量子卡诺循环

以经典理想气体为工质的卡诺热机循环由两个等温和两个绝热过程构成，热机可逆时，它的效率为最大。本文建立一种量子卡诺热机循环模型，该量子卡诺热机循环以一维无限深势阱中极端相对论粒子系统为工质。通过分析，发现该量子卡诺热机循环中的等温和绝热过程和经典卡诺热机的等温和绝热过程具有相似之处，它的效率表达式和经典热力学的可逆卡诺热机的效率表达式也类似，只是用系统的哈密顿量的期望值即系统的能量平均值代替经典热力学中的温度。     

On Hardy’s Theorem on SU(1, 1)

The classical Hardy theorem asserts that ■ and its Fourier transform ■ can not both be very rapidly decreasing.This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform.However,on SU(1,1)there are infinitely many"good"functions in the sense that ■ and its spherical Fourier transform ■ both have good decay. In this paper,we shall characterize such functions on SU(1,1).     

Hyers–Ulam–Rassias stability of Cauchy equation in the space of Schwartz distributions

We reformulate and prove the Hyers–Ulam–Rassias stability of Cauchy equation in the space of Schwartz tempered distributions and Fourier hyperfunctions.     

Action learning versus strategy learning

This article seeks to ascertain whether the strategy‐learning model of Hanaki, Sethi, Erev, and Peterhansl (2003) better accounts for observed behavior than do the various action‐learning models. It does so by measuring the goodness‐of‐fit of the models' predictions against published experimental results for such games as Coordination, Prisoner's Dilemma, and Chicken. The fit is measured via the mean squared deviation (MSD) between the observed behavior and the one predicted by the model. The results show that, for Chicken, the strategy‐learning model fits the observed data much better than do the action‐learning models. The best action‐learning model, on the other hand, fits the observed data well in Coordination. Overall, the strength of the strategy‐learning model is best shown in games where alternations between the two stage‐game Nash equilibria are often observed in the laboratory experiments. © 2004 Wiley Periodicals, Inc. Complexity 9: 41–50, 2004     

Widrow-cellular neural network and optoelectronic implementation

A new type of optoelectronic cellular neural network has been developed by providing the capability of coefficients adjusment of cellular neural network (CNN) using Widrow based perceptron learning algorithm. The new supervised cellular neural network is called Widrow-CNN. Despite the unsupervised CNN, the proposed learning algorithm allows to use the Widrow-CNN for various image processing applications easily. Also, the capability of CNN for image processing and feature extraction has been improved using basic joint transform correlation architecture. This hardware application presents high speed processing capability compared to digital applications. The optoelectronic Widrow-CNN has been tested for classic CNN feature extraction problems. It yields the best results even in case of hard feature extraction problems such as diagonal line detection and vertical line determination.     

积域上一类奇异积分算子的L~p有界性

本文证明,对于Ω∈(1)∩L(log~+L)~2(S~(n-1)×S~(m-1)),h(r,s)∈L~∞(R_+~1×R_+~1)和P_(N_1),P_(N_2)∈(2),带粗糙核的奇异积分算子为L~p有界。     

极紫外望远镜各通道夹角的测量

极紫外望远镜是由四个单通道的望远镜捆绑在一起,以便同时对太阳的相同部分观测,由于受地面装调以及发射过程中的影响,无法保证四个通道光轴严格平行,必然带来观测位置上的误差。只要测出各通道之间的光轴夹角,便可在像面上采取适当的处理方法,以便减小这种误差,但这一夹角的测量精度必须控制在0.1″内。为达到如此高的精度,采用了太阳局部边缘探测的方法,很好地解决了这一问题。     

乘积空间上极大奇异积分算子的Lp有界性

用旋转法结合Fourier估计以及Littlewood-Paley理论给出了乘积空间上带粗糙核的极大奇异积分算子的Lp有界性.证明了对于Ω∈Lq(Sn-1×Sm1),其中q＞1,∫ sn-1Ω(x',y')dx'=0, y'∈Sm-1,∫ sm-1Ω(x',y')dy'=0, x'∈Sn-1,且b,h∈L∞(R1+),则积域上极大奇异积分算子T*(f)=supε1＞0,ε2＞0∫∫|u|＞ε1|v|＞ε2b(|u|)h (|v|)Ω(u',v')/|v|n|v|mf(x-u,y-v)dudv为Lp(Rn×Rm)有界,其中1＜p＜∞.从而改进了以往的结果.     

Analytic continuation and identities involving heat,Poisson, wave and Bessel kernels

In this article we use classical formulas involving the K–Bessel function in two variables to express the Poisson kernel on a Riemannian manifold in terms of the heat kernel. We then use the small time asymptotics of the heat kernel on certain Riemannian manifolds to obtain a meromorphic continuation of the associated Poisson kernel to all values of complex time with identifiable singularities. This result reproves in a different setting by different means a well–known theorem due to Duistermaat and Guillemin [DG 75]. Also, we develop analytic expressions for the heat kernel beyond asymptotic expansions. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)