LINEAR COMPLEXITY AND RANDOM SEQUENCES WITH PERIOD 2~n

Let (?)=(S,S,…)be a binary random sequence with period N=2~n,where S=(S_0,…,S_(N-1))is its one period with N independent and uniformly distributed binary random variables.The main results of this paper are as follows.1)Var c(?)=2-(2N+1)2~(-N)-2~(-2N);2)E|c(?)-c(?)|=[2~(c(?)+1)-2]2~(-N)for any sequence (?) with period 2~n;3)N-1+2~(-N)-(n/2+1-2~(-(N-n)))≤E[(?)c(?)]≤N-1+2~(-N)4)2-2~(-(N-1))≤E[(?)|c(?)-c(?)|]≤2-2~(-N)+n/2-2~(-(N-n)),where E and Var stand for taking expectation and variance respectively,c(?) is the linearcomplexity of the sequence (?) and W(b) the Hamming weight of one period of the seqnence (?).     

SOME THEOREMS OF THE NORDHAUS-GADDUM CLASS

Let the chromatic number of G, the edge chromatic number of G and thetotal chromatic number of G be denoted by x(G), x_1(G) and x_2(G), respectively. Forany simple graph G of order p and its complement G, the following inequalities of theNordhaus-Gaddum class are obtained:(i)|2p~(1/2)|-ε_1≤x(G)+x_1(G)≤2p-2 and 0≤x(G)·x_1(G)≤(p-1)~2 for p≥2,(ii)|2p~(1/2)|+ε_1≤x(G)+x_2(G)≤2p-1 and 0≤x(G)·x_2(G)≤p(p-1) for p≥3,(iii)p≤x_1(G)+x_2(G)≤2p-1 and 0≤x_1(G)·x_2(G)≤p(p-1) for p≥3,where ε_1=0, if p~(1/2) is an odd integer, 1, otherwise,ε_2=1, if p~(1/2) is an even integer, 0, otherwise,and [x] denotes the ceiling of x. We also show that these bounds are sharp for everypositive integer p.     

A Stronger Uniform Consistency Check and Adjustment Method

1　 Uniform CheckL et a judgement matrix A=( aij) n× n.For any i,j,k=1,2 ,… ,n,if followings holdaij>0 ( 1)aij=1aji ( 2 )aijajk=aik ( 3)then AW=n W,where W=( w1 ,w2 ,… ,wn) Tis a weight vector.From the equation AW=n W,we know thata1 1 .( w1 / w1 ) a1 2 .( w2 / w1 ) … a1 n .( wn/ w1 ) =na2 1 .( w1 / w2 ) a2 2 .( w2 / w2 ) … a2 n .( wn/ w2 ) =n　　　　　　　　　　 彙　　　　　　　　n1 .( w1 / wn) an2 .( w2 / wn) … ann.( wn/ wn) =n( 4)　　 If ( 3) does not hold,then ( 4) may …     

APPROXIMATING DISTRIBUTIONS IN DISCRETE DMRL AND NBUE CLASSES

In this paper we discuss the problem of approximating distributions in certain discretelife classes.Let X be a random variable(r.v.)taking nonnegative integers,EX=μ.Suppose Yis a geometric r.v.taking nonnegative integers and with the same mean μ.Denote B_2=(?),α=1-(B_2)/(μ~2),Δ(X,Y)=(?)|P(X≥k)-P(Y≥k)|.The main results are:1)If X∈(D) DMRL (discrete decreasing mean residual life),thenΔ(X,Y)≤max(α,1-e~(-2α)).2)If X∈(D) NBUE (discrete new better than use in expectation) thenΔ(X,Y)≤max(α,1-e~(-(2α)~(1/2)).     

A New Generating Method and Its Application

1 .INTRODUCTIONGreyforecastingisoneoftheimportantelementsinthegreytheory .Ithasbeenusedinmanyfields[1 ,3] ,andalltheseapplicationsarebasedonagreymodel.Intheprocessofmodelbuilding ,usuallytherawse riesismanagedbyaccumulatedgeneratingoperation(AGO) ,thatis,letx(0 ) =(x(0 ) ( 1 ) ,x(0 ) ( 2 ) ,… ,x(0 ) (n) )bearawseries,andx(1 ) =(x(1 ) ( 1 ) ,x(1 ) ( 2 ) ,… ,x(1 ) (n) )isone orderaccumulatedgeneratingseriesofx(0 ) ,wherex(1 ) (k) = Ki=1x(0 ) (i) ,k=1 ,2 ,… ,nIfx(0 ) (k)≥ 0 ,obviously ,…     

ON NICE SEQUENCES CONCERNING HAMILTONICITY OF GRAPHS

In the paper, the (k-1)-traceable-nice ((k-1)-T-nice) and k-homogeneously-traceable-nice (k-HT-nice) sequence are defined similarly to the definition of k-Hamilton-nice (k-H-nice) and (k+1)-Hamilton-connected-nice ((k+1)-HC-nice) sequence. Therelationships among these four nice sequences are discussed. The main results are asfollows: Let_η=(a_1, a_2,…, a_(k+1) be a non-negative rational sequence, k≥2. (1) If η is(k+1)-HC-nice and a_(k+1)=2, then η is k-HT-nice, (2) If η is k-HT-nice and a_(k+1)=2,then η is (k-1)-T-nice, (3) If η is k-H-nice, then η is k-HT-nice. Meanwhile, four unsolvedproblems on these topics are proposed.     

SOME QUALITATIVE PROPERTIES OF SOLUTIONSTO A SECOND-ORDER NONLINEAR BOUNDARY VALUE PROBLEM ON[0, ∞)

1.IntroductionUtilizingthemethodofupperandlowersolutions,WangJunyu,GaoWenneandLinZhenghuahaveestablisedinarecelltpaper[1]thefollowingtheorem:Theorem1.1LetN>0and^2--1.Thenthesecond-oafednonlinearboundaryvalueproblemWesaythatafunctiony(x)isaCIsolutiontotheboundaryvalueproblem(1.1)--(1.3),ifi)bothy(x)andly'(2)I"--,y,(2)areinC'[0, co),n)theequation(1.1)issatisfiedin(0, co),andiii)y(0)=1and:hTOOxl~'] y(x)=0.Furthermore,ifthesolutiony(x)P,,,,,,WcontinuoussecondderiVativein(0, co),thenitiscal…     

A Class of Genetic Algorithms on Bilevel Multi-objective Decision Making Problem

1　ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｂｉｌｅｖｅｌｍｕｌｔｉ ｏｂｊｅｃｔｉｖｅｄｅｃｉｓｉｏｎｍａｋｉｎｇｐｒｏｂｌｅｍ[1] :ｍｉｎｘ Ｆ(ｘ ,ｙ) =ｍｉｎｘ (Ｆ1(ｘ ,ｙ) ,Ｆ2 (ｘ ,ｙ)… ,ＦＭ(ｘ ,ｙ) )　Ｍ 2　ｓ .ｔ.Ｇ(ｘ ,ｙ) 0ｍｉｎｙｉｆｉ(ｘ ,ｙｉ)　ｉ =1 ,2 ,… ,Ｐ　ｓ .ｔ.ｇｉ(ｘ ,ｙｉ) 0　ｉ =1 ,2 ,… ,Ｐ ( 1 )ｗｈｅｒｅｘ =(ｘ1,ｘ2 ,… ,ｘＮ)ａｎｄ ｙｉ=( ｙｉ1,ｙｉ2 ,… ,ｙｉｎｉ)ｓｔａｎｄｆｏｒｔｈｅｄｅｃｉｓｉｏｎｖａｒｉａｂｌｅｏｆｔｈｅｕｐｐｅｒ …     

语法分析中的LL预测分析器改进设计研究

编译方法中的LL(k )文法比LL(1)文法描述的语言范围宽得多 ,同时也具有直观易判定的特点。然而LL(k)分析器的构造要比LL(1)复杂得多 ,在实际的语法分析程序中未能得到广泛使用。改进后的LL(2 )分析方法大大简化了LL(2 )分析器的构造。该方法对于不满足LL(1)条件而满足LL(2 )条件的文法只是对一部分产生式采用向前看一符 ,从而提高了LL(2 )分析器的实用性     

STRONG CONSISTENCY OF THE PERIODIC SMOOTHING SPLINES

Consider the regression model Y_i=u(x_i)+ε_i,i=1,2,…,n,where u(x)∈W_(2,per)~2[0,1],x_i=(i-1)/n,{ε_i}(?)are i.i.d,random variables.We use the periodic smoothing spline u_(λp)(x)toestimate u(x).Under certain conditions,strong consistency results of u_(λp)(x)are obtained,i.e.,forall 0相似文献   

扩展的DEA模型的最优值的研究

讨论扩展的C^2GS^2(C^2R)模型的最优解的存在性，论证在一定条件下其最优值与C^2GS^2(C^2R)模型的最优值相等，讨论用扩展的DEA模型来判断决策单元的DEA有效性(C^2GS^2或C^2R)，证明若所有输入与输出都取正值，则某决策单元的阀值就等于对应的扩展DEA模型的最优值(若它存在)。     

ON NORMAL EULER NUMBERS OF EMBEDDING SURFACES INTO 4-MANIFOLDS

Let N be a closed,orientable 4-manifold satisfying H_1(N,Z)=0,and M be a closed,connected,nonorientable surface embedded in N with normal bundle v.The Euler class e(v)ofv is an element of H_2(M,(?)),where (?) denotes the twisted integer coefficients determined byw_1(v)=w_1(M).We study the possible values of e(v)[M],and prove H_1(N-M)=Z_2 or 0.Underthe condition of H_1(N-M,Z)=Z_2,we conclude that e(v)[M]can only take the followingvalues:2σ(N)-2(n+β_2),2σ(N)-2(n+β_2-2),2σ(N)-2(n+β_2-4),…,2σ(N)+2(n+β_2),where σ(N) is the usual index of N,n the nonorientable genus of M and β_2 the 2nd real Bettinumber.Finally,we show that these values can be actually attained by appropriate embeddingfor N=homological sphere.In the case of N=S~4.this is just the well-known Whitney conjectureproved by W.S.Massey in 1969.     

AHP中(0, 2)EM法与(1/9, 9)EM法的比较研究

本文通过对Saaty提出的(1/9, 9)EM法与左军提出的(0, 2)EM法的比较研究, 认为(0, 2)EM法尚存在三点不足之处：(1)判断信息的损失；(2)累积优势度的损失；(3)一致性的损失。并提出一个判别一种比较标度适应性的指标──随机序隐率。     

USING DISPLACED CONE REPRESENTATION IN DEA MODELS FOR NONDOMINATED SOLUTIONSIN MULTIOBJECTIVE PROGRAMMING

1.IlltroductionBowlin,etal.[2]extendedtheearlierworkofBowlinetal.11]aspartofaresponsetowhatseemstobeagrowinginterestintheuseofefficiencydominance--asreflected,forexampleintheworkofLoved[7],TulkensandVandenEeckaut[lo]andtheirassociates.ThefocusinBowlinetal.[2]turnedtotheuseofan11metricasabasisfor(1)measuringtheamountofefficiencydominancethatmightbepresentinanyDecisionMakingUnit(DMU)aswellasfor(2)dealingwithproblemsinvolvedinthepossiblepresenceofslackswithnon-zerovalues,--whichareimportantas…     

WHAT CAN A PRODUCT OF DISTRIBUTION ZERO AND ITSELF BE?

In this paper,it is proved that,given any standard locally Lebesgue integrable functionF(x)on R,there exist nonstandard representations f_1(x)and f_2(x)of the distribution zero,suchthat,for any φ∈(?),integral from R F(x)φ(x)dx-integral from ~*R f_1(x)f_2(x)φ(x)dx=an infinitesimal.     

REDUCED FORM OF YANG-MILLS EQUATION OFSU(2) ON R~(3,1)

1.NotationsLetR3,1betheMinkowskifour-dimensionalspacewithcoordinatesx=(x')x',x',x').ThemetricdsZ=Zgijdx'dxjofR3'1isgivenbygll=gab=gb3=l,g'=--1,andgij~0fori/j.Letgi(2)betheLiealgebraofgroupSU(2).Theanti-Hermitianrepresentationsofabasisofgi(2)aretakenasfollows:inwhichi=n.Theconnectionisa1-forminwhichThereare12unknownfunctionsA,Thecurvaturetensorsaregivenbyinwhichoj=0/oxj,j=l,2,3,4.TheYang-MillsequationofSU(2)onR3)1is(see[1])TheYang-Millsequationconsistsof12equationsYMjk=0,j~1,2,3,4,k~…     

Design of twodimensional digital filters using neural networks

1.INTRODUCTION Two dimensional(2D)digitalfilteringisoneofthe mostfundamentalandmostimportantprocessing techniquesindigitalimageprocessingandother2D digitalsignalprocessingfields.Comparedwiththe designofone dimensional(1D)digitalfilters,2D digitalfiltersusuallymustbedesignedtosatisfyboth thedesiredmagnitudeandphaseresponsesespecially forimageprocessingapplicationsbecausehumanvi sionsystemismuchmoresensitivethanhumanaudi torysystemtowaveformdistortioncausedbythe phaseresponseoftheapplied2D…     

基于差准则的二维非参数特征分析的SAR目标识别

提出一种基于差准则的二维非参数特征分析(2 dimensional nonparametric feature analysis based on difference criterion,2DDNFA)的图像特征提取方法,它结合了二维线性判决分析(2-dimensional linear discriminant analysis,2DLDA)、最大散度差(maximum scatter difference,MSD)、非参数判决分析(nonparametric feature analysis,NFA)3种方法的思想。首先利用二维图像样本的近邻样本构造类内、类间散布矩阵,再基于差准则计算投影矩阵,最后将二维图像向投影矩阵投影得到特征矩阵。基于实测合成孔径雷达(synthetic aperture radar,SAR)数据的实验结果表明,方法的性能优于基于Fisher准则的2DLDA、二维非参数特征分析(2 dimension nonparametric feature analysis, 2DNFA)方法、也优于基于差准则的二维最大散度差(2-dimensional maximum scatter difference,2DMSD)鉴别分析方法。     

基于IDEAS的联合论证元模型

为统一描述联合论证模式中体系结构数据,基于《国际国防企业体系结构规范》(international defense enterprise architecture specification, IDEAS)提出了联合论证元模型(joint demonstration meta-model, JDM2)。首先,介绍了业务对象参考本体(business object reference ontology, BORO)、IDEAS和国防部元模型(department of defense meta-model,DM2),从设计机理方面剖析了DM2不适用于描述联合论证内容的根本原因以及DM2概念数据模型(conceptual data model,CDM)、逻辑数据模型(logical data model, LDM)和物理交换规范(physical exchange schema, PES)3层结构的优点;然后,借鉴本体理论和DM2设计思想基于联合论证空间提出了JDM2中的概念数据模型;在概念数据模型基础上基于IDEAS规范构建了JDM2中的逻辑数据模型。最后通过实例说明了JDM2的可行性。     

STATISTICAL INFERENCE FOR CONTAMINATION DISTRIBUTION

1 IntroductionThe generaJ model of contamination distribution can be described as follOwing. Let 0 相似文献