Curvature relation of wave front and wave changing in external field

Introduction ThestudiesofexcitablemediaconcernwithBZreaction,slimemoldaggregationand cardiactissue[1].Thepropertiesofthesemediaare:forsmallperturbationsthemediaquickly recovertotheirreststates,whileforstimuliexceedingathresholdthemediawillbeactivated andr…     

Classification of Gauge Orbit Types for SU(n)-Gauge Theories

A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SU(n) in spacetime dimension d4 is presented. The method is based on the one-to-one correspondence between orbit types and holonomy-induced reductions of the underlying principal SU(n)-bundle. It is shown that the orbit types are labelled by certain cohomology elements of spacetime satisfying two relations. Thus, for every principal SU(n)-bundle the corresponding stratification of the gauge orbit space can be explicitly determined. As an application, a criterion characterizing kinematical nodes for physical states in Yang–Mills theory with the Chern–Simons term proposed by Asorey et al. is discussed.     

Approximation Constants in Equidistant Lagrange Interpolation

In this paper we present a new limit relation for the equidistant Lagrange interpolation polynomials to |x|, (0, 1] on the internal [–1, 1]. The result extends a well-known result of D. L. Berman and S. M. Losinskii. Furthermore, we briefly discuss on a possible connection of the limit relation to another prominent constant in best uniform polynomial approximation for |x| - the so-called Bernstein constant.     

外噪声作用下可激发系统中的预测同步现象

采用数值模拟方法研究了由2个完全相同的可激发系统,通过单向延迟反馈耦合连接所组成主动-从动系统中的预测同步现象.结果表明在相等的外噪声作用下,当延迟时间和耦合强度在适当的范围内取值时,从动系统发生放电活动时所产生的动作电位能够预测主动系统发生放电活动时所产生的动作电位,即出现了预测同步现象,并且预测时间不可能大于主动神经元的响应时间.     

Synchronization of complex community networks with nonidentical nodes and adaptive coupling strength

In this Letter, the complex dynamical networks with community structure and nonidentical nodes are considered. The globally asymptotical synchronization of the time-delayed complex community networks onto any uniformly smooth state is studied. Some simple and useful criteria are derived by constructing an effective control scheme and adjusting automatically the adaptive coupling strength. Finally, the developed techniques are applied to two complex community networks which are respectively synchronized to a chaotic trajectory and a periodic orbit, and numerical simulations are provided to show the feasibility of the developed methods.     

ON LAGRANGE INTERPOLATION TO |x|α(1 ＜α＜ 2) WITH EQUALLY SPACED NODES

S.M. Lozinskii proved the exact convergence rate at the zero of Lagrange interpolation polynomials to |x| based on equidistant nodes in [-1, 1]. In 2000, M. Rever generalized S.M. Lozinskii's result to |x|α(0 ≤α≤ 1). In this paper we will present the exact rate of convergence at the point zero for the interpolants of |x|α(1 ＜α＜ 2)..     

Parameterizing the global attractor of the navier-stokes equations by nodal values

In this paper we give an affirmative answer to the conjecture of Foias and Tern am that the elements of the global attractor of the two dimensional Navier Stokes equations are uniquely determined by their nodal values at a finite number of points in the underlying physical domain. This is kind of a sampling theorem for the elements of the the global attractor of the Navier Stokes equations.     

Invariance of stationary probabilities of states for network of multiserver queues

A queueing network consisting of multiserver nodes with different sources of customers is considered. We investigate stationary probability distributions of network states. Their invariance with respect to the functional form of distributions of input and service processes is established under fixed expectations of these distributions and service discipline when any entering customer has a preemptive resume discipline.     

｜x｜^α的Lagrange插值多项式在零点的收敛速度

S.M.Lozinskii指出了函数｜x｜基于等距节点的Lagrange插值多项式在零点的收敛速度.2000年,M.Revers把S.M.Lozinskii的结果推广到｜x｜~α(0<α1).本文考虑的是把等距节点改为修改的Chebyshev节点,从而把零点处的收敛速度从M.Revers证明的O(n-α)提高O(n-2α).     

On the Lebesgue constant of Berrut’s rational interpolant at equidistant nodes

It is well known that polynomial interpolation at equidistant nodes can give bad approximation results and that rational interpolation is a promising alternative in this setting. In this paper we confirm this observation by proving that the Lebesgue constant of Berrut’s rational interpolant grows only logarithmically in the number of interpolation nodes. Moreover, the numerical results suggest that the Lebesgue constant behaves similarly for interpolation at Chebyshev as well as logarithmically distributed nodes.