数学物理学报(英文版)

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DEGREE 3 ALGEBRAIC MINIMAL SURFACES IN THE 3-SPHERE

Joe S. Wang

数学物理学报(英文版). 2012 (6): 2065-2084. DOI: 10.1016/S0252-9602(12)60160-X

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We give a local analytic characterization that a minimal surface in the 3-sphere S³ ( R⁴ defined by an irreducible cubic polynomial is one of the Lawson´s minimal tori. This provides an alternative proof of the result by Perdomo (Characterization of order 3 algebraic immersed minimal surfaces of S³, Geom. Dedicata 129 (2007), 23–34).

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IFP-FLAT DIMENSIONS AND IFP-INJECTIVE DIMENSIONS

卢博, 刘仲奎

数学物理学报(英文版). 2012 (6): 2085-2095. DOI: 10.1016/S0252-9602(12)60161-1

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In basic homological algebra, the flat and injective dimensions of modules play an important and fundamental role. In this paper, the closely related IFP-flat and IFP-injective dimensions are introduced and studied. We show that IFP-fd(M) =IFP-id(M+) and IFP-fd(M⁺)=IFP-id(M) for any R-module M over any ring R. Let IIn (resp., IF_n) be the class of all left (resp., right) R-modules of IFP-injective (resp., IFP-flat) dimension at most n. We prove that every right R-module has an IF_n-preenvelope, (IF_n, IF_n ) is a perfect cotorsion theory over any ring R, and for any ring R with IFP-id(_RR) ≤n, (II_n, II_n ) is a perfect cotorsion theory. This generalizes and improves the earlier work (J. Algebra 242 (2001), 447-459). Finally, some applications are given.

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SOME ASYMPTOTIC PROPERTIES OF THE CONVOLUTION TRANSFORMS OF FRACTAL MEASURES

曹丽

数学物理学报(英文版). 2012 (6): 2096-2104. DOI: 10.1016/S0252-9602(12)60162-3

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We study the asymptotic behavior near the boundary of u(x, y) = K_y* μ (x), defined on the half-space R⁺×R^N by the convolution of an approximate identity K_y(·) (y >0) and a measure μ on R^N. The Poisson and the heat kernel are unified as special cases in our setting. We are mainly interested in the relationship between the rate of growth at boundary of u and the s-density of a singular measure μ. Then a boundary limit theorem of Fatou´s type for singular measures is proved. Meanwhile, the asymptotic behavior of a quotient of K_μ and K_ν is also studied, then the corresponding Fatou-Doob´s boundary relative limit is obtained. In particular, some results about the singular boundary behavior of harmonic and heat functions can be deduced simultaneously from ours. At the end, an application in fractal geometry is given.

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POLYNOMIAL REPRESENTATIONS OF THE AFFINE NAPPI-WITTEN LIE ALGEBRA cH₄

陈雪, 黄智力

数学物理学报(英文版). 2012 (6): 2105-2118. DOI: 10.1016/S0252-9602(12)60163-5

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In this paper, the representation theory for the affine Lie algebra bH₄ associated to the Nappi-Witten Lie algebra H₄ is studied. Polynomial representations of the affine Nappi-Witten Lie algebra bH₄ are given.

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MEIR-KEELER TYPE CONTRACTIONS FOR TRIPLED FIXED POINTS

Hassen Aydi, Erdal Karapmnar, Calogero Vetro

数学物理学报(英文版). 2012 (6): 2119-2130. DOI: 10.1016/S0252-9602(12)60164-7

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In 2011, Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces. In our paper, we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction.

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EXISTENCE OF INFINITE ENERGY SOLUTION TO THE INELASTIC BOLTZMANN EQUATION WITH EXTERNAL FORCE

魏金波, 张显文

数学物理学报(英文版). 2012 (6): 2131-2140. DOI: 10.1016/S0252-9602(12)60165-9

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In this paper, the Cauchy problem for the inelastic Boltzmann equation with external force is considered in the case of initial data with infinite energy. More pre-cisely, under the assumptions on the bicharacteristic generated by external force, we prove the global existence of solution for small initial data compared to the local Maxwellian exp{−p|x − v|²}, which has infinite mass and energy.

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GLOBAL CLASSICAL SOLUTIONS TO THE 3-D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL INITIAL ENERGY

张培欣, 邓雪梅, 赵俊宁

数学物理学报(英文版). 2012 (6): 2141-2160. DOI: 10.1016/S0252-9602(12)60166-0

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We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ||ρ0||_L∞ is appropriate small and 1 << 6/ 5 . Here the initial density could have vacuum and we do not require that the initial energy is small.

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EXISTENCE AND REGULARITY OF SOLUTIONS TO MODEL FOR LIQUID MIXTURE OF ³HE-⁴HE

罗宏, 蒲志林

数学物理学报(英文版). 2012 (6): 2161-2175. DOI: 10.1016/S0252-9602(12)60167-2

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Existence and regularity of solutions to model for liquid mixture of ³He-⁴He is considered in this paper. First, it is proved that this system possesses a unique global weak solution in H¹(Ω, C ×R) by using Galerkin method. Secondly, by using an iteration procedure, regularity estimates for the linear semigroups, it is proved that the model for liquid mixture of ³He-⁴He has a unique solution in H^k(Ω , C × R) for all k ≥ 1.

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MULTIPLE POSITIVE SOLUTIONS FOR FIRST ORDER IMPULSIVE SINGULAR INTEGRO-DIFFERENTIAL EQUATIONS ON THE HALF LINE

郭大钧

数学物理学报(英文版). 2012 (6): 2176-2190. DOI: 10.1016/S0252-9602(12)60168-4

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In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.

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THE SURFACE AREA PRESERVING MEAN CURVATURE FLOW IN QUASI-FUCHSIAN MANIFOLDS

田大平, 李光汉, 吴传喜

数学物理学报(英文版). 2012 (6): 2191-2202. DOI: 10.1016/S0252-9602(12)60169-6

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In this paper, we consider the surface area preserving mean curvature flow in quasi-Fuchsian 3-manifolds. We show that the flow exists for all times and converges exponentially to a smooth surface of constant mean curvature with the same surface area as the initial surface.

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EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS FOR A SEMI-LINEAR HEAT EQUATION WITH FRACTIONAL LAPLACIAN

谭忠, 许勇强

数学物理学报(英文版). 2012 (6): 2203-2210. DOI: 10.1016/S0252-9602(12)60170-2

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In this paper, we are concerned with the existence and non-existence of global solutions of a semi-linear heat equation with fractional Laplacian. We obtain some exten-sion of results of Weissler who considered the case α = 1, and h ≡ 1.

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DECAY ESTIMATES FOR ISENTROPIC COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS IN BOUNDED DOMAIN

Mohamed Ahmed Abdallah, 江飞, 谭忠

数学物理学报(英文版). 2012 (6): 2211-2220. DOI: 10.1016/S0252-9602(12)60171-4

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In this paper, under the hypothesis that ρ is upper bounded, we construct a Lyapunov functional for the multidimensional isentropic compressible magnetohydrody-namic equations and show that the weak solutions decay exponentially to the equilibrium state in L² norm. Our result verifies that the method of Daoyuan Fang, Ruizhao Zi and Ting Zhang [1] can be adapted to magnetohydrodynamic equations.

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VECTORIAL EKELAND´S VARIATIONAL PRINCIPLE WITH A W-DISTANCE AND ITS EQUIVALENT THEOREMS

丘京辉, 李博, 贺飞

数学物理学报(英文版). 2012 (6): 2221-2236. DOI: 10.1016/S0252-9602(12)60172-6

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By using the properties of w-distances and Gerstewitz´s functions, we first give a vectorial Takahashi´s nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland´s variational principle, where the objective function is from a complete metric space into a pre-ordered topological vector space and the perturbation contains a w-distance and a non-decreasing function of the objective function value. From the general vectorial variational principle, we deduce a vectorial Caristi´s fixed point theorem with a w-distance. Finally we show that the above three theorems are equivalent to each other. The related known results are generalized and improved. In particular, some conditions in the theorems of [Y. Araya, Ekeland´s variational principle and its equivalent theorems in vector optimization, J. Math. Anal. Appl. 346(2008), 9–16] are weakened or even completely relieved.

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EXPONENTIAL DECAY FOR A NONLINEAR VISCOELASTIC EQUATION WITH SINGULAR KERNELS

Shun-Tang Wu

数学物理学报(英文版). 2012 (6): 2237-2246. DOI: 10.1016/S0252-9602(12)60173-8

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The nonlinear viscoelastic wave equation
|u_t|^ρ u_tt − Δu − Δu_tt +∫^t₀g(t − s)Δu(s)ds + |u|^p u = 0,
in a bounded domain with initial conditions and Dirichlet boundary conditions is consid-ered. We prove that, for a class of kernels g which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.

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APPROXIMATION OF A CAUCHY-JENSEN ADDITIVE FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN NORMED SPACES

Hassan Azadi Kenary

数学物理学报(英文版). 2012 (6): 2247-2258. DOI: 10.1016/S0252-9602(12)60174-X

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Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation
2f(∑^p_i₌₁x_i+∑^q_j₌₁y_j+ 2∑^d_k₌₁z_k/2) =2f(∑^p_i₌₁x_i+∑^q_j₌₁y_j+ 2∑^d_k₌₁(z_k),

where p, q, d are integers greater than 1, in non-Archimedean normed spaces.

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RIESZ IDEMPOTENT AND BROWDER´S THEOREM FOR ABSOLUTE-(p, r)-PARANORMAL OPERATORS

Salah Mecheri

数学物理学报(英文版). 2012 (6): 2259-2264. DOI: 10.1016/S0252-9602(12)60175-1

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An operator T is said to be paranormal if ||T²x|| ≥ ||Tx||² holds for every unit vector x. Several extensions of paranormal operators are considered until now, for example absolute-k-paranormal and p-paranormal introduced in [10], [14], respectively. Yamazaki and Yanagida [38] introduced the class of absolute-(p, r)-paranormal operators as a further generalization of the classes of both absolute-k-paranormal and p-paranormal operators. An operator T ∈B(H) is called absolute-(p, r)-paranormal operator if |||T|^p|T*|^rx||^r ≥ |||T*|rx||^p+r for every unit vector x ∈ H and for positive real numbers p > 0 and r > 0. The famous result of Browder, that self adjoint operators satisfy Browder´s theorem, is extended to several classes of operators. In this paper we show that for any absolute-(p, r)-paranormal operator T, T satisfies Browder´s theorem and a-Browder´s theorem. It is also shown that if E is the Riesz idempotent for a nonzero isolated point μ of the spectrum of a absolute-(p, r)-paranormal operator T, then E is self-adjoint if and only if the null space of T − μ, N(T − μ) N(T* − μ).

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THE SPACES OF CESÀRO ALMOST CONVERGENT SEQUENCES AND CORE THEOREMS

Kuddusi Kayaduman, Mehmet S?eng¨on¨ul

数学物理学报(英文版). 2012 (6): 2265-2278. DOI: 10.1016/S0252-9602(12)60176-3

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As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new (see [15]). The purpose of this paper is to introduce the new spaces e f and e f₀ consisting of all sequences whose Cesàro transforms of order one are in the spaces f and f₀, respectively. Also, in this paper, we show that e f and e f₀ are linearly isomorphic to the spaces f and f₀, respectively. The β- and γ-duals of the spaces e f and e f₀ are computed. Furthermore, the classes ( f : μ) and (μ : f) of infinite matrices are characterized for any given sequence space μ, and determined the necessary and sufficient conditions on a matrix A to satisfy Bc-core(Ax) K-core(x), K-core(Ax) Bc-core(x), Bc-core(Ax) Bc-core(x), Bc-core(Ax) st-core(x) for all x ∈l₁.

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REFLEXIVITY OF POWERS OF THE MULTIPLICATION OPERATOR ON SPECIAL FUNCTION SPACES

B. Yousefi, Sh. Khoshdel

数学物理学报(英文版). 2012 (6): 2279-2284. DOI: 10.1016/S0252-9602(12)60177-5

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In this paper we present sufficient conditions for reflexivity of any powers of the multiplication operator acting on Banach spaces of formal Laurent series.

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CHARACTERIZATIONS OF SOME MATRIX CLASSES OF QUASI-HOMOGENEOUS OPERATORS

陈爱红, 李容录

数学物理学报(英文版). 2012 (6): 2285-2294. DOI: 10.1016/S0252-9602(12)60178-7

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In this paper, we give a general characterization of a class of matrices of quasi-homogeneous operators between topological vector spaces.

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FINITE GROUPS WHOSE MINIMAL SUBGROUPS ARE WEAKLY H-SUBGROUPS

M. M. Al-Mosa Al-Shomrani, M. Ramadan, A. A. Heliel

数学物理学报(英文版). 2012 (6): 2295-2301. DOI: 10.1016/S0252-9602(12)60179-9

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Let G be a finite group. A subgroup H of G is called an H-subgroup in G if N_G(H)∩H^g ≤ H for all g ∈ G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H∩K is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G. Our results improve and generalize several recent results in the literature.

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THRESHOLD RESULT FOR SEMILINEAR PARABOLIC EQUATIONS WITH INDEFINITE NON-HOMOGENEOUS TERM

谢君辉, 戴求亿, 刘芳

数学物理学报(英文版). 2012 (6): 2302-2314. DOI: 10.1016/S0252-9602(12)60180-5

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In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations
{u_t− Δu = g(u) + λf(x), (x, t) ∈Ω × (0, T),
u = 0, (x, t) ∈ ∂Ω × [0, T),
u(x, 0) = u₀(x) ≥ 0, x ∈Ω (P)
By combining a priori estimate of global solution with property of stationary solution set of problem (P), we prove that the minimal stationary solution U_λ(x) of problem (P) is stable, whereas, any other stationary solution is an initial datum threshold for the existence and
nonexistence of global solution to problem (P).

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CHARACTERIZATION OF MULTIPLIER SPACES WITH DAUBECHIES WAVELETS

杨奇祥

数学物理学报(英文版). 2012 (6): 2315-2321. DOI: 10.1016/S0252-9602(12)60181-7

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We characterize the multiplier spaces from Sobolev spaces to L² with Daubechies wavelets without using capacity.

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ELEMENTARY AND Φ-FREE LIE TRIPLE SYSTEMS

白瑞蒲, 刘丽丽, Li Zhenheng

数学物理学报(英文版). 2012 (6): 2322-2328. DOI: 10.1016/S0252-9602(12)60182-9

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We introduce elementary and Φ-free Lie triple systems and study the proper-ties of these systems. In particular, structures of subsystems of an elementary Lie triple system and a class of Φ-free Lie triple systems are investigated.

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A CHARACTERIZATION OF SCHECHTER´S ESSENTIAL SPECTRUM BY MEAN OF MEASURE OF NON-STRICT-SINGULARITY#br# AND APPLICATION TO MATRIX OPERATOR

Nedra Moalla

数学物理学报(英文版). 2012 (6): 2329-2340. DOI: 10.1016/S0252-9602(12)60183-0

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In this paper we use the notion of measure of non-strict-singularity to give some results on Fredholm operators and we establish a fine description of the Schechter essential spectrum of a closed densely defined linear operator.

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STABILITY AND SUPER CONVERGENCE ANALYSIS OF ADI-FDTD FOR THE 2D MAXWELL EQUATIONS IN A LOSSY MEDIUM

高理平

数学物理学报(英文版). 2012 (6): 2341-2368. DOI: 10.1016/S0252-9602(12)60184-2

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Several new energy identities of the two dimensional(2D) Maxwell equations in a lossy medium in the case of the perfectly electric conducting boundary conditions are proposed and proved. These identities show a new kind of energy conservation in the Maxwell system and provide a new energy method to analyze the alternating direction im-plicit finite difference time domain method for the 2D Maxwell equations (2D-ADI-FDTD). It is proved that 2D-ADI-FDTD is approximately energy conserved, unconditionally sta-ble and second order convergent in the discrete L2 and H1 norms, which implies that 2D-ADI-FDTD is super convergent. By this super convergence, it is simply proved that the error of the divergence of the solution of 2D-ADI-FDTD is second order accurate. It is also proved that the difference scheme of 2D-ADI-FDTD with respect to time t is second order convergent in the discrete H1 norm. Experimental results to confirm the theoretical
analysis on stability, convergence and energy conservation are presented.

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NOTE ON AN OPEN PROBLEM OF HIGHER ORDER NONLINEAR EVOLUTION EQUATIONS

Tujin Kim, 常谦顺, 徐静

数学物理学报(英文版). 2012 (6): 2369-2376. DOI: 10.1016/S0252-9602(12)60185-4

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In view of a new idea on initial conditions, an open problem of nonlinear evolution equations with higher order, which was given by J. L. Lions, is solved. Effect of our results is shown on an example.

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SINGULAR POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION

杨芬

数学物理学报(英文版). 2012 (6): 2377-2387. DOI: 10.1016/S0252-9602(12)60186-6

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The existence and uniqueness of singular solutions decaying like r^−m (see (1.4)) of the equation
Δu +∑^k_Xi=c_i|x|^l_iu^p_i = 0, x ∈ Rⁿ(0.1)
are obtained, where n ≥ 3, c_i> 0, l_i > −2, i = 1, 2, · · · , k, p_i > 1, i = 1, 2, · · · , k and the separation structure of singular solutions decaying like r⁻⁽ⁿ⁻²⁾ of eq. (0.1) are discussed. moreover, we obtain the explicit critical exponent p_s(l) (see (1.9)).

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SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES

甘师信, 陈平炎

数学物理学报(英文版). 2012 (6): 2388-2400. DOI: 10.1016/S0252-9602(12)60187-8

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In this paper the authors study the complete, weak and almost sure conver-gence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].

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UNIFORM APPROXIMATION OF ENTIRE FUNCTIONS OF SLOW GROWTH ON COMPACT SETS

G. S. Srivastava, S. Kumar

数学物理学报(英文版). 2012 (6): 2401-2410. DOI: 10.1016/S0252-9602(12)60188-X

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In the present paper, we study the polynomial approximation of entire func-tions of several complex variables. The characterizations of generalized order and gener-alized type of entire functions of slow growth are obtained in terms of approximation and interpolation errors.

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CONSTRUCTING EXAMPLES WITH 5 EQUILIBRIA FOR SYMMETRIC 3 ×|2 CES / LES PURE EXCHANGE ECONOMIES

黄慧, 石晓军, 张顺明

数学物理学报(英文版). 2012 (6): 2411-2430. DOI: 10.1016/S0252-9602(12)60189-1

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This paper explores the existence of multiple equilibria for symmetric 3 indi-vidual, 2 good CES / LES pure exchange economies. Analytically, we show that there are no more than 5 equilibria in such economies. The number of equilibria varies from 5 to 3 then to 1. We generalize our analytical results of existence of 1, 3, 5 equilibria for a wide range of parametrizations. We also provide concrete examples of 1, 3, 5 equilibria with parameter zones specified.

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ATTRACTORS FOR FULLY DISCRETE FINITE DIFFERENCE SCHEME OF DISSIPATIVE ZAKHAROV EQUATIONS

张法勇, 郭柏灵

数学物理学报(英文版). 2012 (6): 2431-2452. DOI: 10.1016/S0252-9602(12)60190-8

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A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference scheme and the error bounds of optimal order of the difference solutions are obtained in L² ×H¹ ×H² over a finite time interval (0, T]. Finally, the existence of a global attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.

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