数学物理学报(英文版)

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ANNOUNCEMENT

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

数学物理学报(英文版). 2011 (1): 0-0.

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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.

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FURTHER APPLICATIONS OF POLAR COORDINATES IN Cⁿ

余家荣

数学物理学报(英文版). 2011 (1): 1-7. DOI: 10.1016/S0252-9602(11)60201-4

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Simplify the proof on the domain of convergence of multiple power series and consider the case where some of z₁, …, z_n are contained only in a finite number of terms of the series. Obtain some results on holomorphic functions in Cⁿ.

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A SUFFICIENT CONDITION OF CONVERGENCE FOR CLIFFORD CONTINUED FRACTIONS

李永群, 王仙桃

数学物理学报(英文版). 2011 (1): 8-14. DOI: 10.1016/S0252-9602(11)60202-6

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In this article, a sufficient condition for a Clifford continued fraction to be convergent is established, and some applications are given.

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INTERACTION MORAWETZ ESTIMATE AND A SIMPLIFIED PROOF ON THE ENERGY SCATTERING FOR HARTREE EQUAITONS

徐桂香, 苑佳

数学物理学报(英文版). 2011 (1): 15-21. DOI: 10.1016/S0252-9602(11)60203-8

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In this article, we give a simple proof on the energy scattering for the Hartree equations using the interaction Morawetz
estimate that was originally introduced in [5].

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ON F-z-SUPPLEMENTED SUBGROUPS OF FINITE GROUPS

郭文彬, 唐娜, 李保军

数学物理学报(英文版). 2011 (1): 22-28. DOI: 10.1016/S0252-9602(11)60204-X

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A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G=HK and H∩K≤Z^F_∞(G), where Z^F_∞(G) is the F-is the G. We obtain some results about the F-z-supplemented subgroups and use them to determine the structure of some groups.

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TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS

李宇华, 梁占平

数学物理学报(英文版). 2011 (1): 29-38. DOI: 10.1016/S0252-9602(11)60205-1

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In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem: −u′′(t) = λf(t, u(t)) for all t ∈(0, 1) subjecting to u(0)=0 and αu(η)=u(1), where η∈(0,1), α∈[0,1), and λ is a positive parameter. The nonlinear term f(t, u) is nonnegative, and may be singular at t=0, t=1, and u=0. By the fixed point index theory and approximation method, we establish that there exists λ^∗∈ (0,+1], such that the above problem has at least two positive solutions for any λ ∈ (0, λ^∗) under certain conditions on the nonlinear term f.

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ON HASEMAN BOUNDARY VALUE PROBLEM FOR A CLASS OF META-ANALYTIC FUNCTIONS

汪玉峰, 杜金元

数学物理学报(英文版). 2011 (1): 39-48. DOI: 10.1016/S0252-9602(11)60206-3

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In this article, Haseman boundary value problem for a class of meta-analytic functions is studied. The expression of solution and the condition of solvability for Haseman boundary value problem are obtained by changing the problem discussed into the equivalent Haseman boundary value problem of bi-analytic function. And the expression of solution and the condition of solvability depend on the canonical matrix.

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ABSTRACT CAPACITY OF REGIONS AND COMPACT EMBEDDING WITH APPLICATIONS

Veli Shakhmurov

数学物理学报(英文版). 2011 (1): 49-67. DOI: 10.1016/S0252-9602(11)60207-5

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The weighted Sobolev-Lions type spaces W ^l_p, _γ(Ω; E₀, E) = W ^l_p, _γ (Ω; E) \ L_p_, _γ(Ω; E₀) are two Banach spaces and E₀ is continuously and densely embedded on E. A new concept of capacity of region Ω∈Rⁿ in W ^l_p, _γ (Ω; E₀, E) is introduced. Several conditions in terms of capacity of region Ω and interpolations of E₀ and E are found such that ensure the continuity and compactness of embedding operators. In particular, the most regular class of interpolation spaces E_α between E₀ and E, depending of α and l, are found such that mixed differential operators D^α are bounded and compact from W ^l_p, γ(Ω; E₀, E) to E_α-valued L_p, γ spaces. In applications, the maximal regularity for differential-operator equations with parameters are studied.

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UNIVERSAL INTERPOLATING SEQUENCES ON SPACES OF ANALYTIC FUNCTIONS

B.Yousefi

数学物理学报(英文版). 2011 (1): 68-72. DOI: 10.1016/S0252-9602(11)60208-7

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This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of functions analytic on the open unit disk.

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CONTROLLABILITY OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

Bouzahir Hassane, 傅显隆

数学物理学报(英文版). 2011 (1): 73-80. DOI: 10.1016/S0252-9602(11)60209-9

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In this article, we give sufficient conditions for controllability of some partial neutral functional differential equations with infinite delay. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. The results are obtained using the integrated semigroups theory. An application is given to illustrate our abstract result.

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DERIVATIVES OF HARMONIC MIXED NORM AND BLOCH-TYPE SPACES IN THE UNIT BALL OF Rⁿ

唐笑敏, 胡璋剑, 吕小芬

数学物理学报(英文版). 2011 (1): 81-92. DOI: 10.1016/S0252-9602(11)60210-5

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Let H(B) be the set of all harmonic functions f on the unit ball B of Rⁿ. For 0 < p, q ≤ ∞ and a normal weight φ, the mixed norm space H^p,q^, φ'(B) consists of all functions f in H(B) for which the mixed norm ||·||_p,q_, φ < ∞. In this article, we obtain some characterizations in terms of radial, tangential, and partial derivative norms in H^p,q^, φ'(B). The parallel results for the Bloch-type space are also obtained. As an application, the analogous problems for polyharmonic functions are discussed.

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APPLICATION OF TWO OPERATORS TRANSFORM FROM CLASS A OPERATOR TO THE CLASS OF HYPONORMAL OPERATOR

杨长森, 丁艳风

数学物理学报(英文版). 2011 (1): 93-101. DOI: 10.1016/S0252-9602(11)60211-7

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In this article, we give an operator transform T⁽*⁾from class A operator to the class of hyponormal operators. It is different from the operator transform T defined by M. Ch\={o} and T. Yamazaki. Then, we show that σ(T)=σ{T⁽*⁾) and σ_a(T)\{0}=σ_a(T⁽*⁾) \{0}, in case T belongs to class A. Next, we obtain some relations between T and T⁽*⁾.

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METRIC ENTROPY OF HOMEOMORPHISM ON |NON-COMPACT METRIC SPACE

周云华

数学物理学报(英文版). 2011 (1): 102-108. DOI: 10.1016/S0252-9602(11)60212-9

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Let T: X → X be a uniformly continuous homeomorphism on a non-compact metric space (X, d). Denote by X*=X ∪{x*} the one point compactification of X and T*: X*→X* the homeomorphism on X* satisfying T*|_X=T and T*x*=x*. We show that their topological
entropies satisfy h_d(T, X)≥h(T*, X*) if X is locally compact. We also give a note on Katok's measure theoretic entropy on a compact metric space.

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EQUIVALENT CONDITIONS OF LOCAL ASYMPTOTICS FOR THE OVERSHOOT OF A RANDOM WALK WITH HEAVY-TAILED INCREMENTS

王开永, 王岳宝, 尹传存

数学物理学报(英文版). 2011 (1): 109-116. DOI: 10.1016/S0252-9602(11)60213-0

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This article gives the equivalent conditions of the local asymptotics for the overshoot of a random walk with heavy-tailed increments,
from which we find that the above asymptotics are different from the local asymptotics for the supremum of the random walk. To do
this, the article first extends and improves some existing results about the solutions of renewal equations.

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PRODUCTION INVENTORY SYSTEM WITH RANDOM SUPPLY INTERRUPTIONS STATUE AND RANDOM LEAD TIMES

侯玉梅, 刘文远, 张强, 仵凤清

数学物理学报(英文版). 2011 (1): 117-133. DOI: 10.1016/S0252-9602(11)60214-2

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This article analyzes a continuous-review inventory system with random supply interruptions and random lead time which may be interrupted by a random number of supplier's OFF periods. The inventory with constant demand rate is managed by a (r; q₁, q₂, …, q_m) policy and supplies from an unreliable sole supplier. By renewal theory and matrix Geometric method, the long-run average cost function is obtained and some important properties of the function are proved. Furthermore, performance of the inventory is derived.

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SOME DOUBLE SEQUENCE SPACES OF FUZZY NUMBERS DEFINED BY ORLICZ FUNCTIONS

Binod Chandra Tripathy, Bipul Sarma

数学物理学报(英文版). 2011 (1): 134-140. DOI: 10.1016/S0252-9602(11)60215-4

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In this article, we introduce some double sequence spaces of fuzzy real numbers defined by Orlicz function, study some of their properties like solidness, symmetricity, completeness etc, and prove some inclusion results.

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GABOR ANALYSIS OF THE SPACES {\boldmath M( p, q, w) ({R^d) AND S( p, q, r, w, ω) (R^d)

Ayse Sandikci A. Turan G¨urkanli

数学物理学报(英文版). 2011 (1): 141-158. DOI: 10.1016/S0252-9602(11)60216-6

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Let g be a non-zero rapidly decreasing function and w be a weight function. In this article in analog to modulation space, we define
the space M( p, q, w) ( R^d) to be the subspace of tempered distributions f ∈S´(R^d) such that the Gabor transform V_g(f) of f is in the weighted Lorentz space L( p, q, wdμ) (R^2d) . We endow this space with a suitable norm and show that it becomes a Banach space and invariant under time frequence shifts for 1≤p, q≤∞. We also investigate the embeddings between these spaces and the dual space of M( p, q, w) (R^d) . Later we define the space S( p, q, r, w, ω)(R^d) for 1<p<∞, 1≤q ≤∞. We endow it with a sum norm and show that it becomes a Banach convolution algebra. We also discuss some properties of S( p, q, r, w, ω) (R^d) . At the end of this article, we characterize the multipliers of
the spaces M( p, q, w) (R^d) and S( p, q, r, w, ω) ( R^d) .

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DEFORMING METRICS WITH POSITIVE CURVATURE BY A FULLY NONLINEAR FLOW

岳赟, 盛为民

数学物理学报(英文版). 2011 (1): 159-171. DOI: 10.1016/S0252-9602(11)60217-8

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By studying a fully nonlinear flow deforming conformal metrics on a compact and connected manifold, we prove the long time existence and the exponential convergence of the solutions of the flow for any initial metric g₀ with the Schouten tensor A_g₀∈Γ_k.

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HOLDITCH THEOREM FOR THE CLOSED SPACE CURVES IN LORENTZIAN 3-SPACE

Handan Yildirim, Salim Y¨uce, Nuri Kuruoglu

数学物理学报(英文版). 2011 (1): 172-180. DOI: 10.1016/S0252-9602(11)60218-X

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In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L³. For the 1-parameter closed Lorentzian space motion in L³, we obtain a Holditch Theorem taking into account the Lorentzian matrix multiplication for the closed space curves by using their othogonal projections onto the Euclidean plane in the fixed Lorentzian space. Moreover, we generalize this Holditch Theorem for noncollinear three fixed points of the moving Lorentzian space and any other fixed point on the plane which is determined by these three fixed points.

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SEPARATION PROPERTY OF POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION

杨芬, 张丹丹

数学物理学报(英文版). 2011 (1): 181-193. DOI: 10.1016/S0252-9602(11)60219-1

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The asymptotic behavior at infinity and an estimate of positive radial solutions of the equation

Δu +∑^k_i₌₁c_ir^liu^pi = 0, x ∈Rⁿ, (0.1)

are obtained and the structure of separation property of positive radial solutions of Eq. (0.1) with different initial data α is discussed.

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ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH SHARED-SETS IN AN ANGULAR DOMAIN

陈省江, 林伟川

数学物理学报(英文版). 2011 (1): 194-206. DOI: 10.1016/S0252-9602(11)60220-8

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In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.

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ABSOLUTELY |E-PURE MODULES AND E-PURE SPLIT MODULES

阎航宇

数学物理学报(英文版). 2011 (1): 207-220. DOI: 10.1016/S0252-9602(11)60221-X

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We first introduce the concepts of absolutely E-pure modules and E-pure split modules. Then, we characterize the $IF$ rings in terms of absolutely E-pure modules. The E-pure split modules are also characterized.

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MARKOV CHAIN-BASED ANALYSIS OF THE DEGREE DISTRIBUTION FOR A GROWING NETWORK

侯振挺, 童金英, 史定华

数学物理学报(英文版). 2011 (1): 221-228. DOI: 10.1016/S0252-9602(11)60222-1

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In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.

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SOME CLASSES OF DIFFERENCE SEQUENCES OF FUZZY NUMBERS DEFINED BY A SEQUENCE OF MODULI

Ayhan Esi, Mehmet Acikg¨oz

数学物理学报(英文版). 2011 (1): 229-236. DOI: 10.1016/S0252-9602(11)60223-3

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In this article, we introduce and examine some properties of new difference sequence spaces of fuzzy numbers defined using a sequence of modulus functions.

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ON HOLOMORPHIC CURVES OF CONSTANT CURVATURE IN THE COMPLEX GRASSMANN MANIFOLD G(2,5)

焦晓祥, 彭家贵

数学物理学报(英文版). 2011 (1): 237-248. DOI: 10.1016/S0252-9602(11)60224-5

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In this article, it is proved that there doesn't exist any nonsingular holomorphic sphere in complex Grassmann manifold G(2, 5) with constant curvature k=4/7, 1/2, 4/9. Thus, from [7] it follows that if φ: S²→G(2, 5) is a nonsingular holomorphic curve with constant curvature K, then, K=4, 2, 4/3, 1 or 4/5.

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DECAY OF ENERGY FOR A DISSIPATIVE ANISOTROPIC ELASTIC SYSTEM

秦玉明, 刘欣, 邓书显

数学物理学报(英文版). 2011 (1): 249-258. DOI: 10.1016/S0252-9602(11)60225-7

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In this article, we study the large-time behavior of energy for a N-dimensional dissipative anisotropic elastic system. By means of multiplicative techniques, energy method, and Zuazua's estimate technique, we prove the decay property of energy for anisotropic elastic system.

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MULTIPLE POINTS OF IMMERSIONS OF M⁶ \looparrowright R⁷

Mohammad A.Asadi-Golmankhaneh

数学物理学报(英文版). 2011 (1): 259-267. DOI: 10.1016/S0252-9602(11)60226-9

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In this article, we determine the multiple point set of immersions of 6-dimensional manifolds into 7-dimensional Euclidean space R7. The method is to evaluate the charac-teristic numbers of these manifolds. By a certain method, these numbers can be read of from the Hurewicz image of

h : π₇QMO(1) →H₇QMO(1).
In particular, we show that for any immersion of P⁶ in R⁷ the double, 4-fold and 6-fold point manifolds are cobordant to boundaries and triple point manifolds cobordant to P⁴, 5-fold point manifolds cobordant to P²and 7-fold point manifold are odd number.

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BOUNDEDNESS OF DYADIC DERIVATIVE AND CESÀRO MEAN OPERATOR ON SOME B-VALUED MARTINGALE SPACES

陈丽红, 刘培德

数学物理学报(英文版). 2011 (1): 268-280. DOI: 10.1016/S0252-9602(11)60227-0

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In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I* and Ces`aro mean operator σ* are bounded from the B-valued martingale Hardy spaces _p∑_α, D_α, _pL_α, _p ˜H^?_α , _pK_rto L_α (0 < α < 1), respectively. The facts show that it depends on the geometrical properties of the Banach space.

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EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR NONLINEAR SINGULAR 2mth-ORDER CONTINUOUS AND DISCRETE LIDSTONE BOUNDARY VALUE PROBLEMS

苑成军, 文香丹, 蒋达清

数学物理学报(英文版). 2011 (1): 281-291. DOI: 10.1016/S0252-9602(11)60228-2

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By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equa-tions, and provide sufficient conditions for the existence and uniqueness of positive solu-tion to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.

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COMPOSITION OPERATORS BETWEEN SOME WEIGHTED HARDY SPACES

徐丽芳, 邓方文

数学物理学报(英文版). 2011 (1): 292-302. DOI: 10.1016/S0252-9602(11)60229-4

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Let D be the unit disc and H(D) be the set of all analytic functions on D. In[2], C. Cowen defined a space H = {f ∈ H(D) : f(z) =∑^∞_k=0ak(z + 1)^k, ∀z ∈ D, ||f||² =∑^∞_k=0|ak|²4^k < ∞}. In this article, the authors consider the similar Hardy spaces with arbitrary weights and discuss some properties of them. Boundedness and compactness of composition operators between such spaces are also studied.

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ON GENERALIZED BUFFON NEEDLE PROBLEM FOR LATTICES

谢凤繁, 李德宜

数学物理学报(英文版). 2011 (1): 303-308. DOI: 10.1016/S0252-9602(11)60230-0

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Two new concepts, the generalized support function and restricted chord func-tion, both referring to a convex set, were introduced in [1]. General formulae to yield the kinematic measure of a segment of fixed length in a convex set were established based on these concepts. In this article , using the partial intersection method, we consider the generalized Buffon problem for three kinds of lattices. We determine the probability of intersection of a body test needle of length l, l < a.

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A DIFFERENTIABLE SPHERE THEOREM WITH PINCHING INTEGRAL RICCI CURVATURE

王培合, 沈纯理

数学物理学报(英文版). 2011 (1): 321-330. DOI: 10.1016/S0252-9602(11)60232-4

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In this article, we introduce the Hausdorff convergence to derive a differen-tiable sphere theorem which shows an interesting rigidity phenomenon on some kind of manifolds.

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ISOMORPHISMS AND DERIVATIONS IN C*-ALGEBRAS

Lee Jung-Rye, Shin Dong-Yun

数学物理学报(英文版). 2011 (1): 309-320. DOI: 10.1016/S0252-9602(11)60231-2

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In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality:
||f(x) + f(y) + 2f(z) + 2f(w)|| ≤||2f (x + y/2+ z + w) (0.1)
This is applied to investigate isomorphisms between C*-algebras, Lie C*-algebras and JC*-algebras, and derivations on C*-algebras, Lie C*algebras and JC*-algebras, associated with the Cauchy-Jensen functional equation
2f (x + y/2+ z + w )= f(x) + f(y) + 2f(z) + 2f(w). (0.2)

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CYCLIC CODES OVER FORMAL POWER SERIES RINGS

Dougherty Steven T., 刘宏伟

数学物理学报(英文版). 2011 (1): 331-343. DOI: 10.1016/S0252-9602(11)60233-6

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In this article, cyclic codes and negacyclic codes over formal power series rings are studied. The structure of cyclic codes over this class of rings is given, and the relationship between these codes and cyclic codes over finite chain rings is obtained. Using an isomorphism between cyclic and negacyclic codes over formal power series rings, the structure of negacyclic codes over the formal power series rings is obtained.

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LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR SUMS OF NEGATIVELY EPENDENT RANDOM VARIABLES

刘莉, 万成高, 冯艳钦

数学物理学报(英文版). 2011 (1): 344-352. DOI: 10.1016/S0252-9602(11)60234-8

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In this article, we obtain the large deviations and moderate deviations for egatively dependent (ND) and non-identically distributed random variables defined on (∞,+∞). The results show that for some non-identical random variables, precise large deviations and moderate deviations remain insensitive to negative dependence structure.

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COMPLETE HYPERSURFACES WITH CONSTANT MEAN CURVATURE AND FINITE INDEX IN HYPERBOLIC SPACES

邓勤涛

数学物理学报(英文版). 2011 (1): 353-360. DOI: 10.1016/S0252-9602(11)60235-X

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In this article, we prove that any complete finite index hypersurface in the hyperbolic space H⁴(−1)(H⁵(−1)) with constant mean curvature H satisfying H² > 64/63(H² > 175/148 respectively) must be compact. Specially, we verify that any complete and stable hypersurface in the hyperbolic space H⁴(−1) (resp. H⁵(−1)) with constant mean curvature H satisfying H² > 64/63 (resp. H² > 175/148 ) must be compact. It shows that there is no manifold satisfying the conditions of some theorems in [7, 9].

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