Approach Theory in a Category: A Study of Compactness and Hausdorff Separation

In a topological construct endowed with a proper -factorization system and a concrete functor , we study -compactness and -Hausdorff separation, where is a class of “closed morphisms” in the sense of Clementino et al. (A functional approach to general topology. In: Categorical Foundations. Encyclopedia of Mathematics and Its Applications, vol. 97, pp. 103–163. Cambridge University Press, Cambridge, 2004), determined by Λ. In particular, we point out under which conditions on Λ, the notion of -compactness of an object of coincides with 0-compactness of the image in Prap. Our results will be illustrated by some examples: except for some well-known ones, like b-compactness of a topological space, we also capture some compactness notions that were not considered before in the literature. In particular, we obtain a generalization of b-compactness to the setting of approach spaces. This notion is shown to play an important role in the study of uniformizability. The author is research assistant at the Fund of Scientific Research Vlaanderen (FWO).     

A note on the perturbations of compact quantum metric spaces

In this short note,we consider the perturbation of compact quantum metric spaces.We first show that for two compact quantum metric spaces(A,P) and(B,Q) for which A and B are subspaces of an order-unit space C and P and Q are Lip-norms on A and B respectively,the quantum Gromov–Hausdorff distance between(A,P) and(B,Q) is small under certain conditions.Then some other perturbation results on compact quantum metric spaces derived from spectral triples are also given.     

Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories

Let G be a Lie group which is the union of an ascending sequence G₁⊆G₂⊆? of Lie groups (all of which may be infinite-dimensional). We study the question when in the category of Lie groups, topological groups, smooth manifolds, respectively, topological spaces. Full answers are obtained for G the group Diffc(M) of compactly supported C^∞-diffeomorphisms of a σ-compact smooth manifold M; and for test function groups of compactly supported smooth maps with values in a finite-dimensional Lie group H. We also discuss the cases where G is a direct limit of unit groups of Banach algebras, a Lie group of germs of Lie group-valued analytic maps, or a weak direct product of Lie groups.     

LaH分子的X1∑+态的势能函数

应用原子分析反应静力学原理导出ＬａＨ分子的电子状态和可能的离解极限,考虑相对论紧致有效势ＰＣＥＰ（Ｒｅｌａｔｉｖｉｓｔｉｃ Ｃｏｍｐａｃｔ Ｅｆｆｅｃｔｉｖｅ Ｐｏｔｅｎｔｉａｌ）近似下,用ＱＣＩＳＤ方法计算了ＬａＨ分子基态Ｘ＾１Σ＾＋的平衡几何Ｒｅ和离解能Ｄｅ为２．１２５Ａ和２．６２３ｅＶ,并在计算出来的一系列背地里点势能基础上,用正规方程组拟合Ｍｕｒｒｅｌｌ－Ｓｏｒｂｉｅ（Ｍ－Ｓ）势能函数,得     

二维紧致具有非正曲率Riemann流形Euler数的一个计算公式

设Ｍ是二维紧致、曲率Ｋ（Ｍ）≤０的Ｒｉｅｍａｎｎ流形．对任一ｘ　Ｍ,在Ｍ上类数≥３的点集非空且只有有限个点｛α１,α２,…;αｄ｝．用Ｋｊ表示αｊ的类数,即αｊ到ｘ的最短测地线的条数．那么,Ｍ的Ｅｕｌｅｒ数Ｘ（Ｍ）可以表示为：Ｘ（Ｍ）＝（ｄ＋１）＝Ｋｊ．如果Ｍ上类数２３的点只有一个,那么这个点是Ｍ上距离ｘ最远的点．     

A high-order numerical method for the nonlinear Helmholtz equation in multidimensional layered media

We present a novel computational methodology for solving the scalar nonlinear Helmholtz equation (NLH) that governs the propagation of laser light in Kerr dielectrics.     

The Electric Charge Confining in Polyakov’s Compact QED in <Emphasis Type="Italic">R</Emphasis><Superscript>4</Superscript>

We present a Wilson Loop evaluation of the binding energy of electric static charges in A.M. Polyakov’s Compact QED in R ⁴ through path integrals.     

Semilinear fractional integro-differential equations with compact semigroup

In this paper, we study the local and global existence of mild solutions to a class of fractional integro-differential equations in an arbitrary Banach space associated with operators generating compact semigroup on the Banach space.