数学物理学报(英文版)

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ON A BI-HARMONIC EQUATION INVOLVING CRITICAL EXPONENT: EXISTENCE AND MULTIPLICITY RESULTS

Zakaria Boucheche, Ridha Yacoub, Hichem Chtioui

数学物理学报(英文版). 2011 (4): 1213-1244. DOI: 10.1016/S0252-9602(11)60311-1

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In this paper, we consider the problem of existence as well as multiplicity results for a bi-harmonic equation under the Navier
boundary conditions: Δ² u=K(x)u^p, u>0 in Ω, Δu= u=0 on ∂Ω, where Ω is a smooth domain in Rⁿ, n≥5, and p+1 = 2n/n-4 is the critical Sobolev exponent. We obtain highlightly a new criterion of existence, which provides existence results for a dense subset of positive functions, and generalizes Bahri-Coron type criterion in dimension six. Our argument gives also estimates on the Morse index of the obtained solutions and extends some known results. Moreover, it provides, for generic K, Morse inequalities at infinity, which delivers lower bounds for the number of solutions. As further applications of this Morse theoretical approach, we prove more existence results.

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RAZUMIKHIN-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

吴付科, 胡适耕, 毛学荣

数学物理学报(英文版). 2011 (4): 1245-1258. DOI: 10.1016/S0252-9602(11)60312-3

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This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with un-bounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.

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THE POINTWISE ESTIMATES TO SOLUTIONS FOR 1-DIMENSIONAL LINEAR THERMO-VISCO-ELASTIC SYSTEM

郝兴文, 彭少玉

数学物理学报(英文版). 2011 (4): 1259-1271. DOI: 10.1016/S0252-9602(11)60313-5

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In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential sys- tem. The solutions of the system show some decay property due to the parabolicity. Based
on detailed analysis on the Green function of the system, the pointwise estimates of the solutions are obtained, from which the generalized Huygens’principle is shown.

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QUASI-NEUTRAL LIMIT OF THE BIPOLAR NAVIER-STOKES-POISSON SYSTEM

杨秀绘

数学物理学报(英文版). 2011 (4): 1272-1280. DOI: 10.1016/S0252-9602(11)60314-7

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This paper is concerned with the quasi-neutral limit of the bipolar Navier-Stokes-Poisson system. It is rigorously proved, by introducing the new modulated energy functional and using the refined energy analysis, that the strong solutions of the bipolar Navier-Stokes-Poisson system converge to the strong solution of the compressible Navier-Stokes equations as the Debye length goes to zero. Moreover, if we let the viscous coeffi-cients and the Debye length go to zero simultaneously, then we obtain the convergence of the strong solutions of bipolar Navier-Stokes-Poisson system to the strong solution of the compressible Euler equations.

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ON DIFFERENCE EQUATIONS RELATING TO GAMMA FUNCTION

陈宗煊, 黄志波, 张然然

数学物理学报(英文版). 2011 (4): 1281-1294. DOI: 10.1016/S0252-9602(11)60315-9

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We consider the existence, the growth, poles, zeros, fixed points and the Borel exceptional value of solutions for the following difference equations relating to Gamma function y(z + 1) − y(z) = R(z) and y(z + 1) = P(z)y(z).

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THE RECURSION OPERATOR FOR A CONSTRAINED CKP HIERARCHY

李传忠, 田可雷, 贺劲松, 程艺

数学物理学报(英文版). 2011 (4): 1295-1302. DOI: 10.1016/S0252-9602(11)60316-0

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This paper gives a recursion operator for a 1-constrained CKP hierarchy, and by the recursion operator it proves that the 1-constrained CKP hierarchy can be reduced to the mKdV hierarchy under condition q = r.

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GLOBAL WELL-POSEDNESS FOR A FIFTH-ORDER SHALLOW WATER EQUATION ON THE CIRCLE

李用声, 杨兴雨

数学物理学报(英文版). 2011 (4): 1303-1317. DOI: 10.1016/S0252-9602(11)60317-2

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The periodic initial value problem of a fifth-order shallow water equation
∂^tu − ∂²_x∂_tu+ ∂³_xu −∂⁵_xu +3u∂_xu −∂2_xu ∂²_xu -u∂³_xu= 0

is shown to be globally well-posed in Sobolev spaces H^s(T) for s > 2/3 by I-method. For this equation lacks scaling invariance, we first reconsider the local result and pay special attention to the relationship between the lifespan of the local solution and the initial data, and then prove the almost conservation law, and finally obtain the global well-posedness by an iteration process.

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INVERSE COEFFICIENT PROBLEMS FOR PARABOLIC HEMIVARIATIONAL INEQUALITIES

刘振海, I.Szántò

数学物理学报(英文版). 2011 (4): 1318-1326. DOI: 10.1016/S0252-9602(11)60318-4

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This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gra-dient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained.

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EXAMPLES ON EXCEPTIONAL VALUES OF MEROMORPHIC FUNCTIONS

彭炎红, 孙道椿

数学物理学报(英文版). 2011 (4): 1327-1336. DOI: 10.1016/S0252-9602(11)60319-6

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In this paper, by means of the definition of Borel exceptional value method, another exceptional value of meromorphic function which is a T exceptional value is defined by linking the concept of T direction. And we construct a meromorphic function with zero as Borel exceptional value, but not as T exceptional value; and another meromorphic function with zero as T exceptional value, but not as Borel exceptional value.

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THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

Mujeeb ur Rehman, Rahmat Ali Khan, Naseer Ahmad Asif

数学物理学报(英文版). 2011 (4): 1337-1346. DOI: 10.1016/S0252-9602(11)60320-2

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In this paper, we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type
^cD^δ₀+u(t) = f(t, u(t), ^cD^σ₀+u(t)), t ∈ [0, T],
u(0) = ∂u(η), u(T) = βu(η),
where 1 < δ < 2, 0 < σ < 1, α, β∈ R, η ∈ (0, T), αη(1 −β ) + (1 − α)(T − βη) ≠ 0 and ^cD^δ₀+, ^cD^σ₀+ are the Caputo fractional derivatives. We use Schauder fixed point theorem and contraction mapping principle to obtain existence and uniqueness results. Examples
are also included to show the applicability of our results.

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COMPACT COMPOSITION OPERATORS ON GENERALIZED LIPSCHITZ SPACES

戴济能, 欧阳才衡

数学物理学报(英文版). 2011 (4): 1347-1356. DOI: 10.1016/S0252-9602(11)60321-4

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In this paper, boundedness and compactness of the composition operator on the generalized Lipschitz spaces ( > 1) of holomorphic functions in the unit disk are characterized.

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A UNIFIED CLASS OF ANALYTIC FUNCTIONS WITH FIXED ARGUMENT OF COEFFICIENTS

J. Dziok

数学物理学报(英文版). 2011 (4): 1357-1366. DOI: 10.1016/S0252-9602(11)60322-6

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In this paper we introduce new classes of analytic functions with fixed argu-ment of coefficients defined by subordination. Coefficient estimates, distortion theorems, integral means inequalities, and the radii of convexity and starlikeness are investigated. Convolution properties are also pointed out.

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ON COMPACT COMPOSITION OPERATORS ON A CLASS OF HOLOMORPHIC FUNCTION SPACES OVER THE UNIT BALL IN Cⁿ

龙素娟

数学物理学报(英文版). 2011 (4): 1367-1376. DOI: 10.1016/S0252-9602(11)60323-8

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In this paper, a general function space X(Bn) over the unit ball in Cn with norm k · kX(Bn) is introduced. It contains all Hardy space, Bergman space, Besov space etc. The author gives a formulation of a compact composition operator on X(Bn), related to works of [8] and [10].

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SCHWARZ-PICK ESTIMATES FOR BOUNDED HOLOMORPHIC FUNCTIONS ON CLASSICAL DOMAINS

刘洋, 陈志华

数学物理学报(英文版). 2011 (4): 1377-1382. DOI: 10.1016/S0252-9602(11)60324-X

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In this paper, Schwarz-Pick estimates for high order Fr´echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of higher order partial derivatives for bounded holomorphic functions on the disk and unit ball.

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ESTIMATES ON EIGENVALUES FOR THE BIHARMONIC OPERATOR ON A BOUNDED DOMAIN IN Hⁿ(−1)

黄广月, 李兴校

数学物理学报(英文版). 2011 (4): 1383-1388. DOI: 10.1016/S0252-9602(11)60325-1

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In this paper, we consider eigenvalues of the Dirichlet biharmonic operator on a bounded domain in a hyperbolic space. We obtain universal bounds on the (k + 1)th eigenvalue in terms of the first kth eigenvalues independent of the domains.

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DECAY ESTIMATES OF PLANAR STATIONARY WAVES FOR DAMED WAVE EQUATIONS WITH NONLINEAR CONVECTION IN#br# MULTI-DIMENSIONAL HALF SPACE

范丽丽, 刘红霞, 尹慧

数学物理学报(英文版). 2011 (4): 1389-1410. DOI: 10.1016/S0252-9602(11)60326-3

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This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space Rn
?
ut_t− Δu + u_t + divf(u) = 0, t > 0, x = (x₁, x′)∈ Rⁿ₊(:= R₊ × Rⁿ⁻¹),
u(0, x) = u₀(x) → u₊, as x₁ →+∞,
u_t(0, _x) = u₁(x), u(t, 0, x′) = u_b, x′ = (x₂, x₃, · · · , x_n) ∈ Rⁿ−1. (I)
For the non-degenerate case f′₁(u₊) < 0, it was shown in [10] that the above initial-boundary value problem (I) admits a unique global solution u(t, x) which converges to the corresponding planar stationary wave Φ(x₁) uniformly in x₁ ∈R₊ as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u(t, x) for t →+∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f′₁(u_b) < 0. The main purpose of this paper devoted to discussing the case of f′₁(u_b) ≥ 0 and we show that similar results still hold for
such a case. Our analysis is based on some delicate energy estimates.

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C^l -G_V TRIVIALITY OF FUNCTION GERMS AND NEWTON POLYHEDRA

刘恒兴, 张敦穆

数学物理学报(英文版). 2011 (4): 1411-1424. DOI: 10.1016/S0252-9602(11)60327-5

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Weprovideestimates onthedegreeof C^l -G_V determinacy(G is oneofMather’s groups R or K ) of function germs which are defined on analytic variety V and satisfies a non-degeneracy condition with respect to some Newton polyhedron. The result gives lan explicit order such that the C^lgeometrical structure of a function germ is preserved l after higher order perturbations, which generalizes the result on C^l-G triviality of function germs given by M.A.S.Ruas.

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ON F-SENSITIVE PAIRS

谭枫, 张瑞丰

数学物理学报(英文版). 2011 (4): 1425-1435. DOI: 10.1016/S0252-9602(11)60328-7

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In the present paper, we define sensitive pairs via Furstenberg families and
discuss the relation of three definitions: sensitivity, F-sensitivity and F-sensitive pairs,
see Theorem 1. For transitive systems, we give some su?cient conditions to ensure the
existence of F-sensitive pairs. In particular, each non-minimal E system (M system, P sys-
tem) has positive lower density (Fs, Fr resp.)-sensitive pairs almost everywhere. Moreover,
each non-minimal M system is Fts-sensitive. Finally, by some examples we show that: (1)
F-sensitivity can not imply the existence of F-sensitive pairs. That means there exists an
F-sensitive system, which has no F-sensitive pairs. (2) There is no immediate relation be-
tween the existence of sensitive pairs and Li-Yorke chaos, i.e., there exists a system (X,f)
without Li-Yorke scrambled pairs, which has κB-sensitive pairs almost everywhere. (3)
If the system (G,f) is sensitive, where G is a finite graph, then it has κB-sensitive pairs
almost everywhere.

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GENERAL DECAY OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS

吴舜堂

数学物理学报(英文版). 2011 (4): 1436-1448. DOI: 10.1016/S0252-9602(11)60329-9

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The initial boundary value problem for a viscoelastic equation

|u_t|^ρ u_tt -Δu-Δu_tt+∫^t₀g(t-s)Δu(s)ds+|^mu_t| u_t= |u|^p u

in a bounded domain is considered, where ρ,m,p > 0 and g is a nonnegative and decaying
function. The general uniform decay of solution energy is discussed under some conditions
on the relaxation function g and the initial data by adopting the method of [14, 15, 19].
This work generalizes and improves earlier results in the literature.

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CLASSIFICATION OF SOLUTIONS FOR A CLASS OF SINGULAR INTEGRAL SYSTEM

许建开, 谭忠

数学物理学报(英文版). 2011 (4): 1449-1456. DOI: 10.1016/S0252-9602(11)60330-5

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In this paper, we consider the following integral system:
???u(x) = v (y) dy,
? n n-α
R |x-y|
(1.1)
??? up(y)
?v(x) = n-μdy,
n
R |x-y|

where 0 < α, μ < n; p,q ≥ 1. Using the method of moving planes in an integral form which
was recently introduced by Chen, Li, and Ou in [2, 4, 8], we show that all positive solutions
of (0.1) are radially symmetric and decreasing with respect to some point under some
general conditions of integrability. The results essentially improve and extend previously
known results [4, 8].

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DARBOUX TRANSFORMATION OF A NONLINEAR EVOLUTION EQUATION AND ITS EXPLICIT SOLUTIONS

李文敏, 韩有琴, 周高军

数学物理学报(英文版). 2011 (4): 1457-1464. DOI: 10.1016/S0252-9602(11)60331-7

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In this paper, we study a differential-difference equation associated with dis-crete 3 ×3 matrix spectral problem. Based on gauge transformation of the spectral problm, Darboux transformation of the differential-difference equation is given. In order to solve the differential-difference equation, a systematic algebraic algorithm is given. As an appli-cation, explicit soliton solutions of the differential-difference equation are given.

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CHARACTERIZATIONS OF COMPACT OPERATORS ON SOME EULER SPACES OF DIFFERENCE EQUENCES OF ORDER m

Ivana Djolovi′c, Eberhard Malkowsky

数学物理学报(英文版). 2011 (4): 1465-1474. DOI: 10.1016/S0252-9602(11)60332-9

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In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Baffsar ([17]) defined the Euler spaces of m-th order difference sequences e^r₀( Δ^（m）), e^r_c(Δ^（m） ) and e^r_∞(Δ^（m） ) and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that pur-pose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c₀, c and l_∞. The main tool for our characterizations is the Hausdorff measure of noncompactness.

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A CHARACTERIZATION OF ORTHONORMAL WAVELET FAMILIES IN SOBOLEV SPACES

鲁大勇, 李登峰

数学物理学报(英文版). 2011 (4): 1475-1488. DOI: 10.1016/S0252-9602(11)60333-0

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In this paper, a characterization of orthonormal wavelet families in Sobolev spaces H^s(R) is established.

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THE HARDY TYPE INEQUALITY FOR THE MAXIMAL OPERATOR OF THE ONE-DIMENSIONAL DYADIC DERIVATIVE

Ushangi Goginava

数学物理学报(英文版). 2011 (4): 1489-1493. DOI: 10.1016/S0252-9602(11)60334-2

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In this paper we prove that the maximal operator I* of dyadic derivative is not bounded from the Hardy space H_p [0, 1] to the Hardy space H_p [0, 1], when 0 < p 1.

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TRANSPORTATION INEQUALITIES FOR WEAKLY DEPENDENT SEQUENCES

马宇韬

数学物理学报(英文版). 2011 (4): 1494-1502. DOI: 10.1016/S0252-9602(11)60335-4

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In [3], they gave necessary and sufficient condition for T₁C and then as ap-plications T₁C for weakly dependent sequences was established. In this note, based on Gozlan-L´eonard characterization for W₁H-inequalities, we extends this result to W₁H-inequalities.

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A NOTE ON THE INTERACTIONS OF ELEMENTARY WAVES FOR THE AR TRAFFIC FLOW MODEL WITHOUT VACUUM

孙梅娜

数学物理学报(英文版). 2011 (4): 1503-1512. DOI: 10.1016/S0252-9602(11)60336-6

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In this note, we consider the interactions of elementary waves for the traffic flow model proposed by Aw and Rascle when the vacuum is not involved. The solutions are obtained constructively and globally when the initial data consist of three pieces of constant states. Furthermore, it can be found that the Riemann solutions are stable with respect to such small perturbations of the initial data in this particular situation by investigating the limits of the solutions as the perturbed parameter " goes to zero.

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A NOTE ON GENERALIZED ABSOLUTE SUMMABILITY FACTORS FOR A TRIANGULAR MATRIX

Ekrem Savas

数学物理学报(英文版). 2011 (4): 1513-1516. DOI: 10.1016/S0252-9602(11)60337-8

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In this paper, a general theorem on |A, δ|k-summability factors of infinite series is proved under different conditions.

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L^p CONTINUITY OF HÖRMANDER SYMBOL OPERATORS O_pS^m_0,0 AND NUMERICAL ALGORITHM

杨奇祥

数学物理学报(英文版). 2011 (4): 1517-1534. DOI: 10.1016/S0252-9602(11)60338-X

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If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for H¨ormander symbol operators O_pS^m_0,0, which is different to the case S^m_ρ,δ (0 ≤δ < ρ ≤ 1). In this paper, we use a special numerical algorithm based on wavelets to study the L^pcontinuity of non infinite smooth operators O_pS^m_0,0; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L²→L²continuity for scale operators. By considering the influence region of scale operator, we get H¹(= F^0,2₁ ) → L¹ continuity and L¹ →BMO continuity. By interpolation theorem, we get also L^p(= F^0,2_p ) → L^p continuity for 1 < p < ∞. Our results are sharp for F^0,2_p →L^pcontinuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for
which the symbols can ensure the resulting operators to be bounded on these spaces.

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NASH EQUILIBRIA WITHOUT CONTINUITY OF THE CHOICE RULES

José C.R. Alcantud

数学物理学报(英文版). 2011 (4): 1535-1540. DOI: 10.1016/S0252-9602(11)60339-1

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The proposal in Alcantud and Al´os-Ferrer [1], where players that express their tastes according to choice rules facing a competitive situation, is further exploited here. We prove that, under lack of continuity of the choice rules it is also possible to ensure the existence of equilibrium. We shall appeal to general situations that are fulfilled by well-established models, where players have non-transitive preferences of various types.

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SOME RESULTS ON PRODUCT COMPLEX FINSLER MANIFOLDS

吴志成, 钟春平

数学物理学报(英文版). 2011 (4): 1541-1552. DOI: 10.1016/S0252-9602(11)60340-8

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Let (M, F) be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds (M₁, F₁) and (M₂, F₂). In this paper, we obtain the relationship between the Chern Finsler connection coefficients Γⁱ_;k associated to F and the Chern Finsler connection coefficients ˜ Γ^a_;c,˜ Γ^α_;_γassociated to F₁, F₂, respectively. As applications we prove that, if both (M₁, F₁) and (M₂, F₂) are strongly Kähler Finsler (complex Berwald, or locally complex Minkowski, respectively) manifolds, so does (M, F). Furthermore,
we prove that the holomorphic curvature KF = 0 if and only if K_F₁= 0 and K_F₂ = 0.

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A FIXED POINT APPROACH TO THE STABILITY OF A GENERALIZED APOLLONIUS TYPE QUADRATIC FUNCTIONAL EQUATION

王志华

数学物理学报(英文版). 2011 (4): 1553-1560. DOI: 10.1016/S0252-9602(11)60341-X

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Using the fixed point method, this article proves the Hyers-Ulam-Rassias sta-bility of a generalized Apollonius type quadratic functional equation in Banach spaces. The conditions of these results are demonstrated by the quadratic functional equation of Apollonius type.

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AMBARZUMYAN’S THEOREM WITH EIGENPARAMETER IN THE BOUNDARY CONDITIONS

杨传富, 杨孝平

数学物理学报(英文版). 2011 (4): 1561-1568. DOI: 10.1016/S0252-9602(11)60342-1

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In this paper, the classical Ambarzumyan’s theorem for the regular Sturm-Liouville problem is extended to the case in which the boundary conditions are eigenpa-rameter dependent. Specifically, we show that if the spectrum of the operator −D2+q with
eigenparameter dependent boundary conditions is the same as the spectrum belonging to the zero potential, then the potential function q is actually zero.

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NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH#br# STRUM-LIOUVILLE BOUNDARY CONDITIONS

赵增勤

数学物理学报(英文版). 2011 (4): 1569-1582. DOI: 10.1016/S0252-9602(11)60343-3

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This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C²ⁿ⁻²[0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C²ⁿ⁻¹[0, 1] positive solutions. Relations between the positive solutions and the Green’s functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems.

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IMPROVED GAGLIARDO-NIRENBERG INEQUALITIES ON HEISENBERG TYPE GROUPS

罗光洲

数学物理学报(英文版). 2011 (4): 1583-1590. DOI: 10.1016/S0252-9602(11)60344-5

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Motivated by the idea of M. Ledoux who brings out the connection between Sobolev embeddings and heat kernel bounds, we prove an analogous result for Kohn’s sub-Laplacian on the Heisenberg type groups. The main result includes features of an inequality of either Sobolev or Galiardo-Nirenberg type.

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SOME REMARKS ON (L)-GREEN’S RELATIONS AND STRONGLY RPP SEMIGROUPS

杜兰, 郭聿琦, K.P. Shum

数学物理学报(英文版). 2011 (4): 1591-1599. DOI: 10.1016/S0252-9602(11)60345-7

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In order to study rpp semigroups, in particular, some special cases, several facts on (l)-Green’s relations and strongly rpp semigroups are given as some remarks.

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LOCAL AUTOMORPHISMS OF SEMISIMPLE ALGEBRAS AND GROUP ALGEBRAS

王登银, 关琦, 张冬菊

数学物理学报(英文版). 2011 (4): 1600-1612. DOI: 10.1016/S0252-9602(11)60346-9

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Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F-algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to be an algebraically closed field of characteristic zero, K a finite group, FK the group algebra of K over F, then all local automorphisms of FK are also characterized.

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DE MORGAN ALGEBRAS WITH DOUBLE DEMI-PSEUDOCOMPLEMENTATION

方捷, 王雷波

数学物理学报(英文版). 2011 (4): 1613-1623. DOI: 10.1016/S0252-9602(11)60347-0

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The variety ddpM of de Morgan algebras with double demi-pseudocomplem-entation consists of those algebras (L;∧,∨,^{? ,* ,+} , 0, 1) of type (2, 2, 1, 1, 1, 0, 0) where (L; ∧,∨,^? , 0, 1) is a de Morgan algebra, (L;∧,∨, ^*,+ , 0, 1) is a double demi-p-lattice and the operations x → x^?, x → x^* and x → x⁺ are linked by the identities x^*?= x^?*, x^+? = x^?+ and x^*+ = x^+*. In this paper, we characterize congruences on a ddpM-algebra, and give a description of the subdirectly irreducible algebras.

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SCHWARZ-PICK ESTIMATES FOR PARTIAL DERIVATIVES OF ARBITARY ORDER OF BOUNDED HOLOMORPHIC FUNCTIONS#br# IN THE UNIT BALL OF Cⁿ

戴绍虞, 陈怀惠

数学物理学报(英文版). 2011 (4): 1624-1632. DOI: 10.1016/S0252-9602(11)60348-2

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This paper gives a Schwarz-Pick estimate for bounded holomorphic functions in the unit ball of Cⁿ.

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ON THE STABILITY OF FUSION FRAMES (FRAMES OF SUBSPACES)

Mohammad Sadegh Asgari

数学物理学报(英文版). 2011 (4): 1633-1642. DOI: 10.1016/S0252-9602(11)60349-4

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A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame (frame of subspaces) is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space
by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3(iii)] with extra information about the bounds.

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SOME INEQUALITIES OF HERMITE–HADAMARD TYPE FOR s-CONVEX FUNCTIONS

Mohammad W. Alomari, Maslina Darus, Uˇgur S. Kirmaci

数学物理学报(英文版). 2011 (4): 1643-1652. DOI: 10.1016/S0252-9602(11)60350-0

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In this paper several inequalities of the left-hand side of Hermite-Hadamard’s inequality are obtained for s-convex functions.

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