ON TOPOLOGICAL LINEAR CONTRACTIONS ON NORMED SPACES AND APPLICATION

51.IntroductionandPreliminariesThroughoutthispaper(X,11'if)denotesanormedspaceandN(11'II)denotesthecollectionofallnormsonXwhichareequivalentto11'11.Foreach11'if'6N(II'II)andeachr>0,letX.(ll'II')~{xEX:Ilxll'5r}andX?(ll'if')~{xEX.Ilxll'相似文献   

ON THE CONSISTENCY OF CROSS-VALIDATION IN NONLINEAR WAVELET REGRESSION ESTIMATION

1IntroductionConsidernonparametricregressiollwherextli=;E[O,1],En1,.',Ejl1larei.d.d.errorswitl11llea11o,a11dgisanunkl1ownfunctiontobeestimated-Nouparametricregressionestil11ationaimstoesti111atetl1euukllow11regressionfunctiong(x).Tl1enolllinearwaveletesti111atorshavebeenintroducedalldstudiedbyDonoho(1995).DonohoandJohnstoue(1994,1995).Do11oho,Johnstolle-KerkyachariallandPicard(1995)andDelyollandJuditsky(l996).Tl1eseauthorshavedenlo11stratedthevirtuesofllonlineaxwaveletmetl1odsf1o1llthev…     

STRONG LAW OF LARGE NUMBERS AND SHANNON-MCMILLAN THEOREM FOR MARKOV CHAINS FIELD ON CAYLEY TREE

1 lntroductionA tr(t(t is a grapl1 G = {T, E) wllicl1 is co1l11ected a11d colltai1ls no cir(.uits. Give11 a11y twov(irtic'is 't / P E T, let crP bc tl1e ullique patl1 col111ecti11g,v aIld /]. Defille tl1e graph distal1cc(l(rr, p) to hc the Ilu1llber of edges co11tained in the path crP.We discuss ulainly tl1e rooted Cayley tree TC,2(i.e.,binary tree. See Fig.1). In tlle Cayleytree Tc,2,tl1e root (denoted by 0) llas OIlly two 11(tiglll)(irs al1d all otller vertices have threeneighbors. A…     

THE FINITE ELEMENT METHOD FOR SEMILINEAR PARABOLIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS

1.IntroductionLetxbepointsonplaneR',andfibeapolygonaldomain,wedenotetheboundaryoffibyOff.Thereinfiarefinitemanybrokelineswhichdivideitilltofinitepolygonalsubdomainsall,I=1,''jL.Thefunctionp(x)EL'(fl)isassumedtohaveboundedfirstderivativesinallsubdomainsall,whilepisallowedtobediscontinuousontheinterfacesoflinOflj.AndthereexistsapositiveconstantTsuchthatp(x)2T)Vxefi.WeadopttheusualnotationsoftheSobolevspacesinthispaper,thatis,denotebyH'(fl)andHI(fl)thespacesand11'11.thenorms,l'1.theseminor…     

A Solution of Inverse Eigenvalue Problems for Unitary Hessenberg Matrices

Let H∈Cn×n be an n×n unitary upper Hessenberg matrix whose subdiagonal elements are all positive. Partition H as H=[H11 H12 H21 H22],(0.1) where H11 is its k×k leading principal submatrix; H22 is the complementary matrix of H11. In this paper, H is constructed uniquely when its eigenvalues and the eigenvalues of (H|^)11 and (H|^)22 are known. Here (H|^)11 and (H|^)22 are rank-one modifications of H11 and H22 respectively.     

The Higher Derivatives of Bianalytic Functions

Bianalyticfunctionsisanewkif1doffunctionspresentedrecently-PapersL1j'[2Jdls-cussedson1ebaslcpropertiesofbianalyticfunctions-Inthispaper,wewillgetthehigherdt'rivD'-tivesandWeierstrassTheorembytheresultsofpapers[lj.[2j.5l.TheFormulaofHigherDerivativesFromF2j,wehavetherepresentatlonformulaofbianalytlcfu11ctionsProvidedthattheintegralcanbedifferentiatedunderthesignofintegrationwefi11dFronlti1edefinitionofthe(ierivativeofl)ia11alyticfu11ctionlwehaveWearegoingtc)IJrovetlIeaboveformulainfollowi…     

A FINITE DIMENSIONAL METHOD FOR SOLVING NONLINEAR ILL-POSED PROBLEMS

1.IntroductionInthispaperweconsiderthenonlinearproblemsoftheformF(x)=co,(1)whereF:D(F)CX-- YisanonlinearoperatorbetweenrealHilbertspacesXandYandcoER(F).ThenormsinXandYwillbedenotedby11'IIxand11'flyrespectively.Wearemainlyinterestedinthoseproblemsofth...     

p为偶数时p-级数的和

推导p-级数∑∞n=11np在p=4,6,8情形下的和,并给出∑∞n=11(2n-1)2k(k∈瓔*)的递推计算公式,进而得出∑∞n=11n2k(k∈瓔*)的和.结果显示,∑∞n=11n2k的和与π2k成正比.     

Subspace subcodes of generalized reed-solomon codes

1. IntroductionTlle subfield subcodes of RS Cud('s a11(l tl1" tra('e-sIlurtened RS codes are introducedill [1] al1d [2], respe(!tiv'lly. II1 [3] the subsI)acc subcodes ()f RS codes over GF(2"') areintrodllced, which caIl be rcgarded as a ge11eralizatio11 of the subfield subcodes of RS codesa11d tlle trace-shorte1led RS codes, a11d tl1c fOrll1ulas t() ('oIllI)llte tl1e diInensions of thesubsPace subc(,des ()f RS c()des ()ver GF(2"' ) are given. llut what we call get if, i11stead ()fR…     

争鸣

问题问题97数列{an}中,a1=2,2an=an-1 an1-1(n≥2),求an.解由特征方程2x=x 1x得x=±1.∴2(an-1)=an-1 a1n-1-2=(ana-n1--11)2(1)2(an 1)=an-1 a1n-1 2=(ana-n1- 11)2(2)由((21))得aann -11=(aann--11 -11)2=[(aann--22- 11)2]2n-1=(aann--22 -11)4=…=(aa11- 11)2n-1.∵a1=2,∴aann- 11=(13)2n-1,即an=21-3-2n-1-1.上面解法是找特征根后,通过化简变形后得出规律的.但递推式变为:3an=an-1 an1-1(n≥2)后,用上面方法失效.我也曾试过好多种方法均告失败.请同行们参与讨论:“已知数列{an}中,a1=2,3an=an-1 an1-1(n≥2),求an”问题.an怎样求呢?是…     

L^∞（G）中的一个闭凸不变集

设G是局部紧群,f是G上的右一致连续函数.本文讨论L(G)中一个闭凸不变集的关系式Co{Lxfx∈G}11@11={φ*fφ∈P＇(G)}11@11(f∈R∪C(G)).由此式易得出RUC(G)上的左不变平均与拓扑左不变平均的等价关系.     

L~∞(G)中的一个闭凸不变集

设 G是局部紧群 ,f 是 G上的右一致连续函数 .本文讨论 L∞ (G)中一个闭凸不变集的关系式Co{ Lxf :x∈ G} 11· 11∞ ={* f∶∈ P′(G) } 11· 11∞ (f∈ R∪ C(G) ) .由此式易得出 R∪ C(G)上的左不变平均与拓扑左不变平均的等价关系 .     

ON A THEOREM OF BERNSTEIN AND ITS APPLICATIONS TO WEIGHTED MINIMAX SERIES

1.IntroductionLetfbeacontinuousfunctionon[a,b].L[.willdesignatethesetofallpolynomialsofdegreelessorequalthannand11thesetofallpolyflomials.Asiswellknown,foreachntheminimaxoffisgivenby:wherepnisthebestuniformapproximationoffin11..LetusalsoconsidertileminimaxseriesgivenbytheexpressionThesetoffunctionsforwhichS*(f)=ZEd(f)相似文献   

两道不等式题的统一推广

本短文旨在建立以下命题　已知ｘ ,ｙ∈Ｒ+ ,且ｘｙ =1.若λ >1,则 11+λｘ+ 11+λｙ≥ 2λ + 1;若 0 <λ <1,则 11+λｘ+ 11+λｙ≤ 2λ + 1.证　 11+λｘ + 11+λｙ =2 +λ(ｘ + ｙ)(1+λｘ) (1+λｙ)= 2 +λ(ｘ + ｙ)λ2 + 1+λ(ｘ + ｙ) =1- λ2 - 1λ2 + 1+λ(ｘ + ｙ) .λ>1时 ,11+λｘ+ 11+λｙ≥ 1- λ2 - 1λ2 + 1+ 2λｘｙ=1- λ2 - 1(λ + 1) 2 =2λ + 1;0 <λ <1时 ,11+λｘ + 11+λｙ ≤ 1-λ2 - 1λ2 + 1+ 2λｘｙ=2λ + 1.所以 ,命题成立 .于命题中取λ =2 ,ｘ =ｂａ ,ｙ =ａｂ (ａ ,ｂ∈Ｒ+ )和λ =12 ,可分别得到文 [1]中…     

MULTIPLIERS AND TENSOR PRODUCTS OF WEIGHTED L~p-SPACES

1 IntroductionLet G be a locally compact uninrodular gloup witI1 Haar nseasure dx. In this paperCo (G) deuotes the spare of colltillou8, comPlex-valued functiolls oll G which vanish at illfillityand Cc (G) de11otes the 8pace of all contiuuous, complexvaued function8 oll G wit11 colllpactsllpport. Tlle left (right) trall8latiou operators Ly (%) are giveu byL.f(x) = f (y--'x), (Ruf(x) = f(xy)) for x,y E G.For a Beurliug weight function on G (ffeiter, t10]) i.e. a conti11uou8 f1lllction w …     

ON UNIVALENT BLOCH FUNCTIONS

Let A = {z: lzl < 1} be the unit disk of complex plane C. For a 6 A, let W.(z) = isbe the M5biu8 transfOrlnation of A and let g(z, a) = log Ieel be the Green's functiou on Awith logarithlllic sillgularity at a E a. FOr 0 < p < oo, tl1e space Q. consists of all fuuctiolls fa11alytic il1 A for w11ichsup / I If'(z)l'(g(z, a))P dA(z) < oo, (1)aea j ja If'(z)l'(g(z, a))P dA(z) < oo, (1)wllere dA(z) is tlle Euclidcan area eIelllent o11 A.Q.-spaces have been i11vestigated by n1any authors (…     

一个不等式的简证及其几何直观

文 [1 ]对不等式2 (n 1 - 1 ) <∑nk=11k<2 n - 1(n >1 )进行了指数推广 ,其结果是 :定理　 11 - p[(n 1 ) 1-p - 1 ]<∑nk=11kp<11 - p. n1-p - 11 - p 1(p∈ R且 p >0 ,p≠ 1 ,n >1 ) .上述定理证明的依据是如下两个引理 :引理 1　 1kp <11 - p[k1-p - (k -1 ) 1-p]　 (p∈ R且 p >0 ,p≠ 1 ,k >1 ) .引理 2　 1kp >11 - p[(k 1 ) 1-p -k1-p]　 (p∈ R且 p >0 ,p≠ 1 ,k≥ 1 ) .文 [1 ]的证明方法是借助于算术—几何均值不等式 ,分 0

1进行讨论证明 ,读者不难看出 ,不仅过程繁琐 ,而且对其证明思路难以把握 .文 [2 ]中利…     

一道课本习题结论的推广

人教版全日制普通高级中学教科书(必修),《数学》第一册(上)中,复习参考题三,B组第4题是:有两个等差数列{an},{bn},满足ba11 ba22 …… bann=7nn 32,求ab55的值.解答如下:ab55=22ab55=ab11 ab99=92×(a1 a9)92×(b1 b9)=ab11 ab22 …… ba99=7×99 3 2=1625,现将本题的结论作如下推广.结论1若两等差数列{an},{bn}的前n项和分别为Sn,Tn,且TSnn=cann db(ac≠0),则bann=ST22nn--11=ca××((22nn--11)) db.证bann=22abnn=ab11 ab22nn--11=2n-12×(a1 a2n-1)2n-12×(b1 b2n-1)=TS22nn--11=ca××((22nn--11)) db,结论2若两等差数…     

一个六点九边图的图设计

令Kv表示v个顶点的完全图,G是一个不含孤立点的简单连通图.一个v阶的G-设计是将Kv划分成互不相交的子图,使得每个子图都和G同构,记为G-GD(v).研究六点九边图G11的图设计存在性问题.利用标准的递推构造并结合必要的直接构造,证明除去G11-GD(9)不存在以及G11-GD(18)的存在性未知外,G11-GD(v...     

A SIMPLE PROOF OF THE INEQUALITY FFD (L)≤11/9 OPT(L) 1, ■L FOR THE FFD BIN-PACKING ALGORITHM

The first fit decreasing (FFD) heuristic algorithm is one of the most famous and moststudied methods for an approximative solution of the bin-packing problem. For a list L, letOPT(L) denote the minimal number of bins into which L can be packed, and let FFD(L)denote the number of bins used by FFD. Johnson showed that for every list L, FFD(L)≤11/9OPT(L) 4. His proof required more than 100 pages. Later, Baker gave a much shorterand simpler proof for FFD(L)≤11/9OPT(L) 3. His proof required 22 pages. In this paper,we give a proof for FFD(L)≤11/9 OPT(L) 1. The proof is much simpler than the previousones.