Nine Point Circle

The nine point circle is a geometrical concept that links some of a triangle'S parts that one would initially feel could not be interconnected. This circle was discovered by Charles Julien Brian- chon(1783-1864)and Jean Victor Poncelet(1788- 1867).     

On Fixed Point and Almost Fixed Point Problems of Lower Semicontinuous Type Multivalued Mappings

In the present paper, some new almost fixed point theorems and fixed point theorems for lower semicontinuous type multivalued mappings are obtained in metrizable H-spaces.     

The “Point” Goalie Problem

Suppose you are given a collection of discs of radius εand you are asked to place them in the plane so that any straight linethat crosses the unit disc willhit one or more of them. Furthermore, you are asked to do thiswith as few discs as possible. How many do you need? This problem can be cast as an (infinite) integer programming (IP) problem.Often, for such problems, one can obtain a lowerbound by considering thelinear programming (LP) relaxation.For the above problem the relaxed problem allows discs with positive weight,requires that each line crossing the unit disc accumulates weight 1from discs it hits,and asks that the total weight be minimized.This LP problem has a simple asymptotically optimal solutionwith total weight 1/ε.Clearly, this is the best possible since blockingall the lines in a single direction requires total weight 1/ε.Although it is quite intuitive that the IP version cannothavesuch a “perfect” solution, achieving the lower bound, it is surprisinglydifficult to obtain a better lower bound.Here we improve the lower bound to 1.001/ε.The true answer is probably considerably larger.We believe this is the first example of a problem in this class where it has been proven that the LP and IP versions have different answers.     

An Abstract Critical Point Theorem and Applications

In this paper,we prove a following critical point theorem by using linkmethod in [1]. Theorem 1.1. Let X be a real Banach space,X_1,X_2 be subspaces of X.X=X_1+X_2 and dim X_2=m<+∞,f(x)∈ C~1(X,R)satisfies Palais-Smale conditionand following three conditions: i)There exist ρ>0,β>a such that f|βρηx_1≥β, ii)There exist e∈β_R∩X_1,R>ρ such that     

Inductive Proof of a Saddle Point Theorem

Many proofs have been published for the minimax theorem, and all the published inductive proofs have been indirect ones. It has been pointed out that a direct inductive proof is needed, especially for instructional purposes, since indirect proofs are more or less implicit in nature. Such a direct proof is given in [4]: Now the minimax theorem can be stated equivalently in terms of saddle point. And it is the object of the present paper to give a direct inductive proof for the saddle point version of this theorem.     

Weakly Almost Periodic Point and Measure Centre

In studying a dynamical system, one finds that there frequently exist some pertur-bations or false phenomena. In order to exclude them, we introduce the notion ofmeasure centre which is defined as the least compact invariant absolutely measure 1set. According to the ergodic theory, all of the important dynamical behaviors of asystem are embeded over its measure centre. In order to determine the structure of     

多媒体课件制作工具Power Point简介

可以用来制作多媒体课件的工具软件很多 ,我们之所以首先介绍ＰｏｗｅｒＰｏｉｎｔ,是因为ＰｏｗｅｒＰｏｉｎｔ具有两大特点 :一是它能与Ｗｉｎｄｏｗｓ,Ｗｏｒｄ ,Ｅｘｃｅｌ密切配合 ,二是它最简单易学 ,在提倡教师自己制作课件的背景下 ,对于非专业性的软件制作者的教师来说 ,学习ＰｏｗｅｒＰｏｉｎｔ应当是最佳选择之一 .ＰｏｗｅｒＰｏｉｎｔ是微软公司的办公套件Ｏｆｆｉｃｅ中的三大核心组件之一 (另两大核心组件是Ｗｏｒｄ和Ｅｘｃｅｌ) .本文将以已汉化的Ｏｆｆｉｃｅ97中的ＰｏｗｅｒＰｏｉｎｔ97为准 .1　启动菜单与选择1.1　…     

Using Stopping Point to Describe Stopping Line

The stopping line and the stopping point are very important concepts. However few relations between the two concepts have been proved. In this short article, we manage to recount some relations between the two concepts. We also obtain another result. Wc know that if{λ_i}_(i∈Λ)be a family of stopping line, and Λ is a countable index set, λ_i must be a stopping line; if Λ is not a countable index set, what is the λ_i ? Here wc will point out that λ_i is a stopping line too.     

Fixed Point Theorems on a Non-convex Set

ＦｉｘｅｄＰｏｉｎｔＴｈｅｏｒｅｍｓｏｎａＮｏｎ－ｃｏｎｖｅｘＳｅｔ￥ＺｈａｏＸｉａｏｑｕａｎ（赵晓全）ａｎｄＳｕｎＸｕｅｓｉ（孙学思）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃａ，ＨａｒｂｉｎＩｎｓｔｉｔｕｔｅｏｆＥｌｅｃｔｒｉｃａｌＴｅｃｈｎ...     

Equivalence Relations from a Geometrical Point of View

ＥｑｕｉｖａｌｅｎｃｅＲｅｌａｔｉｏｎｓｆｒｏｍａＧｅｏｍｅｔｒｉｃａｌＰｏｉｎｔｏｆＶｉｅｗ￥ＣｈｅｎＺｈｅｎｇｔｉｎｇ（ＬｕｏｙａｎｇＥｄｕｃａｔｉｏｎａｌＩｎｓｔｉｔｕｔｅ）Ａｂｓｔｒａｃｔ：ＷｅＰｒｏｖｅａｔｈｅｏｒｅｍａｂｏｕｔｔｈｅｇｅｏ...     

Vietoris–Rips Complexes of Planar Point Sets

Fix a finite set of points in Euclidean n-space \mathbbEⁿ\mathbb{E}^{n} , thought of as a point-cloud sampling of a certain domain D ì \mathbbEⁿD\subset\mathbb{E}^{n} . The Vietoris–Rips complex is a combinatorial simplicial complex based on proximity of neighbors that serves as an easily-computed but high-dimensional approximation to the homotopy type of D. There is a natural “shadow” projection map from the Vietoris–Rips complex to \mathbbEⁿ\mathbb{E}^{n} that has as its image a more accurate n-dimensional approximation to the homotopy type of D.     

Fixed Point Tehorems in Fuzzy Inner Product Spaces

In this paper, we obtain some new fixed point theorems in fuzzy-Banach spaces by considering the t-norms of h-type and a linear mapping of weakly demicompact.     

Critical Point Theorems and Applications to Differential Equations

This paper contains a generalization of the well-known Palais-Smale and Cerami compactness conditions. The compactness condition introduced is used to prove some general existence theorems for critical points. Some applications are given to differential equations.     

The Fixed Point Theorem for Some Contraction Mappings

The fixed point theorem has many important application in the theory of differential equations. The book of Kolmogorov and Fomin [9] provides excellent illustration of the use of fixed point theorem in analysis. Various contraction mappings and their fixed point theorem are given in B.E. Rhoades [10].     

Explicit Hierarchical Fixed Point Approach to Variational Inequalities

An explicit hierarchical fixed point algorithm is introduced to solve monotone variational inequalities, which are governed by a pair of nonexpansive mappings, one of which is used to define the governing operator and the other to define the feasible set. These kinds of variational inequalities include monotone inclusions and convex optimization problems to be solved over the fixed point sets of nonexpansive mappings. Strong convergence of the algorithm is proved under different circumstances of parameter selections. Applications in hierarchical minimization problems are also included.     

Fixed Point Theorems of Mixed Monotone Operators with Applications

61.IntroductionThefixedPOinttheoremsofmixedmonotoneoperatorsaregotinpaper[1jandF2j-Inthispaper,regularconeanddemicontinuousofoperatorareweakenedinTheorem1ofpaper[1j.Theformerisweakenedtonormalconeandthelattertoweakerandweakercontinuous.Separabilityandweaklysequentiallycompactofimagesetofoperatorareweakenedtoquasi-separabilityandquasiweaklysequentiallycompactinTheorem1ofpaper[2j,Westillget'thefixedpointtheoremsofmixedmonotoneoperators.Wea1sogiveson1eapplicationstono11-monoteoperatorsanddiffe…     

Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces

The purpose of this paper is to introduce some types of compatibility of maps, and we prove some common fixed point theorems for mappings satisfying some conditions on intuitionistic fuzzy metric spaces which defined by J.H.Park.     

Packing Constant and Strong Extreme Point in Orlicz Spaces

Packing constant is an important and interesting geometric parameter.Packingconstant A_x of Banach space is a real number such that if r≤A_x,then a infinitenumber of spheres of radius r can be packed in the unit ball U(X),and if r>A_x,only a finite number of spheres can be done.It began in the 1950 studyingpacking constant of special sequence spaces.Rankin found A_2 and A_p of space l_2and l_p(p>1)respectively in 1955 and in 1958.In 1976,Cleaver discussed Orliczsequence space equipped with Orlicz norm [l_M, ||·||_M]·under a strong condition,     

The Soft Point and Its Applications in Body Falling

From the mesoscopic point of view, a definition of soft point is introduced by considering the attributes of geometric profile and mass distribution. After that, this concept is used to develop the soft matching technique to simulate the chaotic behaviors of the equations. Especially, a tennis model with deformation factor a(t) is proposed to derive a generalized Newton-Stokes equation v′(t) = λ(v T-a(t)v(t)). Furthermore, a concept of duality of deformation factor a(t) and velocity v(t) with re...