关于一个级数问题的思考

关于正项级数的Du Bois Reymond定理及Abel定理指出：没有一种最精确的标准能够用以衡量一切正项级数的敛散性。本文给出了以上两个定理的两种形式,并作简捷证明。     

向量优化问题局部近似解的等价性

主要研究两种不同序关系下向量优化问题的近似解.一种是正锥序关系下的近似解,另一种是多面体锥序关系下的近似解.针对这两种序关系下向量优化问题的近似解,建立了局部近似最优解和μ阶严格局部近似最优解之间的等价关系,同时构建了这两种序关系下近似有效点集之间的等价关系.     

梵塔问题的两个定理

本文首次证明了梵塔问题的两个定理,建立了一种梵塔问题新算法．     

新型混联机床动力学正问题研究

研究了新型混联机床的动力学正问题,得到了动力学正问题方程.针对两种情况进行了仿真研究,一种是刀具没有承受力和力矩的作用;一种是端铣刀进行铣削.分别给出了各个变量的时间历程图和相轨图.     

Darcy-Stokes问题的统一稳定化有限体积法分析

本文对Darcy-Stokes问题提出了一种统一的稳定化有限体积法.在离散问题中,采用两种剖分,一种为三角形剖分,一种为其对偶四边形剖分.速度及压力分别采用非协调线性元及分片常数元来做逼近.经证明,文中的统一格式,具有稳定性及最优误差估计.最后用数值算例验证了本文的理论结果.     

产品回收逆向物流网络设计问题的两阶段启发式算法

针对产品回收逆向物流网络设计问题,设计了一种嵌套了模拟退火算法的两阶段启发式算法。第一阶段确定回收点的选址-分配-存储的联合决策;第二阶段确定回收中心的选址-运输的联合决策,两个阶段相互迭代,从而实现最优解的搜索。通过与遗传算法比较,证明了两阶段启发式算法是一种有效的算法。     

正多边形的密铺问题

<正>所谓密铺(也可以叫做平面图形的镶嵌),是用大小和形状都一样的一种或几种平面图不留空白也不重叠地拼接在一起,比如地板、蜂巢、马赛克、砖瓦的墙,都是生活中常见的密铺图案.以往在学校接触到的密铺,多是以习题的形式询问某正多边形或两种正多边形否可以平铺,没有系统的知识讲解和讨论分析.本文是我校的研究性课题之一,在老师的指导下,通过不定方程的讨论并结合"几何画板"软件,研究总结了一种正多边形和两种正多边形的平铺规     

复杂网络的Buffon概率问题

本文研究了两种复杂网格的几何概率问题,通过利用凸域内定长线段的运动测度,得到了这两种复杂网格的Buffon概率.     

农夫过河问题新解

以一种新视角讨论了趣味逻辑题"农夫过河问题",通过引入位置状态向量与运送过程向量,建立了一个向量方程,它对应于一个线性方程组,其解是唯一确定的.考虑到运送过程的顺序,这个唯一解对应于两种安全过河运送方案.最后,用线性代数建模方法重新表述趣味问题"嫉妒的丈夫"及其矩阵表示.     

按比例分配问题

按比例分配问题是把一个数量按照一定的比进行分配。它是平均分问题的发展,平均分是按比例分配的一种特例。按比例分配问题的解法主要有两种：     

Indecomposable continua and the Julia sets of polynomials, II

We find necessary and sufficient conditions for the connected Julia set of a polynomial of degree d?2 to be an indecomposable continuum. One necessary and sufficient condition is that the impression of some prime end (external ray) of the unbounded complementary domain of the Julia set J has nonempty interior in J. Another is that every prime end has as its impression the entire Julia set. The latter answers a question posed in 1993 by the second two authors.We show by example that, contrary to the case for a polynomial Julia set, the image of an indecomposable subcontinuum of the Julia set of a rational function need not be indecomposable.     

The jump number of suborders of the power set order

Let P be an ordered set induced by several levels of a power set. We give a formula for the jump number of P and show that reverse lexicographic orderings of P are optimal. The proof is based on an extremal set result of Frankl and Kalai.     

Computing a Minimum Weight Triangulation of a Sparse Point Set*

Investigating the minimum weight triangulation of a point set with constraint is an important approach for seeking the ultimate solution of the minimum weight triangulation problem. In this paper, we consider the minimum weight triangulation of a sparse point set, and present an O(n ⁴) algorithm to compute a triangulation of such a set. The property of sparse point set can be converted into a new sufficient condition for finding subgraphs of the minimum weight triangulation. A special point set is exhibited to show that our new subgraph of minimum weight triangulation cannot be found by any currently known methods.     

Tight Gabor Sets on Discrete Periodic Sets

This paper addresses Gabor analysis on a discrete periodic set. Such a scenario can potentially find its applications in signal processing where signals may present on a union of disconnected discrete index sets. We focus on the Gabor systems generated by characteristic functions. A sufficient and necessary condition for a set to be a tight Gabor set in discrete periodic sets is obtained; discrete periodic sets admitting a tight Gabor set are also characterized; the perturbation of tight Gabor sets is investigated; an algorithm to determine whether a set is a tight Gabor set is presented. Furthermore, we prove that an arbitrary Gabor frame set can be represented as the union of a tight Gabor set and a Gabor Bessel set.     

Subdifferential properties of the minimal time function of linear control systems

We present several formulae for the proximal and Fréchet subdifferentials of the minimal time function defined by a linear control system and a target set. At every point inside the target set, the proximal/Fréchet subdifferential is the intersection of the proximal/Fréchet normal cone of the target set and an upper level set of a so-called Hamiltonian function which depends only on the linear control system. At every point outside the target set, under a mild assumption, proximal/Fréchet subdifferential is the intersection of the proximal/Fréchet normal cone of an enlargement of the target set and a level set of the Hamiltonian function.     

Weak convergence theorem for monotone mappings and a countable family of nonexpansive mappings

In this paper, we introduce an iterative process for finding the common element of the set of common fixed points of a countable family of nonexpansive mappings and the set of solutions of the variational inequality problem for an α$\alpha$-inverse-strongly-monotone mapping. We obtain a weak convergence theorem for a sequence generated by this process. Moreover, we apply our result to the problem for finding a common element of the set of equilibrium problems and the set of solutions of the variational inequality problem of a monotone mapping.     

Set containment characterization with strict and weak quasiconvex inequalities

Dual characterizations of the containment of a convex set, defined by infinite quasiconvex constraints, in an evenly convex set, and in a reverse convex set, defined by infinite quasiconvex constraints, are provided. Notions of quasiconjugate for quasiconvex functions, λ-quasiconjugate and λ-semiconjugate, play important roles to derive the characterizations of the set containments.     

N-free orders and minimal interval extensions

We investigate problems related to the set of minimal interval extensions of N-free orders. This leads us to a correspondence between this set for an arbitrary order and a certain set of its maximal N-free reductions. We also get a 1-1-correspondence between the set of linear extensions of an arbitrary order and the set of minimal interval extensions of the linegraph of that order. This has an algorithmic consequence, namely the problem of counting minimal interval extensions of an N-free order is #P-complete. Finally a characterization of all N-free orders with isomorphic root graph is given in terms of their lattice of maximal antichains; the lattices are isomorphic iff the root graphs agree.This work was supported by the PROCOPE Program. The first author is supported by the DFG.     

On the existence of maximal ω-limit sets for dendrite maps

For interval maps and also for graph maps, every ω-limit set is a subset of a maximal one. In this note we construct a continuous map on a dendrite with no maximal ω-limit set. Moreover, the set of branch points is nowhere dense, every ω-limit set of the map is nowhere dense, the set of periodic points and the set of recurrent points are equal and the set of ω-limit points is not closed (an example with the last property was constructed by the authors already in [Ko?an Z, Kornecká-Kurková V, Málek M. On the centre and the set of omega-limit points of continuous maps on dendrites. Topol Appl 2009;156:2923-2931]).