Model and empirical study on some collaboration networks

In this paper we present an empirical study of a few practical systems described by cooperation networks, and propose a model to understand the results obtained. We study four non-social systems, which are the Bus Route Networks of Beijing and Yangzhou, the Travel Route Network of China, Huai-Yang recipes of Chinese cooked food, and a social system, which is the Collaboration Network of Hollywood Actors. In order to explain the results related to the degree distribution, act-degree distribution and act-size distribution (especially about the degree distribution, which may be better fitted using a stretched exponential distribution (SED)), we suggest a simple model to show a possible evolutionary mechanism for the emergence of such networks. The analytic and numerical results obtained from the model are in good agreement with the empirical results.     

经济增长与宏观经济运行模型

对国民经济进行宏观调控，如同经济增长问题一样是一个永恒问题，对宏观调控的基本内容，手段，方法，国内外学者已进行了较多的规范性讨论，尤其是在数理分析方面，也已有许多具有普遍意义的成果，但是，要把那些成果转化为“生产力”从而变成清晰的，简明的，可操作的手段和方法，尚需人们不断的探索，本文通过对国民经济运行过程中若干宏观经济变量之间的数量关系分析，并以此建立了的国民经济宏观数量模型，就是尝试性的探索。     

超快光电测量技术

本文综述了近年来趔快光电测量技术的新进展，其中包括扭快光电材料的特性、高速光电器件的基本原理，着重介绍了若干主要的用快光电测量技术．     

Effective potential for local composite operators and the problem of factorization of multi-field condensates

A new formulation of effective potential for local composite operators is given. The two-fermion condensate \(\langle \bar \Psi \Psi \rangle \) and four-fermion condensate \(\langle \bar \Psi \Psi \bar \Psi \Psi \rangle \) are calculated simultaneously in the Gross-Neveu model up to next-to-the-leading order in 1/N expansion. It is shown that factorization \(\langle \bar \Psi \Psi \bar \Psi \Psi \rangle = C_1 \langle \bar \Psi \Psi \rangle ^2 \) holds only in theN→∞ limit and the non-factorized part of \(\langle \bar \Psi \Psi \bar \Psi \Psi \rangle \) contributed by the order-1/N terms is comparable to \(C_1 \langle \bar \Psi \Psi \rangle ^2 \) when takingN=3.     

Exponential approximations in the classes of life distributions

In this paper we discuss the approximation of life distributions by exponential ones. The main results are: (1) F NBUE, where its mean is 1, we have , 0, where = 1 - ₂/2, ₂ being the second moment ofF. The inequality is sharp. (2) In the case ofFIFR, the upper bound is . (3) For the HNBUE class, the upper bound is min . Furthermore, the improved upper bound is . In addition, we show 0} |\bar G(t) - e^{ - t} | \leqslant \sqrt {\frac{\rho }{2}} $$ " align="middle" border="0"> , where (4) For the IMRL class, the upper bound is /(1+) ([1]). Here we give a simple proof.Project supported by the National Natural Science Fund of China.     

Indirect laser photoacoustic detection for trace samples on membranes

An indirect laser photoacoustic technique is described. The basic principle, the experimental set-up and the influencing factors are discussed in detail. This method was used to quantify phenylamine, arginine and methylene blue on membranes. The linear ranges of the calibration curve are up to two orders of magnitude. With 1 microliter of sample solution, the detection limits are 0.25, 1.52 and 0.14 pmol for phenylamine, arginine and methylene blue, respectively.