Group actions and covering maps in the uniform category

In Rips complexes and covers in the uniform category (Brodskiy et al. [4]) we define, following James (1990) [9], covering maps of uniform spaces and introduce, inspired by Berestovskii and Plaut (2007) [2], the concept of generalized uniform covering maps. In this paper we investigate when these covering maps are induced by group actions which allows us to relate our covering maps to those in Berestovskii and Plaut (2007) [2]. Also, as an application of our results we present an exposition of Prajs' (2002) [16] homogeneous curve that is path-connected but not locally connected.     

Composite genus one Belyi maps

Motivated by a demand for explicit genus 1 Belyi maps from theoretical physics, we give an efficient method of explicitly computing genus one Belyi maps by (1) composing covering maps from elliptic curves to the Riemann sphere with simpler (univariate) genus zero Belyi maps, as well as by (2) composing further with isogenies between elliptic curves. The computed examples of genus 1 Belyi maps has doubly-periodic dessins d’enfant that are listed in the physics literature as so-called brane-tilings in the context of quiver gauge theories.     

决策模糊集覆盖系数的实用计算方法

研究了经济学中广泛应用的决策模糊理论中模糊集覆盖系数的性质,并据此提出了无须通过繁杂的统计实验就能够计算覆盖系数的实用方法,进而提出了模糊集交并运算算子.用两个算例说明了该方法和算子与实际情形相符,具有可行性.     

两类赋予w~＊-可分对偶的空间的BCP

在对偶w~＊-可分的情况下,证明了两类Banach空间具有球覆盖性质,即：它们是1）光滑空间;2）具有MIP的空间.     

THE LARGEST SOLUTION OF LINEAR EQUATION OVER THE COMPLETE HEYTING ALGEBRA

Let (L, ≤, ∨, ∧) be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by ∨ and ∧ respectively, is studied. We obtain: (i) the necessary and suffcient conditions for S(A, b)≠■l; (ii) the necessary conditions for |S(A, b)| = 1. We also obtain the vector  ∈ Ln and prove that it is the largest element of S(A, b) if S(A, b)≠■.     

Surrogate constraint normalization for the set covering problem

The set covering problem (SCP) is central in a wide variety of practical applications for which finding good feasible solutions quickly (often in real-time) is crucial. Surrogate constraint normalization is a classical technique used to derive appropriate weights for surrogate constraint relaxations in mathematical programming. This framework remains the core of the most effective constructive heuristics for the solution of the SCP chiefly represented by the widely-used Chvátal method. This paper introduces a number of normalization rules and demonstrates their superiority to the classical Chvátal rule, especially when solving large scale and real-world instances. Directions for new advances on the creation of more elaborate normalization rules for surrogate heuristics are also provided.     

Accessibility of partially hyperbolic endomorphisms with 1D center-bundles

We prove that partially hyperbolic endomorphisms with one dimensional center-bundles and non-trivial unstable bundles are stably accessible. And there is residual subset $\Res$ of partially hyperbolic volume preserving endomorphisms with one dimensional center-bundles such that every $f \in \Res$ is stably accessible. In the end, we prove the accessibility of Gan''s example.     

Chromatic numbers of spheres

The chromatic number of a subset of Euclidean space is the minimal number of colors sufficient for coloring all points of this subset in such a way that any two points at the distance 1 have different colors. We give new upper bounds on chromatic numbers of spheres. This also allows us to give new upper bounds on chromatic numbers of any bounded subsets.     

On fixed-points and singular values of transcendental meromorphic functions

In this paper we make a further discussion of a relationship between the number of fixed-points and distribution of singular values along the round annuli centered at the origin of a transcendental meromorphic function. To attain our purpose we first establish a fundamental inequality for the modulus of derivative of a holomorphic covering mapping whose image is an annulus by virtue of the hyperbolic metric. The inequality is of independent significance. We make a simple survey on some domain constants for ...     

A note on maximal covering location games

In this note we introduce and analyze maximal covering location games. As the core may be empty, several sufficient conditions for core non-emptiness are presented. For each condition we provide an example showing that when the condition is not satisfied, core non-emptiness is not guaranteed.