorems, and fixed point theorems of contractive mappings in this generalized setting are proved as well as some theorems related to topological…

The notions of convexity and convex polytopes are introduced in the setting of tropical geometry. Combinatorial types of tropical polytopes are shown to be in bijection with regular triangulations of products of two simplices. Applications…

The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.

Convex roof extensions are widely used to create entanglement measures in quantum information theory. The aim of the article is to present some tools which could be helpful for their treatment. Sections 2 and 3 introduce into the subject.…

Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…

These are notes on twisted K-homology theory and twisted Ext-theory from the C*-algebra viewpoint, part of a series of talks on ``C*-algebras, noncommutative geometry and K-theory'', primarily for physicists.