JavaStatSoft: design patterns and features

JavaStatSoft, implemented using Java, is an open-source software for performing statistics. The current features of JavaStatSoft are described. Several well-known patterns the software used are introduced. In addition, based on these patterns and the experience in developing the software, a new framework, referred to as Data Analysis Module, is proposed to help programmers develop a user-friendly software for data analysis.     

Schreier rewriting beyond the classical setting Dedicated to our teacher Alfred Lvovich Shmelkin on his 70th birthday

Using actions of free monoids and free associative algebras, we establish some Schreier-type formulas involving ranks of actions and ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish a generalization of the Schreier formula in the case of subgroups of infinite index. We also study and apply large modules over free associative and free group algebras.     

基于RM型通用门ULM3的对称函数综合

阐述了基本RM型对称函数的定义和性质，给出了任意”变量对称函数在n-1变量基本RM型对称函数完备集中展开系数的计算公式，在此基础上，提出了基于RM型三变量通用逻辑门ULM3的变量数为奇数或偶数的对称函数综合方法，实例验证了上述方法的有效性．     

走进IC卡

介绍了IC卡技术特点及其应用，并展望了我国IC卡的发展前景。     

Modules and Behaviours in nD Systems Theory

This paper is intended both as an introduction to the behavioural theory of nD systems, in particular the duality of Oberst and its applications, and also as a bridge between the behavioural theory and the module-theoretic approach of Fliess, Pommaret and others. Our presentation centres on Pommaret's notion of a system observable, and uses this concept to provide new interpretations of known behavioural results. We discuss among other subjects autonomous systems, controllable systems, observability, transfer matrices, computation of trajectories, and system complexity.     

On the subspaces of JF and JT with non-separable dual

It is proved that every subspace of James Tree space (JT) with non-separable dual contains an isomorph of James Tree complemented in JT. This yields that every complemented subspace of JT with non-separable dual is isomorphic to JT. A new JT like space denoted as TF is defined. It is shown that every subspace of James Function space (JF) with non-separable dual contains an isomorph of TF. The later yields that every subspace of JF with non-separable dual contains isomorphs of c₀ and ?p for 2?p<∞. The analogues of the above results for bounded linear operators are also proved.     

套代数模上的线性保秩映射

主要讨论作用在复Hilbert空间弱闭 AlgN-模上的线性保秩映射，并给出在各种情况下保秩一性线性映射的刻画．作为应用，最后讨论了弱闭 AlgN-模上的模同构，并得出这样的同构是平凡的．     

Formation of individual protein channels in lipid bilayers suspended in nanopores

Free-standing lipid bilayers are formed in regularly arranged nanopores of 200, 400 and 800 nm in a 300 nm thin hydrophobic silicon nitride membrane separating two fluid compartments. The extraordinary stability of the lipid bilayers allows us to monitor channel formation of the model peptide melittin and α-hemolysin from Staphylococcus aureus using electrochemical impedance spectroscopy and chronoamperometry. We observed that melittin channel formation is voltage-dependent and transient, whereas transmembrane heptameric α-hemolysin channels in nano-BLMs persist for hours. The onset of α-hemolysin-mediated conduction depends on the applied protein concentration and strongly on the diameter of the nanopores. Heptameric channel formation from adsorbed α-hemolysin monomers needs more time in bilayers suspended in 200 nm pores compared to bilayers in pores of 400 and 800 nm diameters. Diffusion of sodium ions across α-hemolysin channels present in a sufficiently high number in the bilayers was quantitatively and specifically determined using ion selective electrodes. The results demonstrate that relatively small variations of nano-dimensions have a tremendous effect on observable dynamic biomolecular processes. Such nanopore chips are potentially useful as supports for stable lipid bilayers to establish functional assays of membrane proteins needed in basic research and drug discovery.     

Shannon sampling II: Connections to learning theory

We continue our study [S. Smale, D.X. Zhou, Shannon sampling and function reconstruction from point values, Bull. Amer. Math. Soc. 41 (2004) 279–305] of Shannon sampling and function reconstruction. In this paper, the error analysis is improved. Then we show how our approach can be applied to learning theory: a functional analysis framework is presented; dimension independent probability estimates are given not only for the error in the L² spaces, but also for the error in the reproducing kernel Hilbert space where the learning algorithm is performed. Covering number arguments are replaced by estimates of integral operators.