On vector-valued random Fourier series

Consider a (complex) Banach spaceX, such thatX C_O, and vectors(X _i ) _i ofX. Consider an independent standard normal sequence(g _i ) _i . Then if anX-valued random Fourier series _{|k| n} e ^ikt g _k x _k satisfies

On the ?ojasiewicz-Simon gradient inequality

We prove a general version of the ?ojasiewicz-Simon inequality, and we show how to apply the abstract result to study energy functionals E of the form

     

On the Differential Properties of Temlyakov-Type and Temlyakov-Bavrin-Type Integrals

We establish a formula that expresses the value of the density of the Temlyakov-type integral with defining domain of type A in terms of the integral itself by means of a differential operator. We extend this operator connection to the Temlyakov–Bavrin-type integral of order k. Our study bases on the method of linear differential operators with variable coefficients which is developed by A. V. Nelaev.     

Strongly inequivalent representations and Tutte polynomials of matroids

We develop constructive techniques to show that non-isomorphic 3-connected matroids that are representable over a fixed finite field and that have the same Tutte polynomial abound. In particular, for most prime powers q, we construct infinite families of sets of 3-connected matroids for which the matroids in a given set are non-isomorphic, are representable over GF(q), and have the same Tutte polynomial. Furthermore, the cardinalities of the sets of matroids in a given family grow exponentially as a function of rank, and there are many such families.In Memory of Gian-Carlo Rota     

A note on the isotopy problem for $$ \mathbb{R}^2 $$ -planes

For a class of stable planes we define a notion of isotopy equivalence with respect to that class and prove that any two planes of a certain class of -planes comprising all affine -planes are isotopy equivalent. Furthermore we obtain that all affine -planes are isotopy equivalent in the class of affine -planes. Finally we give an example which shows that this approach cannot be easily generalized to 2-dimensional projective planes, and we outline a different way for a possible generalization.Received: 27 April 2001     

Combings of groups and the grammar of reparameterization

A new construction of combings is used to distinguish between several previously indistinguishable classes of groups associated to the theory of automatic groups and non-positive curvature in group theory. We construct synchronously bounded combings for a class of groups that are neither bicombable nor automatic. The linguistic complexity of these combings is analysed: in many cases the language of words in the combing is an indexed language.     

电化学方法研究(phen)2Cu2+配合物与DNA的相互作用

用电化学循环伏安法和微分脉冲伏安法研究了1,10-邻菲咯啉铜配合物[（phen）2Cu^2＋]与小牛胸腺DNA（CTDNA）的相互作用。结果发现,在pH=7．4的三羟甲基胺基甲烷-盐酸缓冲溶液（Tris—HCl）中,（phen）2Cu^2＋配合物的铜离子在循环伏安图上呈现明显的准可逆氧化-还原波。当加入一定量的小牛胸腺DNA时,配合物（phen）,Cu^2＋的氧化和还原峰电流均有所下降。通过比较（phen）2Cu^2＋配合物中加入单链DNA和双链DNA后的氧化和还原峰电流下降的程度,前者比后者F降的程度小,可以得出（phen）2Cu^2＋配合物与小牛胸腺双链DNA的作用方式存在着插入式的沟槽结合模式。这个结论在本实验中由盐效应进一步得到证实。由此可知,（phen）2Cu^2＋配合物与小牛胸腺DNA形成了一种插入式的电惰性结合物,从而导致氧化还原峰电流下降。     

拟次酉阵与拟次Hermite阵

提出了拟次酉阵、拟(反)次Hermite阵概念，研究了它们的性质及其相互间的关系，将正交矩阵广义Gayley分解推广到拟次酉阵上。