Edge proximity and matching extension in projective planar graphs

A graph $G$ with at least $2m+2$ vertices is said to be distance $d$ $m$-extendable if, for any matching $M$ of $G$ with $m$ edges in which the edges lie at distance at least $d$ pairwise, there exists a perfect matching of $G$ containing $M$. In this paper we prove that every 5-connected triangulation on the projective plane of even order is distance 3 7-extendable and distance 4 $m$-extendable for any $m$.     

EPR‐Based Approach for the Localization of Paramagnetic Metal Ions in Biomolecules

Metal ions play an important role in the catalysis and folding of proteins and oligonucleotides. Their localization within the three‐dimensional fold of such biomolecules is therefore an important goal in understanding structure–function relationships. A trilateration approach for the localization of metal ions by means of long‐range distance measurements based on electron paramagnetic resonance (EPR) is introduced. The approach is tested on the Cu²⁺ center of azurin, and factors affecting the precision of the method are discussed.     

Matching Extension Missing Vertices and Edges in Triangulations of Surfaces

Let G be a 5‐connected triangulation of a surface Σ different from the sphere, and let be the Euler characteristic of Σ. Suppose that with even and M and N are two matchings in of sizes m and n respectively such that . It is shown that if the pairwise distance between any two elements of is at least five and the face‐width of the embedding of G in Σ is at least , then there is a perfect matching M₀ in containing M such that .     

基于Delaunay三角剖分的地表平均温度模拟

利用Delaunay三角网对目标区域进行剖分,在对地表温度进行高度插值后,运用二重积分的思想建立了基于Delaunayr三角剖分的地表平均温度测量模型.同时以南极地表平均温度的测量为例,将67个自动气象地表台站、46个气象地表台站以及56个高空气象观测站的加权平均温度与地表平均温度的数据进行分析,得到南极2015全年地表平均温度均在-8℃以下,最低温约为-20℃,符合南极大陆地表温度的实际情况.     

No optimal 1‐planar graph triangulates any nonorientable closed surface

Suzuki [Discrete Math. 310 (2010), 6–11] proved that for any orientable closed surface F² other than the sphere, there exists an optimal 1‐planar graph which can be embedded on F² as a triangulation. However, for nonorientable closed surfaces, the existence of such graphs is unknown. In this article, we prove that no optimal 1‐planar graph triangulates a nonorientable closed surface.     

Accurate integration over atomic regions bounded by zero‐flux surfaces

The approach for the integration over a region covered by zero‐flux surface is described. This approach based on the surface triangulation technique is efficiently realized in a newly developed program TWOE . The elaborated method is tested on several atomic properties including the source function. TWOE results are compared with those produced by using well‐known existing programs. Absolute errors in computed atomic properties are shown to range usually from 10^?6 to 10^?5 au. The demonstrative examples prove that present realization has perfect convergence of atomic properties with increasing size of angular grid and allows to obtain highly accurate data even in the most difficult cases. It is believed that the developed program can be bridgehead that allows to implement atomic partitioning of any desired molecular property with high accuracy. © 2012 Wiley Periodicals, Inc.     

Interpolating minimal energy C1‐Surfaces on Powell–Sabin Triangulations: Application to the resolution of elliptic problems

In this article, we present a method to obtain a C¹‐surface, defined on a bounded polygonal domain Ω, which interpolates a specific dataset and minimizes a certain “energy functional.” The minimization space chosen is the one associated to the Powell–Sabin finite element, whose elements are C¹‐quadratic splines. We develop a general theoretical framework for that, and we consider two main applications of the theory. For both of them, we give convergence results, and we present some numerical and graphical examples. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 798–821, 2015     

An efficient adaptive analysis procedure for node-based smoothed point interpolation method (NS-PIM)

This paper presents an efficient adaptive analysis procedure being able to operate in the framework of the node-based smoothed point interpolation method (NS-PIM). The NS-PIM uses three-node triangular cells and is very easy to be implemented, which make it an ideal candidate for adaptive analysis. In the present adaptive procedure, a new error indicator is devised for NS-PIM settings; two ways are proposed to calculate the local critical value; a simple h-type local refinement scheme is adopted and Delaunay technology is used for regenerating optimal new mesh. A number of typical numerical examples involving stress concentration and solution singularities have been tested. The results demonstrate that the present procedure achieves much higher convergence rate results compared to the uniform refinement, and can obtain upper bound solution in strain energy.