A Note on Single Machine Scheduling with Coefficient of Completion Time Variation Minimization

1.IntroductionGivenasetN~{1,2,...,n},n>1,ofindependentandsimultaneouslyavailablejobswhicharetobeprocessednonpreemptivelyonasinglemachine,jobirequiresapositiveprocessingtimepiandisassignedapositiveweightfi,iEN.Let11bethesetofn!possiblepermutationsofintegers1,2,...,n,and7~{[l],[2]!...I[n]}E11beajobsequencewhichdenotesthatjob[k]isthekthjobtobeprocessedonthemachine.Assumethatthemachinestratstoprocessthefirstjobattimezero.TheproblemistofindajobsequenceT*E11tominimizewhereC[i]isthecompletiontime…     

增算子不动点的迭代求法及其应用

设E是Banach空间 ,本文在空间C[I,E]中得到了若干新的增算子不动点的存在性定理及其不动点的迭代求法 .作为应用 ,我们研究了Banach空间上非线性积分方程最大解和最小解及其单调迭代方法     

A QP-FREE AND SUPERLINEARLY CONVERGENT ALGORITHM FOR INEQUALITY CONSTRAINED OPTIMIZATIONS

1 IntroductionConsider tl1e optimizatioll problemndn{f(x): gj(x) 5 0, j e I, x E R"}, j1)where f(x), gj(x): R" - R, j E I = {l,2,...,m}.We know tl1e quasi-Newton meth.d[1]'[9]1[5]1[1O1 is one of the most effective methods to solveproblenl (1) due to its property of superlinear convergence and is still all hot topic at presenttime, which attracts a Iot of authors to make iInprovemellt both in theory a1ld app1ication.Fechinei and Lucidi[3] in 1995 proposed a locally superlinearly convergell…     

增算子不动点定理及其对含间断项非线性脉冲方程的应用

设E是Banach空间,本文在比C[I,E]更一般的Banach空间中得到了几个新的非连续增算子不动点定理.作为应用,我们研究了Banach空间中含间断项的非线性脉冲积分方程和微分方程的最大解和最小解的存在性.     

一个定理的另证与推广

文[1]给出了如下定理： 定理△ABC的内切圆与BC,CA,AB依次相切于点D，E，F，圆心为I，BC=a，CA=b。AB=c。     

一道奧数题的简证

<正>题目[1]如图1,在Rt△ABC中,已知CD为斜边AB上的高,I、I1、I2分别为△ABC、△ADC、△BDC的内心,IE⊥AB于点E,直线AI与BC、BI与AC、MN与CD分别交于点N、M、Q.证明QE∥=CI.在文[1]的证明中,作了很多辅助线,使证明过程比较迂回而繁琐.经笔者研究发现,证明此题不须作辅助线,其证明过程简洁而明快.     

四面体内心与旁心的一个有趣性质

文 [1 ]给出了三角形内心与旁心的一个充要条件 .文 [2 ]与文 [3]将其作了改进 ,文 [3]的结论简洁而明快 .即定理　设a ,b ,c为△ABC的三边 ,则点P为△ABC的内心的充要条件是aPA→ +bPB→ +cPC→ =0 .本文将此性质推广到四面体 .约定 :△表示三角形面积 ,△1 ,△2 ,△3,△4 依次表示四面体ABCD四个顶点A ,B ,C ,D所对的三角形面积 .定理 1　点P为四面体ABCD内心 (内切球球心 )的充要条件是△1 PA→ +△2 PB→ +△3PC→ +△4PD→ =0 .图 1　定理 1图证　如图 1 ,设I为四面体ABCD的内心 .延长AI交面BCD于E .设I,E到面ABC…     

在皮亚诺算术模型上方括号划分的一个定理

本文解决文献[1]中提出的问题:如果I是半正则的,m,n∈ω,则I→[I]_m~n(?)I→[I]_(m 1)~(n 1),下文中所引用的术语和记号在[1]—[3]中均可找到。引理1 如果I是半正则的,I→[I]_m~n,则I→[I]_(m 1)~n。证.设F:[I]~n→(m 1)是规则划分函数,定义函数G如下:     

Linear Oprator Between D[a, b]and A Banach Space E

Let g(t) denote an element of D[a, b] which is the space of all functions having discontinuities of the first kind. Theorem I . Every Iinear continuous oprator T from E to D[a, b], may be expressed by an abstract functionft Whose Values Iie in E and Which is Weakly quasicontinuous, and ‖T‖= sup ‖f_t‖.     

度量空间中的完全覆盖定理

<正> 文[1]给出了如下概念和定理: 定义1 [a,b]的一个闭子区间族C叫做[a,b]的一个完全覆盖,如果对每个x属于[a,b]都存在一个正数δ_x,使对[a,b]的每一个包含x的闭子区间I,当I的长度|I|小于δ_x时,I属于     

Common fixed point theorems of Gregus type for weakly compatible mappings satisfying generalized contractive conditions

We prove a common fixed point theorem of Gregus type for four mappings satisfying a generalized contractive condition in metric spaces using the concept of weak compatibility which generalizes theorems of [I. Altun, D. Turkoglu, B.E. Rhoades, Fixed points of weakly compatible mappings satisfying a general contractive condition of integral type, Fixed Point Theory Appl. 2007 (2007), article ID 17301; A. Djoudi, L. Nisse, Gregus type fixed points for weakly compatible mappings, Bull. Belg. Math. Soc. 10 (2003) 369-378; A. Djoudi, A. Aliouche, Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl. 329 (1) (2007) 31-45; P. Vijayaraju, B.E. Rhoades, R. Mohanraj, A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 15 (2005) 2359-2364; X. Zhang, Common fixed point theorems for some new generalized contractive type mappings, J. Math. Anal. Appl. 333 (2) (2007) 780-786]. We prove also a common fixed point theorem which generalizes Theorem 3.5 of [H.K. Pathak, M.S. Khan, T. Rakesh, A common fixed point theorem and its application to nonlinear integral equations, Comput. Math. Appl. 53 (2007) 961-971] and common fixed point theorems of Gregus type using a strict generalized contractive condition, a property (E.A) and a common property (E.A).     

Einige Eigenschaften monotoner Matrizen

In [5]Ky Fan derived several theorems on real square matrices from well-known covering theorems on simplexes given byE. Sperner [13] andB. Knaster-C. Kuratowski-S. Mazurkiewicz [9]. In this note some theorems on monotone matrices and nonsingularM-matrices are presented which extend some ofFan's results. The proofs will be based on certain topological theorems on simplexes which were recently established by the author in [12] and which include the mentioned covering theorems.     

One-dimensional maps via complex analysis in several variables

In this article we use elements from the theory of several complex variables to establish dynamical properties of certain one-dimensional maps (e.g. decay of correlations, central limit theorems, etc.). I am grateful to David Ruelle for introducing me to the Bochner theorem in September 1984 and for making a copy of his article [15] available to me prior to publication. I would also like to thank S. Krantz, E. Bedford and H. Weiss for advice on the complex analysis and G. Keller for comments on interval maps. The author currently holds a Royal Society University Research Fellowship.     

Some common fixed point theorems for weakly compatible mappings

Jungck's [G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986) 771-779] notion of compatible mappings is further extended and used to prove some common fixed point theorems for weakly compatible non-self mappings in complete convex metric spaces. We improve on the method of proof used by Rhoades [B.E. Rhoades, A fixed point theorem for non-self set-valued mappings, Int. J. Math. Math. Sci. 20 (1997) 9-12] and Ahmed and Rhoades [A. Ahmed, B.E. Rhoades, Some common fixed point theorems for compatible mappings, Indian J. Pure Appl. Math. 32 (2001) 1247-1254] and obtain generalization of some known results. In particular, a theorem by Rhoades [B.E. Rhoades, A fixed point theorem for non-self set-valued mappings, Int. J. Math. Math. Sci. 20 (1997) 9-12] is generalized and improved.     

New fixed point theorems for <Emphasis Type="Italic">P</Emphasis><Subscript>1</Subscript>-compact mappings in Banach spaces

E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.     

Rings characterized by injectivity classes

Recently, there are a number of well known theorems which char­acterize rings in terms of injective modules (cf. [2], [3], [5] and [8]). The purpose of this paper is to give general theorems which show that some similar results remain true when many other classes of general injective modules are considered in place of injective modules. Our results encompass several well known results by Huynh and Smith, Liu, and Xue. In particular we answer negatively the question of Yue Chi Ming [11] and an example is given to show that E—injective modules form an intermediate class between continuous and quasi-continuous modules(cf. Example 3).     

Positional dimension-like functions of the type Ind

In Iliadis (2005) [4] positional dimension-like functions of the type ind are given. All these functions are studied only with respect to the property of universality. In a later paper by the present authors, and in two papers by V.V. Tkachuk (1981, 1982) (see [7] and [8]), these dimension-like functions have been studied with respect to the other standard properties of dimension theory. In R. Koga, Subspace-dimension with respect to total spaces, Master Thesis, Osaka Kyoiku University, 1998 (see also K.P. Hart, Jun-iti Nagata, J.E. Vaughan, Encyclopedia of General Topology, Elsevier Science Publishers, B.V., Amsterdam, 2004) a positional dimension-like function of the type Ind is given. Here we define new positional dimension-like functions of the type Ind, and present for all these functions, theorems concerning subspace theorems, partition theorems, sum theorems, and product theorems. Finally, we give some open questions concerning these functions.     

Approximating fixed points of Suzuki-generalized nonexpansive mappings

In this paper, we prove weak and strong convergence theorems for Ishikawa iteration of Suzuki-generalized nonexpansive mappings in uniformly convex Banach spaces. Furthermore, we extend the results to CAT(0) spaces. Our work extends the results of Suzuki [T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mapping, J. Math. Anal. Appl. 340 (2008) 1088–1095] and Takahashi and Kim [W. Takahashi, G.E. Kim, Approximating fixed points of nonexpansive mappings in Banach spaces, Math. Jpn. 48 (1998) 1–9].     

Fixed point theorems for nonexpansive mappings

In this paper, we shall extend two fixed point theorems of F. E. Browder [4, Corollary to Theorem 1] and J. T. Markin [6, Theorem 1].