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．     

固体样品进样技术中汞量定标方法的研究

在原子吸收光谱分析中,固体样品直接进样是目前的研究课题之一。本文主要报道作者在分析汞中所进行的固体直接进样技术工作和讨论。在我们研制成功的KT—81型塞曼效应测汞仪中,针对元素汞蒸气压高的特点,用饱和汞蒸气作为汞量标准,实现了固体样品,如土壤、污泥、毛发、煤、食品等汞含量的直接进样测定。汞蒸气一次制备后可长期使用。分析汞时,只要用标准气体任意校验一次就可测量。1～2分钟能分析一个样品,S<0.3ng。r<5%。此法用NBS标准物质验证过。     

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.     

由肉桂酸生物合成L-苯丙氨酸

本文评述了Ｌ－苯丙氮酸的各种合成路线、国内外的研究现状及工业化情况，重点讨论了由肉桂酸和氨生物合成Ｌ－苯丙氨酸的路线，提出了在国内进一步工作的建议。