What is the maximum stretching for C–C single bond?

The objective of this work is to determine the maximum stretch of the C–C bond before it misses the character of single bond, employing both the Atoms in Molecules (AIM) and Electron Localization Function (ELF) methods. It was concluded that C–C distances up to 2.0 Å could be considered single bonds.     

<Emphasis Type="Italic">ϕ</Emphasis>-pairs and common fixed points in cone metric spaces

In this paper we introduce a contractive condition, called ϕ-pair, for two mappings in the framework of cone metric spaces and we prove a theorem which assures existence and uniqueness of common fixed points for ϕ-pairs. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature. The authors are supported by Università degli Studi di Palermo, R. S. ex 60%.     

The area within a curve

The area of a simple closed convex curve can be estimated in terms of the number of points of a square lattice that lie within the curve. We obtain the usual error bound without integration using a form of the Hardy—Littlewood—Ramanujan circle method, and also present simple estimates for the mean square error.     

Global G-Manifold Reductions and Resolutions

The purpose of this note is to exhibit some simple and basic constructions for smooth compact transformation groups, and some of their most immediate applications to geometry.     

具有变号非线性项的奇异二阶三点边值问题的三个非零正解

该文研究一类具有变号非线性项的奇异二阶三点边值问题多个正解的存在性. 运用Leggett-Williams不动点定理在$f$满足一定的增长条件下, 获得了至少三个非零正解存在的结果.     

Infinitely Many Contact Process Transitions on a Tree

We continue our study of the ergodic behavior of the contact process on infinite connected graphs of bounded degree. Examples are provided of trees on which, as the infection parameter increases, complete convergence alternates between holding and failing infinitely many times.     

改进的最小费用理论在盲竖井选址中的应用

在网络的任意点求解绝对中心等特殊点是网络流研究的一个难点.在目前最小费用理论的基础上引入平面几何理论,把网络等效于几何图形,建立了数学模型.通过求解,得出了网络间的最佳连接点,从而确定出盲竖井的位置.最后以云南锡业集团个旧东区两个生产平台之间的连接为一算例,得出了理想的结果,验证了该方法的有效可行性.     

Fix-Mahonian Calculus, II: Further statistics

Using classical transformations on the symmetric group and two transformations constructed in Fix-Mahonian Calculus I, we show that several multivariable statistics are equidistributed either with the triplet (fix, des, maj), or the pair (fix, maj), where “fix,” “des” and “maj” denote the number of fixed points, the number of descents and the major index, respectively.     

参数曲线的全局凸性判别条件

基于平面曲线的二次微商,导出了二重点的判别条件,结合参数曲线的局部凸性条件,得到了参数闭曲线的充要条件。给出了参数曲线的拐点判别条件,从而得到了参数曲线局部凸的充要条件。     

A method for minimizing the sum of a convex function and a continuously differentiable function

This paper presents a method for minimizing the sum of a possibly nonsmooth convex function and a continuously differentiable function. As in the convex case developed by the author, the algorithm is a descent method which generates successive search directions by solving quadratic programming subproblems. An inexact line search ensures global convergence of the method to stationary points.