数学物理学报(英文版)

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COMPLEX RATIONAL TYPE INTERPOLATION AT DISTURBED FEJ´|ER POINTS ON A CURVE

涂天亮, 莫炯

数学物理学报(英文版). 2012 (2): 441-454. DOI: 10.1016/S0252-9602(12)60028-9

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The results of accurate order of uniform approximation and simultaneous ap-proximation in the early work “Jackson Type Theorems on Complex Curves” are improved from Fej´er points to disturbed Fej´er points in this article. Furthermore, the stability of convergence of T^*_n,ε(f, z) with disturbed sample values f(z^*_k) +ε_k are also proved in this article.

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BEST APPROXIMATION FOR WEIERSTRASS TRANSFORM CONNECTED WITH SPHERICAL MEAN OPERATOR

L.T. Rachdi, N. Msehli

数学物理学报(英文版). 2012 (2): 455-470. DOI: 10.1016/S0252-9602(12)60029-0

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Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked.

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MULTIVARIATE WEIGHTED BERNSTEIN-TYPE INEQUALITY AND ITS APPLICATIONS

曹飞龙, 林绍波

数学物理学报(英文版). 2012 (2): 471-482. DOI: 10.1016/S0252-9602(12)60030-7

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Bernstein inequality played an important role in approximation theory and Fourier analysis. This article first introduces a general system of functions and the so-called multivariate weighted Bernstein, Nikol’skiÏ, and Ul’yanov-type inequalities. Then, the relations among these three inequalities are discussed. Namely, it is proved that a family of functions equipped with Bernstein-type inequality satisfies Nikol’skiÏ-type and Ul’yanov-type inequality. Finally, as applications, some classical inequalities are deduced from the obtained results.

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A NOTE ON THE DRAZIN INVERSE OF A MODIFIED MATRIX

Dragana S. Cvetkovic, Jelena Ljubisavljevic

数学物理学报(英文版). 2012 (2): 483-487. DOI: 10.1016/S0252-9602(12)60031-9

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In this article, the expression for the Drazin inverse of a modified matrix is considered and some interesting results are established. This contributes to certain recent results obtained by Y.Wei [9].

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CONFOUNDING STRUCTURE OF TWO-LEVEL NONREGULAR FACTORIAL DESIGNS

任俊柏

数学物理学报(英文版). 2012 (2): 488-498. DOI: 10.1016/S0252-9602(12)60032-0

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In design theory, the alias structure of regular fractional factorial designs is elegantly described with group theory. However, this approach cannot be applied to nonregular designs directly. For an arbitrary nonregular design, a natural question is how to describe the confounding relations between its effects, is there any inner structure similar to regular designs? The aim of this article is to answer this basic question. Using coefficients of indicator function, confounding structure of nonregular fractional factorial designs is obtained as linear constrains on the values of effects. A method to estimate the sparse significant effects in an arbitrary nonregular design is given through an example.

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A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM, FIXED POINT#br# PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS, AND QUASI-VARIATIONAL INCLUSION PROBLEM

刘敏, 张石生

数学物理学报(英文版). 2012 (2): 499-519. DOI: 10.1016/S0252-9602(12)60033-2

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In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone map-pings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Takahashi and Toyoda [9], Takahashi and Takahashi [10] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [11], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].

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SOME PROPERTIES OF m-ISOMETRIES AND m-INVERTIBLE OPERATORS ON BANACH SPACES

Ould Ahmed Mahmoud Sid Ahmed

数学物理学报(英文版). 2012 (2): 520-530. DOI: 10.1016/S0252-9602(12)60034-4

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This article has two purposes: the first is to give some structure results for the class of m-isometries, and the second purpose is to extend the notions of left and right inverses to m-left and m-right inverses respectively.

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MAPS PRESERVING STRONG SKEW LIE PRODUCT ON FACTOR VON NEUMANN ALGEBRAS

崔建莲, Choonkil Park

数学物理学报(英文版). 2012 (2): 531-538. DOI: 10.1016/S0252-9602(12)60035-6

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Let A be a factor von Neumann algebra and Φ be a nonlinear surjective map from A onto itself. We prove that, if Φ satisfies that Φ(A)Φ(B) − Φ(B)Φ(A)* =AB − BA* for all A, B ∈ A, then there exist a linear bijective map Ψ : A → A satisfying (A) (B) − (B) (A)* = AB − BA* for A, B ∈ A and a real functional h on A with h(0) = 0 such that Φ(A) = (A) + h(A)I for every A ∈ A. In particular, if A is a type I factor, then, Φ(A) = cA + h(A)I for every A ∈ A, where c = ±1.

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WEYL’S TYPE THEOREMS AND HYPERCYCLIC OPERATORS

M.H. M. Rashid

数学物理学报(英文版). 2012 (2): 539-551. DOI: 10.1016/S0252-9602(12)60036-8

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For a bounded operator T acting on an infinite dimensional separable Hilbert space H, we prove the following assertions: (i) If T or T*∈ SC, then generalized a-Browder’s theorem holds for f(T) for every f ∈Hol(σ(T)). (ii) If T or T* ∈ HC has topological uniform descent at all λ∈ iso(σ(T)), then generalized Weyl’s theorem holds for f(T) for every f ∈ Hol(σ(T)). (iii) If T ∈ HC has topological uniform descent at all
λ∈ E(T), then T satisfies generalized Weyl’s theorem. (iv) Let T ∈HC. If T satisfies the growth condition G_d(d ≥ 1), then generalized Weyl’s theorem holds for f(T) for every f ∈ Hol(σ(T)). (v) If T ∈ SC, then, f(σ_SBF±(T)) = σ_SBF±(f(T)) for all f ∈ Hol(σ(T)). (vi) Let T be a-isoloid such that T* ∈ HC. If T − λI has finite ascent at every λ ∈ E^a(T) and if F is of finite rank on H such that TF = FT, then T +F obeys generalized a-Weyl’s theorem.

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DIFFEOMORPHISMS WITH VARIOUS C¹ STABLE PROPERTIES

田学廷, 孙文祥

数学物理学报(英文版). 2012 (2): 552-558. DOI: 10.1016/S0252-9602(12)60037-X

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Let M be a smooth compact manifold and ∧ be a compact invariant set. In this article, we prove that, for every robustly transitive set ∧, f|_∧ satisfies a C¹-generic-stable shadowable property (resp., C¹-generic-stable transitive specification property or C¹-generic-stable barycenter property) if and only if ∧ is a hyperbolic basic set. In partic-ular, f|_∧ satisfies a C¹-stable shadowable property (resp., C¹-stable transitive specification property or C¹-stable barycenter property) if and only if ∧ is a hyperbolic basic set. Similar results are valid for volume-preserving case.

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EXTENDED CESÀRO OPERATORS AND MULTIPLIERS ON BMOA

吕小芬

数学物理学报(英文版). 2012 (2): 559-567. DOI: 10.1016/S0252-9602(12)60038-1

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In this article, we characterize the boundedness and compactness of extended Cesàro operators on the spaces BMOA by the Carleson measures in the unit ball. Mean-while, we study the pointwise multipliers on BMOA.

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L^p BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRÖDINGER OPERATORS ON HEISENBERG GROUP

李澎涛, 彭立中

数学物理学报(英文版). 2012 (2): 568-578. DOI: 10.1016/S0252-9602(12)60039-3

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Let L = −△Hⁿ+V be a Schr¨odinger operator on Heisenberg group Hⁿ, where △Hⁿ is the sublaplacian and the nonnegative potential V belongs to the reverse H¨older class B_Q_/2, where Q is the homogeneous dimension of Hⁿ. Let T₁= (−△Hⁿ+V )−1V , T₂ =(−△Hⁿ+V ^)−1/2V ^1/2, and T₃ = (−△Hⁿ+V )^−1/2∇Hⁿ, then we verify that [b, T_i], i = 1, 2, 3 are bounded on some L^p(Hⁿ), where b ∈ BMO(Hⁿ). Note that the kernel of T_i, i = 1, 2, 3 has no smoothness.

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REPRESENTATIONS OF A LOOP LIE ALGEBRA ASSOCIATED WITH QUANTUM PLANE

梁俊平, 吴月柱

数学物理学报(英文版). 2012 (2): 579-585. DOI: 10.1016/S0252-9602(12)60040-X

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In this article, some modules over a loop Lie algebra associated to quantum plane are constructed. The isomorphism classes among these modules are also determined.

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HYPERHOLOMORPHIC THEORY ON KAEHLER MANIFOLDS

汤冬梅, 钟同德, 邱春晖

数学物理学报(英文版). 2012 (2): 586-604. DOI: 10.1016/S0252-9602(12)60041-1

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First of all, using the relations (2.3), (2.4), and (2.5), we define a complex Clifford algebra W_n and the Witt basis. Secondly, we utilize the Witt basis to define the operators ∂and ∂^ on Kaehler manifolds which act on W_n-valued functions. In addition, the relation between above operators and Hodge-Laplace operator is argued. Then, the Borel-Pompeiu formulas for W_n-valued functions are derived through designing a matrix Dirac operator D and a 2× 2 matrix–valued invariant integral kernel with the Witt basis.

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INVARIANTS UNDER STABLE EQUIVALENCES OF MORITA TYPE

李方, 孙隆刚

数学物理学报(英文版). 2012 (2): 605-618. DOI: 10.1016/S0252-9602(12)60042-3

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The aim of this article is to study some invariants of associative algebras under stable equivalences of Morita type. First of all, we show that, if two finite-dimensional self-injective k-algebras are stably equivalent of Morita type, then their orbit algebras are isomorphic. Secondly, it is verified that the quasitilted property of an algebra is invariant under stable equivalences of Morita type. As an application of this result, it is obtained that if an algebra is of finite representation type, then its tilted property is invariant under stable equivalences of Morita type; the other application to partial tilting modules is given in Section 4. Finally, we prove that when two finite-dimensional k-algebras are stably equivalent of Morita type, their repetitive algebras are also stably equivalent of Morita type under certain conditions.

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ISOPERIMETRIC PROBLEMS OF THE CALCULUS OF VARIATIONS WITH FRACTIONAL DERIVATIVES

Ricardo Almeida, Rui A. C. Ferreira, Delfim F. M. Torres

数学物理学报(英文版). 2012 (2): 619-630. DOI: 10.1016/S0252-9602(12)60043-5

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In this article, we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide and do not coincide with the lower bound of the fractional derivatives are considered.

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SOME PROPERTIES OF COMMUTING AND ANTI-COMMUTING m-INVOLUTIONS

Mark Yasuda

数学物理学报(英文版). 2012 (2): 631-644. DOI: 10.1016/S0252-9602(12)60044-7

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We define an m-involution to be a matrix K ∈ C^n×nfor which K^m= I. In this article, we investigate the class Sm (A) of m-involutions that commute with a diagonalizable matrix A ∈ C^n×n. A number of basic properties of S_m (A) and its related subclass S_m (A, X) are given, where X is an eigenvector matrix of A. Among them, S_m (A) is shown to have a torsion group structure under matrix multiplication if A has distinct eigenvalues and has non-denumerable cardinality otherwise. The constructive definition of S_m (A, X) allows one to generate all m-involutions commuting with a matrix with distinct eigenvalues. Some related results are also given for the class ˜ S_m (A) of m-involutions that anti-commute with a matrix A ∈ C^n×n.

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ON ALMOST PRIME SUBMODULES

Hani A. Khashan

数学物理学报(英文版). 2012 (2): 645-651. DOI: 10.1016/S0252-9602(12)60045-9

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In this article, we define almost prime submodules as a new generalization of prime and weakly prime submodules of unitary modules over a commutative ring with identity. We study some basic properties of almost prime submodules and give some char-acterizations of them, especially for (finitely generated faithful) multiplication modules.

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UNIQUE CONTINUATION AND PERSISTENCE PROPERTIES OF SOLUTIONS OF THE 2-COMPONENT DEGASPERIS-PROCESI#br# EQUATIONS

付英, 屈长征

数学物理学报(英文版). 2012 (2): 652-662. DOI: 10.1016/S0252-9602(12)60046-0

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In this article, the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed. It is shown that strong solutions of the 2-component Degasperis-Procesi equations, initially decaying exponentially
together with its spacial derivative, must be identically equal to zero if they also decay exponentially at a later time.

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SOME APPLICATIONS OF PLANAR GRAPH IN KNOT THEORY

程志云, 高红铸

数学物理学报(英文版). 2012 (2): 663-671. DOI: 10.1016/S0252-9602(12)60047-2

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The relationship between a link diagram and its corresponding planar graph is briefly reviewed. A necessary and sufficient condition is given to detect when a planar graph corresponds to a knot. The relationship between planar graph and almost planar Seifert surface is discussed. Using planar graph, we construct an alternating amphicheiral prime knot with crossing number n for any even number n 4. This gives an affirmative answer to problem 1.66(B) on Kirby’s problem list.

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POSITIVE SOLUTIONS FOR SINGULAR BVPs ON THE POSITIVE HALF-LINE ARISING FROM EPIDEMIOLOGY AND COMBUSTION THEORY

Sma?l Djebali, Ouiza Sa?fi, 闫宝强

数学物理学报(英文版). 2012 (2): 672-694. DOI: 10.1016/S0252-9602(12)60048-4

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In this work, we are concerned with the existence and multiplicity of positive solutions for singular boundary value problems on the half-line. Two problems from epi-demiology and combustion theory set on the positive half-line are investigated. We use upper and lower solution techniques combined with fixed point index on cones in appro-priate Banach spaces. The results complement recent ones in the literature.

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THE INTERIOR LAYER FOR A NONLINEAR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATION

王爱峰, 倪明康

数学物理学报(英文版). 2012 (2): 695-709. DOI: 10.1016/S0252-9602(12)60049-6

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In this article, the interior layer for a second order nonlinear singularly per-turbed differential-difference equation is considered. Using the methods of boundary func-tion and fractional steps, we construct the formula of asymptotic expansion and point out that the boundary layer at t = 0 has a great influence upon the interior layer at t = σ. At the same time, on the basis of differential inequality techniques, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of our result. The result of this article is new and it complements the previously known ones.

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ILL-POSEDNESS OF MODIFIED KAWAHARA EQUATION AND KAUP-KUPERSHMIDT EQUATION

闫威, 李用声

数学物理学报(英文版). 2012 (2): 710-716. DOI: 10.1016/S0252-9602(12)60050-2

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In this article, we consider the Cauchy problems for the modified Kawahara
equation
∂_tu +μ∂_x(u³) + α∂⁵_xu + β∂³_xu + γ∂_xu = 0
and the Kaup-Kupershmidt equation
∂_tu + μu∂²_xu + α∂⁵_xu + β∂³_xu + γ∂_xu = 0.
Using the general well-posedness principle introduced by I. Bejenaru and T. Tao, we prove that the modified Kawahara equation is ill-posed for the initial data in Hs(R) with s < −1/4 and that the Kaup-Kupershmidt equation is ill-posed for the initial data in H^s(R) with
s < 0.

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RESULTS ON A QUESTION OF ZHANG AND YANG

李升, 高宗升

数学物理学报(英文版). 2012 (2): 717-723. DOI: 10.1016/S0252-9602(12)60051-4

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For a meromorphic function f, let N_(l+1(r, 1/f ) denote the counting function of zeros of f of order l at least. Let f be a nonconstant meromorphic function, such that N(r, f) = S(r, f). Denote F = fⁿ. Suppose that F and F′ share 1 CM. If (1) n ≥ 3, or (2) n = 2 and N(r, 1/
f ) = O(N₍₃(r, 1/f )), then, F = F′, and f assumes the form

f(z) = ce^{1/n z},
where c is a nonzero constant. This main result of this article gives a positive answer to a question raised by Zhang and Yang [1] for the meromorphic functions case in some sense. And a relative result is proved.

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ON PROPERTIES OF q-DIFFERENCE EQUATIONS

郑秀敏, 陈宗煊

数学物理学报(英文版). 2012 (2): 724-734. DOI: 10.1016/S0252-9602(12)60052-6

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In this article, we consider some type of q-difference equations, which have meromorphic solutions with Borel exceptional zeros and poles. We also give a precise result in the finite order case and some further results in a particular case where qⁱ= qⁱ.

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CONVERGENCE OF WEIGHTED AVERAGES OF MARTINGALES IN NONCOMMUTATIVE BANACH FUNCTION SPACES

张超, 侯友良

数学物理学报(英文版). 2012 (2): 735-744. DOI: 10.1016/S0252-9602(12)60053-8

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Let x = (x_n)_n≥1 be a martingale on a noncommutative probability space (M, τ ) and (w_n)_n≥1 a sequence of positive numbers such that W_n =
∑ⁿ_k₌₁w_k →∞ as n →1. We prove that x = (x_n)_n≥1 converges in E(M) if and only if (σ_n(x))_n≥1 converges in E(M), where E(M) is a noncommutative rearrangement invariant Banach function space with the Fatou property and σ_n(x) is given by
σ_n(x) =1/W_n∑ⁿ_k₌₁w_kx_k, n = 1, 2, · · · . If in addition, E(M) has absolutely continuous norm, then, (σn(x))_n≥1 converges in E(M) if and only if x = (x_n)_n≥1 is uniformly integrable and its limit in measure topology x_∞ ∈E(M).

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ESTIMATES ON THE FIRST TWO POLY-LAPLACIAN EIGENVALUES ON SPHERICAL DOMAINS

马冰清

数学物理学报(英文版). 2012 (2): 745-751. DOI: 10.1016/S0252-9602(12)60054-X

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In this article, we study the first two eigenvalues of the higher order buckling problem on a domain in the unit sphere. We obtain an estimate on the second eigenvalue in terms of the first eigenvalue. In particular, the estimate on first two eigenvalues of the higher order buckling problem of Huang, Li and Qi [5] is included in our results.

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THE SHARP ESTIMATE OF THE THIRD HOMOGENEOUS EXPANSION FOR A CLASS OF STARLIKE MAPPINGS OF ORDER ON THE#br# UNIT POLYDISK IN Cⁿ

刘小松, 刘太顺

数学物理学报(英文版). 2012 (2): 752-764. DOI: 10.1016/S0252-9602(12)60055-1

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In this article, first, a sufficient condition for a starlike mapping of order f(x) defined on the unit ball in a complex Banach space is given. Second, the sharp estimate of the third homogeneous expansion for f is established as well, where f(z) =(f₁(z), f₂(z), · · · , f_n(z))′ is a starlike mapping of order or a normalized biholomorphic starlike mapping defined on the unit polydisk in Cⁿ, and D²fk(0)(z²)/2! = z_k(∑_ⁿl=1a_klz_l), k =1, 2, · · · , n, here, a_kl= 1/2！∂²f_k(0)/∂z_k∂z_l,k, l = 1, 2, · · · , n. Our result states that the Bieberbach conjecture in several complex variables (the case of the third homogeneous expansion for starlike mappings of order and biholomorphic starlike mappings) is partly proved.

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CLASSES OF MEROMORPHIC FUNCTIONS ASSOCIATED WITH CONIC REGIONS

J. Dziok

数学物理学报(英文版). 2012 (2): 765-774. DOI: 10.1016/S0252-9602(12)60056-3

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The object of this article is to introduce new classes of meromorphic functions associated with conic regions. Several properties like the coefficient bounds, growth and distortion theorems, radii of starlikeness and convexity, partial sums, are investigated. Some consequences of the main results for the well-known classes of meromorphic functions are also pointed out.

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ENTROPY FUNCTIONAL FOR CONTINUOUS SYSTEMS OF FINITE ENTROPY

M. Rahimi, A. Riazi

数学物理学报(英文版). 2012 (2): 775-782. DOI: 10.1016/S0252-9602(12)60057-5

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In this article, we introduce the concept of entropy functional for continuous systems on compact metric spaces, and prove some of its properties. We also extract the Kolmogorov entropy from the entropy functional.

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APPROXIMATION OF ADJOINT OF A MULTIPLIER ON BANACH ALGEBRAS

A. Ghaffari, S. Javadi, H. Khodaei

数学物理学报(英文版). 2012 (2): 783-792. DOI: 10.1016/S0252-9602(12)60058-7

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For a Banach algebra A, we denote by A* and A the first and the second duals of A respectively. Let T be a mapping from A* to itself. In this article, we will investigate some stability results concerning the equations

T(αf + βg) = αT(f) + βT(g), T(af) = aT(f)

and

T(αf + βg) + T(αf − βg) = 2α²T(f) + 2β²T(g)
where f, g ∈ A*, a ∈ A, and α, β∈ Q \ {0}.

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SINGULARLY PERTURBED SEMI-LINEAR BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS FUNCTION

丁海云, 倪明康, 林武忠, 曹扬

数学物理学报(英文版). 2012 (2): 793-799. DOI: 10.1016/S0252-9602(12)60059-9

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A class of singularly perturbed semi-linear boundary value problems with discontinuous functions is examined in this article. Using the boundary layer function method, the asymptotic solution of such a problem is given and shown to be uniformly effective. The existence and uniqueness of the solution for the system is also proved. Numerical result is presented as an illustration to the theoretical result.

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ON MEROMORPHIC SOLUTIONS OF A TYPE OF SYSTEM OF COMPOSITE FUNCTIONAL EQUATIONS

高凌云

数学物理学报(英文版). 2012 (2): 800-806. DOI: 10.1016/S0252-9602(12)60060-5

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In this article, we mainly investigate the growth and existence of meromor-phic solutions of a type of systems of composite functional equations, and obtain some interesting results. It extends some results concerning functional equations to the systems of functional equations.

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CONTINUOUS FRAME WAVELETS

Ali Akbar Arefijamaal, Narguess Tavallaei

数学物理学报(英文版). 2012 (2): 807-812. DOI: 10.1016/S0252-9602(12)60061-7

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Let π be a unitary representation of a locally compact topological group G on a separable Hilbert space H. A vector Ψ ∈ H is called a continuous frame wavelet if there exist A, B > 0 such that
A||Φ||² ≤∫_G|<π(g)Ψ ,Φ|²dg ≤ B||Φ||² (Φ ∈ H),

in which dg is the left Haar measure of G. Similar to the study of wavelets, an essential problem in the study of continuous frame wavelets is how to characterize them under the given unitary representation. Moreover, we investigate a relation between admissible vectors of π and its components.

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ON REDUCIBILITY OF THE SELF-HOMOTOPY EQUIVALENCES OF WEDGE SPACES

俞海波, 沈文淮

数学物理学报(英文版). 2012 (2): 813-817. DOI: 10.1016/S0252-9602(12)60062-9

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Reducibility of the self-homotopy equivalences of wedge spaces is studied and some conditions implying the reducibility are obtained.

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COMMON FIXED POINT THEOREMS FOR MULTI-VALUED MAPS

Boˇsko Damjanovi′c, Bessem Samet, Calogero Vetro

数学物理学报(英文版). 2012 (2): 818-824. DOI: 10.1016/S0252-9602(12)60063-0

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We establish some results on coincidence and common fixed points for a two-pair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and several results existing in the literature.

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