IMPLICIT DEGREES AND CHVATAL'S CONDITION FOR HAMILTONICITY

Based on the ideas in[9],an integer d~0(v),called the implicit degree of v whichsatisfies d~0(v)≥d(v),is associated with each vertex v of a graph G.It is proved that if theimplicit degree sequence d_1~0,d_2~0,…,d_n~0(where d_1~0≤d_2~0≤…≤d_n~0)of a simple graph G on n≥3vertices satisfiesd_i~0≤i相似文献   

寻找满足Fletcher算法要求的初始点的方法

让我们着一个非线性约束规划中最简单,但应用最广泛的二次规划问题: min f(x)=1/2x~TQx-c~Tx(1)受制于约束: a_1~Tx≥b_i,i=1,2,…,p (2)其中Q是一个一般的实n阶对称矩阵,c和     

ON THE BOUNDEDNESS OF SOLUTIONS,EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF CUBIC DIFFERENTIAL SYSTEM

In this paper, we discuss the boundedness of the solutions, the existence andthe uniqueness of the limit cycle of the following cubic differential system:x'=y, y'=-x+δy+a_2xy+a_4x+a_5x~2y. (*)We obtain the following results:(1) System (*) is bounded if and only if (i) a_5<0, a_4=0; or (ii) a_5=0, a_4<0, δ≤0,-(-8a_4)~(1/2)相似文献   

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.     

随机截断下基于多个混合分布样本的非参数推断

设有K族(K≥2)i.i.d.(独立同分布)随机变量{Xij,j=1,2,…,ni},i=1,2,…,K,分别来自于分布Gi(x)=(1-iα)F1(x)+iαF2(x),其中iα∈[0,1].每族随机变量同时被另一列i.i.d.随机变量Yij,j=1,2,…,ni截断.本文分别用经验分布和Kaplan-meier估计构造了分布F1,F2的估计,并证明了估计量的性质.最后用数值例子对两种方法作了比较,验证了Kaplan-meier估计的精确有效性.     

EXISTENCE OF CONSISTENT ESTIMATES OF LINEAR REGRESSION COEFFICIENTS WHEN THE ERROR VARIANCES ARE UNEQUAL

Consider the linear regression model Y_i=x_i′β+σ_ie_i,i=1,…,n,…,where E(e_i)=0,E(e_ie_j)=δ_(ij),0<σ_1~2(?)σ_2~2(?)…and {x_i} satisfies A_1(?)sum from i=1 to n x_ix_i′/n(?)A_2,for n large,A_1>0,A_2>0.This paper shows that (i) ifσ_i~2,i=1,2…,are known,then the necessary and sufficient condition for theconsistency of the best unbiased linear estimate of β is sum from i=1 to ∞σ_i~(-2)=∞;(ii)if{σ_i~2}is only known to belong to the set {(h_1,h_2,…)∶0相似文献   

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。     

HEAVY RANDOM CENSORING LIMIT THEOREMS

1.IntroductionOurproblemistoestimatethedistributionfunctionFandthecumulativehazardfunctionAofsomenonnegativerandomvariableX,whereXisthelifetimeinaparticularstateofanindividual.Samplinglifetimehasanumberofrestrictions.Asanexample,thelifetimedatacanberightcensored.TObespecific,supposeXI,X2,...Xuarei.i.d.nonnegativerandomvariableswhicharecensoredontherightbynfollow-upi.i.d.timesYI,Y2,...Yn.LetF(x)=P(XI5x),A(x)~I"Mic1~F-bethedistributionfUnctionandcumulativehazardfunctionofX.Wesaythatthe…     

Persistence in A Three Species Predator-Prey System

1IntroductionItistheauthor'sknowledgethatfewerliteraturescanbefoundonthethreespeciespredatorpreysystem.Themainpurposeofthispaperistoprovethatthesystemcanbepersistentundersomecondition,toobtainsufficientconditionforthepersistenceofthefollowingpredator-preysystemwherethefunctions6i(t),a,j(t),i,j=1,2,3arecontinuousboundedaboveandbelowbypositiveconstantsoilthehalfinfiniteinterval05t< co.Thisthreespeciessystem(l.1)showsthatthethirdspeciesisthepredatorofthefirstspeciesandthesecondspeciesthatisthepre…     

A Class of Parallel Runge-Kutta Methods for Differential-Algebraic Systems of Index 2

1-INTHODUCTIONWeconsiderthedifferential-algebraicsystemwherefandgaresufficientIydifferentiable.Inorderthat(1a)isanindex2problemwesupposethatinaneighbourhoodoftheexactsolution.wefurtherassumethattheinitialva1uesyo,zoareconsistentwith(l),i.e.,(yo,zo)satisfies(lb)andThesolutionof(1a)isdenotedby(y(t),z(t)).Problemsoftheform(l)arefrequentlyencounteredinpractice.Forexamp1e,problem(l)hasthetypicalstructureofacontrolproblemwherethez-variableactsascontrolparameterwhichforcesthesolutionofthediffer…     

Weighted L~2-Estimates of Solutions for Damped Wave Equations with Variable Coefficients

The authors establish weighted L~2-estimates of solutions for the damped wave equations with variable coefficients utt-div A(x)▽u + au_t = 0 in IR~nunder the assumption a(x) ≥ a_0[1 + ρ(x)]~(-l),where a_0 0, l 1, ρ(x) is the distance function of the metric g = A~(-1)(x) on IR~n. The authors show that these weighted L~2-estimates are closely related to the geometrical properties of the metric g = A~(-1)(x).     

BAHADUR'S REPRESENTATION FOR NEAREST NEIGHBOR MEDIAN ESTIMATES: THE FIXED DESIGN CASE

1.IntroductionConsiderthefixeddesignnonparametricregressionmodelK=g(xi) ei,i21,(1.l)whereg(x)isanunknownregressionfunctiondefinedontheinterval[0,if,{xi,iZ1}arefixeddesignpoilltsdrawnfromtheinterval[0,1],{ei,i21}arei.i.d.randomvariablesfromapopulationhavingunknownsymmetricdistributionF(x)withsymmetricpoint0andK(i21)istheobservationatxi(i21).Forestimatingtheunknownregressionfunctiong(x),takethefirstnobservationsYI,'',Ye.WithoutlossofgeneralityjletalSxZS''5xu.LetD.i(x)denotethei-thnearestn…     

图上博弈的Page-Shapley值

对合作博弈(N,v)和交流图(N,L)所产生的交流局面(N,v,L),现有的分配法则都是重新定义一个特征函数,再归结为新特征函数的Shapley值.为了避免定义新特征函数时的失真(从而使得计算Shapley值出现一定偏差),本文提出一个新的分配法则.设原博弈(N,v)的Shapley值为Sh(N,v)=(S_1,S_2,…,s_n),其中s_i可视为参与者i的实力.类似于Google的网络搜索算法,对连通的交流图L和表示参与者相互合作程度的转移矩阵P,定义参与者的PageRank (参与者的级别或地位),记为(r_1,r_2,…,r_n),其中r_i表示参与者i在合作交流中的地位.新的分配法则,称为Page-Shapley值:其中参与者i所得为c_Nr_is_iv(N),而C_N取为1/Σ_(j∈N)r_jS_j以便保证值的有效性.当L不连通时,其Page-Shapley值由各分支的Page-Shapley值拼接而成.     

THE EQUIVALENCE CLASSES OF LRS OVER Z_p~e

1.IntroductionLetpbeaprasenumber,eapositivenumber,ZretheresidueringofZmoduloP".Letfi=(Zve)oo={g=(al)iZolaiEZap}.Asequenceg=(al)iZoinniscalledalinearrecurringsequence(LRSinshort)overZPeifitsatisfiesthelinearrecurrencerelationan i=on--fan--1 i '' toal,i=0,1,...(1.1)whereCiEZreffor0SiSn--1,andthemonicpolynomialiscalledthecharacteristicpolynomialofg.Denotethesetofailsequencessatisfyinglinearrecurrencerelation(1.l)byn(f).Next,werequirethatj(x)satisfiesgcd(f(0),p)=1,theneverysequenceg=(ac)i…     

NONMRAMETRIC AND SEMIPARAMETRICREGRESSION MODELS WITH LOCALLYGENERALIZED GAUSSIAN ERROR

1.IntroductionLetpbeanaturalnumberandAbeacompactsetinW,K(")~g(xj")) e(")ti~1)2,...5acwherexln),x;n),''t.in)EAaredesignpoints,gisanunknownfunction,ej")arerandomerrors.Georgiovil]definedg.(x)~fWu.(x)K(")asanestimateofg,whereWei(x)=i=1Wei(x,xl"),xln),''5x;…     

LAWS OF THE ITERAFED LOGARITHM FOR TRIMMED SUM

1.IntroductionLetX,X1,X2,''beasequenceofn0n-degenerateindependelltidenticallydistributedra-n-domVarableswithcommondistributionfunctionF,andletXl,'',X2beanarrangementofXl,'Xnindecreasingorderofmagnitude,i.e.IX:l2''2IX2I.SetS;=Z:. ,X;.Forx>0,defineandforx=0,setG(O)=Q(O)=P(IXI>O),K(0)=0-DeAneLetrnbeanynon-decreasingsequenceofilltegerssuchthatwheref>0andwewritel2nforloglogn.By(1.1)and(l.2),forsufficientlylargentwecandeflneasequenceb.byP.S.Griffinl1Jobtainedthefollowingtheorem:R…     

ON THE CONDITION FOR CONSISTENCY OF RESAMPLING ESTIMATORS OF VARIANCE OF TRIMMED L-STATISTICS

1.IntroductionLetXI,X2,''tX.beani.i.d.randomsamplewithcommondistributionfunction(c.d.f.)F(unknown),andFibetheempiricaldistributionfunction(e.d.f.)basedonthesample.ConsiderthefollowingfunctionalofFwhereF--'(t)ginf{x:F(x)2t}istheinversefunctionofF(inversef…     

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.     

MUCLTIVARIATE RESISTANT REGRESSION SPLINES FOR ESTIMATING MULTIVARIATE FUNCTIONS FROM NOISY DATA

1.IntroductionMultivariatesurfaceestimationisanimportantproblemforwhichseveralmethodologieshavebeendevelopedwiththeaimofconstructinganestimatorg,,(x)ofaJ--dimensionalsurfacego(x)basedonnoisyobservations{(Xi,K),15i5n}.Existingestimatorsofgoareobtainedonthe…     

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…