具有双不变拟Riemann度量的Lie群

本文讨论了其有双不变拟Riemann度量的Lie群及其等距变换群的一些性质,证明了:1)具有双不变拟Riemann度量的Lie群的等距变换群一定非单;2)具有双不变拟Riemann度量的Lie群半单的充要条件是其等距变换群半单且非单.     

无穷维随机微分方程的最优宽松控制

W.H.Flcmng—M.Nisio在文[3]中讨论了n维空间上如下形式随机微分方程的最优宽松控制问题:本文利用A.Bensoussan—M.Nisiso在文[1]中引入的测度的殆紧性,将文[3]中最优宽松控制的存在性定理推广到无穷维情形.     

The Renormalization Group and Its Finite Lattice Approximations

We investigate finite lattice approximations to the Wilson renormalization group in models of unconstrained spins. We discuss first the properties of the renormalization group transformation (RGT) that control the accuracy of this type of approximation and explain different methods and techniques to practically identify them. We also discuss how to determine the anomalous dimension of the field. We apply our considerations to a linear sigma model in two dimensions in the domain of attraction of the Ising fixed point using a Bell–Wilson RGT. We are able to identify optimal RGTs which allow accurate computations of quantities such as critical exponents, fixed-point couplings and eigenvectors with modest statistics. We finally discuss the advantages and limitations of this type of approach.     

Extraction of subsystems “Majorized” by the rademacher system

In this paper it is proved that from any uniformly bounded orthonormal system {f _n} _n=1 ^∞ of random variables defined on the probability space (Ω, ε, P), one can extract a subsystem {fni} _i ^{Emphasis>=1/∞} majorized in distribution by the Rademacher system on [0, 1]. This means that {

Weak Copositive and Intertwining Approximation

It is known that shape preserving approximation has lower rates than unconstrained approximation. This is especially true for copositive and intertwining approximations. ForfL_p, 1p<∞, the former only has rateω(f, n⁻¹)_p, and the latter cannot even be bounded byC f_p. In this paper, we discuss various ways to relax the restrictions in these approximations and conclude that the most sensible way is the so-calledalmostcopositive/intertwining approximation in which one relaxes the restriction on the approximants in a neighborhood of radiusΔ_n(y_j) of each sign changey_j.     

Multiple Wick Product Chaos Processes

Let u(x) xR ^q be a symmetric nonnegative definite function which is bounded outside of all neighborhoods of zero but which may have u(0)=. Let p _x, (·) be the density of an R ^q valued canonical normal random variable with mean x and variance and let {G _x, ; (x, )R ^q ×[0,1 ]} be the mean zero Gaussian process with covariance

Menger概率n-度量空间中的不动点定理

引进了概率ｎ－度量空间,并将文「１」、「２」的某些主要结果拓广至Ｍｅｎｇｅｒ概率ｎ－度量空间。     

On linearly Lindelöf and strongly discretely Lindelöf spaces

We prove that the cardinality of every first countable linearly Lindelöf Tychonoff space does not exceed , and every strongly discretely Lindelöf Tychonoff space of countable tightness is Lindelöf.

     

Constructive decomposition of functions of finite central mean oscillation

The space CMO of functions of finite central mean oscillation is an analogue of BMO where the condition that the sharp maximal function is bounded is replaced by the convergence of the sharp function at the origin. In this paper it is shown that each element of CMO is a singular integral image of an element of the Beurling space of functions whose Hardy-Littlewood maximal function converges at zero. This result is an analogue of Uchiyama's constructive decomposition of BMO in terms of singular integral images of bounded functions. The argument shows, in fact, that to each element of CMO one can construct a vector Calderón-Zygmund operator that maps that element into the proper subspace .