15 April 2008, Volume 24 Issue 4

    

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  The FENE Dumbbell Model near Equilibrium

  Fang Hua LIN, Ping ZHANG

  Acta Mathematica Sinica. 2008, 24(4): 529-538. https://doi.org/10.1007/s10114-007-1034-5

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  We study the global existence of smooth solutions near the equilibrium to a coupled microscopic-macroscopic FENE dumbbell model which arises from the kinetic theory of diluted solutions of polymeric liquids with noninteracting polymer chains.
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  The Dichotomy Between Traces on d-sets Γ in Rⁿ and the Density of D(Rⁿ\Γ)in Function Spaces

  Hans TRIEBEL

  Acta Mathematica Sinica. 2008, 24(4): 539-554. https://doi.org/10.1007/s10114-007-7007-x

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  A space A_pq^s(Rⁿ) with A=B or A=F and s∈R,0<p,q<∞ either has a trace in L_p(Γ),where Γ is a compact d-set in Rⁿ with 0<d<n,or D(Rⁿ\Γ) is dense in it.Related dichotomy numbers are introduced and calculated.
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  Symplectic Convexity for Orbifolds

  Qi Lin YANG

  Acta Mathematica Sinica. 2008, 24(4): 555-564. https://doi.org/10.1007/s10114-007-5234-9

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  Let a connected compact Lie group G act on a connected symplectic orbifold of orbifold fundamental group Γ.If the action preserves the symplectic structure and there is a G-equivariant and mod-Γ proper momentum map for the lifted action on the universal branch covering orbifold,and if the lifted G-action commutes with that of Γ,then the symplectic convexity theorem is still true for this kind of lifted Hamiltonian action.
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  Discrete Time Mean-variance Analysis with Singular Second Moment Matrixes and an Exogenous Liability

  Wen Cai CHEN, Zhong Xing YE

  Acta Mathematica Sinica. 2008, 24(4): 565-576. https://doi.org/10.1007/s10114-007-5261-6

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  We apply the dynamic programming methods to compute the analytical solution of the dynamic mean-variance optimization problem affected by an exogenous liability in a multi-periods market model with singular second moment matrixes of the return vector of assets.We use orthogonal transformations to overcome the difficulty produced by those singular matrixes,and the analytical form of the efficient frontier is obtained.As an application,the explicit form of the optimal mean-variance hedging strategy is also obtained for our model.
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  On the Rotating Navier-Stokes Equations with Mixed Boundary Conditions

  Kai Tai LI, Rong AN

  Acta Mathematica Sinica. 2008, 24(4): 577-598. https://doi.org/10.1007/s10114-007-1032-7

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  The stationary and nonstationary rotating Navier-Stokes equations with mixed boundary conditions are investigated in this paper.The existence and uniqueness of the solutions are obtained by the Galerkin approximation method.Next,θ-scheme of operator splitting algorithm is applied to rotating Navier-Stokes equations and two subproblems are derived.Finally,the computational algorithms for these subproblems are provided.
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  Existence of Weakly Effcient Solutions in Vector Optimization

  Lucelina BATISTA SANTOS, Marko ROJAS-MEDAR, Gabriel RUIZ-GARZÓN

  Acta Mathematica Sinica. 2008, 24(4): 599-606. https://doi.org/10.1007/s10114-007-5649-3

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  In this paper,we present an existence result for weak efficient solution for the vector optimization problem.The result is stated for invex strongly compactly Lipschitz functions.
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  The Semisimplicity of L¹(K,w) of a Weighted Commutative Hypergroup K

  M. LASHKARIZADEH BAMI

  Acta Mathematica Sinica. 2008, 24(4): 607-610. https://doi.org/10.1007/s10114-007-0979-8

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  In the present paper,it is shown that,for a locally compact commutative hypergroup K with a Borel measurable weight function w,the Banach algebra L¹(K,w) is semisimple if and only if L¹(K) is semisimple.Indeed,we have improved a well-krown result of Bhatt and Dedania from locally compact groups to the general setting of locally compact hypergroups.
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  Convergence Rates for Probabilities of Moderate Deviations for Moving Average Processes

  Ping Yan CHEN, Ding Cheng WANG

  Acta Mathematica Sinica. 2008, 24(4): 611-622. https://doi.org/10.1007/s10114-007-6062-7

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  The present paper first shows that,without any dependent structure assumptions for a sequence of random variables,the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence.Then this paper investigates the convergence rates and refined convergence rates (or complete moment convergence) for probabilities of moderate deviations of moving average processes.The results in this paper extend and generalize some well-known results.
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  Analytic Invariant Curves for a Planar Mapping

  Wen RongRong LI, Han Ze LIU, Li YIN

  Acta Mathematica Sinica. 2008, 24(4): 623-630. https://doi.org/10.1007/s10114-007-6221-x

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  This paper is concerned with the existence of analytic invariant curves for a planar mapping.By constructing a convergent power series solution of an auxiliary equation,analytic solutions of the original equation are obtained.In this paper,we discuss not only the general case,but also the critical cases as well,in particular,the case where β is a unit root is discussed.
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  Precise Asymptotics in Chung’s Law of the Iterated Logarithm

  Li Xin ZHANG

  Acta Mathematica Sinica. 2008, 24(4): 631-646. https://doi.org/10.1007/s10114-007-1033-6

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  Let X,X₁,X₂,…be i.i.d.random variables with mean zero and positive,finite variance σ²,and set S_n=X₁+…+X_n,n ≥ 1.The author proves that,if EX²I{|X|≥t}=o((log logt)^-1)as t→∞,then for any a>-1 and b>-1,
  
  whenever a_n=o(1/loglogn).The author obtains the suffcient and necessary conditions for this kind of results to hold.
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  On s-Quasinormal and c-Normal Subgroups of a Finite Group

  Shi Rong LI

  Acta Mathematica Sinica. 2008, 24(4): 647-654. https://doi.org/10.1007/s10114-007-6283-9

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  Let F be a saturated formation containing the class of supersolvable groups and let G be a finite group.The following theorems are shown: (1) G∈F if and only if there is a normal subgroup H such that G/H∈F and every maximal subgroup of all Sylow subgroups of H is either c-normal or s-quasinormally embedded in G; (2) G∈F if and only if there is a soluble normal subgroup H such that G/H∈F and every maximal subgroup of all Sylow subgroups of F(H),the Fitting subgroup of H,is either c-normally or s-quasinormally embedded in G.
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  The Limit Theorems for Random Walk with State Space R in a Space-time Random Environment

  Wei Gang WANG, Zhen Long GAO, Di He HU

  Acta Mathematica Sinica. 2008, 24(4): 655-662. https://doi.org/10.1007/s10114-007-6332-4

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  We consider a discrete time random walk on real number space in a space-time random environment.We state that when the random environment is i.i.d.,under the marginal annealed law,the law of large numbers,iterated law and CLT of the process are correct.Using a martingale approach,we also state an a.s.invariance principle for random walks in general random environment whose hypothesis requires a subdiffusive bound on the variance of the quenched mean,under an ergodic invariant measure for the environment chain.
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  Irrationality of Some p-adic L-values

  Frits BEUKERS

  Acta Mathematica Sinica. 2008, 24(4): 663-686. https://doi.org/10.1007/s10114-007-1029-2

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  We give a proof of the irrationality of p-adic zeta-values ζ_p(k) for p=2,3 and k=2,3.Such results were recently obtained by Calegari as an application of overconvergent p-adic modular forms.In this paper we present an approach using classical continued fractions discovered by Stieltjes.In addition we show the irrationality of some other p-adic L-series values,and values of the p-adic Hurwitz zeta-function.
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  Highest Weight Representations of a Family of Lie Algebras of Block Type

  Xiao Qing YUE, Yu Cai SU

  Acta Mathematica Sinica. 2008, 24(4): 687-696. https://doi.org/10.1007/s10114-007-0986-9

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  For an additive subgroup G of a field F of characteristic zero,a Lie algebra B(G) of Block type is defined with basis {L_α,i|α∈G,i∈Z₊} and relations [L_α,i,L_β,j]=(β-α)L_α+β,i+j (αj-βi)L_α+β,i+j-1.It is proved that an irreducible highest weight B(Z)-module is quasifinite if and only if it is a proper quotient of a Verma module.Furthermore,for a total order  on G and any Λ∈B(G)₀^*(the dual space of B(G)₀=span{L_0,#em/em#|#em/em#∈Z₊}),a VermaB(G)-module M(Λ,) is defined,and the irreducibility of M(Λ,) is completely determined.
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  Integral Formula of Minkowski Type and NewCharacterization of the Wulff Shape

  Yi Jun HE, Hai Zhong LI

  Acta Mathematica Sinica. 2008, 24(4): 697-704. https://doi.org/10.1007/s10114-007-7116-6

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  Given a positive function F on Sⁿ which satisfies a convexity condition,we introduce the r-th anisotropic mean curvature M_r for hypersurfaces in Rⁿ⁺¹ which is a generalization of the usual r-th mean curvature H_r.We get integral formulas of Minkowski type for compact hypersurfaces in Rⁿ⁺¹.We give some new characterizations of the Wulff shape by the use of our integral formulas of Minkowski type,in case F=1 which reduces to some well-known results.