Maximum principle at infinity for complete minimal surfaces in flat 3-manifolds

The main result of this paper is the following maximum principle at infinity:Theorem.Let M ₁ and M ₂ be two disjoint properly embedded complete minimal surfaces with nonempty boundaries, that are stable in a complete flat 3-manifold. Then dist(M ₁,M ₂)=min(dist(M ₁,M ₂), dist(M ₂,M ₁)).In case one boundary is empty, e.g. M ₁,then dist(M ₁,M ₂)=dist(M ₂,M ₁).If both boundaries are empty, then M ₁ and M ₂ are flat.     

Sur les metriques admettant les plans comme surfaces minimales

We establish the system of partial differential equations satisfied by the riemannian metrics on open subsets of which admit planes as minimal surfaces. This is a nonlinear system of 10 partial differential equations, with the euclidian metric as a particular solution. In a previous work, we solved this system for axially symmetrical metrics. In this paper we linearize the system at the euclidian metric and solve the linear system. We obtain a 20-dimensional space of solutions.

     

All-glass open-split interface for capillary GC/MS

This paper describes a design for an all-glass GC/MS interface. The design has advantages due to low dead volume, lack of column effluent adsorption and degradation, simple interface production and installation, and ease of column mounting/dismounting.     

Determination/estimation of an optimal replacement interval under minimal repair

In this paper the problem of estimation of an optimal replacement interval for a system which is minimally repaired at failures is studied. The problem is investigated both under a parametric and a nonparametric form of the failure intensity of the system. It is assumed that observational data from n systems are available. Some asymptotic results are shown. A graphical procedure for determining/estimating an optimal replacement interval is presented. The procedure is particularly valuable for sensitivity analyses, for example with respect to the costs involved.     

Low-energy points on the sphere and the real projective plane

We present a generalization of a family of points on ${\mathbb{S}}^2$, the Diamond ensemble, containing collections of N points on ${\mathbb{S}}^2$ with very small logarithmic energy for all $N\in \mathbb{N}$. We extend this construction to the real projective plane ${\mathbb{RP}}^2$ and we obtain upper and lower bounds with explicit constants for the Green and logarithmic energy on this last space.     

Explicit maximal and minimal curves over finite fields of odd characteristics

In this work we present explicit classes of maximal and minimal Artin–Schreier type curves over finite fields having odd characteristics. Our results include the proof of Conjecture 5.9 given in [1] as a very special subcase. We use some techniques developed in [2], which were not used in [1].     

There is no upper bound for the diameter of the commuting graph of a finite group

We construct a family of finite 2-groups which have commuting graph of increasing diameter.     

基于有限非阿贝尔群的密钥交换

从一般线性群GL（n,F）和对称群Sn上的困难问题出发,构造了几个密钥交换算法,新算法具有更高的效率.同时,指出基于一般线性群的密钥交换算法的安全性直接依赖于广义矩阵覆盖问题,基于对称群的密钥交换协议的安全性直接依赖于置换群上的共轭问题.