关于《代微积拾级》的一个注记

对我国第一部微积分课本《代微积拾级》中曲线凹凸性概念和拐点判定方法作了历史考察,指出其中的缺陷,并试图说明清代数学家未能发现这一缺陷的原因。     

动态裂纹尖端弹粘塑性场的研究

本文利用弹-粘-塑性材料力学模型,对动态扩展裂纹尖端的指数奇异性和对数奇异性进行了渐近分析.文中假定,弹性阶段的粘性效应可以略去,仅在塑性应变中粘性才起作用,对于这种模型,推导出了其率敏感型的本构关系.以Ⅱ型裂纹为例,进一步推导了两种奇异性下裂纹尖端场的渐近微分控制方程,并进行了数值仿真分析.同时讨论了粘性系数α、马赫数M2对裂纹尖端应力应变场的影响,即,弹粘塑性材料扩展裂纹的奇异性取决于其粘性系数和马赫数,粘性系数较大时,裂纹尖端场具有对数奇异性;粘性系数较小时,裂纹尖端场具有指数奇异性.修正了文献[1]中对数奇异性区域的大小;解释了文献[1]中过渡区的成因;给出了过渡区尖端应力场解的形式,从而建立了裂纹尖端场的统一解.     

Z箍缩等离子体K壳层X射线自辐射单色成像

采用针孔配接对数螺线柱面晶体方案,研制了一种小型、靶室内置X射线单色成像器,用于获取Z箍缩等离子体K壳层自辐射单色图像。在阳加速器上对该成像器进行了测试,成功地获取了铝丝阵负载Z箍缩等离子体K壳层自辐射的类氢线与类氦线单色图像。实验结果表明：该成像器具有优异的单色性（能谱带宽小于1 eV）,适合于中低原子序数Z箍缩内爆负载的特征谱线单色图像诊断。     

Application in stochastic volatility models of nonlinear regression with stochastic design

In regression model with stochastic design, the observations have been primarily treated as a simple random sample from a bivariate distribution. It is of enormous practical significance to generalize the situation to stochastic processes. In this paper, estimation and hypothesis testing problems in stochastic volatility model are considered, when the volatility depends on a nonlinear function of the state variable of other stochastic process, but the correlation coefficient |ρ|≠±1. The methods are applied to estimate the volatility of stock returns from Shanghai stock exchange. Copyright © 2009 John Wiley & Sons, Ltd.     

Gravitational Field as a Pressure Force from Logarithmic Lagrangians and Non-Standard Hamiltonians:The Case of Stellar Halo of Milky Way

Recently,the notion of non-standard Lagrangians was discussed widely in literature in an attempt to explore the inverse variational problem of nonlinear differential equations.Different forms of non-standard Lagrangians were introduced in literature and have revealed nice mathematical and physical properties.One interesting form related to the inverse variational problem is the logarithmic Lagrangian,which has a number of motivating features related to the Li′enard-type and Emden nonlinear differential equations.Such types of Lagrangians lead to nonlinear dynamics based on non-standard Hamiltonians.In this communication,we show that some new dynamical properties are obtained in stellar dynamics if standard Lagrangians are replaced by Logarithmic Lagrangians and their corresponding non-standard Hamiltonians.One interesting consequence concerns the emergence of an extra pressure term,which is related to the gravitational field suggesting that gravitation may act as a pressure in a strong gravitational field.The case of the stellar halo of the Milky Way is considered.     

高斯型空间光孤子相互作用的数值研究

通过数值模拟的方法,对高斯孤子在对数型饱和非线性介质中的相互作用进行了研究,考查了两光束间的相对振幅和相对相位对其相互作用的影响。结果表明：高斯孤子之间的相互作用敏感地依赖于两光束间的相对振幅和相对相位。在不同的振幅差异范围内,光束间的主要作用交替地表现为相互排斥和相互吸引,并由于高斯孤子的不稳定性,导致了光束在碰撞后以一种尺寸周期性变化的呼吸模式传输。随着相对相位的增大,两光束间始终持续地表现出强烈的排斥作用,直到相对相位增加到一个2π周期之后。而且碰撞之后,光束也都以呼吸模式进行传输,其分离的角度越大,呼吸就越明显。     

The role of linear objective functions in barrier methods

Received December 10, 1994 / Revised version received April 29, 1998 Published online October 21, 1998