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.     

Chaotic motion of the dynamical system under both additive and multiplicative noise excitations

With both additive and multiplicative noise excitations, the effect on the chaotic behaviour of the dynamical system is investigated in this paper. The random Melnikov theorem with the mean-square criterion that applies to a type of dynamical systems is analysed in order to obtain the conditions for the possible occurrence of chaos. As an example, for the Duffing system, we deduce its concrete expression for the threshold of multiplicative noise amplitude for the rising of chaos, and by combining figures, we discuss the influences of the amplitude, intensity and frequency of both bounded noises on the dynamical behaviour of the Duffing system separately. Finally, numerical simulations are illustrated to verify the theoretical analysis according to the largest Lyapunov exponent and Poincaré map.     

Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings

In this paper we shall show that the boundary of the hyperbolic building considered by M. Bourdon admits Poincaré type inequalities. Then by using Heinonen-Koskela's work, we shall prove Loewner capacity estimates for some families of curves of and the fact that every quasiconformal homeomorphism is quasisymmetric. Therefore by these results, the answer to questions 19 and 20 of Heinonen and Semmes (Thirty-three YES or NO questions about mappings, measures and metrics, Conform Geom. Dyn. 1 (1997), 1-12) is NO.

     

一类Pointaré差分方程解的渐近性质

以二阶的情形讨论了Ｐｏｉｎｃａｒ差分方程ｙ（ｎ＋ｍ）十（ａ１＋ｐ１（ｍ））ｙ（ｎ＋ｍ－１）＋…＋（ａｎ＋ｐｎ（ｍ））ｙ（ｍ）＝０当其常系数部分ｘ（ｎ＋ｍ）＋ａ１ｘ（ｎ＋ｍ－１）＋…＋ａｎｘ（ｍ）＝０的特征方程有相同的根时，解的渐近性质．通过不动点方法给出了Ｐｏｉｎｃａｒ差分方程的解渐近于其常系数方程解的条件，并给出了渐近式高阶项的估计．     

Differentiable conjugacy of the Poincaré type vector fields on

We prove that on , except for those germs of vector fields whose linear parts are conjugated to , any two Poincaré type vector fields are at least conjugated to each other provided their linear approximations have the same eigenvalues and the nonlinear parts are generic.

     

Poincaré duality in P.A. Smith theory

Let , or more generally be a finite -group, where is an odd prime. If acts on a space whose cohomology ring fulfills Poincaré duality (with appropriate coefficients ), we prove a mod congruence between the total Betti number of and a number which depends only on the -module structure of . This improves the well known mod congruences that hold for actions on general spaces.

     

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.