Sturm-Liouville operators with indefinite weight functions and eigenvalue depending boundary conditions

We consider a class of boundary value problems for Sturm-Liouville operators with indefinite weight functions. The spectral parameter appears nonlinearly in the boundary condition in the form of a function τ which has the property that λ?λτ(λ) is a generalized Nevanlinna function. We construct linearizations of these boundary value problems and study their spectral properties.     

Scalar Derivatives in Hilbert Spaces

Computational formulae for scalar derivatives of mappings and pairs of mappings in the direction of a set will be given. These formulae are very important for explicitly verifying conditions of existence for fixed point theorems, surjectivity theorems, integral equations, variational inequalities and complementarity problems under additional differentiability conditions. To emphasize this idea at the end of the paper we give an application to complementarity problems. Some theorems which extend the correspondence between monotone mappings and scalar derivatives from Euclidean spaces to Hilbert spaces will also be given.     

On Spencer Cohomologies of Affine Algebraic Varieties

This paper contains proofs and examples for some key facts about algebraic Spencer cohomologies preannounced elsewhere. The author hopes that here he has managed to build a more systematic discourse of the issues raised in earlier works.     

高炉冶炼过程的混沌性解析

根据Grassberger和Procaccia提出的Kolmogorov熵计算方法，以山东莱芜钢铁集团公司1号 高炉和山西临汾钢铁集团公司6号高炉测得的铁水硅含量时间序列为样本，计算了各自的Kol mogorov熵分别为（01453±00151）nats·h-1^-1和（01553±0014 0）nats·h-1^-1，并估计了两座高炉铁水硅含量可预测的时间尺度分别约为6 88和644h.由Kolmogorov熵均为大于零的有限值，定量地说明了这两座高炉 关键词： 混沌 Kolmogorov熵 高炉冶炼过程 铁水硅含量     

The Approximation Properties of Certain Interpolation Operators of Entire Exponential Type （Ⅱ）

ＴｈｅＡｐｐｒｏｘｉｍａｔｉｏｎＰｒｏｐｅｒｔｉｅｓｏｆＣｅｒｔａｉｎＩｎｔｅｒｐｏｌａｔｉｏｎＯｐｅｒａｔｏｒｓｏｆＥｎｔｉｒｅＥｘｐｏｎｅｎｔｉａｌＴｙｐｅ（Ⅱ）￥ＴｉａｎＪｉｓｈａｎ；ＬｉｕＪｉｕｆｅｎ（ＨｅｎａｎＵｎｉｔｉｖｅｒｓｉｔｙ）（Ｐ...     

Wiener's lemma for twisted convolution and Gabor frames

We prove non-commutative versions of Wiener's Lemma on absolutely convergent Fourier series (a) for the case of twisted convolution and (b) for rotation algebras. As an application we solve some open problems about Gabor frames, among them the problem of Feichtinger and Janssen that is known in the literature as the ``irrational case'.

     

EXISTENCE OF LIMIT CYCLES FOR A CUBIC KOLMOGOROV SYSTEM WITH A PARABOLIC SOLUTION WHICH DOES NOT CONTACT AND INTERSECT THE COORDINATE AXES

This paper is concerned with a cubic Kolmogorov system with a parabolicsolution which does not contact and intersect the coordinates. The conclusionis that such a system may possess limit cycles.     

Existence Results for Evolution Noncoercive Hemivariational Inequalities

This paper is devoted to the existence of solutions for evolution hemivariational inequalities as generalizations of evolution variational inequalities to nonconvex functionals. The operators involved are taken to be multivalued and noncoercive. Using the notion of the generalized gradient of Clarke and the recession method, some existence results of solutions are proved.     

Positive linear operators which preserve x 2

A sequence of positive linear operators which approximate each continuous function on [0,1] while preserving the functione ₂ (x) =x ² is presented. Quantitative estimates are given and are compared with estimates of approximation by Bernstein polynomials. Connections with summability are discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Continuous integral kernels for unbounded Schrödinger semigroups and their spectral projections

By suitably extending a Feynman-Kac formula of Simon (Canad. Math. Soc. Conf. Proc. 28 (2000) 317), we study one-parameter semigroups generated by (the negative of) rather general Schrödinger operators, which may be unbounded from below and include a magnetic vector potential. In particular, a common domain of essential self-adjointness for such a semigroup is specified. Moreover, each member of the semigroup is proven to be a maximal Carleman operator with a continuous integral kernel given by a Brownian-bridge expectation. The results are used to show that the spectral projections of the generating Schrödinger operator also act as Carleman operators with continuous integral kernels. Applications to Schrödinger operators with rather general random scalar potentials include a rigorous justification of an integral-kernel representation of their integrated density of states—a relation frequently used in the physics literature on disordered solids.