非线性守恒律高阶谱粘性法的收敛性

讨论守恒型方程周期边界问题的高阶谱粘性方法逼近解的收敛性.在逼近解一致有界的假设下,通过建立其高阶导数的上界估计,证明了高阶谱粘性方法逼近解具有同二阶谱粘性方法逼近解相类似的高频衰减性质.以此为基础,用补偿列紧法证明了高阶谱粘性方法逼近解收敛于守恒型方程的物理解.     

有限时区最优控制问题的值函数的逼近

对于有限时区最优连续－转换－脉冲控制问题的情函数满足的拟变分不等式，本文给出了其关于时间的离散化逼近系统，以及逼近解和原粘性解之间的估计．     

Eikonal型方程粘性解的表达式

对于圆锥型和棱锥型Hamiltonian的Eikonal型方程,本文给出了一种几何方法,得出其初值问题解的表达式并且说明由此式给出的解为原初值问题的粘性解．首先用一个凸函数序列逼近Eikonal型方程中的Hamiltonian,再由Hopf-Lax公式给出方程序列的粘性解,最后证明了该粘性解序列会收敛到Eikonal方程的粘性解．     

含无穷拉普拉斯算子的渗流问题的李普希兹估计

本文研究含无穷拉普拉斯算子的渗流问题.运用改进的Bernstein方法和光滑逼近,分别建立了该问题严格正粘性解和非负粘性解关于空间变量的李普希兹估计.     

具有奇性与真空粘性依赖于密度的非牛顿流局部强解的存在唯一性

研究一维有界区间上粘性依赖于密度且具有奇性、初始允许真空的可压缩非牛顿流.通过正则化奇性项以及逐步迭代构造初边值问题的逼近解,对逼近解取极限得到其局部强解的存在唯一性,进一步推广了相关文献中关于非牛顿流解的存在性结果.     

一类广义KdV－Burgers型方程的初边值问题

本文研究了一类带三阶粘性项的广义ＫｄＶ－Ｂｕｒｇｅｒｓ型方程的初边值问题．运用Ｇａｌｅｒｋｉｎ逼近方法，结合能量估计，得到了问题整体解的存在性，正则性，唯一性和稳定性等结果．并在一定条件下讨论了问题的解的渐近行为和“爆破”现象．     

无限时区最优控制系统的逼近

对于无限时区最优连续－转换－脉冲控制系统值函数满足的拟变分不等式，本文给出了其关于时间的离散化逼近系统，以及逼近解和原粘性解之间的估计．另外，相对于连续－转换控制系统，本文给出了其空间离散化方程，并且给出了解的估计以及求解的算法．     

具有截断势的空间齐次Boltzmann方程的L2逼近

本文证明了在一定条件下,粘性Boltzmann方程■_tf=Q(f,f) δ△_vf的解当粘性系数δ趋于0~ 时,依L_k~2范数逼近于齐次方程■_tf=Q(f,f)的解。     

一类广义KdV—Burgers型方程的初边值问题

本文研究了一类带三阶粘性项的广义ＫｄＶ－Ｂｕｒｇｅｒｓ型方程的初边值问题，运用Ｇａｌｅｒｋｉｎ逼近方法，结合能量估计，得到了问题整体解的存在性，正则性，唯一性和稳定性等结果，并在一定条件下讨论了问题的解的渐边行为和“爆破”现象。     

一类流固耦合系统强解的存在性问题

本文主要讨论一类多刚体与粘性系数依赖于密度的不可压缩流体耦合系统的强解存在性问题.首先,利用变量替换建立本文研究对象对应的非线性微分方程,然后,利用Garlerkin逼近方法获得线性化问题的光滑解,从而可以构造出原问题的逼近解.通过估计逼近解的一致有界性,最后证明了一类描述多刚体在不可压缩流体中运动的耦合系统强解的存在性问题.特别要指出的是在初始密度满足相容性条件下,此结论允许流体内部出现真空.     

The Derksen invariant vs. the Makar-Limanov invariant

In this article it is shown that the Makar-Limanov invariant of a ring (or variety) can be trivial while the Derksen invariant is not, and vice versa.

     

On the ratio integral formula for the likelihood ratio of a maximal invariant

The usual ratio of an integral formula for the likelihood ratio of a maximal invariant in a group model is shown to be correct under assumption that the denominator integral is finite almost everywhere. The limitation of this assumption is discussed, and an application to invariant suffciency is given.     

Invariant ordering on the simply connected covering of the Shilov boundary of a symmetric domain

The Shilov boundary of a symmetric domain D = G/K of tube type has the form G/P, where P is a maximal parabolic subgroup of the group G. We prove that the simply connected covering of the Shilov boundary possesses a unique (up to inversion) invariant ordering, which is induced by the continuous invariant ordering on the simply connected covering of G and can readily be described in terms of the corresponding Jordan algebra.     

强共振情况下不变环面的分支

本文利用周期变换和积分流形理论研究平面周期扰动系统，在强共振情况下获得了从一阶细焦点分支出不变环面的简洁条件，本文中的非共振条件不同于［５］中所给出的非共振条件．     

互素作用下的不变块(英文)

令A,G为有限群且(|A|,|G|)=1.设A通过自同构作用在G上.令B是G的A-不变块.若B的每一个指标都是A-不变的,且B的亏群是循环群,则A中心化B的某一亏群.     

Existence and bifurcation of integral manifolds with applications

In this paper a bifurcation theorem on the existence of integral manifolds is obtained by using contracting principle. As an application, sufficient conditions for a higher dimensional system to have an integral manifold are given. Especially the existence and uniqueness of a 3-dimensional invariant torus appearing in a 4-dimensional autonomous system with singularity of codimension two are proved.     

A smooth invariant not a smooth function of the invariant polynomials

An explicit example is given of a smooth function invariant under a linear group action that is not a smooth function of the invariant polynomials.

     

On Fridman Invariants and Generalized Squeezing Functions*

In this paper, the authors introduce the notion of generalized squeezing function and study the basic properties of generalized squeezing functions and Fridman invariants.They also study the comparison of these two invariants, in terms of the so-called quotient invariant.     

On testing the coefficient of variation in an inverse Gaussian population

Here we prove that the LR test for one sided hypotheses concerning the coefficient of variation in an inverse Gaussian family is the UMP invariant test under scale transformation. Some approximations to the CDF of the test statistic are investigated.