The U—property of Orlicz Sequence Spaces

LetXbeaBanachspace,X'bethedualofX,S(X)={xeX:IIxII=l},B(X)={x6X:llxIlS1}betheunitsphereandunitballofX,respectively.ForxeX,let7xdenotethesetofsupportingfunctionalsfofS(X.)atx.Inl978,LauKa-singintroducedthefollowingnotiontostudytheChebyshevsubsetofX[1j:DefinitionABanachspaceXissaidtohaveU-propertyifforanyE>O,thereexists3>osuchthatSomeoftheresultsofU-propertyin[ljaresummarizedinthefollowing.Theorem(I)IfXhasU-property,thenXisuniformlynonSquare,inparticular,Xissuper-reflexive(infactr…     

Some Characterizations of Nil Ideals in BCI—algebras

51.IntrodcutionIn[1j,thenotionsofnilidealinBCI-algebrasandinlBCI-algebrawereintreduced.WeshowthatnilBCI-algebraisageneralizationofassociativeandquasi-associativeBCIalgebra([2J,[3j).lnthispaper,somecharacterizationsofnilidealsinBCI-algebraswereproved.Moreover,theBCI-algebrassatifyingO*x.=xwerediscussedandvariousproPertieswereproved.Werecallsomedefinitionsande1ementaryproperties.ThefollowingsaretrueinaBCI-al-gebra:(l)x o=x;(2)(x*y)*z=(x z) y;(3)x相似文献   

k—严格凸与k—UR空间

本文讨论k—严格凸Banach空间的各种性质,并证明,对于有限维空间,k—严格凸与k—UR是等价的.另外若x,Y分别是k₁—严格凸k₂—严格凸的Banach空间,11+k₂-1)—严格凸的Banach空间.     

Approximation Properties of a Special Class of Mathematical Expectation Operators

61-IntroductionLet(X.}"cNbeasequenceofindependentrandomvariableseachhavingthesamelatticepointdistributionwithprobabilityfunctionP(X,=a kh)=P*,expectationEX"=),l(x)andvarianceE(X"-ax")'=a2(x).WhereKeZ:={o,tl,l2,..'},a,harethepositivecon-stants,xeI=Y'=Ri8arealcontinuousparameter.LettheprobabilitydistributionofS,=ZX,beForacontinuousfunctionfontheinterval7'(possiblyinfinite)definethemathematicalex-pectationoperatorRemarks(l)UsingChebychev,sinequalitywegeteasily.(See[1,P,,,f,,.j)-(2)Manyo…     

有向图的L(j,k)数的上界

给定正整数j≥k,有向图D的一个L(j,k)-标号是指从V(D)到非负整数集的一个函数f,使得当x在D中邻接到y时|f(x)-f(y)|≥j,当x在D中到y距离为二时|f(x)-f(y)|≥k.f的像元素称为标号.L(j,k)一标号问题就是确定(?)j,k-数(?)j,k(D),这个参数等于(?) max{f(x)|x∈V(D)},这里f取遍D的所有L(j,k)-标号.本文根据有向图的有向着色数及最长有向路的长度来研究(?)j,k-数,证明了:(1)对任何有向着色数为(?)(D)的有向图D,(?)j,k(D)≤((?)(D)-1)j;(2)对任何最长有向路的长度为l的有向图D,如果不含有向圈或者D中最长有向圈长度为l 1,则(?)j,k(D)≤lj.并且这两个界都是可达的.最后我们对l=3的有向图给出了3j-L(j,k)-labelling的一个有效算法.     

糙度和k—覆盖图

一、引言 我们所考虑的图是指没有环和重边的有限无向图。在本文中未加说明的定义和记号请参见文献[2]。设G是一个具有顶点集V(G)和边集E(G)的图。对V(G)的一个子集S,用G[S]表示G的由S导出的子图且令G—S=G[V(G)\S]。若G[S]不含边,则称S为独立集。我们用d_G(x)表示G中顶点x的次数,用Γ_G(x)表示G中与顶点x邻接的顶点集合。对令.我们分别用△(G)和ω(G)表示G的顶点的最大次数和连通分支数。若对任意的且ω(G—S)>1有     

Generalized Convexity and Generalized Quasi—variational Inequality

51.PreliminaryLetXbeaset.Througho11ttl1lspaperweshalldenoteby2xthefaruilyofallsubsetsofX,by(X)thefamilyofallnoneruptyfinitesuhsetsof'X.lfXlsasul,setofavectorspace,co(X)denotestheconvexhu1lofX.IfXisatopologicalspaceandA=X,thenwedenotebyintx(A)theil1teriorofAinXandc.l.(A)theclosureofAinXrespectively.Definitionl.1LetXandYl)etoI3ologicalspacesandT:X-2"isaset-vail1edmapping.(i)Tissaidtobeuppersemicontin\1ous(resp.lowersemicontinuo1Js)atxo6X,ifforeachopensetGinYwithG=T(x,)(resI3.Gn7'(x,…     

一致光滑Banach空间中Φ-半压缩映象的不动点的迭代逼近

1　引言与预备知识设X为实Banach空间,X*为其共轭空间.正规对偶映象J:X→2X*定义为:Jx={x*∈X*:〈x,x*〉=‖x‖2=‖x*‖2},其中〈·,·〉表示广义对偶组.熟知,若X*为严格凸的,则J为单值正齐次的;若X*为一致凸的(等价地,X为一致光滑的),则J在X的任何有界子集上是一致连续的.我们用j表示单值的正规对偶映象.用R+表示正半实轴.以F(T)表示T的不动点集,即F(T)={x∈D(T):Tx=x}.映象T:D(T)X→X称为φ-半压缩的,如果F(T)≠,且存在严格增加函数φ:R+→R+,φ(0)=0,使得x∈D(T),y∈F(T),相应地存在某j(x-y)∈J(x-y)满足不等式〈Tx-y,j(…     

可极化Carnot群上一类非散度型方程的非平凡解

§1Introduction WebeginbyquotingsomepreliminaryfactsontheCarnotgroupandreferthein estedreaderto[1-3]formorepreciseinformationonthissubject.ALiegroupG=(Rn,o)isaCarnotgroupifthefollowingproperties(G1)(G2)hold.(G1)RncanbesplitintorsubspacesRn=Rn1×...×Rnrandthedilations(δλdefinedbyδλ(x)=(λx(1),λ2x(2),...,λrx(r)),x(j)∈Rnj areautomorphismsofG.(G2)TheLiealgebragofGisgeneratedbytheleftinvariantvectorfieldsX1,.Xn1satisfying Xj(0)=xj,j=1,...,n1.Thenaturalnumbersrand Q=n1+2n2+...+rnr…     

A CLASS OF NONLOCAL BOUNDARY VALUE PROBLEMS OF NONLINEAR ELLIPTIC SYSTEMS IN UNBOUNDED DOMAINS

We consider the following boundary value problem ill the unbounded donain Liui = fi(x,u, Tu), i = 1, 2,' ! N,x E fl, (1) olLi "i0n Pi(x)t'i = gi(x,u), i = l, 2,',N,x E 0fl, (2) where x = (x i,', x.), u = (u1,' f uN), Th = (T1tti,', TNi'N) and [ n. 1 L, = -- I Z ajk(X)the i0j(X)C], Li,k=1' j=1 J] l Ltti = / K(x,y)ui(y)dy, x E n. jn K(x, y)ui(y)dy, x E n. Q denotes an unbounded dolllain in R", including the exterior of a boullded doinain and 0…     

多目标规划的ak—较多有效点与ak—较多最优点

在[1]中,作引入了多目标规划的较多有效点及较多最优点的概念,并讨论了它们的性质,本首次提出了ak-较多有效点与ak-较多最优点的概念,并讨论了ak-较多有效点,ak-较多最优点、ak-较多有效解,ak-较多最优解的相关性质。     

区间映射的链回归点的可链点集

主要讨论区间映射的链回归点的可链点集与链等价集的关系,证明了:若区间映射的拓扑熵是零,则它的链回归点的可链点集与链等价集相等.此外还得到了区间映射有正拓扑熵的几个等价条件.     

圆柱面绕任意轴回转形成的包络面分析

在分析及计算椭圆上距离任意已知点最远或最近的点基础上,分析了最远点及最近点在圆柱面绕任意轴回转形成包络面过程中的作用,从而由最远点及最近点的计算公式导出了多种形式的包络面方程,并由此找出了包络面受各种因素影响的规律.     

正态分布在学生学习成绩评估中的应用

本文将正态分布应用于学生学习成绩评估中，将原始分数转换为标准分数后，各科的分数方可比较或相加，从而改变了将原始分数直接相加比较的那种不够科学也不甚合理的传统做法。     

不动点在讨论驻点存在性问题中的应用

本文通过建立不动点与驻点之间的关系，从而利用不动点的存在性来确定函数驻点的存在性。     

A short note about exposed points in real banach spaces

We express the set of exposed points in terms of rotund points and non-smooth points.As long as we have Banach spaces each time＂bigger＂,we consider sets of non-smooth points each time＂smaller＂.     

关于有效点与真有效点的几个定理

本文推广了Ｂｅｎｓｏｎ真有效点的定义，给出了凸锥相对内部的一个刻划，并在无尖性假设情况下，利用凸锥相对内部的刻划，证明了Ｈａｒｔｌｅｙ真有效点与改进的Ｂｅｎｓｏｎ真有效点是等价的；同时给出了一些有效点与真有效点标量化的一些结果．     

一种基于二部图的试题知识点标注方法

针对在线教育中试题知识点自动标注问题,本文提出了一种基于二部图的试题知识点标注方法。首先,为了合理划分知识点粒度,本文构建了知识点知识图谱来融合知识点;其次,基于教材等语料抽取知识点与特征词二部图和试题与特征词二部图,并利用TF-IDF公式计算知识点与特征词、试题与特征词之间的边权,以构建试题-知识点二部图模型;再次,提出词频加权的相似性度量方法计算试题和知识点之间的相似度,将相似度最高的知识点作为试题知识点标签。最后,以某在线教育平台提供的高中历史试题为实验数据集进行数值实验,实验结果表明该方法的效果显著优于朴素贝叶斯、K最近邻、随机森林以及支持向量机。     

A result in asymmetric Euclidean Ramsey theory

It is proved that if the points of the three-dimensional Euclidean space are coloured with red and blue, then there exist either two red points at unit distance, or six collinear blue points with distance one between any two consecutive points.     

A branch-and-cut-and-price approach for the pickup and delivery problem with shuttle routes

The Pickup and Delivery Problem with Shuttle routes (PDPS) is a special case of the Pickup and Delivery Problem with Time Windows (PDPTW) where the trips between the pickup points and the delivery points can be decomposed into two legs. The first leg visits only pickup points and ends at some delivery point. The second leg is a direct trip – called a shuttle – between two delivery points. This optimization problem has practical applications in the transportation of people between a large set of pickup points and a restricted set of delivery points.