数学物理学报(英文版)

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THE BOREL DIRECTIONS OF ALGEBROIDAL FUNCTION AND ITS COEFFICIENT FUNCTIONS

张少华, 张晓梅, 孙道椿

数学物理学报(英文版). 2014 (2): 241-251. DOI: 10.1016/S0252-9602(14)60001-1

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In this article, the relationship between the Borel direction of algebroidal function and its coefficient functions is studied for the first time. To begin with, several theorems of algebroidal functions in unit disk are proved. By these theorems, some interesting conclusions are obtained.

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CONSTRUCTING POINTED WEAK HOPF ALGEBRAS BY ORE-EXTENSION

曹海军, 李方, 张棉棉

数学物理学报(英文版). 2014 (2): 252-262. DOI: 10.1016/S0252-9602(14)60002-3

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The main work of this article is to give a nontrivial method to construct pointed semilattice graded weak Hopf algebra A_t =
ⁿ_i₌₀A ^α_t from a Clifford monoid S = [Y ; G_α, φ_α, β ]by Ore-extensions, and to obtain a co-Frobenius semilattice graded weak Hopf algebra H(S, n, c, χ, a, b) through factoring At by a semilattice graded weak Hopf ideal.

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THE LERAY-SCHAUDER CONDITION FOR 1-SET WEAKLY-CONTRACTIVE AND (ws)-COMPACT OPERATORS

Afif BEN AMAR

数学物理学报(英文版). 2014 (2): 263-273. DOI: 10.1016/S0252-9602(14)60003-5

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The main purpose of this article is to prove a collection of new fixed point theorems for (ws)-compact and so-called 1-set weakly contractive operators under Leray-Schauder boundary condition. We also introduce the concept of semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators. As consequences, we get new fixed point existence for (ws)-compact (in particular nonexpansive) self mappings unbounded closed convex subset of Banach spaces. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. Later on, we give an application to generalized Hammerstein type integral equations.

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A RESULT OF SUZUKI TYPE IN PARTIAL G-METRIC SPACES

Peyman SALIMI, Pasquale VETRO

数学物理学报(英文版). 2014 (2): 274-284. DOI: 10.1016/S0252-9602(14)60004-7

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Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and char-acterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki´s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric 0-completeness. In this article, we introduce the notion of partial G-metric spaces and prove a result of Suzuki type in the setting of partial G-metric spaces. We deduce also a result of common fixed point.

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A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS

李尤发, 杨守志

数学物理学报(英文版). 2014 (2): 285-300. DOI: 10.1016/S0252-9602(14)60005-9

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This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R*, s > 1. We give a sufficient condition for a two-direction refinable function belonging to L²(R*). Then, two theorems are given for constructing biorthogonal (orthogonal) two-direction refinable functions in L²(R*) and their biorthogonal (orthogo-nal) two-direction wavelets, respectively. From the constructed biorthogonal (orthogonal) two-direction wavelets, symmetric biorthogonal (orthogonal) multiwaveles in L²(R*) can be obtained easily. Applying the projection method to biorthogonal (orthogonal) two-direction wavelets in L²(R*), we can get dual (tight) two-direction wavelet frames in L²(R^m), where
m ≤s. From the projected dual (tight) two-direction wavelet frames in L²(R^m), symmetric dual (tight) frames in L²(Rm) can be obtained easily. In the end, an example is given to illustrate theoretical results.

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ASYMPTOTIC PROPERTIES OF THE MOMENT CONVERGENCE FOR NA SEQUENCES

赵月旭

数学物理学报(英文版). 2014 (2): 301-312. DOI: 10.1016/S0252-9602(14)60006-0

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It is well-known that the complete convergence theorem for i.i.d. random vari-ables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4]obtained a moment version of Hsu and Robbins series. However, the series tends to infinity whenever ε goes to zero, so it is of interest to investigate the asymptotic behavior of the series
as ε goes to zero. This note gives some limit theorems of the series generated by moments for NA random variables.

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SUPERSYMMETRIC INVARIANCE AND UNIVERSAL CENTRAL EXTENSIONS OF LIE SUPERTRIPLE SYSTEMS

张庆成, 魏竹, 褚颖娜, 张永平

数学物理学报(英文版). 2014 (2): 313-330. DOI: 10.1016/S0252-9602(14)60007-2

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In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to its standard imbedding Lie superalgebras. Furthermore, we generalize Garland´s theory of universal central extensions for Lie supertriple systems following the classical one for Lie superalgebras. We solve the problems of lifting automorphisms and lifting derivations.

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INVOLUTIONS WITH FIXED POINT SET RP(2m) ? P(2m, 2n + 1)

孟媛媛, 王彦英

数学物理学报(英文版). 2014 (2): 331-342. DOI: 10.1016/S0252-9602(14)60008-4

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Let (M, T) be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism classes of (M, T) are determined.

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I₂-CONVERGENCE AND I₂-CAUCHY DOUBLE SEQUENCES

ErdinC DUNDAR, Bilal ALTAY

数学物理学报(英文版). 2014 (2): 343-353. DOI: 10.1016/S0252-9602(14)60009-6

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In this article, we prove a decomposition theorem for I₂-convergent double sequences and introduce the notions of I₂-Cauchy and I*₂ -Cauchy double sequence, and then study their certain properties. Finally, we introduce the notions of regularly (I₂, I)-convergence and (I₂, I)-Cauchy double sequence.

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ALMOST CONVERGENCE AND DOUBLE SEQUENTIAL BAND MATRIX

Murat CANDAN

数学物理学报(英文版). 2014 (2): 354-366. DOI: 10.1016/S0252-9602(14)60010-2

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The class f of almost convergent sequences was introduced by G.G. Lorentz, using the idea of the Banach limits [A contribution to the theory of divergent sequences, Acta Math. 80(1948), 167–190]. Let f₀(B) and f(B) be the domain of the double sequentialband matrix B(r, s) in the sequence spaces f₀ and f. In this article, the β− and −duals of the space f(B) are determined. Additionally, we give some inclusion theorems concerning with the spaces f₀(B) and f(B). Moreover, the classes (f(B) : μ) and (μ : f(B)) of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where μ is an arbitrary sequence space.

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SUBORDINATION PROPERTIES OF MULTIVALENT FUNCTIONS INVOLVING AN EXTENDED FRACTIONAL DIFFERINTEGRAL OPERATOR

Mohamed K. AOUF, Teodor BULBOACA, Rabha M. EL-ASHWASH

数学物理学报(英文版). 2014 (2): 367-379. DOI: 10.1016/S0252-9602(14)60011-4

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The object of this article is to investigate inclusion, radius, and other various properties of subclasses of multivalent analytic functions, which are defined by using an extended version of the Owa-Srivastava fractional differintegral operator
Ω^{( λ, p)}.

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AN INEQUALITY ON THE ZEROS AND POLES OF VECTOR VALUED MEROMORPHIC FUNCTIONS

吴昭君

数学物理学报(英文版). 2014 (2): 380-386. DOI: 10.1016/S0252-9602(14)60012-6

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The author proves that if f : C→Cⁿ is a transcendental vector valued mero-morphic function of finite order and assume ∑_{a∈Cⁿ∪{∞}}δ(a) = 2, then,
1 − δ(∞)/2 − δ(∞)≤K(f′) ≤2(1 − δ(∞)/2 − δ(∞),
where
K(f ′) = limsup _r→+∞N(r, f ′) + N (r, 0, f′)T(r, f ′).
This result extends the related results for meromorphic function by Singh and Kulkarni.

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ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS

杨杰, 王宇钊, 陈文艺

数学物理学报(英文版). 2014 (2): 387-393. DOI: 10.1016/S0252-9602(14)60013-8

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It is well known that the commutator T_bof the Calder´on-Zygmund singular integral operator is bounded on L^p(Rⁿ) for 1 < p < +∞ if and only if b ∈ BMO [1]. On the other hand, the commutator T_b is bounded from H¹(Rⁿ) into L¹(Rⁿ) only if the function b is a constant [2]. In this article, we will discuss the boundedness of commutator of certain pseudo-differential operators on Hardy spaces H¹. Let T^σ be the operators that its symbol is S⁰_1,δ with 0 ≤δ < 1, if b∈ LMO1, then, the commutator [b, T^σ] is bounded from H¹(Rⁿ) into L¹(Rⁿ) and from L¹(Rⁿ) into BMO(Rⁿ); If [b, T^σ ] is bounded from H¹(Rⁿ) into L¹(Rⁿ) or L¹(Rⁿ) into BMO(Rⁿ), then, b ∈ LMOloc.

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DOMAIN OF THE DOUBLE SEQUENTIAL BAND MATRIX B(r, s) ON SOME MADDOX´S SPACES

Faruk OZGER, Feyzi BASAR

数学物理学报(英文版). 2014 (2): 394-408. DOI: 10.1016/S0252-9602(14)60014-X

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The domain of generalized difference matrix B(r, s) in the classical spaces l_∞, c, and c₀ was recently studied by Kiri¸s¸ci and Ba¸sar in [16]. The main goal of this article is to introduce the paranormed sequence spaces l_∞(B, p), c( B, p), and c₀(B, p), which are more general and comprehensive than the corresponding consequences of the matrix domain of B(r, s), as well as other studies in literature. Besides this, the alpha-, beta-, and gamma-duals of the spaces l_∞(B, p), c(B, p), and c₀(eB , p) are computed and the bases of the spaces c(B , p) and c₀(B, p) are constructed. The final section of this article is devoted to the characterization of the classes (λ(B, p) : μ) and (μ : λ(B, p)), where λ∈ {c, c₀, l_∞} and μ is any given sequence space. Additionally, the characterization of some other classes which are related to the space of almost convergent sequences is obtained by means of a given lemma.

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APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN#br# BANACH SPACES

Yekini SHEHU

数学物理学报(英文版). 2014 (2): 409-423. DOI: 10.1016/S0252-9602(14)60015-1

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Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gˆateaux differentiable norm. Assume that every nonempty closed con-vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map-pings which is also a unique solution to variational inequality problem involving-strongly
pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con-vex optimization problems, and split feasibility problems. Our result extends many recent important results.

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GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR THE 3D COMPRESSIBLE NON–ISENTROPIC EULER EQUATIONS WITH DAMPING

张映辉, 吴国春

数学物理学报(英文版). 2014 (2): 424-434. DOI: 10.1016/S0252-9602(14)60016-3

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We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.

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UNIFORMLY STARLIKE MAPPINGS AND UNIFORMLY CONVEX MAPPINGS ON THE UNIT BALL Bⁿ

冯淑霞, 刘太顺

数学物理学报(英文版). 2014 (2): 435-443. DOI: 10.1016/S0252-9602(14)60017-5

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In this article, we extend the definition of uniformly starlike functions and uni-formly convex functions on the unit disk to the unit ball in Cn, give the discriminant criterions for them, and get some inequalities for them.

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UNIQUENESS OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS

刘永, 祁晓光

数学物理学报(英文版). 2014 (2): 444-452. DOI: 10.1016/S0252-9602(14)60018-7

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In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible.

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CONSENSUS OF THE SECOND-ORDER MULTI-AGENT SYSTEMS WITH AN ACTIVE LEADER AND COUPLING TIME DELAY

郭万里, 肖海军, 陈士华

数学物理学报(英文版). 2014 (2): 453-465. DOI: 10.1016/S0252-9602(14)60019-9

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This article investigates the consensus problem of the second-order multi-agent systems with an active leader and coupling time delay in direct graph. One decentralized state control rule is constructed for each agent to track the active leader and it is proved that the proposed control scheme enables the consensus to be obtained when the adjacency
topology is fixed/switched. Simulation results show effectiveness of the proposed theoretical analysis.

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MEROMORPHIC FUNCTIONS WITH BOUNDED BOUNDARY ROTATION

Jacek DZIOK

数学物理学报(英文版). 2014 (2): 466-472. DOI: 10.1016/S0252-9602(14)60020-5

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In this article, we generalize the class of meromorphic functions with bounded boundary rotation and related classes. Characterizations and some properties of these classes of functions are given.

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ON LACUNARY STATISTICAL CONVERGENCE OF ORDER α

Hacer SENGüL, Mikail ET

数学物理学报(英文版). 2014 (2): 473-482. DOI: 10.1016/S0252-9602(14)60021-7

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In this article, we introduce the concept of lacunary statistical convergence of order α of real number sequences and give some inclusion relations between the sets of lacu-nary statistical convergence of order α and strong N^α_θ (p)-summability. Furthermore, some relations between the spaces N^α_θ (p)- and S^α_θ are examined.

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EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS INVOLVING m CRITICAL HARDY-SOBOLEV EXPONENTS AND m SIGN-CHANGING WEIGHT FUNCTION

Nemat NYAMORADI, Tsing-San HSU

数学物理学报(英文版). 2014 (2): 483-500. DOI: 10.1016/S0252-9602(14)60022-9

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In this article, we consider a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy-Sobolev exponent and one sign-changing function. The existence and multiplicity results of positive solutions are obtained by variational methods.

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CENTRAL LIMIT THEOREMS FOR A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME

高志强, 刘全升, 汪和松

数学物理学报(英文版). 2014 (2): 501-512. DOI: 10.1016/S0252-9602(14)60023-0

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We consider a branching random walk with a random environment in time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The envi-ronment is supposed to be independent and identically distributed. For A （R, let Z_n(A) be the number of particles of generation n located in A. We show central limit theorems for the counting measure Z_n(·) with appropriate normalization.

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3-LIE BIALGEBRAS

白瑞蒲, 程宇, 李佳倩, 孟伟

数学物理学报(英文版). 2014 (2): 513-522. DOI: 10.1016/S0252-9602(14)60024-2

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3-Lie algebras have close relationships with many important fields in mathemat-ics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied. And the classification of 4-dimensional 3-Lie coalgebras and 3-dimensional 3-Lie bialgebras over an algebraically closed field of char-acteristic zero are provided.

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THE SUPER-BIHAMILTONIAN REDUCTION ON C^∞(S¹, OSP(1|2))

张玲, 左达峰

数学物理学报(英文版). 2014 (2): 537-545. DOI: 10.1016/S0252-9602(14)60026-6

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In this article, we will show that the super-bihamiltonian structures of the Kuper-KdV equation in [3], the Kuper-CH equation in [17, 18] and the super-HS equation in [11, 16, 19] can be obtained by applying a super-bihamiltonian reduction of different super-Poisson pairs defined on the loop algebra of osp(1|2).

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RELATIVE ESSENTIAL SPECTRA INVOLVING RELATIVE DEMICOMPACT UNBOUNDED LINEAR OPERATORS

Bilel KRICHEN

数学物理学报(英文版). 2014 (2): 546-556. DOI: 10.1016/S0252-9602(14)60027-8

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In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation
results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter´s and approximate essential spectrum.

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ON THE INVERTIBILITY OF HILBERT SPACE IDEMPOTENTS

邓春源

数学物理学报(英文版). 2014 (2): 523-536. DOI: 10.1016/S0252-9602(14)60025-4

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This note is to present some results on the group invertibility of linear combina-tions of idempotents when the difference of two idempotents is group invertible.

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RIEMANN-HILBERT CHARACTERIZATION FOR MAIN BESSEL POLYNOMIALS WITH VARYING LARGE NEGATIVE PARAMETERS

段萍, 杜金元

数学物理学报(英文版). 2014 (2): 557-567. DOI: 10.1016/S0252-9602(14)60028-X

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In this article, we establish the Bessel polynomials with varying large negative parameters and discuss their orthogonality based on the generalized Bessel polynomials. By using the Riemann-Hilbert boundary value problem on the positive real axis, we get the Riemann-Hilbert characterization of the main Bessel polynomials with varying large negative parameters.

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LOGARITHMICALLY IMPROVED REGULARITY CRITERION FOR THE 3D GENERALIZED MAGNETO-HYDRODYNAMIC EQUATIONS

赵继红, 刘桥

数学物理学报(英文版). 2014 (2): 568-574. DOI: 10.1016/S0252-9602(14)60029-1

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This article proves the logarithmically improved Serrin´s criterion for solutions of the 3D generalized magneto-hydrodynamic equations in terms of the gradient of the velocity field, which can be regarded as improvement of results in [10] (Luo Y W. On the regularity of generalized MHD equations. J Math Anal Appl, 2010, 365: 806–808) and [18] (Zhang Z J. Remarks on the regularity criteria for generalized MHD equations. J Math Anal Appl, 2011, 375: 799–802).

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SUFFICIENT CONDITION FOR FUNCTIONS TO BE IN A CLASS OF MEROMORPHIC MULTIVALENT SAKAGUCHI TYPE SPIRAL-LIKE FUNCTIONS

Muhammad ARIF, Janusz SOK′O l, Muhammad AYAZ

数学物理学报(英文版). 2014 (2): 575-578. DOI: 10.1016/S0252-9602(14)60030-8

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In this article, we define a subclass of meromorphic multivalent Sakaguchi type functions and obtain certain sufficient conditions for functions to be in this class. The main result presented here includes a number of consequences as its special cases.

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MODEL SELECTION METHOD BASED ON MAXIMAL INFORMATION COEFFICIENT OF RESIDUALS

谭秋衡, 蒋杭进, 丁义明

数学物理学报(英文版). 2014 (2): 579-592. DOI: 10.1016/S0252-9602(14)60031-X

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The traditional model selection criterions try to make a balance between fitted error and model complexity. Assumptions on the distribution of the response or the noise, which may be misspecified, should be made before using the traditional ones. In this ar-ticle, we give a new model selection criterion, based on the assumption that noise term in the model is independent with explanatory variables, of minimizing the association strength between regression residuals and the response, with fewer assumptions. Maximal Information Coefficient (MIC), a recently proposed dependence measure, captures a wide range of associ-ations, and gives almost the same score to different type of relationships with equal noise, so MIC is used to measure the association strength. Furthermore, partial maximal information coefficient (PMIC) is introduced to capture the association between two variables removing a third controlling random variable. In addition, the definition of general partial relationship is given.

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