数学物理学报(英文版)

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A RIEMANN-HILBERT APPROACH TO THE INITIAL-BOUNDARY PROBLEM FOR DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION

徐建, 范恩贵

数学物理学报(英文版). 2014 (4): 973-994. DOI: 10.1016/S0252-9602(14)60063-1

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We use the Fokas method to analyze the derivative nonlinear Schr¨odinger (DNLS) equation iq_t(x, t) = −q_xx(x, t)+(rq²)_x on the interval [0, L]. Assuming that the solution q(x, t) exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter ξ. This problem has explicit (x, t) dependence, and it has jumps across {ξ ∈ C|Imξ⁴ = 0}. The relevant jump matrices are explicitely given in terms of the spectral functions {a(ξ), b(ξ)}, {A(ξ), B(ξ)}, and {A(ξ), B(ξ)}, which in turn are defined in terms of the initial data q₀(x) = q(x, 0), the boundary data g₀(t) = q(0, t), g₁(t) = q_x(0, t), and another boundary values f₀(t) = q(L, t), f₁(t) =q_x(L, t). The spectral functions are not independent, but related by a compatibility condition, the so-called global relation.

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THE MAIN INVARIANTS OF A COMPLEX FINSLER SPACE

Nicoleta ALDEA, Gheorghe MUNTEANU

数学物理学报(英文版). 2014 (4): 995-1011. DOI: 10.1016/S0252-9602(14)60064-3

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In this paper we extend the results obtained in [3], where are investigated the general settings of the two-dimensional complex Finsler manifolds, with respect to a local complex Berwald frame. The geometry of such manifolds is controlled by three real invariants which live on T′M: two horizontal curvature invariants K and W and one vertical curvature invariant I. By means of these invariants are defined both the horizontal and the vertical holomorphic sectional curvatures. The complex Landsberg and Berwald spaces are of particular interest. Complex Berwald spaces coincide with K¨ahler spaces, in the two -dimensional case. We establish the necessary and sufficient condition under which K is a constant and we obtain a characterization for the K¨ahler purely Hermitian spaces by the fact K =W= constant and I = 0. For the class of complex Berwald spaces we have K =W= 0. Finally, a classification of two-dimensional complex Finsler spaces for which the horizontal curvature satisfies a special property is obtained.

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IDENTIFYING AN UNKNOWN SOURCE IN SPACE-FRACTIONAL DIFFUSION EQUATION

杨帆, 傅初黎, 李晓晓

数学物理学报(英文版). 2014 (4): 1012-1024. DOI: 10.1016/S0252-9602(14)60065-5

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In this paper, we identify a space-dependent source for a fractional diffusion equation. This problem is ill-posed, i.e., the solution (if it exists) does not depend continu-ously on the data. The generalized Tikhonov regularization method is proposed to solve this problem. An a priori error estimate between the exact solution and its regularized approxi-mation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained. Numerical examples are presented to illustrate the validity and effectiveness of this method.

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HARMONIC OSCILLATORS AT RESONANCE, PERTURBED BY A NON-LINEAR FRICTION FORCE

Philip KORMAN, Yi LI

数学物理学报(英文版). 2014 (4): 1025-1028. DOI: 10.1016/S0252-9602(14)60066-7

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This note is an addendum to the results of Lazer and Frederickson [1], and Lazer [4] on periodic oscillations, with linear part at resonance. We show that a small modification of the argument in [4] provides a more general result. It turns out that things are different for the corresponding Dirichlet boundary value problem.

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CONSENSUS FORMATION OF TWO-LEVEL OPINION DYNAMICS

Yilun SHANG

数学物理学报(英文版). 2014 (4): 1029-1040. DOI: 10.1016/S0252-9602(14)60067-9

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Opinion dynamics have received significant attention in recent years. This pa-per proposes a bounded confidence opinion model for a group of agents with two different confidence levels. Each agent in the population is endowed with a confidence interval around her opinion with radius αd or (1 − α)d, where α∈ (0, 1/2] represents the differentiation of
confidence levels. We analytically derived the critical confidence bound d_c= 1/(4α) for the two-level opinion dynamics on Z. A single opinion cluster is formed with probability 1 above this critical value regardless of the ratio p of agents with high/low confidence. Extensive numerical simulations are performed to illustrate our theoretical results. Noticed is a clear impact of p on the collective behavior: more agents with high confidence lead to harder agreement. It is also experimentally revealed that the sharpness of the threshold d_c increases with α but does not depend on p.

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STOCHASTIC SIMPLIFIED BARDINA TURBULENT MODEL: EXISTENCE OF WEAK SOLUTION

邱华, 房少梅

数学物理学报(英文版). 2014 (4): 1041-1054. DOI: 10.1016/S0252-9602(14)60068-0

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In this paper, we consider the stochastic version of the 3D Bardina model arising from the turbulent flows of fluids. We obtain the existence of probabilistic weak solution for the model with the non-Lipschitz condition.

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STABILITY RESULTS OF RANDOM IMPULSIVE SEMILINEAR DIFFERENTIAL EQUATIONS

M. GOWRISANKAR, P. MOHANKUMAR, A. VINODKUMAR

数学物理学报(英文版). 2014 (4): 1055-1071. DOI: 10.1016/S0252-9602(14)60069-2

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In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilinear differential equations un-der sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.

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LPS´S CRITERION FOR INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

陈卿, 谭忠, 吴国春

数学物理学报(英文版). 2014 (4): 1072-1080. DOI: 10.1016/S0252-9602(14)60070-9

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In this paper we derive LPS´s criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in R3. We show that if 0 < T < +∞ is the maximal time interval for the unique smooth solution u ∈ C^∞([0, T),R³),
then |u| + |∇d| /∈ L^q([0, T], L^p(R³)), where p and q safisfy the Ladyzhenskaya-Prodi-Serrin´s condition: 3/p+2/q= 1 and p ∈ (3,+∞].

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CONVERGENCE ANALYSIS FOR SYSTEM OF EQUILIBRIUM PROBLEMS AND LEFT BREGMAN STRONGLY RELATIVELY NONEXPANSIVE MAPPING

Yekini SHEHU

数学物理学报(英文版). 2014 (4): 1081-1097. DOI: 10.1016/S0252-9602(14)60071-0

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In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.

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ON THE WEIGHTED VARIABLE EXPONENT AMALGAM SPACE W(L^p^(x), L^q_m)

A. Turan GüRKANLI, Ismail AYDIN

数学物理学报(英文版). 2014 (4): 1098-1110. DOI: 10.1016/S0252-9602(14)60072-2

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In [4] , a new family W(L^p^(x), L^q_m) of Wiener amalgam spaces was defined and investigated some properties of these spaces, where local component is a variable exponent Lebesgue space L^p^(x) (R) and the global component is a weighted Lebesgue space L^q_m (R). This present paper is a sequel to our work [4]. In Section 2, we discuss necessary and sufficient conditions for the equality W(L^p^(x), L^q_m)= L^q (R) . Later we give some characterization of Wiener amalgam space W(L^p^(x), L^q_m). In Section 3 we define the Wiener amalgam space W(FL^p^(x), L^q_m) and investigate some properties of this space, where FL^p^(x) is the image of L^p^(x) under the Fourier transform. In Section 4, we discuss boundedness of the Hardy-Littlewood maximal operator between some Wiener amalgam spaces.

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MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF QUASI-LINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENT

范海宁, 刘晓春

数学物理学报(英文版). 2014 (4): 1111-1126. DOI: 10.1016/S0252-9602(14)60073-4

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In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.

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EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF PARABOLIC EQUATIONS WITH NATURAL GROWTH TERMS AND L¹ DATA

Kaouther AMMAR, Hicham REDWANE

数学物理学报(英文版). 2014 (4): 1127-1144. DOI: 10.1016/S0252-9602(14)60074-6

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We study a class of nonlinear parabolic equations of the type:
∂b(u)/∂t− div(a(x, t, u)∇u)+ g(u)|∇u|² = f,
where the right hand side belongs to L¹(Q), b is a strictly increasing C¹-function and −div(a(x, t, u)∇u) is a Leray-Lions operator. The function g is just assumed to be con-tinuous on R and to satisfy a sign condition. Without any additional growth assumption on u, we prove the existence of a renormalized solution.

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AN UPPER BOUND OF THE ESSENTIAL NORM OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES

陈志华, 江良美, 颜启明

数学物理学报(英文版). 2014 (4): 1145-1156. DOI: 10.1016/S0252-9602(14)60075-8

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In this paper, we define the generalized counting functions in the higher dimen-sional case and give an upper bound of the essential norms of composition operators between the weighted Bergman spaces on the unit ball in terms of these counting functions. The sufficient condition for such operators to be bounded or compact is also given.

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APPROXIMATION BY COMPLEX SZ´ASZ-DURRMEYER OPERATORS IN COMPACT DISKS

Sorin G. GAL, Vijay GUPTA

数学物理学报(英文版). 2014 (4): 1157-1165. DOI: 10.1016/S0252-9602(14)60076-X

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In the present paper, we deal with the complex Sz´asz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.

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CERTAIN FAMILY OF INTEGRAL OPERATORS PRESERVING SUBORDINATION AND SUPERORDINATION

Mohamed K. AOUF, Teodor BULBOACA, Tamer M. SEOUDY

数学物理学报(英文版). 2014 (4): 1166-1178. DOI: 10.1016/S0252-9602(14)60077-1

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We obtain subordination, superordination and sandwich-preserving new theo-rems for certain integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also derived, and the results generalize some recently ones.

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EKELAND´S PRINCIPLE FOR SET-VALUED VECTOR EQUILIBRIUM PROBLEMS

龚循华

数学物理学报(英文版). 2014 (4): 1179-1192. DOI: 10.1016/S0252-9602(14)60078-3

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In this paper, we introduce a concept of quasi C-lower semicontinuity for set-valued mapping and provide a vector version of Ekeland´s theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient so-lution for set-valued vector equilibrium problems without the assumption of convexity of the
constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of "-approximate solution for set-valued vector equi-librium problems without the assumptions of compactness and convexity of the constraint set.

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ON INVERSES AND ALGEBRAIC LOOPS OF CO-H-SPACES

Dae-Woong LEE

数学物理学报(英文版). 2014 (4): 1193-1211. DOI: 10.1016/S0252-9602(14)60079-5

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In this paper we study the properties of homotopy inverses of comultiplications and algebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old ones by using a group action. We are primar-ily interested in the algebraic loops which have inversive, power-associative and Moufang
properties for some comultiplications.

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SPECTRAL MAPPING THEOREM FOR ASCENT, ESSENTIAL ASCENT, DESCENT AND ESSENTIAL DESCENT SPECTRUM OF LINEAR RELATIONS

Ezzeddine CHAFAI, Maher MNIF

数学物理学报(英文版). 2014 (4): 1212-1224. DOI: 10.1016/S0252-9602(14)60080-1

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In [7], Cross showed that the spectrum of a linear relation T on a normed space satisfies the spectral mapping theorem. In this paper, we extend the notion of essential ascent and descent for an operator acting on a vector space to linear relations acting on Banach spaces. We focus to define and study the descent, essential descent, ascent and essential ascent spectrum of a linear relation everywhere defined on a Banach space X. In particular, we show that the corresponding spectrum satisfy the polynomial version of the spectral mapping theorem.

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SOLUTIONS TO DISCRETE MULTIPARAMETER PERIODIC BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN VIA CRITICAL POINT THEORY

高承华

数学物理学报(英文版). 2014 (4): 1225-1236. DOI: 10.1016/S0252-9602(14)60081-3

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In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [G. Bonanno and P. Candito, Appl. Anal., 88(4) (2009), pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for and μ in some suitable intervals. The approaches we use are the critical point theory.

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FIXED POINT RESULTS ON METRIC-TYPE SPACES

Monica COSENTINO, Peyman SALIMI, Pasquale VETRO

数学物理学报(英文版). 2014 (4): 1237-1253. DOI: 10.1016/S0252-9602(14)60082-5

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In this paper we obtain fixed point and common fixed point theorems for self-mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.

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EXPONENTIAL STABILITY FOR NONLINEAR HYBRID STOCHASTIC PANTOGRAPH EQUATIONS AND NUMERICAL APPROXIMATION

周少波, 薛明皋

数学物理学报(英文版). 2014 (4): 1254-1270. DOI: 10.1016/S0252-9602(14)60083-7

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The paper develops exponential stability of the analytic solution and convergence in probability of the numerical method for highly nonlinear hybrid stochastic pantograph equation. The classical linear growth condition is replaced by polynomial growth conditions, under which there exists a unique global solution and the solution is almost surely exponen-tially stable. On the basis of a series of lemmas, the paper establishes a new criterion on convergence in probability of the Euler-Maruyama approximate solution. The criterion is very general so that many highly nonlinear stochastic pantograph equations can obey these conditions. A highly nonlinear example is provided to illustrate the main theory.

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BOUNDARY LAYER AND VANISHING DIFFUSION LIMIT FOR NONLINEAR EVOLUTION EQUATIONS

彭艳

数学物理学报(英文版). 2014 (4): 1271-1286. DOI: 10.1016/S0252-9602(14)60084-9

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In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameter α goes to zero.

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ADDITIVE MAPS ON SOME OPERATOR ALGEBRAS BEHAVING LIKE (α, β)-DERIVATIONS OR GENERALIZED (α, β)-DERIVATIONS AT ZERO-PRODUCT ELEMENTS

Hoger GHAHRAMANI

数学物理学报(英文版). 2014 (4): 1287-1300. DOI: 10.1016/S0252-9602(14)60085-0

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Let A be a subalgebra of B(X) containing the identity operator I and an idem-potent P. Suppose that Let A be a subalgebra of B(X) containing the identity operator I and an idem-potent P. Suppose that α, β : A → A are ring epimorphisms and there exists some nest N on X such that α(P)(X) and β(P)(X) are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ : A →B(X) be an additive mapping. It is shown that, if δ is (α, β)-derivable at zero point, then there exists an additive (α, β)-derivation τ : A →B(X) such that δ(A) =τ (A) + α(A)δ(I) for all A ∈ A. It is also shown that if δ is generalized (α, β)-derivable at zero point, then δis an additive generalized (α, β)-derivation. Moreover,
by use of this result, the additive maps (generalized) (α, β)-derivable at zero point on several nest algebras, are also characterized.

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FUNCTIONAL ANALYSIS METHOD FOR THE M/G/1 QUEUEING MODEL WITH OPTIONAL SECOND SERVICE

艾尼·吾甫尔, 艾合买提·卡斯木

数学物理学报(英文版). 2014 (4): 1301-1330. DOI: 10.1016/S0252-9602(14)60086-2

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By studying the spectral properties of the underlying operator corresponding to the M/G/1 queueing model with optional second service we obtain that the time-dependent solution of the model strongly converges to its steady-state solution. We also show that the time-dependent queueing size at the departure point converges to the corresponding steady-
state queueing size at the departure point.

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A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES

Hung Viet LE

数学物理学报(英文版). 2014 (4): 1331-1344. DOI: 10.1016/S0252-9602(14)60087-4

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Let h be a measurable function defined on R⁺×R⁺. Let Ω∈ L(log L⁺)^ν_q (Sⁿ¹⁻¹×Sⁿ²⁻¹) (1 ≤ ν_q ≤2) be homogeneous of degree zero and satisfy certain cancellation condi-tions. We show that the singular integral

Tf(x₁, x₂) = p. v.∫∫_Rn1+n2Ω(y´₁, y´₂)h(|y₁|, |y₂|)/|y₁|ⁿ¹ |y₂|ⁿ²f(x₁ − y₁, x₂ − y₂)dy₁dy₂maps from S^α_¹, ^α^₂_{p, q}F(R^n₁ × R^n₂) boundedly to itself for 1 < p, q <∞, α₁, α₂ ∈R.

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COMMON FIXED POINT OF GENERALIZED WEAKLY CONTRACTIVE MAPS IN PARTIAL METRIC SPACES

Vesna COJBASIC RAJIC, Stojan RADENOVIC, Sunny CHAUHAN

数学物理学报(英文版). 2014 (4): 1345-1356. DOI: 10.1016/S0252-9602(14)60088-6

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In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized (φ, ψ )-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results.

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