Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable

We prove that finite quotients of the multiplicative group of a finite dimensional division algebra are solvable. Let be a finite dimensional division algebra having center , and let be a normal subgroup of finite index. Suppose is not solvable. Then we may assume that is a minimal nonsolvable group (MNS group for short), i.e. a nonsolvable group all of whose proper quotients are solvable. Our proof now has two main ingredients. One ingredient is to show that the commuting graph of a finite MNS group satisfies a certain property which we denote Property . This property includes the requirement that the diameter of the commuting graph should be , but is, in fact, stronger. Another ingredient is to show that if the commuting graph of has Property , then is open with respect to a nontrivial height one valuation of (assuming without loss of generality, as we may, that is finitely generated). After establishing the openness of (when is an MNS group) we apply the Nonexistence Theorem whose proof uses induction on the transcendence degree of over its prime subfield to eliminate as a possible quotient of , thereby obtaining a contradiction and proving our main result.

     

一种采用分段线性函数的图像增强方法

提出了一种采用分段线性函数实现图像增强的方法.为了避免在图像增强过程中的过度平滑或锐化,定义一个7段线性函数.函数的自变量是输入图像的某一像素灰度值与其3×3邻域一像素灰度值之差,函数的输出反映了这个差值对输出像素灰度值的贡献.分段函数还通过两个参数分别调整平滑或锐化的程度.实验结果表明,这种方法是一种灵活、有效的图像增强方法.     

框式约束凸二次规划的预估校正光滑算法

研究了框式约束凸二次规划的一种光滑算法，算法中应用了牛顿法及其变形形式，证明了算法的全局收敛性．     

Exponential smoothing — I

Some new insights and results for exponential smoothing with application to forecasting and parameter estimation. Multidimensional exponential smoothing is described by a Kalman filter model with a limiting stationary gain matrix.     

Local smoothing property and Strichartz inequality for Schrödinger equations with potentials superquadratic at infinity

We study smoothing properties for time-dependent Schrödinger equations , , with potentials which satisfy V(x)=O(|x|^m) at infinity, m?2. We show that the solution u(t,x) is 1/m times differentiable with respect to x at almost all , and explain that this is the result of the fact that the sojourn time of classical particles with energy λ in arbitrary compact set is less than CTλ^−1/m during [0,T] when λ is very large. We also show Strichartz's inequality with derivative loss for such potentials and give its application to nonlinear Schrödinger equations.     

Predictor-Corrector Smoothing Methods for Monotone LCP

In this paper, we analyze the global and local convergence properties of two predictor-corrector smoothing methods, which are based on the framework of the method in [1], for monotone linear complementarity problems (LCPs). The difference between the algorithm in [1] and our algorithms is that the neighborhood of smoothing central path in our paper is different to that in [1]. In addition, the difference between Algorithm 2.1 and the algorithm in [1] exists in the calculation of the predictor step. Comparing with the results in [1],the global and local convergence of the two methods can be obtained under very mild conditions. The global convergence of the two methods do not need the boundness of the inverse of the Jacobian. The superlinear convergence of Algorithm 2.1‘ is obtained under the assumption of nonsingularity of generalized Jacobian of Φ(x,y) at the limit point and Algorithm 2.1 obtains superlinear convergence under the assumption of strict complementarity at the solution. The efficiency of the two methods is tested by numerical experiments.     

Smoothing Properties and Approximation of Time Derivatives for Parabolic Equations: Variable Time Steps

We study smoothing properties and approximation of time derivatives for time discretization schemes with variable time steps for a homogeneous parabolic problem formulated as an abstract initial value problem in a Banach space. The time stepping methods are based on using rational approximations to the exponential function which are A()-stable for suitable (0,/2] with unit bounded maximum norm. First- and second-order approximations of time derivatives based on using difference quotients are considered. Smoothing properties are derived and error estimates are established under the so-called increasing quasi-quasiuniform assumption on the time steps.     

基于WEB的数字信号处理虚拟系统

基于WEB的虚拟系统为研究数字信号处理提供了一种新的方式,采用虚拟系统对数字信号的频谱分析及语音编码进行研究,通过ASP和ActiveX技术实现系统的动态交互和实时传输,初步实现了信号在网上的实时交互处理,该系统的研究成果已开始应用于教学,科研中。     

Adaptive Smoothing Method,Deterministically Computable Generalized Jacobians,and the Newton Method

In this note, we show that a well-known integral method, which was used by Mayne and Polak to compute an -subgradient, can be exploited to compute deterministically an element of the plenary hull of the Clarke generalized Jacobian of a locally Lipschitz mapping regardless of its structure. In particular, we show that, when a locally Lipschitz mapping is piecewise smooth, we are able to compute deterministically an element of the Clarke generalized Jacobian by the adaptive smoothing method. Consequently, we show that the Newton method based on the plenary hull of the Clarke generalized Jacobian can be implemented in a deterministic way for solving Lipschitz nonsmooth equations.