非对称双稳耦合网络系统的尺度随机共振研究

研究了不同周期信号调制下非对称双稳耦合网络系统的尺度随机共振问题. 针对该网络系统, 首先运用高斯近似和役使原理对其进行了降维, 推导了其简化模型. 在绝热近似条件下, 利用Fokker-Planck方程分别得到了余弦信号和矩形信号调制下信噪比的解析表达式. 在此基础上, 研究了系统的尺度随机共振行为, 并讨论了非对称性、噪声强度、周期信号的振幅和耦合系数对系统尺度随机共振的影响. 结果表明, 两种情形下信噪比均是系统尺度的非单调函数, 说明在此网络系统中产生了共振现象. 关键词： 尺度随机共振 非对称双稳耦合网络系统 余弦信号 矩形信号     

On a parabolic‐elliptic chemotaxis system with periodic asymptotic behavior

We study a parabolic‐elliptic chemotactic PDEs system, which describes the evolution of a biological population “u” and a chemical substance “v” in a bounded domain . We consider a growth term of logistic type in the equation of “u” in the form μu(1 ? u + f(t,x)). The function “f,” describing the resources of the systems, presents a periodic asymptotic behavior in the sense where f ^? is independent of x and periodic in time. We study the global existence of solutions and its asymptotic behavior. Under suitable assumptions on the initial data and f ^?, if the constant chemotactic sensitivity χ satisfies we obtain that the solution of the system converges to a homogeneous in space and periodic in time function.     

On the blow‐up phenomena for a 1‐dimensional equation of ion sound waves in a plasma: Analytical and numerical investigation

The initial‐boundary value problem for an equation of ion sound waves in plasma is considered. A theorem on nonextendable solution is proved. The blow‐up phenomena are studied. The sufficient blow‐up conditions and the blow‐up time are analysed by the method of the test functions. This analytical a priori information is used in the numerical experiments, which are able to determine the process of the solution's blow‐up more accurately.     

Superconvergence of the Composite Rectangle Rule for Computing Hypersingular Integral on Interval

The generalized middle rectangle rule for the computation of certain hypersingular integrals is discussed. A generalized middle rectangle rule with the density function approximated and the singular kernel analysis calculated is presented and the asymptotic expansion of error functional is obtained. When the special function in the error functional equals to zero, the superconvergence point is obtained and the superconvergence phenomenon which is one order higher than the general case is presented. At last, numerical examples are given to confirm the theoretical results.     

AN ANALOGUE OF A THEOREM OF FERENC LUKÁCS FOR DOUBLE WALSH—FOURIER SERIES

A theorem of Ferenc Lukács states that if a periodic function is integrable in Lebesgue"s sense and has a discontinuity of first kind at some point , then the th partial sum of the conjugate series to its trigonometric Fourier series at divided by converges to as . An analogue of this theorem for Walsh–Fourier series was proved by Rafat Riad. The main aim of the present paper is to extend the latter result from single to double Wals–Fourier series. We consider also functions of two variables which are of bounded variation over a rectangle in the sense of Hardy and Krause. Among others, we present a proof of the existence of the so-called sector limits of such functions at each point.     

Local Asymptotic Normality for Linear Homogeneous Difference Equations with Non-Gaussian Noise

This paper considers the problem of estimation of drift parameter for linear homogeneous stochastic difference equations. The Local Asymptotic Normality (LAN) for the problem is proved. LAN implies the Hajek–Le Cam minimax lower bound. In particular, it is shown that the Fisher's information matrix for the problem can be expressed in terms of the stationary distribution of an auxiliary Markov chain on the projective space P(^d).     

Stimulated emission from two-dimensional nested rectangle photonic crystal fibers

In this paper, we use the theory of spontaneous emission of two-level atoms embedded in photonic crystals. The unavoidable existence of a localized field with a defect mode and its basic properties are confirmed, which enables one to study the inherent laws of spontaneous emission from doped media. We combine the theory of spontaneous emission with numerical simulation for studying stimulated emission in a doped localized field and conditions for increasing the emission. The inherent laws for the cases where transmissivity is larger than unity and the negative imaginary part of the complex refractive index in doped compound lattices appears are also studied. The analysis of two-dimensional nested rectangle photonic crystal fibers (PCFs) with and without active impurities was performed using the finite-difference time-domain (FDTD) method. We find that, when active impurities are introduced into photonic crystal fibers, the negative imaginary part of the complex refractive index appears and the doped mode with high quality factor and great mode density occurs in the photonic forbidden band, thus amplifying substantially the stimulated emission.     

Non-radial flow of an incompressible fluid of second grade in a contracting channel

The steady non-radial flow of an incompressible fluid of second grade in a contracting channel is studied. The dependence of the flow on the material parameters of the fluid and on the channel angle is investigated. A similarity transformation is introduced for the streamfunction which reduces the P.D.E. to a sequence of O.D.E.s. A series solution is employed to solve the problem.

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Sommario Si studia il flusso stazionario non radiale di un fluido di secondo grado incomprimibile in un canale convergente, esaminandone la dipendenza dai parametri materiali del fluido e dall'angolo di apertura del canale. Si introduce una trasformazione di similitudine per la funzione di corrente che riduce l'equazione di moto ad una serie di equazioni differenziali ordinarie, risolte numericamente.

     

A N. Bourbaki type General Theory and the Properties of Contracting Symbols and Corresponding Contracted Forms

A system of contracting symbols is introduced for a N. Bourbaki type general mathematical theory corresponding to a general classical mathematical theory T.     

On the Stokes entry flow into a semi-infinite circular cylindrical tube

The problem of Stokes entry flow into a semi-infinite circular cylindrical tube was studied in this paper. A new kind of series solutions was derived. Their evident difference from the solutions in References [1,2] is that the present solutions don ’t involve infinite integral. So they are favourable for calculation. We calculated an example by allocated method and obtained satisfied results.