空间参数曲线的双目标能量极小化方法及其应用

能量极小化方法已广泛用于平面曲线的构造,而在空间曲线构造方面的应用尚少。首先介绍了空间参数曲线的弯曲能和扭曲能,然后提出了一种以弯曲能和扭曲能同时极小为目标的空间参数曲线构造方法,最后以空间三次Bézier曲线为例,探讨了该方法在曲线的构造、延拓、平滑等问题中的应用。所提出的方法更符合空间参数曲线既需考虑弯曲又需考虑扭曲的特点。     

Non-Noether Conserved Quantity of Poincaré-Chetaev Equations of a Generalized Classical Mechanics

In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré-Chetaev equations of a generalized classical mechanics under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced. Finally, an example is given to illustrate the application of the results.     

可反映射的性质及其应用

对可反映射的性质进行了研究 ,利用其性质对混沌系统 Hénon映射的同宿轨进行了讨论     

重分数布朗运动的列维连续模

重分数布朗运动是布朗运动的一种推广，有较强的实用背景.该过程的增量既不是独立的，也不是平稳的. 本文研究了它的列维连续模.     

一类高次多项式系统极限环的存在性和唯一性

通过变换将一类高次多项式系统转化为广义Liénard系统,并利用广义Liénard系统的结果研究了其极限环存在性问题,推广了相关文献的结果.     

Option Pricing and Hedging under a Markov Switching Lévy Process Model

In this paper,we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to option pricing and hedging.In this model,the market interest rate,the volatility of the underlying risky assets and the N-state compensator,depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process.We use the MEMM(minimal entropy martingale measure) as the equivalent martingale measure.The option price using this model is obtained by the Fourier transform method.We obtain a closed-form solution for the hedge ratio by applying the local risk minimizing hedging.     

Bolzano's Theorems for Holomorphic Mappings

The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple way from Cauchy's theorem for holomorphic functions.A more complicated proof,using Cauchy's argument principle,provides uniqueness of the zero,when the sign conditions on the boundary are strict.Applications are given to corresponding Brouwer fixed point theorems for holomorphic functions.Extensions to holomorphic mappings from Cn to Cn are obtained using Brouwer degree.     

由Lévy过程驱动的BSDE定义的一般非线性期望

本文研究了平凡可积随机变量的一类非线性期望f-期望.利用陈增敬推广g-期望的方法,扩张了f-期望的定义空间.     

一类广义Liénard系统解的有界性

获得了广义 Liénard系统dxdt=p(y) -F(x) ,　 dydt=-g(x) q(y)所有正半轨线有界的若干充分条件 ,推广改进了已有文献 [1— 1 2 ]中的相应结果 .     

Clifford分析中奇异积分的Poincaré-Bertrand置换公式

借助于多元复分析的思想，本文证明了Ｃｌｉｆｏｒｄ分析中奇异积分的Ｐｏｉｎｃａｒé－Ｂｅｒｔｒａｎｄ置换公式．