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2017年, 第37卷, 第3期　刊出日期：2017-06-25 上一期    下一期

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GLOBAL WEAK SOLUTIONS TO ONE-DIMENSIONAL COMPRESSIBLE VISCOUS HYDRODYNAMIC EQUATIONS 郭柏灵, 席肖玉 数学物理学报(英文版). 2017 (3):  573-583.  DOI: 10.1016/S0252-9602(17)30023-1 摘要 ( 62 )   RICH HTML PDF   收藏 In this article, we are concerned with the global weak solutions to the 1D compressible viscous hydrodynamic equations with dispersion correction δ2ρ((ϕ(ρ))xxϕ'(ρ))x with ϕ(ρ)=ρα. The model consists of viscous stabilizations because of quantum Fokker-Planck operator in the Wigner equation and is supplemented with periodic boundary and initial conditions. The diffusion term εuxx in the momentum equation may be interpreted as a classical conservative friction term because of particle interactions. We extend the existence result in[1] (α=1/2) to 0 < α ≤ 1. In addition, we perform the limit ε → 0 with respect to 0 < α ≤ 1/2. 参考文献 | 相关文章 | 计量指标

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A NONCONFORMING QUADRILATERAL FINITE ELEMENT APPROXIMATION TO NONLINEAR SCHRODINGER EQUATION 石东洋, 廖歆, 王乐乐 数学物理学报(英文版). 2017 (3):  584-592.  DOI: 10.1016/S0252-9602(17)30024-3 摘要 ( 129 )   RICH HTML PDF   收藏 In this article, a nonconforming quadrilateral element (named modified quasiWilson element) is applied to solve the nonlinear schrödinger equation (NLSE). On the basis of a special character of this element, that is, its consistency error is of order O(h3) for broken H1-norm on arbitrary quadrilateral meshes, which is two order higher than its interpolation error, the optimal order error estimate and superclose property are obtained. Moreover, the global superconvergence result is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis. 参考文献 | 相关文章 | 计量指标

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SIGN-CHANGING SOLUTIONS FOR p-BIHARMONIC EQUATIONS WITH HARDY POTENTIAL IN RN 杨瑞瑞, 张薇, 刘祥清 数学物理学报(英文版). 2017 (3):  593-606.  DOI: 10.1016/S0252-9602(17)30025-5 摘要 ( 71 )   RICH HTML PDF   收藏 In this article, by using the method of invariant sets of descending flow, we obtain the existence of sign-changing solutions of p-biharmonic equations with Hardy potential in RN. 参考文献 | 相关文章 | 计量指标

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REFINEMENTS OF TRANSFORMATION INEQUALITIES FOR ZERO-BALANCED HYPERGEOMETRIC FUNCTIONS 王淼坤, 褚玉明 数学物理学报(英文版). 2017 (3):  607-622.  DOI: 10.1016/S0252-9602(17)30026-7 摘要 ( 91 )   RICH HTML PDF   收藏 In the article, we present some refinements of three classes of transformation inequalities for zero-balanced hypergeometric functions by use of the updated monotonicity criterion for the quotient of power series. 参考文献 | 相关文章 | 计量指标

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NORMAL FAMILY OF MEROMORPHIC FUNCTIONS SHARING HOLOMORPHIC FUNCTIONS AND THE CONVERSE OF THE BLOCH PRINCIPLE Nguyen Van THIN 数学物理学报(英文版). 2017 (3):  623-656.  DOI: 10.1016/S0252-9602(17)30027-9 摘要 ( 93 )   RICH HTML PDF   收藏 In 1996, C. C. Yang and P. C. Hu[8] showed that:Let f be a transcendental meromorphic function on the complex plane, and a ≠0 be a complex number; then assume that n ≥ 2, n1, …, nk are nonnegative integers such that n1 + … + nk ≥ 1; thus fn(f')n1 … (f(k))nk -a has infinitely zeros. The aim of this article is to study the value distribution of differential polynomial, which is an extension of the result of Yang and Hu for small function and all zeros of f having multiplicity at least k ≥ 2. Namely, we prove that fn(f')n1 … (f(k))nk -a(z) has infinitely zeros, where f is a transcendental meromorphic function on the complex plane whose all zeros have multiplicity at least k ≥ 2, and a(z) ? 0 is a small function of f and n ≥ 2, n1, …, nk are nonnegative integers satisfying n1 + … + nk ≥ 1. Using it, we establish some normality criterias for a family of meromorphic functions under a condition where differential polynomials generated by the members of the family share a holomorphic function with zero points. The results of this article are supplement of some problems studied by J. Yunbo and G. Zongsheng[6], and extension of some problems studied X. Wu and Y. Xu[10]. The main result of this article also leads to a counterexample to the converse of Bloch's principle. 参考文献 | 相关文章 | 计量指标

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SELF-SIMILAR SOLUTIONS TO THE HYPERBOLIC MEAN CURVATURE FLOW 何春蕾, 黄守军, 邢晓敏 数学物理学报(英文版). 2017 (3):  657-667.  DOI: 10.1016/S0252-9602(17)30028-0 摘要 ( 57 )   RICH HTML PDF   收藏 This article concerns the self-similar solutions to the hyperbolic mean curvature flow (HMCF) for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity. 参考文献 | 相关文章 | 计量指标

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CHARACTERIZATION OF DERIVATIONS ON B(X) BY LOCAL ACTIONS 薛天娇, 安润玲, 侯晋川 数学物理学报(英文版). 2017 (3):  668-678.  DOI: 10.1016/S0252-9602(17)30029-2 摘要 ( 65 )   RICH HTML PDF   收藏 Let A be a unital algebra and M be a unital A-bimodule. A linear map δ:A → M is said to be Jordan derivable at a nontrivial idempotent P ∈ A if δ(A) ◦ B + A ◦ δ(B)=δ(A ◦ B) for any A, B ∈ A, with A ◦ B=P, here A ◦ B=AB + BA is the usual Jordan product. In this article, we show that if A=AlgN is a Hilbert space nest algebra and M=B(H), or A=M=B(X), then, a linear map δ:A → M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P ∈ B(X) if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained. 参考文献 | 相关文章 | 计量指标

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LIFE-SPAN OF CLASSICAL SOLUTIONS TO HYPERBOLIC GEOMETRY FLOW EQUATION IN SEVERAL SPACE DIMENSIONS 孔德兴, 刘琦, 宋长明 数学物理学报(英文版). 2017 (3):  679-694.  DOI: 10.1016/S0252-9602(17)30030-9 摘要 ( 57 )   RICH HTML PDF   收藏 In this article, we investigate the lower bound of life-span of classical solutions of the hyperbolic geometry flow equations in several space dimensions with "small" initial data. We first present some estimates on solutions of linear wave equations in several space variables. Then, we derive a lower bound of the life-span of the classical solutions to the equations with "small" initial data. 参考文献 | 相关文章 | 计量指标

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DISTRIBUTIONS ON ALMOST CONTACT MANIFOLDS Hyunjoo CHO 数学物理学报(英文版). 2017 (3):  695-702.  DOI: 10.1016/S0252-9602(17)30031-0 摘要 ( 76 )   RICH HTML PDF   收藏 It is known that any hypersurface in an almost complex space admits an almost contact manifold[11, 14]. In this article we show that a hyperplane in an almost contact manifold has an almost complex structure. Along with this result, we explain how to determine when an almost contact structure induces a contact structure, followed by examples of a manifold with a closed G2-structure. 参考文献 | 相关文章 | 计量指标

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AN EFFICIENT PARALLEL PROCESSING OPTIMAL CONTROL SCHEME FOR A CLASS OF NONLINEAR COMPOSITE SYSTEMS A. JAJARMI, M. HAJIPOUR 数学物理学报(英文版). 2017 (3):  703-721.  DOI: 10.1016/S0252-9602(17)30032-2 摘要 ( 88 )   RICH HTML PDF   收藏 This article presents an efficient parallel processing approach for solving the optimal control problem of nonlinear composite systems. In this approach, the original high-order coupled nonlinear two-point boundary value problem (TPBVP) derived from the Pontryagin's maximum principle is first transformed into a sequence of lower-order decoupled linear time-invariant TPBVPs. Then, an optimal control law which consists of both feedback and forward terms is achieved by using the modal series method for the derived sequence. The feedback term specified by local states of each subsystem is determined by solving a matrix Riccati differential equation. The forward term for each subsystem derived from its local information is an infinite sum of adjoint vectors. The convergence analysis and parallel processing capability of the proposed approach are also provided. To achieve an accurate feedforward-feedback suboptimal control, we apply a fast iterative algorithm with low computational effort. Finally, some comparative results are included to illustrate the effectiveness of the proposed approach. 参考文献 | 相关文章 | 计量指标

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FEKETE AND SZEGÖ INEQUALITY FOR A SUBCLASS OF STARLIKE MAPPINGS OF ORDER α ON THE BOUNDED STARLIKE CIRCULAR DOMAIN IN Cn 刘太顺, 徐庆华 数学物理学报(英文版). 2017 (3):  722-731.  DOI: 10.1016/S0252-9602(17)30033-4 摘要 ( 57 )   RICH HTML PDF   收藏 In this article, first, we establish the Fekete and Szegö inequality for an interesting subclass of biholomorphic functions in the open unit disk U. Second, we generalize this result to the bounded starlike circular domain in Cn. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied. 参考文献 | 相关文章 | 计量指标

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MEROMORPHIC SOLUTIONS OF SOME TYPES OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS 王钥 数学物理学报(英文版). 2017 (3):  732-751.  DOI: 10.1016/S0252-9602(17)30034-6 摘要 ( 57 )   RICH HTML PDF   收藏 Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some properties of meromorphic solutions, and we obtain some results, which are the improvements and extensions of some results in references. Examples show that our results are precise. 参考文献 | 相关文章 | 计量指标

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ON SUBSONIC AND SUBSONIC-SONIC FLOWS IN THE INFINITY LONG NOZZLE WITH GENERAL CONSERVATIVES FORCE 顾旭旻, 王天怡 数学物理学报(英文版). 2017 (3):  752-767.  DOI: 10.1016/S0252-9602(17)30035-8 摘要 ( 51 )   RICH HTML PDF   收藏 In this article, we study irrotational subsonic and subsonic-sonic flows with general conservative forces in the infinity long nozzle. For the subsonic case, the varified Bernoulli law leads a modified cut-off system. Because of the local average estimate, conservative forces do not need any decay condition. Afterwards, the subsonic-sonic limit solutions are constructed by taking the extract subsonic solutions as the approximate sequences. 参考文献 | 相关文章 | 计量指标

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IMPROVE EFFICIENCY OF BIOGAS FEEDBACK SUPPLY CHAIN IN RURAL CHINA 贾晓菁, 贾仁安 数学物理学报(英文版). 2017 (3):  768-785.  DOI: 10.1016/S0252-9602(17)30036-X 摘要 ( 71 )   RICH HTML PDF   收藏 Feedback supply chain is a key structure in the supply chain system, and the development of feedback supply chain for biogas biomass energy is one of the important ways of the rural ecological civilization construction. Presently, the efficiency problem of biogas supply chain in rural China has been restricting the development of biogas biomass energy business. This article, on the basis of combination of regulation parameters, describes the dynamic changes in the system, using differential equations integrated with simulation to reveal the rules of regulation parameters to investigate the efficiency problem in the biogas supply chain. First of all, on the basis of the actual situation, the flow level and flow rate system structure model and simulation equation set are established for the biogas energy feedback supply chain from a scale livestock farm to peasant households; On the basis of the differentiability of the simulation equation a third order inhomogeneous differential equation with constant coefficients containing regulative parameters is established for the quantity of biogas stored in the feedback supply chain. A theorem and its corollaries are established for the operating efficiency of supply chain to reveal the change law of the quantity of biogas, the quantity of biogas consumed daily by peasant households and its standard-reaching rate as well as other variables. 参考文献 | 相关文章 | 计量指标

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ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION CM WITH THEIR SHIFTS AND DIFFERENCE OPERATORS 崔宁, 陈宗煊 数学物理学报(英文版). 2017 (3):  786-798.  DOI: 10.1016/S0252-9602(17)30037-1 摘要 ( 115 )   RICH HTML PDF   收藏 In this article, we mainly devote to proving uniqueness results for entire functions sharing one small function CM with their shift and difference operator simultaneously. Let f(z) be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f(z), f(z+c), and Δcnf(z) share 0 CM, then f(z + c) ≡ Af(z), where A(≠0) is a complex constant. Moreover, let a(z), b(z)(? 0) ∈ S(f) be periodic entire functions with period c and if f(z) -a(z), f(z + c) -a(z), Δcnf(z) -b(z) share 0 CM, then f(z + c) ≡ f(z). 参考文献 | 相关文章 | 计量指标

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OUTER OPERATORS FOR THE NONCOMMUTATIVE SYMMETRIC HARDY SPACES ASSOCIATED WITH FINITE SUBDIAGONAL ALGEBRA Kanat S. TULENOV, Madi RAIKHAN 数学物理学报(英文版). 2017 (3):  799-805.  DOI: 10.1016/S0252-9602(17)30038-3 摘要 ( 71 )   RICH HTML PDF   收藏 In this article, we extended main results on outer operators of[6] to the symmetric Hardy spaces, when associated subdiagonal algebra is finite. 参考文献 | 相关文章 | 计量指标

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LARGE TIME BEHAVIOR OF SOLUTIONS TO 1-DIMENSIONAL BIPOLAR QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS 李杏, 雍燕 数学物理学报(英文版). 2017 (3):  806-835.  DOI: 10.1016/S0252-9602(17)30039-5 摘要 ( 66 )   RICH HTML PDF   收藏 In this article, we study the 1-dimensional bipolar quantum hydrodynamic model for semiconductors in the form of Euler-Poisson equations, which contains dispersive terms with third order derivations. We deal with this kind of model in one dimensional case for general perturbations by constructing some correction functions to delete the gaps between the original solutions and the diffusion waves in L2-space, and by using a key inequality we prove the stability of diffusion waves. As the same time, the convergence rates are also obtained. 参考文献 | 相关文章 | 计量指标

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NONEXISTENCE AND SYMMETRY OF SOLUTIONS TO SOME FRACTIONAL LAPLACIAN EQUATIONS IN THE UPPER HALF SPACE 郭艳艳 数学物理学报(英文版). 2017 (3):  836-851.  DOI: 10.1016/S0252-9602(17)30040-1 摘要 ( 81 )   RICH HTML PDF   收藏 In this article, we consider the fractional Laplacian equation where 0 < α < 2, R+n:={x=(x1, x2,…, xn)|xn > 0}. When K is strictly decreasing with respect to|x'|, the symmetry of positive solutions is proved, where x'=(x1, x2, …, xn-1) ∈ Rn-1. When K is strictly increasing with respect to xn or only depend on xn, the nonexistence of positive solutions is obtained. 参考文献 | 相关文章 | 计量指标

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THE FOKAS-LENELLS EQUATION ON THE FINITE INTERVAL 肖羽, 范恩贵, 徐建 数学物理学报(英文版). 2017 (3):  852-876.  DOI: 10.1016/S0252-9602(17)30041-3 摘要 ( 77 )   RICH HTML PDF   收藏 Using the Fokas unified method, we consider the initial boundary value problem for the Fokas-Lenells equation on the finite interval. We present that the Neumann boundary data can be explicitly expressed by Dirichlet boundary conditions prescribed, and extend the idea of the linearizable boundary conditions for equations on the half line to Fokas-Lenells equation on the finite interval. 参考文献 | 相关文章 | 计量指标

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MULTIPLICATIVE PERTURBATIONS OF LOCAL α-TIMES INTEGRATED C-SEMIGROUPS Nai-Sher YEH, Chung-Cheng KUO 数学物理学报(英文版). 2017 (3):  877-888.  DOI: 10.1016/S0252-9602(17)30042-5 摘要 ( 68 )   RICH HTML PDF   收藏 We establish some left and right multiplicative perturbations of a local α-times integrated C-semigroup S(·) on a complex Banach space X with non-densely defined generator, which can be applied to obtain some additive perturbation results concerning S(·). Some growth conditions of the perturbations of S(·) are also established. 参考文献 | 相关文章 | 计量指标