15 July 2009, Volume 25 Issue 7

    

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  Hyperbolic Conservation Laws on Manifolds.An Error Estimate for Finite Volume Schemes

  Philippe G.LeFLOCH, Baver OKUTMUSTUR, Wladimir NEVES

  Acta Mathematica Sinica. 2009, 25(7): 1041-1066. https://doi.org/10.1007/s10114-009-8090-y

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  Following Ben–Artzi and LeFloch,we consider nonlinear hyperbolic conservation lawsposed on a Riemannian manifold,and we establish an L¹-error estimate for a class of finite volumeschemes allowing for the approximation of entropy solutions to the initial value problem.The errorin the L¹ norm is of order h^1/4 at most,where h represents the maximal diameter of elements in thefamily of geodesic triangulations.The proof relies on a suitable generalization of Cockburn,Coquel,and LeFloch's theory which was originally developed in the Euclidian setting.We extend the argumentsto curved manifolds,by taking into account the e?ects to the geometry and overcoming several newtechnical diffculties.
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  On Heat Kernel Estimates and Parabolic Harnack Inequality for Jump Processes on Metric Measure Spaces

  Zhen-Qing CHEN, Panki KIM, Takashi KUMAGAI

  Acta Mathematica Sinica. 2009, 25(7): 1067-1086. https://doi.org/10.1007/s10114-009-8576-7

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  In this paper,we discuss necessary and suffcient conditions on jumping kernels for a classof jump-type Markov processes on metric measure spaces to have scale-invariant finite range parabolicHarnack inequality.
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  Harmonic Moments of Branching Processes in Random Environments

  Wei Gang WANG, Ping LV, Di He HU

  Acta Mathematica Sinica. 2009, 25(7): 1087-1096. https://doi.org/10.1007/s10114-009-8137-0

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  We consider harmonic moments of branching processes in general random environments.For a sequence of square integrable random variables,we give some conditions such that there is apositive constant c that every variable in this sequence belong to A_c or A_c uniformly.
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  Finite Groups with Its Power Automorphism Groups Having Small Indices

  Jun Xin WANG, Xiu Yun GUO

  Acta Mathematica Sinica. 2009, 25(7): 1097-1108. https://doi.org/10.1007/s10114-009-8060-4

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  In this paper,a finite group G with|Aut(G):P(G)|=p or pq is determined,where P(G)is the power automorphism group of G,and p,q are distinct primes.Especially,we prove that a finitegroup G satisfies|Aut(G):P(G)|=pq if and only if Aut(G)/P(G)S₃.Also,some other classes offinite groups are investigated and classified,which are necessary for the proof of our main results.
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  Every Weakly Compact Set Can Be Uniformly Embedded into a Reflexive Banach Space

  Li Xin CHENG, Qing Jin CHENG, Zheng Hua LUO, Wen ZHANG

  Acta Mathematica Sinica. 2009, 25(7): 1109-1112. https://doi.org/10.1007/s10114-009-7545-5

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  Based on an application of the Davis–Figiel–Johnson–Pelzyski procedure,this note showsthat every weakly compact subset of a Banach space can be uniformly embedded into a reflexive Banachspace.As its application,we present the recent renorming theorems for reflexive spaces of Odell–Schlumprecht and Hajek–Johanis can be extended and localized to weakly compact convex subsets ofan arbitrary Banach space.
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  Portfolio Optimization under Entropic Risk Management

  Wei ZHONG

  Acta Mathematica Sinica. 2009, 25(7): 1113-1130. https://doi.org/10.1007/s10114-009-7524-x

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  In this paper,properties of the entropic risk measure are examined rigorously in a generalframework.This risk measure is then applied in a dynamic portfolio optimization problem,appearingin the risk management constraint.By considering the dual problem,we prove the existence anduniqueness of the solution and obtain an analytic expression for the solution.
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  Isometric Isomorphisms in Proper CQ*-algebras

  Choonkil PARK, Jong Su AN

  Acta Mathematica Sinica. 2009, 25(7): 1131-1138. https://doi.org/10.1007/s10114-009-7454-7

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  In this paper,we prove the Hyers–Ulam–Rassias stability of isometric homomorphisms inproper CQff-algebras for the following Cauchy–Jensen additive mapping:2f((x1+x2)/2+y)=f(x1)+f(x2)+2f(y).appeared in the paper:On the stability of the linear mapping in Banach spaces,Proc.Amer.Math.Soc.,72(1978),297–300.This is applied to investigate isometric isomorphisms between proper CQff-algebras.
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  On Extension of Isometries Between the Unit Spheres of Normed Space E and l^p(p>1)

  Ji Jin YI, Rui Dong WANG

  Acta Mathematica Sinica. 2009, 25(7): 1139-1144. https://doi.org/10.1007/s10114-009-7376-4

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  In this paper,we study the extension of isometries between the unit spheres of normedspace E and l^p(p>1).We arrive at a conclusion that any surjective isometry between the unit sphereof normed space l^p(p>1)and E can be extended to be a linear isometry on the whole space l^p(p>1)under some condition.
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  Hua’s Theorem with s Almost Equal Prime Variables

  Qing Feng SUN, Heng Cai TANG

  Acta Mathematica Sinica. 2009, 25(7): 1145-1156. https://doi.org/10.1007/s10114-009-7251-3

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  It is proved unconditionally that every suffciently large positive integer satisfying somenecessary congruence conditions can be represented as the sum of s almost equal k-th powers of primenumbers for 2 k 10 and s=2^k+1,which gives a short interval version of Hua’s theorem.
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  Large Deviation for Stochastic Cahn–Hilliard Partial Di?erential Equations

  Ke Hua SHI, Dan TANG, Yong Jin WANG

  Acta Mathematica Sinica. 2009, 25(7): 1157-1174. https://doi.org/10.1007/s10114-009-7224-6

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  In this paper,we prove a large deviation principle for a class of stochastic Cahn–Hilliardpartial differential equations driven by space-time white noises.
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  On Multifractal of Cantor Dust

  In-Soo BAEK

  Acta Mathematica Sinica. 2009, 25(7): 1175-1182. https://doi.org/10.1007/s10114-009-7111-1

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  We consider quasi-self-similar measures with respect to all real numbers on a Cantor dust.We define a local index function on the real numbers for each quasi-self-similar measure at each point ina Cantor dust.The value of the local index function at the real number zero for all the quasi-self-similarmeasures at each point is the weak local dimension of the point.We also define transformed measures ofa quasi-self-similar measure which are closely related to the local index function.We compute the localdimensions of transformed measures of a quasi-self-similar measure to find the multifractal spectrumof the quasi-self-similar measure.Furthermore we give an essential example for the theorem of localdimension of transformed measure.In fact,our result is an ultimate generalization of that of a self-similar measure on a self-similar Cantor set.Furthermore the results also explain the recent resultsabout weak local dimensions on a Cantor dust.
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  Prinjective Ringel–Hall Algebras for Posets of Finite Prinjective Type

  Justyna KOSAKOWSKA

  Acta Mathematica Sinica. 2009, 25(7): 1183-1190. https://doi.org/10.1007/s10114-009-6541-0

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  In the present paper we investigate prinjective Ringel–Hall algebras,for prinjective modulesover incidence algebras of posets of finite prinjective type.Results we obtain are analogous to these,given by C.M.Ringel,for representations of Dynkin quivers.In particular we give a description ofprinjective Ringel–Hall algebras by generators and relations.
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  On Permutation Polynomials in Two Variables over Z/p²Z

  Qi Jiao WEI, Qi Fan ZHANG

  Acta Mathematica Sinica. 2009, 25(7): 1191-1200. https://doi.org/10.1007/s10114-009-6526-z

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  We give a good characterization of the permutation polynomials in two variables overZ/p²Z.
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  Zero-Sum Stochastic Games with Average Payoffs:New Optimality Conditions

  Jie YANG, Xian Ping GUO

  Acta Mathematica Sinica. 2009, 25(7): 1201-1216. https://doi.org/10.1007/s10114-009-6274-0

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  In this paper we study zero-sum stochastic games.The optimality criterion is the long-runexpected average criterion,and the payofffunction may have neither upper nor lower bounds.We givea new set of conditions for the existence of a value and a pair of optimal stationary strategies.Ourconditions are slightly weaker than those in the previous literature,and some new suffcient conditionsfor the existence of a pair of optimal stationary strategies are imposed on the primitive data of themodel.Our results are illustrated with a queueing system,for which our conditions are satisfied butsome of the conditions in some previous literatures fail to hold.
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  On Pointwise Bounded Approximation

  Zhijian QIU

  Acta Mathematica Sinica. 2009, 25(7): 1217-1222. https://doi.org/10.1007/s10114-009-7058-2

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  Let G be an open subset in the extended complex plane and let A(G)denote the algebraof all functions analytic on G and continuous on G.We call a domain multi-nicely connected if thereis a circular domain W and a conformal mapφfrom W onto G such that the boundary value functionofφis univalent almost everywhere with respect to the arclength on∂W.Suppose that every component of G is finitely connected and none of the components of G havesingle point boundary components.We show that for every bounded analytic function on G to bethe pointwise limit of a bounded sequence of functions in A(G),it is necessary and suffcient thateach component of G is multi-nicely connected and the harmonic measures of G are mutually singular.This generalizes the corresponding result of Davie for the case when the components of G are simplyconnected.