A Multidimensional Generalization of Shukla's 8ψ8 Summation

   Abstract. We give an r -dimensional generalization of H. S. Shukla's very-well-poised ₈ ψ ₈ summation formula. We work in the setting of multiple basic hypergeometric series very-well-poised over the root system A _r-1 or, equivalently, the unitary group U(r) . Our proof, which is already new in the one-dimensional case, utilizes an A _r-1 nonterminating very-well-poised ₆ φ ₅ summation by S. C. Milne, a partial fraction decomposition, and analytic continuation.     

SOME REMARKS ON HOLOMORPHIC FUNCTIONS AND TAYLOR SERIES IN Cn

Some previous results on convergence of Taylor series in Cn [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy-Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in Cn are constructed and the Taylor series expansion is deduced.     

Dirichlet级数与连带级数

本文研究了右半平面内解析的Dirichlet级数的增长性,利用凸函数和一致收敛数的性质和几个引理,证明了连带级数的奇异点与原级数的增长性有关,并得到该连带级数的一些性质.     

二阶时滞小波神经网络的全局指数稳定性分析

通过构造李雅谱诺夫泛函,对具有时滞的二阶神经网络的稳定性进行分析,利用Eazumikhin定理得到了网络平衡点全局指数稳定的时滞相关与无关的充分条件,当衰减率依赖于时间时,得出了它们之间的一个线性关系,并进行了简明扼要的分析.     

High-Order Leap-Frog Based Discontinuous Galerkin Method for the Time-Domain Maxwell Equations on Non-Conforming Simplicial Meshes

A high-order leap-flog based non-dissipative discontinuous Galerkin timedomain method for solving Maxwell's equations is introduced and analyzed. The proposed method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements, with a Nth-order leap-frog time scheme. Moreover, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary level hanging nodes. The method is proved to be stable under some CFL-like condition on the time step. The convergence of the semi-discrete approximation to Maxwell's equations is established rigorously and bounds on the global divergence error are provided. Numerical experiments with highorder elements show the potential of the method.     

Strong approximation for the general Kesten-Spitzer random walk in independent random scenery

This paper is to prove that, if a one-dimensional random wa lkcan be approximated by a Brownian motion, then the related random walk in a g eneral independent scenery can be approximated by a Brownian motion in Brownian scenery.     

Relaxation in cooperative systems: Use of mixture virial coefficients

The coefficients in power series in the variable time that describe relaxation in a cooperative system can be calculated using a combinatorial approach where one considers how many ways one can introduce a given number of properly defined events in a system. The coefficients obtained in this manner can be related to the equilibrium virial coefficients for a mixture. If one assumes rapid internal equilibration, the relaxation process can be expressed completely in terms of the viral coefficients for a mixture with at most one solute particle, or, in some cases, just the virial coefficients for a single-component system. Thus, equilibrium virial coefficients can give useful information about the time evolution of processes in cooperative systems.     

35Cl NQR studies of 1‐chloro‐2,4‐dinitrobenzene and 1,2‐dichloro‐3‐nitrobenzene as a function of pressure and temperature

The temperature and pressure dependences of ³⁵Cl nuclear quadrupole resonance (NQR) frequency and spin–lattice relaxation time (T₁) were investigated for 1‐chloro‐2,4‐dinitrobenzene and 1,2‐dichloro‐3‐nitrobenzene. T₁ was measured in the temperature range 77–300 K. Furthermore, the NQR frequency (ν) and T₁ for these compounds were measured as a function of pressure up to 5.1 kbar at 300 K. Relaxation was found to be due to the torsional motion of the molecule and the reorientation motion of the nitro group. By analysing the temperature dependence of T₁, the activation energy for the reorientation motion of the nitro group was obtained. The temperature dependence of the average torsional lifetimes of the molecules and the transition probabilities W₁ and W₂ for the Δm = ±1 and Δm = ±2 transitions, were also obtained. Both compounds showed a non‐linear variation of NQR frequency with pressure. The pressure coefficients were observed to be positive. A thermodynamic analysis of the data was carried out to determine the constant‐volume temperature coefficients of the NQR frequency. The spin–lattice relaxation time T₁ for both the compounds was found to be weakly dependent on pressure, showing that the relaxation is mainly due to the torsional motions. Copyright © 2002 John Wiley & Sons, Ltd.     

Large deviations: An introduction to 2007 Abel prize

2007 Abel prize has been awarded to S R S Varadhan for creating a unified theory of large deviations. We attempt to give a flavour of this branch of probability theory, highlighting the role of Varadhan.