THE CHARACTERISTIC OF EVENTUALLY UNIFORMLY CONTINUOUS C0 SEMIGROUPS ON A HILBERT SPACE

1.IntroductionA.Pazy[1]hastwicepointedoutthatsofar,therearenoknownnecessaryandsufficientconditions,intermsofAortheresolventR(A;A),whichassurethecontinuityfort>0ofT(t)intheuniformoperatortopology.Dr.PengfeiYaol2]hasobtainedthecharacteristicconditionsofaCOsemigroupT(t)onaHilbertspace,whichassurethecontinuityofT(t)fort>0intheuniformoperatortopology.InthispaperweconsiderthecharacteristicconditionsofaCOsemigroupT(t)onaHilbertspace,whichassurethecontinuityofT(t)fort>to(to20)intheuniformoper…     

ON TOURNAMENTS OF SMALL ORDERS AND THEIR APPLICATIONS

In this paper, we generate all nonisomorphic tournaments of order at most nine, all nonisomorphic almost regular tournaments of order 10 and all nonisomorphic regular tournaments of order 11. For each of these tournaments~ we have given its scorelist, connectivity, diameter, the minimal number of feedbacks, automorphisms and spectra.Moreover, we have verified the well-known Kelly‘s Conjecture for n = 2k 1≤11. And we also determine the n-universal tournaments for n≤θ. However ，several related results are given and some related open problems are raised.     

APPROXIMATION OF SOLUTION OF RELAXED DIFFERENTIAL INCLUSION ON COMPACT SET

ＡＰＰＲＯＸＩＭＡＴＩＯＮＯＦＳＯＬＵＴＩＯＮＯＦＲＥＬＡＸＥＤＤＩＦＦＥＲＥＮＴＩＡＬＩＮＣＬＵＳＩＯＮＯＮＣＯＭＰＡＣＴＳＥＴ￥ＳＯＮＧＷｅｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨａｒｂｉｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｈａｒｂ...     

ON THE EXISTENCE OF FIXED POINTS FOR MAPPINGS OF ASYMPTOTICALLY NONEXPANSIVE TYPE

Let C be a nonempty weakly compact convex subset of a Banach space X, and T : C →C a mapping of asymptotically nonexpansive type. Then there hold the following conclusions: (i) if X has uniform normal structure and limsup |||TjN||| < N(X)~1/(N(X)) , where|||TjN||| is the exact Lipschitz constant of TjN , N is some positive integer, and N(X) is the normal structure coefficient of X, then T has a fixed point; (ii) if X is uniformly convex in every direction and has weak uniform normal structure, then T has a fixed point.     

ON THE BEST UNIFORM CONVERGENCE RATE OF EB ESTIMATORS

ＯＮＴＨＥＢＥＳＴＵＮＩＦＯＲＭＣＯＮＶＥＲＧＥＮＣＥＲＡＴＥＯＦＥＢＥＳＴＩＭＡＴＯＲＳＬＩＡＮＧＨｕａ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）ＹＵＡＮＹａｈｕａ（...     

ON EVALUATING THE RUN LENGTH PROPERTIES OF  CHARTS WITH ESTIMATED CONTROL LIMITS

(?) charts with estimated control limits are commonly used in practice and treated as if the in-control process parameters were known. However, the former can behave quite differently from the latter. To understand the differences, it is necessary to study the run length distribution (RLD), its mean (ARL) and standard deviation (SDRL) of the (?) charts when the control limits are estimated. However, ARL and SDRL are integrals over an infinite region with a boundless integrand, the finiteness has not been proved in literature. In this paper, we show the finiteness and uniform integrability of ARL and SDRL. Furthermore, we numerically evaluate the ARL, SDRL and the RLD using number theory method. A numerical study is conducted to assess the performance of the proposed method and the results are compared with those given by Quesenberry and Chen.     

ON THE CONVERGENCE OF SAMPLING ALGORITHMS FOR SOWING DYNAMIC STOCHASTIC PROGRAMMING

1. IntroductionStochajstic prggramming is a very flexible, powerful modelling paradigm that allows decisionmaking models to incorporate uncertain parameters or outcomes, the range of its application isas wide as any in optimization['] 5 such as finance, telecommunications, power system models andtransportation, etc. One class of popular models in stochastic programming is the multistage(or dynamic ) stochastic programming with recouxse because it can be used to properly describelong-term decis…