Distortion theorems for subclasses of starlike mappings along a unit direction in ℂ

In this paper, we obtain a distortion theorem of Jacobian matrix for biholomorphic subclasses of starlike mappings along a unit direction on the unit polydisc. These results extend the classical distortion theorem of starlike mappings to higher dimensions. We then give an upper bound estimate for biholomorphic subclasses of starlike mappings along a unit direction in a complex Banach space.     

Average Width and Optimal Recovery of Some Anisotropic Classes of Smooth Functions Defined on the Euclidean Space R~d

§ 1.Introduction and Main Results　 In[1 ] ,[2 ] ,the authors studied some problems of optimal recovery of functions de-fined on a cube,for a class of functions with partial derivatives of a fixed order havingmoduli of continuity not exceeding a given modules of continuity,and for the unit ballsSHαp in the spaces Hαp satisfying the mixed Holder conditionα,respectively.They ob-tained some weak asymptotic results.　 In[3 ] ,[4 ] and[5] ,Magarill-Il' yaev,Liu and Sun studied some proble…     

稀疏矢量阵信号栅瓣及对称伪峰干扰抑制

稀疏矢量阵进行宽带信号处理时,强目标的栅瓣及对称伪峰会干扰弱目标的检测,提出了一种基于理论干扰预测的加权抑制方法。方法利用矢量阵波束形成先获得强目标的波达方向(Direction Of Arrival,DOA)信息以及目标所在方位各频率的幅度谱信息,再利用理论计算公式获得强目标的栅瓣和对称伪峰角度上对应的各频率点的幅度谱强度信息,通过在方位、频率维度加权的方式对强目标的栅瓣和伪峰干扰进行抑制,来改善在强干扰下的弱目标检测能力。方法也适用于多目标情况,对各个目标依次使用,减少多目标时栅瓣和对称伪峰对方位历程的影响,净化了时间方位历程图。对所提方法给出了理论推导过程并进行了仿真和实验验证,实验结果验证可行。结果表明,新方法可以有效地抑制强目标的栅瓣和对称伪峰干扰,提高弱目标的检测能力,此外,净化后的时间方位历程图更利于弱目标检测和目标数量的估计。     

Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type

In this paper we study hybrid iterative scheme for finding a common element of set of solutions of generalized mixed equilibrium problem, set of common fixed points of finite family of weak relatively nonexpansive mapping and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. Our results extend, improve and generalize the results of several authors which are announced recently. Application of our theorem to solution of equations of Hammerstein-type is of independent interest.     

Interaction of solitary waves for the generalized KdV equation

We consider a class of generalized KdV equations with a small parameter and nonlinearities of the type u^m. We create a finite differences scheme to simulate the solution of the Cauchy problem and present some numerical results for the problem of the solitary waves interaction. In particular, we consider sufficient condition under which pairs of solitary waves interact, in the asymptotic sense, in accordance with the soliton scenario.     

Ultimate boundedness and an attractor for stochastic Hopfield neural networks with time-varying delays

This paper investigates ultimate boundedness and a weak attractor for stochastic Hopfield neural networks (HNN) with time-varying delays. By employing the Lyapunov method and the matrix technique, some novel results and criteria on ultimate boundedness and an attractor for stochastic HNN with time-varying delays are derived. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.     

Extension Operators Preserving Biholomorphic Mappings on Hartogs Domains*

In this paper, the authors extend the Roper-Suffridge operator on the generalized Hartogs domains. They mainly research the properties of the extended operator.By the characteristics of Hartogs domains and the geometric properties of subclasses of spirallike mappings, they obtain the extended Roper-Suffridge operator preserving almost starlikeness of complex order λ, almost spirallikeness of type β and order α, parabolic spirallikeness of type β and order ρ on the Hartogs domains in different co...     

Excellent扩张和弱维数

在这篇文章里，我们证明了，当环Ｓ是Ｒ的ｅｘｃｅｌｌｅｎｔ扩张，Ｍ是Ｓ－模时，Ｍ做为Ｓ－模的弱维数与Ｍ做为Ｒ－模的弱维数相等。     

An order-by-disorder process in the cyclic phase of spin-2 condensate with a weak magnetic field

We present in this paper a model study on the “order-by-disorder” process in the cyclic phase of spin-2 condensate, which forms a family of incommensurable, spiral degenerate ground states. On the basis of the ordering mechanism of entropic splitting, it is demonstrated that the energy corrections resulting from quantum fluctuations of disorder lift the accidental degeneracy of the cyclic configurations and thus lead to an eventual spiral order called the cyclic order. The order-by-disorder phenomenon is then realized even if the magnetic field exists. Finally, we show that our theoretic observations can be verified experimentally by direct detection of the cyclic order in the ⁸⁷Rb condensate of a spin-2 manifold with a weak magnetic field.     

扩散过程中弱相干光场的退相干

研究了扩散过程中弱相干光场量子特性的演化.利用正规乘积、反正规乘积和Weyl编序算符内的积分技术,采用热纠缠态表象求解密度矩阵主方程,利用Kraus算符给出扩散过程中密度算符解的表达式,导出初态为弱相干态的量子态密度算符演化规律.讨论了扩散对光场压缩效应和反聚束效应的影响.结果表明:随着扩散过程的进行,弱相干场压缩深度和压缩范围均在减小;扩散初期光场呈反聚束效应,扩散时间大于一定值后反聚束效应消失.