拓扑序列复杂性和混合

本文给出动力系统的拓扑序列复杂函数和族.F-扩散的概念,利用序列复杂函数给出一致刚性、等度连续性和F-混合的特征,并讨论了族F-混合与一致刚性、相关族扩散、混沌及序列等度连续点存在性的关系.     

关于P-凸性与F-凸性的一些注记（英文）

本文得到在赋Orlicz范数(或Luxemburg范数)下Orlicz-Bochner序列空间l_M(X_s)为P-凸的当且仅当l_M是P-凸的,且{X_s}为等度P-凸的.据此可得l_M(X_s)为F-凸的当且仅当l_M是F-凸的,且{X_s}为等度F-凸的.本文也讨论了Orlicz-Bochner函数空间L_M(μ,X)中的F-凸性.     

关于随机解析算子函数的正族性质

该文在经典函数的正族理论基础上建立了随机解析算子函数的正族、一致有界和等度连续等概念，并在此意义下，给出了随机解析算子函数族内闭一致有界与等度连续、正族与一致有界的关系，以及随机解析算子函数族为正族的一个充分必要条件。     

函数S-粗集对偶与F-粗边际规律

函数单向S粗集对偶(dual offunction one direction singular rough sets)是函数S粗集的基本形式之一,函数单向S-粗集对偶具有动态特性与规律(函数)特性.函数S粗集(function singular rough sets)是把函数概念引入到S粗集内(singular rough sets)改进S粗集得到的把导数概念与函数单向S粗集对偶交叉、渗透给出粗边际规律F-粗边际规律概念;给出粗边际规律F-粗边际规律特征;给出F-粗边际规律与粗边际规律的关系;给出F-粗边际规律在经济信息系统中的应用     

复值度量空间中F-压缩映射的叠合点

将F-压缩的概念从度量空间推广到复值度量空间中,并引进F-拟压缩的概念.说明了每个F-压缩是F-拟压缩,但反之不真.运用序列逼近的方法,对两个满足某种F-压缩条件的映射,证明了 一些叠合点结果,同时得到了一些不动点结果,这些结果推广了 Wardowski的结果.给出了几个说明性例子以突出这种推广.     

富足半群上的F-好同余

引入了富足半群上F-好同余的概念,给出了富足半群上F-好同余的性质和特征.在此基础上,得到了富足半群上F-好同余的并为F-好同余的相关条件.最后,进一步对拟适当半群上的F-好同余作了讨论并得到了一些性质.     

F-本质子模与F-多余子模

本文研究了F-本质子模和F-多余子模.利用同调的方法,得到了F-本质与F-包络,F-多余与F-复盖之间的关系,另外还得到了F-本质子模,F-多余子模的相关性质,从而推广了文献[3,10]中的部分结果.     

一元F-粗积分的概率估计

在函数单向S-粗集生成的一元F-粗积分的基础上,结合元素迁移的概率特征,提出了依概率p-粗积分的概念,给出了依概率p-粗积分上下关系链定理和依概率p-粗积分关系链定理,讨论了依概率p-粗积分和F-粗积分及牛顿积分间的关系.     

无限差集类及其应用

若S为Z+的一无限子集,称S-S={n-m|n,m∈S,n>m}为一无限差集.本文研究Z+的子集族F生成的无限差集类(?)F-△={S-S|S∈F)及其对偶族K(?)F-△的性质,并讨论它们在动力系统研究中的应用.     

可换随机变量序列的弱收敛

本文讨论可换随机变量序列部分和适当正则化以后的一致稳定依分布收敛问题,求出了在这种收敛意义下的全部极限混合分布函数。给出了收敛的充要条件。     

Topologically weakly mixing homeomorphisms of the Klein bottle that are uniformly rigid

In this paper we prove that there is a large family of topologically weakly mixing homeomorphisms of the Klein bottle that are uniformly rigid. We do this by viewing the Klein bottle as the quotient of the two-torus by an appropriate group action and producing topologically weakly mixing homeomorphisms of the two-torus that are uniformly rigid and equivariant with respect to the action.     

Absolute and relative choreographies in rigid body dynamics

For the classical problem of motion of a rigid body about a fixed point with zero area integral, we present a family of solutions that are periodic in the absolute space. Such solutions are known as choreographies. The family includes the well-known Delone solutions (for the Kovalevskaya case), some particular solutions for the Goryachev-Chaplygin case, and the Steklov solution. The “genealogy” of solutions of the family naturally appearing from the energy continuation and their connection with the Staude rotations are considered. It is shown that if the integral of areas is zero, the solutions are periodic with respect to a coordinate frame that rotates uniformly about the vertical (relative choreographies).      

On the existence of consistent estimates and tests

The paper concerns estimates of probability measures (=p-measures) determined from a countable number of independent realizations. The main results are:

1. For suitable topologies, the existence of a consistent sequence of estimates implies the existence of a sequence of estimates which is strongly consistent a. e. with respect to an arbitrary finite prior measure. In the case of a measurable parameter the existence of a consistent sequence of estimates implies strong consistency of the Bayes estimates for the quadratic loss function.
2. If a family ofp-measures is separable with respect to the supremum metric, there exists a sequence of strict estimates which is uniformly consistent with respect to the supremum metric on any totally bounded subset ofp-measures.
3. IfB is totally σ-bounded with respect to the supremum metric there exists a density-consistent sequence of estimates. IfB is separable with respect to the supremum metric there exists a sequence of estimates which is density consistent a. e. with respect to an arbitrary finite prior measure.
4. A sequence of uniformly consistent tests exists for all compact hypotheses in the case of an abstract sample space and for all weakly closed hypotheses in the case of a separable metric sample space.

     

Pure adaptive search in global optimization

Pure adaptive seach iteratively constructs a sequence of interior points uniformly distributed within the corresponding sequence of nested improving regions of the feasible space. That is, at any iteration, the next point in the sequence is uniformly distributed over the region of feasible space containing all points that are strictly superior in value to the previous points in the sequence. The complexity of this algorithm is measured by the expected number of iterations required to achieve a given accuracy of solution. We show that for global mathematical programs satisfying the Lipschitz condition, its complexity increases at mostlinearly in the dimension of the problem.This work was supported in part by NATO grant 0119/89.     

Exponentially decaying wavelets with uncertainty constants uniformly bounded with respect to the smoothness parameter

We construct a family of wavelet functions whose scaling functions decay exponentially and have uncertainty constants uniformly bounded with respect to the smoothness parameter.     

Some improvements of the S-adic conjecture

In [S. Ferenczi, Rank and symbolic complexity, Ergodic Theory Dynam. Systems 16 (1996) 663-682], S. Ferenczi proved that the language of any uniformly recurrent sequence with an at most linear complexity is S-adic. In this paper we adapt his proof in a more structured way and improve this result stating that any such sequence is itself S-adic. We also give some properties on the constructed morphisms.     

Approximating Boolean functions by OBDDs

In learning theory and genetic programming, OBDDs are used to represent approximations of Boolean functions. This motivates the investigation of the OBDD complexity of approximating Boolean functions with respect to given distributions on the inputs. We present a new type of reduction for one-round communication problems that is suitable for approximations. Using this new type of reduction, we improve a known lower bound on the size of OBDD approximations of the hidden weighted bit function for uniformly distributed inputs to an asymptotically tight bound and prove new results about OBDD approximations of integer multiplication and squaring for uniformly distributed inputs.     

Strongly relatively nonexpansive sequences in Banach spaces and applications

We introduce the concept of a strongly relatively nonexpansive sequence in a Banach space and investigate its properties. Then we apply our results to the problem of approximating a common fixed point of a countable family of relatively nonexpansive mappings in a uniformly convex and uniformly smooth Banach space.      

Convergence Theorems for Pointwise Asymptotically Strict Pseudo-Contractions in Hilbert Spaces

A new class of contractive mappings called pointwise asymptotically ?-strict pseudo-contractions in Hilbert spaces is introduced and weak convergence of the sequence generated by Mann's iterative scheme to a fixed point of a uniformly Lipschitzian and pointwise asymptotically ?-strict pseudo-contractive mapping T in a Hilbert space is established. Also, a new kind of monotone hybrid method which is a modification of Mann's iterative scheme for finding a common fixed point of an infinitely countable family of uniformly Lipschitzian and pointwise asymptotically ?-strict pseudo-contractive mappings is proposed. Strong convergence of the sequence generated by the proposedmonotone hybrid method for an infinitely countable family of uniformly Lipschitzian and pointwise asymptotically ?-strict pseudo-contractive mappings in a Hilbert space is also shown. The results presented in this article extend and improve some known results in the literature.     

A category of kernels for equivariant factorizations and its implications for Hodge theory

Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesàro averages. Nonlinear spectral gaps of graphs are also shown to behave sub-multiplicatively under zigzag products. These results yield a combinatorial construction of super-expanders, i.e., a sequence of 3-regular graphs that does not admit a coarse embedding into any uniformly convex normed space.