灰色预测模型的进一步拓广

一、引言 文献[2]中提出了用对数函数对原始数据列{x~((0))(k)}进行变换,提高了离散数据的光滑度,从而拓宽了灰色预测模型的应用范围。文献[2]还给出了预测全国电视机产量的结果,并使这个预测结果的平均误差由不作变换进行预测的263.16％减少到23.6％。 提高灰色预测精度关键在于增加数据列的光滑性。为此,笔者提出用幂函数对原始数据{x~((0))(k)}进     

网络中的优势有效点与选址问题

一、引言 设N=(V,A)为一个有限、简单、无向的连通网络,其顶点集为V,连杆集为A。 设U={u_1,u_2,…,u_p}V,每个u_i对应一个定义在N中点集上的函数d_i(i=1,2,…,p),其定义如下: 这里d(x,u_i)表示x与u_i之间在网络中的最短距离(即连接x与u_i的任一条最短路径的长度)。 我们的问题是求x~*N,使每个函数d(x,u_i)在x~*都取“极小”值(i=1,2,…,p)。这显然是一个多目标决策问题。     

新离散verhulst模型的建模机理及其优化

在对verhulst模型求解方法的误差分析以后,通过对verhulst模型的白化方程的特殊变化,得到了离散的verhulst模型;推导了可以取x~((1))序列中任意一项x~((1))(k)作为初始值的时间响应式,并给出了可行的选取方法;给出了使用最小一乘法与平均相对误差最小的目标函数下的模型参数求解方法;在文中归纳了本文新离散verhulst模型的求解方法及建模步骤;证明了本文新模型的无偏性。最后通过实例分析比较了新模型与几种已有模型的模拟预测精度,结果表明,本文提出新离散verhulst模型能够有效提高模拟预测精度,并且计算过程更加简便。     

ON THE ONE-SIDED LOGARITHMIC LAW FOR ARRAYS

1.IntroductionLet{X.,n2l}beasequenceofindependentandidenticallydistributed(i.i.d.)randomvariables.TheHartmanandWintner,sllllawoftheiteratedlogarithmstatesthatifEXI~0andEX7=1Moreover,itisprovedin[2]and[3]that(1)holdsifandonlyifEXI~0andEX7=1.Nowlet{Xnk,k=1,2,''tntn~1,2,'.}beanarrayofi.i.d.randomvariables.FOreveryn21setS.~Z:--,X.k'ThealmostsureconvergenceofSahasbeenstlldiedbyHu,MoriczandTaylor[41,HuandWeb.rls]andQi[6].HuandWeber[5]showedundertheconditionsEXll=0,EX7,=1andEXt,相似文献   

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 ,…     

EB RULES FOR SELECTING THE BEST EXPONENTIAL POPULATION

In this paper,we obtain empirical Bayes(EB)procedures for selecting the bestamong k different exponential populations(the form of the conditional probability densitye.g.each population is f_4(x_i/b_i)=b_i exp(-b_ix_i),x_i,b_i∈(0,∞),i=1,2,…,k).These rulesare based on the EB estimators of b_i.We show that,under the squared error loss,the Bayesrisk of the EB estimators converges to the related minimum Bayes risks with rates of conver-gence at Jeast of order O(n~(-q)).Further,for the selection problem,the rates of convergenceof the proposed selection rules are shown to be at least of order O(n~((-q)/2) where q can bearbitrarily close to 1/5 or 1 under suitable conditions.     

QUEUEING NETWORKS WITH INSTANTANEOUS SEQUENTIAL TRANSITIONS

1 IntroductionQueueing networks have been one of the most importallt techniques in the modeling andanalysis of computer, communication, transportation, and Iogistics systems. The first queueingnetwork model was introduced by J..k,..[i'2], in which Jackson considers a network with Nnodes, and transitions of the typex -- x -- ej ek5 i,k = 0,1,'',N, (1)where x = (x1, x2)'' 5 XN) denotes the number of customers at the N nodes, ej is the unitvector with a 1 at the j-th position and 0 elsewh…     

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 …     

DGM(1,1)模型的特性及其在技术创新领域中的应用

本文首先提出了以前文献对DCM(1,1)与GM(1,1)模型关系的证明错误,否定了以前文献的一些观点.第二,证明了DGOM(1,1)模型的MAPE值与边值x~((1))(m)(1≤m≤n)无关.第三,发现DGOM(1,1)模型的MAPE值变劣现象并分析其原因.第四,用最小一乘法,构建了边值优化的DGOMII(1,1)模型,其效果优于DGOM(1,1)模型.最后,将DGM(1,1)及DGOMII(1,1)模型应用于技术创新领域中.     

A NOTE ON THE PAPER“A NEW SUFFICIENT CONDITION FOR HAMILTONIAN GRAPHS”

We prove that if G is a graph of order n and connectivity k,and thereexists some t,t(?)k,such that for every independent set S={x_0,x_1,…x_t} ofcardinality t+1,we havesum from i=0 to t |N(S/{x_i}|>t(n-1),then G is Hamiltonian.     

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.     

The Priority Problem of the Cumulative Preponderance and the Maximum Covariance

1　PrincipleandMethod:ForsomecriterionCthecomparativeimportanceofnprojectsisdenotedbyagroupofweightsω1,ω2,…,ωn,whereωi>0,∑ni=1ωi=1.Thelargerweightismoreimportant.Apositiven-dimensionvetorω=(ω1,…,ωn)Tcomprisedbyagroupofweightsiscalledapri-orityvector.ThesetofallpriorityvectorsisdenotedbyVn.IfthejudgementmatrixA=(aij)isconstructedbypointwisecomparisonsofnprojects,thenAisapositivereciprocaln×nmatrix,satisfying:aij>0,aij=1aji　i,j=1,2,…,n.　　LetR ndenotethesetofallpositiverecipro…     

STRONGLY CONSISTENT ESTIMATION FOR A MULTIVARIATE LINEAR RELATIONSHIP MODEL WITH ESTIMATED COVARIANCES MATRIX

1 IntroductionSuppose that the true values Of a set of variables satisfy exact linear relationships, but theyare unobserved. We can Obtain the Observed values which are the sums of the true values anderrors of measurement. The model is described as follows. A set of rmdimensional vectors {xh}satisfyB'xk or = 0, k = 1,2,'' t (1.1)where B is an m x p parameter mains with rank p < m and o is a p x 1 parameter vector. Weobserved {Zk}, which are m x 1 random vectors and satisfyZk = ac ed, …     

A MUCLTI-PARAMETER SPLITTING EXTRAPOLATION AND A PARALLEL ALGORITHM

1.IntroductionConsidertheone-dimensionalDirichletproblemwherethecoefficientsoftheproblemaresmoothandsatisfyp(x)2c>0,q(x)30,xE(0,1).Let[0,1]bedividedintopsubintervalsT={(aj--1,aj):j=1,2,'',p},ac=0,ap--1.Oneach(aj--1)aj),auniformmeshrefinementwithsizehiisi…     

IMPROVEMENT ON THE TEST IN THE EXPONENTIAL FAMILY

Let x_1,…, x_n be the life spans of n items. Suppose that we start the experi-ment at the time t=0 for all the items simultaneuously aud stop the experiment at the timet=r, where r is a stopping time. The observed data set is Z_n=(x_(1),…, x_(k), r(x)),where x_(i)(i=1,…, n) is the order statistic of x_i, i=1,…, n and k=k(x) is the num-ber of the observed data. Suppose that the distribution family of x_i, i=1,…, n is i.i.d.exponential with life expectation θ>0. For testing the hypothesis H_0: θ≤θ_0 againstH_1: θ>θ_0, we use the total time of experiment S_r=sub from i=1 to k x_(i) +(n-k)r (x) as the teststatistic. We reject H_0 as large value of S_r is observed. In this paper for a given stoppingtime r we construct a stopping time ro so that the resulting test is a best improvement ofthe one, which is based on r, in the sense that the power functions of the two tests are thesame but the test based on r_0 is the one which has the minimnm total experiment time.     

On the Meromorphic Solutions of Linear Differential Equations

In this paper, we investigate the growth of meromorphic solutions of higher order linear differential equation f^（k） ＋Ak-1 （z）e^Pk-1^（z） f^（k-1） ＋…＋A1 （z）e^P1（z） f′ ＋Ao（z）e^Po（z） f = 0 （k ≤ 2）, where Pj（z） （j = 0, 1,..., k - 1） are nonconstant polynomials such that deg Pj = n （j = 0, 1,..., k - 1） and Aj（z）（≠ 0） （j = 0, 1,..., k - 1） are meromorphic functions with order p（Aj） 〈 n （j = 0, 1,..., k - 1）.     

On the Solutions of the Matrix Equations in Optimal Stochastic Control

1.INTRoDUCTIoNoFTHEPRoBLEMConsiderthetime-invariantlinearIt6stochasticsystemwherexER,uCRm,FER""",BER""m,a=const.(i=1,2,'',k)arenaturalnumbers;W(t)=[W(t),W2(t),Wk(t)]"(tSo)isak-dimensionalstandardWienerprocesswithindependentcomponentsdefinedonthecompleteprobabilityspace(fl,FP),(A,B)iscontrollable.SupposethatRERm"m,QERmxmaregivenpositivedefiniteweightingmatrices,Ereferstothemathematicalexpectation.ConsidertheoptimalstochasticcontrolDroblemItiswell-knownthatifthereisapositive…     

A REMARK ABOUT TARTAR''''S LEMMA

Let ■Ω=Γ=Γ_1+Γ_2 (see Fig.1),meas(Γ_1)>0,V={v|v∈H~1(Ω),v|Γ_1=0},and V_0={ω|Δω=h in Ω,ω|Γ=0,(?)h∈V}.Let V_0′=thedual space of V_0,a(u,v)=∫_Ω▽u·▽Δvdx,and F(v)=∫_Ω fvdx+∫_(Γ_2)g1Δvds-∫_Γg2(?)ds,f∈V′_0,g1∈H~(-(1/2))(Γ_2),g2∈H~(-(3/2))(Γ).Consider the variational problem:find u ∈ V such thata(u,v)=F(v),(?)v∈V_0. (1)Using Tartar's lemma,we prove that for problem (1) there exists a unique u∈Vsatisfying■     

On the Star Chromatic Number of Graph Products

1　 IntroductionThroughout this paper,we only consider simple graphs.Letkanddbe natural numberssuch thatk 2 d.A ( k,d) -coloring of a graph G=( V,E) is a map c:V|→ Zk,such thatforeach edge( u,v)∈ E,|c( u) -c( v) |k d,where|x|k=min{|x|,k-|x|},and Zk={0 ,1 ,2 ,… ,k-1 }.Itis obvious thata( k,1 ) -coloring ofa graph is justan ordinaryk-coloringof G.The star-chromatic numberχ* ( G) of a graph G is defined by:χ* ( G) =inf{k/ d∶ G has a ( k,d) -coloring}.　　It is proved in[1 ,2 ] that th…     

ON A PROPERTY OF SOLUTIONS OF M-MATRIXEQUATIONS

1.IntroductionConsideringthefollowingsystemoflinearequationsAx~b(l.1)whereAisannxnM-matrix,bisanndimensionalvectorandbeRang(A).Theresearchonthesolutionofequation(1.1)isveryimportantinLeontiefmodelofinput-outputanalysis(see[1,2]).G.St..k.ma[Zjstudiestheabo…