A note on fast Fourier transforms for nonequispaced grids

In this paper, we are concerned with fast Fourier transforms for nonequispaced grids. We propose a general efficient method for the fast evaluation of trigonometric polynomials at nonequispaced nodes based on the approximation of the polynomials by special linear combinations of translates of suitable functions ϕ. We derive estimates for the approximation error. In particular, we improve the estimates given by Dutt and Rokhlin [7]. As a practical consequence, we obtain a criterion for the choice of the parameters involved in the fast transforms. This revised version was published online in August 2006 with corrections to the Cover Date.     

静磁场中双极化态弱平面引力波对高斯束的扰动能量

讨论了处于静磁场中双极化态弱平面引力波对高斯束的一阶和二阶扰动能量，数值计算表明，引力波对整个电磁体系的能量扰动很小.换言之，背景电磁场在引力波作用下其总能量不会发生明显改变，但在局部区域中产生的扰动能流则可能引起可供观测的效应. 关键词： 双极化态弱平面引力波 高斯束 电磁响应 扰动能量     

Internal viscosity in polymer kinetic theory: shear flows

The Gaussian closure method and Brownian dynamics simulations have been used to calculate the shear material properties of a dilute solution of Hookean dumbbells with internal viscosity. Results for the zero-shear-rate material properties and small amplitude oscillatory shear material properties have been found analytically, and numerical results for the steady state shear material properties are also presented. Two interpretations of the stress tensor are investigated and results are compared. Brownian dynamics simulations are used to obtain material properties of the Hookean dumbbell with internal viscosity without approximations. These simulation results are compared with the perturbation solution of Booij and van Wiechen as well as with a new Gaussian closure solution. Also presented are the contracted distribution functions as derived from the Gaussian closure method and from Brownian dynamics simulations.     

A heavy-traffic analysis of a closed queueing system with a GI/∞ service center

This paper studies the heavy-traffic behavior of a closed system consisting of two service stations. The first station is an infinite server and the second is a single server whose service rate depends on the size of the queue at the station. We consider the regime when both the number of customers, n, and the service rate at the single-server station go to infinity while the service rate at the infinite-server station is held fixed. We show that, as n→∞, the process of the number of customers at the infinite-server station normalized by n converges in probability to a deterministic function satisfying a Volterra integral equation. The deviations of the normalized queue from its deterministic limit multiplied by √n converge in distribution to the solution of a stochastic Volterra equation. The proof uses a new approach to studying infinite-server queues in heavy traffic whose main novelty is to express the number of customers at the infinite server as a time-space integral with respect to a time-changed sequential empirical process. This gives a new insight into the structure of the limit processes and makes the end results easy to interpret. Also the approach allows us to give a version of the classical heavy-traffic limit theorem for the G/GI/∞ queue which, in particular, reconciles the limits obtained earlier by Iglehart and Borovkov. This revised version was published online in June 2006 with corrections to the Cover Date.     

一种新的光束概念—无衍射光束

本文介绍了国际学术界新近提出的无衍射光束概念,对该光束的物理机制和应用前景进行了讨论。     

Useful Monte Carlo optimization

This contribution to the debate on Monte Carlo optimization methods shows that there exist techniques that may be useful in many technical applications.     

On a Class of Covariance Operators

This paper is the continuation of [1] in which complex symmetries of distributions and their covariance operators are investigated. Here we also study the most general quaternion symmetries of random vectors. Complete classification theorems on these symmetries are proved in terms of covariance operator spectra.     

Optical propagation of the HE11 mode and Gaussian beams in hollow circular waveguides

The propagation of the HE₁₁ mode and Gaussian beams in hollow oversized circular waveguides is analyzed using optical theories. Different types of waveguides are considered : hollow dielectric or conducting waveguides, dielectric-lined waveguides, corrugated waveguides. General formulas are derived which give the power transmission through these different guides. The best wall materials and structures are determined from a comparison of the waveguide transmissions, at the infrared and millimeter wavelengths. The question of the coupling between the HE₁₁ mode and Gaussian beams is discussed and from a review of coupling coefficients derived before, an optimum value is pointed out. The problem of matching a Gaussian beam into circular waveguides in order to achieve the maximum power transmission is analyzed. These results are of interest for infrared lasers or waveguide applications and for Electron Cyclotron Wave (ECW) systems at the millimeter wavelength.     

INDO-MO Model with s-p-d Separation

A newly developed semiempirical method, “the INDO-MO model with s-p-d separation” is introduced. Based on the assumption of the equivalent basis functions in the set for each angular-momentum quantum number, the average type electronic repulsion integrals of 3d orbitals are suggested. Similar to our former s-p-d separation CNDO-MO formulation, the proportionality factor K₀₁ for the bonding parameter for each period of the periodic table is proposed for our method of semiempirical calculation.     

ANALYTIC FUNCTIONALS AND A NEW DISTRIBUTION THEORY OVER INFINITE DIMENSIONAL SPACES

§1.ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＢａｃｋｇｒｏｕｎｄ　　ＴｈｅｄｉｓｔｒｉｂｕｔｉｏｎｔｈｅｏｒｙｏｖｅｒｉｎｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎａｌＧａｕｓｓｉａｎｓｐａｃｅｈａｓｂｅｅｎｄｅｖｅｌｏｐｅｄｉｎｔｗｏｄｉｒｅｃｔｉｏｎｓ:Ｇｉｖｅｎａｄｅｎｓｅｌｙｄｅｆｉｎｅｄｎｏｎ-ｎｅｇａｔｉｖｅｓｅｌｆａｄｊｏｉｎｔｏｐｅｒａｔｏｒＡｉｎｔｈｅＨｉｌｂｅｒｔｓｐａｃｅＬ2(Ｒ),ｂｙｔｈｅｗｅｌｌ-ｋｎｏｗｎｉｓｏｍｏｒｐｈｉｓｍｂｅｔｗｅｅｎ(Ｌ2),ｔｈｅＨｉｌｂｅｒｔｓｐａｃｅｏｆｓｑｕａｒｅｉ…