数学物理学报(英文版)

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ANNOUNCEMENT

数学物理学报(英文版). 2011 (2): 0-0. DOI: 10.1016/S0252-9602(11)60236-1

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A special issue of Acta Mathematica Scientia, to be published in 2011, will be dedicated to the 85th birthday of Peter D. Lax, who is one of
the most prominent mathematicians of the past hundred years. Peter Lax has made important and seminal contributions in many areas of pure and applied mathematics, including the theory of integrable systems and solitons, with applications to fluid dynamics and physics, scattering theory, and the theory of shock waves in hyperbolic conservation laws, with applications to gas dynamics. He also exerted a great influence in launching the field of scientific computation. Over the years, Peter Lax has been a great supporter of mathematics in China, having helped numerous Chinese mathematicians. We invite contributions to the special issue from students, postdocs and other colleagues and friends of Peter Lax. If you plan to contribute a paper, please inform the Standing Editors of the special issue, by March 31, 2011.

Standing Editors: Gui-Qiang Chen, Constantine Dafermos, Xiaqi Ding, Tai-Ping Liu

Gui-Qiang Chen: chengq@maths.ox.ac.uk

Constantine Dafermos: Constantine_Dafermos@brown.edu

Xiaqi Ding: xqding@amt.ac.cn

Tai-Ping Liu: liu@math.stanford.edu

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ON THE WILLMORE'S THEOREM FOR CONVEX HYPERSURFACES

周家足

数学物理学报(英文版). 2011 (2): 361-366. DOI: 10.1016/S0252-9602(11)60237-3

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Let M be a compact convex hypersurface of class C², which is assumed to bound a nonempty convex body K in the Euclidean space Rⁿ and H be the mean curvature of M. We obtain a lower bound of the total square of mean curvature ∫_M H²dA. The bound is the Minkowski quermassintegral of the convex body K. The total square of mean curvature attains the lower bound when M is an (n-1)-sphere.

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A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

石东洋, 任金城, 龚伟

数学物理学报(英文版). 2011 (2): 367-382. DOI: 10.1016/S0252-9602(11)60238-5

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In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix-Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L²-norm are established, as well as one in broken H¹-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.

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ON A REGULARIZATION OF INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH PROPERLY STATED LEADING TERM

刘红, 宋永忠

数学物理学报(英文版). 2011 (2): 383-398. DOI: 10.1016/S0252-9602(11)60239-7

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In this article, linear regular index 2 DAEs A(t)[D(t)x(t)]'+B(t)x(t)=q(t) are considered. Using a decoupling technique, initial condition and boundary condition are properly formulated. Regular index 1DAEs are obtained by a regularization method. We study the behavior of the solution of the regularization system via asymptotic expansions. The error analysis between the solutions of the DAEs and its regularization system is given.

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DENSITY PROPERTIES OF MAPPING SPACES FOR OPERATOR SPACES

董浙, 姜海益

数学物理学报(英文版). 2011 (2): 399-407. DOI: 10.1016/S0252-9602(11)60240-3

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In this article, we give the sufficient and necessary conditions for which several important mapping spaces are weak* dense in the
corresponding completely bound mapping spaces.

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EXACT EVALUATIONS OF FINITE |TRIGONOMETRIC SUMS BY SAMPLING THEOREMS

M.H. Annaby, R.M. Asharabi

数学物理学报(英文版). 2011 (2): 408-418. DOI: 10.1016/S0252-9602(11)60241-5

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We use the sampling representations associated with Sturm-Liouville difference operators to derive generalized integral-valued
trigonometric sums. This extends the known results where zeros of Chebyshev polynomials of the first kind are involved to the use of
the eigenvalues of difference operators, which leads to new identities. In these identities Bernoulli's numbers play a role similar to that of Euler's in the old ones. Our technique differs from that of Byrne-Smith (1997) and Berndt-Yeap (2002).

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A RISK-SENSITIVE STOCHASTIC MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL OF JUMP DIFFUSIONS AND ITS APPLICATIONS

史敬涛, 吴臻

数学物理学报(英文版). 2011 (2): 419-433. DOI: 10.1016/S0252-9602(11)60242-7

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A stochastic maximum principle for the risk-sensitive optimal control problem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.

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CYCLIC VECTORS AND CELLULAR INDECOMPOSABLE OPERATORS ON Q_p SPACES

叶善力, 娄增建

数学物理学报(英文版). 2011 (2): 434-440. DOI: 10.1016/S0252-9602(11)60243-9

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We identify the functions whose polynomial multiples are weak* dense in Q_p spaces and prove that if |f(z)|≥|g(z)| and g is cyclic in Q_p, then f is cyclic in Q_p. We also show that the multiplication operator M_z on Q_p spaces is cellular indecomposable.

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OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U₆(2)

张良才, 施武杰

数学物理学报(英文版). 2011 (2): 441-450. DOI: 10.1016/S0252-9602(11)60244-0

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Let G be a finite group and π(G)={p₁, p₂, …, p_k} be the set of the primes dividing the order of G. We define its prime graph Γ(G) as follows. The vertex set of this graph is π(G), and two distinct vertices p, q are joined by an edge if and only if pq ∈π_e(G). In this case, we write p～q. For p ∈π(G), put deg(p):=|{q ∈π(G) | p～q|, which is called the degree of p. We also define D(G):=(deg(p₁), deg(p₂), … , deg(p_k)), where p₁<p₂<…<p_k, which is called the degree pattern of G. We say a group G is k-fold OD-characterizable if there exist exactly k non-isomorphic finite groups with the same order and degree pattern as G. Specially, a 1-fold OD-characterizable group is simply called an OD-characterizable group. Let L:=U₆(2). In this article, we classify all finite groups with the same order and degree pattern as an almost simple groups related to L. In fact, we prove that L and L.2 are OD-characterizable, L.3 is 3-fold OD-characterizable, and L.S₃ is 5-fold OD-characterizable.

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A HEAT KERNEL VERSION OF HARDY'S THEOREM FOR THE LAGUERRE HYPERGROUP

黄际政, 刘和平

数学物理学报(英文版). 2011 (2): 451-458. DOI: 10.1016/S0252-9602(11)60245-2

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In this article, we prove a heat kernel version of Hardy's theorem for the Laguerre hypergroup.

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POINCARÉSERIES AND AN APPLICATION TO WEYL ALGEBRAS

王志华, 魏俊潮, 李立斌

数学物理学报(英文版). 2011 (2): 459-467. DOI: 10.1016/S0252-9602(11)60246-4

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Let A_n be the n-th Weyl algebra over a field of characteristic 0 and M a finitely generated module over A_n. By further exploring the relationship between the Poincaré series and the dimension and the multiplicity of M, we are able to prove that the tensor product of two finitely generated modules over A_n has the multiplicity equal to the product of the multiplicities of both modules. It turns out that we can compute the dimensions and the multiplicities of some homogeneous subquotient modules of A_n.

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COMPACT COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES ON BOUNDED SYMMETRIC DOMAINS

吕小芬, 胡璋剑

数学物理学报(英文版). 2011 (2): 468-476. DOI: 10.1016/S0252-9602(11)60247-6

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In this article, we borrow the idea of using Schur's test to characterize the compactness of composition operators on the weighted Bergman spaces in a bounded symmetric domain Ω, and verify that C_φ is compact on L^q_a(Ω, d^v_β) if and only if K(φ(z), φ(z))/K(z, z)→0 as z→∂Ω under a mild condition, where K(z, w) is the Bergman kernel.

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COMMUTATORS OF BOCHNER-RIESZ OPERATORS FOR A CLASS OF RADIAL FUNCTIONS

夏霞, 陆善镇

数学物理学报(英文版). 2011 (2): 477-482. DOI: 10.1016/S0252-9602(11)60248-8

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In this article, we prove the boundedness of commutators generated by Bochner-Riesz operators below the critical index and BMO functions on the class of radial functions in L^p (Rⁿ) with |1/p-1/2|<(1+2α)/(2n).

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OPTIMAL PORTFOLIO ON TRACKING THE EXPECTED WEALTH PROCESS WITH LIQUIDITY CONSTRAINTS

罗葵, 王光明, 胡亦钧

数学物理学报(英文版). 2011 (2): 483-490. DOI: 10.1016/S0252-9602(11)60249-X

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In this article, the authors consider the optimal portfolio on tracking the expected wealth process with liquidity constraints. The constrained optimal portfolio is first formulated as minimizing the cumulate variance between the wealth process and the expected wealth process. Then, the dynamic programming methodology is applied to reduce the whole problem to solving the Hamilton-Jacobi-Bellman equation coupled with the liquidity constraint, and the method of Lagrange multiplier is applied to handle the constraint. Finally, a numerical method is proposed to solve the constrained HJB equation and the constrained optimal strategy. Especially, the explicit solution to this optimal
problem is derived when there is no liquidity constraint.

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ON COMPACTNESS FOR ITERATED COMMUTATORS

刘永民, 于燕燕

数学物理学报(英文版). 2011 (2): 491-500. DOI: 10.1016/S0252-9602(11)60250-6

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The authors study the iterated commutators on the weighted Bergman spaces A²(Φ), and prove that C^n/h is compact on A²(Φ) if and only if h ∈B₀.

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ON SPACELIKE AUSTERE SUBMANIFOLDS IN PSEUDO-EUCLIDEAN SPACE

东瑜昕, 韩英波

数学物理学报(英文版). 2011 (2): 501-511. DOI: 10.1016/S0252-9602(11)60251-8

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In this article, we construct some spacelike austere submanifolds in pseduo-Euclidean spaces. We also get some indefinite special Lagrangian submanifolds by constructing twisted normal bundle of spacelike austere submanifolds in pseduo-Euclidean spaces.

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ON THE GLOBAL STABILITY CONJECTURE OF THE GENOTYPE SELECTION MODEL

S.H. Saker

数学物理学报(英文版). 2011 (2): 512-528. DOI: 10.1016/S0252-9602(11)60252-X

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In 1994, Grove, Kocic, Ladas, and Levin conjectured that the local stability and global stability conditions of the fixed point y =1/2 in the genotype selection model should be equivalent. In this article, we give an affirmative answer to this conjecture and prove that local stability implies global stability. Some illustrative examples are included to demonstrate the validity and applicability of the results.

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RANDOM ATTRACTORS FOR A STOCHASTIC HYDRODYNAMICAL EQUATION IN HEISENBERG PARAMAGNET

郭柏灵, 郭春晓, 蒲学科

数学物理学报(英文版). 2011 (2): 529-540. DOI: 10.1016/S0252-9602(11)60253-1

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This article studies the asymptotic behaviors of the solution for a stochastic hydrodynamical equation in Heisenberg paramagnet in a
two-dimensional periodic domain. We obtain the existence of random attractors in H¹.

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EXPRESSION OF MEROMORPHIC SOLUTIONS OF SYSTEMS OF ALGEBRAIC DIFFERENTIAL EQUATIONS WITH EXPONENTIAL COEFFICIENTS

高凌云

数学物理学报(英文版). 2011 (2): 541-548. DOI: 10.1016/S0252-9602(11)60254-3

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Using the Nevanlinna theory of the value distribution of meromorphic functions and theory of differential algebra, we investigate the problem of the forms of meromorphic solutions of some specific systems of generalized higher order algebraic differential equations with exponential coefficients and obtain some results.

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A DEGENERACY THEOREM FOR MEROMORPHIC MAPPINGS WITH TRUNCATED MULTIPLICITIES

颜启明, 陈志华

数学物理学报(英文版). 2011 (2): 549-560. DOI: 10.1016/S0252-9602(11)60255-5

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In this article, we prove a degeneracy theorem for three linearly non-degenerate meromorphic mappings from Cⁿ into P^N(C), sharing 2N+2 hyperplanes in general position, counted with multiplicities truncated by 2.

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AN IMPROVEMENT OF THE OCTONIONIC TAYLOR TYPE THEOREM

廖建全, 李兴民

数学物理学报(英文版). 2011 (2): 561-566. DOI: 10.1016/S0252-9602(11)60256-7

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We prove that the octonionic polynomials V ^k_l1 …lkare independent of the associative orders _k. This improves the octonionic Taylor type theorem.

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RANDOM ATTRACTOR FOR A TWO-DIMENSIONAL INCOMPRESSIBLE NON-NEWTONIAN FLUID\\ WITH MULTIPLICATIVE NOISE

赵才地, 李用声, 周盛凡

数学物理学报(英文版). 2011 (2): 567-575. DOI: 10.1016/S0252-9602(11)60257-9

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This article proves that the random dynamical system generated by a two-dimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the
phase space.

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ON A CLASS OF KÖTHE SEQUENCE SPACES WITH NORMAL STRUCTURE

B.Zlatanov

数学物理学报(英文版). 2011 (2): 576-590.

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In this note, we investigate the generalized modulus of convexity δ^(λ) and the generalized modulus smoothness ρ^(λ). We obtain some estimates of these moduli for X=l_p. We obtain inequalities between WCS coefficient of a K\"othe sequence space X and δ_X^(λ). We show that, for a wide class of K\"othe sequence spaces X, if for some ε ∈(0, 9/10] holds δ_X(ε)>1/3(1-√3/2)ε, then X has normal structure.

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ON THE REGULARITY CRITERIA OF THE 3D NAVIER-STOKES EQUATIONS IN CRITICAL SPACES

董柏青, Sadek Gala, 陈志敏

数学物理学报(英文版). 2011 (2): 591-600. DOI: 10.1016/S0252-9602(11)60259-2

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Regularity criteria of Leray-Hopf weak solutions to the three-dimensional Navier-Stokes equations in some critical spaces such as Lorentz space, Morrey space and multiplier space are derived in terms of two partial derivatives, ∂₁u₁, ∂₂u₂, of velocity fields.

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A COUPLED CONTINUOUS-DISCONTINUOUS FEM APPROACH FOR CONVECTION DIFFUSION EQUATIONS

祝鹏, 谢资清, 周叔子

数学物理学报(英文版). 2011 (2): 601-612. DOI: 10.1016/S0252-9602(11)60260-9

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In this article, we introduce a coupled approach of local discontinuous Galerkin and standard finite element method for solving convection diffusion problems. The whole domain is divided into two disjoint subdomains. The discontinuous Galerkin method is adopted in the subdomain where the solution varies rapidly, while the standard finite element method is used in the other subdomain due to its lower computational cost. The stability and a priori error estimate are established. We prove that the coupled method has O((ε^1/2}+h^1/2)h^k) convergence rate in an associated norm, where ε is the diffusion coefficient, h is the mesh size and k is the degree of polynomial. The numerical results verify our theoretical results. Moreover, 2k-order superconvergence of the numerical traces at the nodes, and the optimal convergence of the errors under L² norm are observed numerically on the uniform mesh. The numerical results also indicate that the coupled method has the same convergence order and almost the same errors as the purely LDG method.

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FORCED OSCILLATION OF SECOND ORDER DIFFERENTIAL EQUATIONS WITH MIXED NONLINEARITIES

Taher S.Hassan, Lynn Erbe, Allan Peterson

数学物理学报(英文版). 2011 (2): 613-626. DOI: 10.1016/S0252-9602(11)60261-0

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This article is concerned with the oscillation of the forced second order differential equation with mixed nonlinearities

(a(t)( x´(t)^γ)´+p₀(t) x^γ( g₀(t))+∑_i=1ⁿp_i(t)l x(g_i(t))|^αisgn x (g_i(t)) =e(t),
where γ is a quotient of odd positive integers, α_i>0, i=1, 2, …, n, a, e, and p_i∈C([ 0, ∞) , {R}, α(t) >0, g_i: R→R are positive continuous functions on R with lim_t→∞g_i(t)=∞, i=0, 1, …, n. Our results generalize and improve the results in a recent article by Sun and Wong [29].

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ON PROPERTIES OF DIFFERENCE POLYNOMIALS

陈宗煊, 黄志波, 郑秀敏

数学物理学报(英文版). 2011 (2): 627-633. DOI: 10.1016/S0252-9602(11)60262-2

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We study the value distribution of difference polynomials of meromorphic functions, and extend classical theorems of Tumura-Clunie type to difference polynomials. We also consider the value distribution of f(z)f(z+c).

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MINIMUM CONGESTION SPANNING TREES IN BIPARTITE AND RANDOM GRAPHS

M.I.Ostrovskii

数学物理学报(英文版). 2011 (2): 634-640. DOI: 10.1016/S0252-9602(11)60263-4

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The first problem considered in this article reads: is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs? It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n^3/2, where n is the number of vertices. The second problem is to estimate spanning tree congestion of random graphs. It is proved that the standard model of random graphs cannot be used to find graphs whose spanning tree congestion has order
greater than n^3/2.

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WEIGHTED COMPOSITION OPERATORS BETWEEN DIRICHLET SPACES

王茂发

数学物理学报(英文版). 2011 (2): 641-651. DOI: 10.1016/S0252-9602(11)60264-6

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In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are ifferent counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.

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A DUAL-RELAX PENALTY FUNCTION APPROACH FOR SOLVING NONLINEAR BILEVEL PROGRAMMING WITH LINEAR LOWER LEVEL PROBLEM

万仲平, 王广民, 吕一兵

数学物理学报(英文版). 2011 (2): 652-660. DOI: 10.1016/S0252-9602(11)60265-8

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The penalty function method, presented many years ago, is an important numerical method for the mathematical programming
problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty function
approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our
algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.

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FRACTIONAL ORDER BOUNDARY |VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL

Hussein A.H.Salem

数学物理学报(英文版). 2011 (2): 661-672. DOI: 10.1016/S0252-9602(11)60266-X

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In this article, we investigate the existence of Pseudo solutions for some fractional order boundary value problem with integral
boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems
constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value
problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function. To encompass the full scope of this article, we give an example illustrating the main result.

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THE BANACH ALGEBRAS GENERATED BY OPERATORS WITH ONE-POINT SPECTRUM

H.Seferoglu, N.Simsek

数学物理学报(英文版). 2011 (2): 673-680. DOI: 10.1016/S0252-9602(11)60267-1

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In this article, we present some results related to the structure of Banach algebras generated by operators with one-point spectrum.

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GLOBAL EXISTENCE AND NONEXISTENCE FOR A DOUBLY DEGENERATE PARABOLIC SYSTEM COUPLED VIA NONLINEAR BOUNDARY FLUX

陈波涛, 米永生, 穆春来

数学物理学报(英文版). 2011 (2): 681-693. DOI: 10.1016/S0252-9602(11)60268-3

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This article deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve and the critical Fujita curve for the problem. Especially for the blow-up case, it is rather technical. It comes from the construction of the so-called Zel'dovich-Kompaneetz-Barenblatt profile.

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ON MULTIPLICATION AND COMULTIPLICATION MODULES

H. Ansari-Toroghy, F. Farshadifar

数学物理学报(英文版). 2011 (2): 694-700. DOI: 10.1016/S0252-9602(11)60269-5

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This article deals with some results concerning multiplication and comultiplication modules over a commutative ring.

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ON THE BRAIDED STRUCTURES OF RADFORD'S BIPRODUCT

马天水, 李海英, 赵文正

数学物理学报(英文版). 2011 (2): 701-715. DOI: 10.1016/S0252-9602(11)60270-1

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We obtain the necessary and sufficient conditions for Radford's biproduct to be a braided Hopf algebra. As an application, a nontrivial example is given.

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VISCOSITY ITERATIVE METHODS FOR COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS WITHOUT COMMUTATIVITY ASSUMPTION IN HILBERT SPACES

Eknarin Jankaew, Somyot Plubtieng, Anutep Tepphun

数学物理学报(英文版). 2011 (2): 716-726. DOI: 10.1016/S0252-9602(11)60271-3

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In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces. We also prove, without
commutativity assumption, that the iterates converge to a common fixed point of the mappings which solves some variational
inequality. The results presented extend the corresponding results of Shimizu and Takahashi [T. Shimizu, W. Takahashi, Strong
convergence to common fixed point of families of nonexpansive mappings, J. Math. Anal. Appl. 211 (1997), 71-83], and Yao and Chen[Y. Yao, R. Chen, Convergence to common fixed points of average mappings without commutativity assumption in Hilbert spaces,Nonlinear Analysis 67(2007), 1758-1763].

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PARTIAL COMPACTNESS FOR LANDAU-LIFSHITZ MAXWELL EQUATION IN TWO-DIMENSION

寇艳蕾, 丁时进

数学物理学报(英文版). 2011 (2): 727-748. DOI: 10.1016/S0252-9602(11)60272-5

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We study the partial regularity of weak solutions to the 2-dimensional Landau-Lifshitz equations coupled with time dependent
Maxwell equations by Ginzburg-Landau type approximation. Outside an energy concentration set of locally finite 2-dimensional parabolic
Hausdorff measure, we prove the uniform local C^∞ bounds for the approaching solutions and then extract a subsequence converging to a global weak solution of the Landau-Lifshitz-Maxwell equations which are smooth away from finitely many points.

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