On images of Borel measures under Borel mappings

Let and be metric spaces. We show that the tight images of a (fixed) tight Borel probability measure on , under all Borel mappings , form a closed set in the space of tight Borel probability measures on with the weak-topology. In contrast, the set of images of under all continuous mappings from to may not be closed. We also characterize completely the set of tight images of under Borel mappings. For example, if is non-atomic, then all tight Borel probability measures on can be obtained as images of , and as a matter of fact, one can always choose the corresponding Borel mapping to be of Baire class 2.

     

New Families in the Stable Homotopy of Spheres Revisited

This paper constructs a new family in the stable homotopy of spheres π _{t −6} S represented by h _n g ₀γ₃∈E ^{6 t} ₂ in the Adams spectral sequence which revisits the b _{n −1} g ₀γ₃-elements ∈π _{t −7} S constructed in [3], where t = 2p ⁿ (p− 1) + 6(p ² + p + 1)(p− 1) and p≥ 7 is a prime, n≥ 4. Received October 7, 1998, Revised May 8, 2000, Accepted August 8, 2000.     

Some Classes of L 1-Convergence of Fourier Series

In this paper equivalent classes of the classes M and S _pr , p > 1, > 0. r { 0,1,2, ... ,[]} defined by Shuyun [3] are obtained. Then, it is shown that the class S _pr , 1 > p 2, 0, r {0,1,2,...,[]} is a subclass of BVC _r , where S _pr is the equivalent class of the Shuyun's class S _pr , BV is the class of null sequences of bounded variation and C _r is the extension of the Garrett--Stanojevic class. As a corollary of this result, we have obtained the theorem, proved in [7].     

Folding of lattice protein chains with modified Gō potential

We propose a modified Gō model in which the pairwise interaction energies vary as local environment changes. The stability difference between the surface and the core is also well considered in this model. Thermodynamic and kinetic studies suggest that this model has improved folding cooperativity and foldability in contrast with the Gō model. The free energy landscape of this model has broad barriers and narrow denatured states, which is consistent with that of the two-state folding proteins and is lacked for the Gō model. The role of non-native interactions in protein folding is also studied. We find that appropriate consideration of the contribution of the non-native interactions may increase the folding rate around the transition temperature. Our results show that conformation-dependent interaction between the residues is a realistic representation of potential functions in protein folding. Received 10 April 2002 / Received in final form 20 August 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: wangwei@nju.edu.cn     

Unconditional structures of weakly null sequences

The following dichotomy is established for a normalized weakly null sequence in a Banach space: Either every subsequence admits a convex block subsequence equivalent to the unit vector basis of , or there exists a subsequence which is boundedly convexly complete.

     

Microstructure of glycidylmethacrylate/vinyl acetate copolymers by two‐dimensional nuclear magnetic resonance spectroscopy

Glycidylmethacrylate/vinyl acetate copolymers were prepared by solution polymerization with benzene as a solvent and benzoyl peroxide as an initiator. Copolymer compositions were determined from ¹H NMR spectra, and comonomer reactivity ratios were determined by the Kelen–Tudos (KT) method and the nonlinear least‐squares error‐in‐variable method (EVM). The reactivity ratios obtained from KT and EVM were r_G = 37.4 ± 12.0 and r_V = 0.036 ± 0.019 and r_G = 35.2 and r_V = 0.03, respectively. Complete spectral assignments of ¹³C and ¹H NMR spectra were done with the help of distortionless enhancement by polarization transfer and two‐dimensional ¹³C–¹H heteronuclear single quantum coherence and total correlation spectroscopy. The methyl, methine, and methylene carbon resonance showed both stereochemical and compositional sensitivity. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 4051–4060, 2001     

对－氯苯乙烯和丙烯酸甲酯梯度共聚物的微观结构表征

对由原子转移自由基聚合(ATRP)方法得到的具有“活性”聚合特征的对－氯苯乙烯(S)和丙烯酸甲酯(M)梯度共聚物结构进行了表征．通过¹H、¹³C 核磁共振(NMR)方法和对羰基¹³C峰峰面积的拟合积分研究了该共聚物的单体以及以M为中心的三元组序列结构的组成含量随转化率的变化．研究结果表明：共聚物链中S和M单体含量随着转化率的增加分别表现出减小和增大的变化趋势;三元组序列结构的含量变化中,SMS和MMM分别呈现出单调下降和上升的变化,而MM/MMS则随着转化率的增加达到一个最大值,然后呈现下降趋势．本文还尝试运用了以M为中心的五元组序列结构对羰基¹³C峰峰面积进行更精确的拟合积分,其拟合峰面积的计算结果显示了与上述三元组序列结果相同的变化规律．     

两个渐近非扩张映射公共不动点的迭代程序

在一致凸Banach空间中,研究了迭代序列逼近收敛于两个渐近非扩张映射的公共不动点。所得结果推广了已有的一些结果。     

On the Common Substring Alignment Problem

The Common Substring Alignment Problem is defined as follows: Given a set of one or more strings S₁, S₂ … S_c and a target string T, Y is a common substring of all strings S_i, that is, S_i = B_iYF_i. The goal is to compute the similarity of all strings S_i with T, without computing the part of Y again and again. Using the classical dynamic programming tables, each appearance of Y in a source string would require the computation of all the values in a dynamic programming table of size O(nℓ) where ℓ is the size of Y. Here we describe an algorithm which is composed of an encoding stage and an alignment stage. During the first stage, a data structure is constructed which encodes the comparison of Y with T. Then, during the alignment stage, for each comparison of a source S_i with T, the pre-compiled data structure is used to speed up the part of Y. We show how to reduce the O(nℓ) alignment work, for each appearance of the common substring Y in a source string, to O(n)-at the cost of O(nℓ) encoding work, which is executed only once.     

Galois环上本原序列压缩映射的单性

设Ω是 Ｇａｌｏｉｓ环 ＧＲ（２~ｄ,ｒ）的 Ｔｅｉｃｈｍｕｌｌｅｒ代表集,则 ＧＲ（２~ｄ,ｒ）上每条序列ａ有唯一的权位分解,　其中ａ-ｉ是Ω上序列,同时也可自然视为有限域Ｆ-（２~ｒ）,上序列．设ｆ（ｘ）是环 ＧＲ（２~ｄ,ｒ）上强本原多项式,Ｇ（ｆ（ｘ））表示 ＧＲ（２~ｄ,ｒ）上以ｆ（ｘ）为特征多项式的序列的全体,是Ｆ-（２~ｒ）上一类ｄ－１元多项式, 　本文证明了压缩映射是单射,即对 ａ＝ ｂ当且仅当对所有 ａ,ｂ ∈ Ｇ（ｆ（ｘ））．