Coburn Type Operators and Compact Perturbations

A bounded linear operator T acting on a Hilbert space is called Coburn operator if ker(T ? λ) = {0} or ker(T ? λ)^*= {0} for each λ ∈ C. In this paper, the authors define other Coburn type properties for Hilbert space operators and investigate the compact perturbations of operators with Coburn type properties. They characterize those operators for which has arbitrarily small compact perturbation to have some fixed Coburn property.Moreover, they study the stability of these properties under small compact perturbations.     

Stability of impulsive time-varying systems and compactness of the operators mapping the input space into the state and output spaces

This paper is concerned with time-varying systems with non-necessarily bounded everywhere continuous time-differentiable time-varying point delays. The delay-free and delayed dynamics are assumed to be time-varying and impulsive, in general, and the external input may also be impulsive. For given bounded initial conditions, the (unique) homogeneous state-trajectory and output trajectory are equivalently constructed from three different auxiliary homogeneous systems, the first one being delay-free and time-invariant, the second one possessing the delay-free dynamics of the current delayed system and the third one being the homogeneous part of the system under study. In this way, the constructed solution trajectories of both the unforced and forced systems are obtained from different (input-state space/output space and state space to output space) operators. The system stability and the compactness of the operators describing the solution trajectories are investigated.     

Incompressibility of strange matter

Strange stars (ReSS) calculated from a realistic equation of state (EOS), that incorporate chiral symmetry restoration as well as deconfinement at high density [Phys. Lett. B 438 (1998) 123; Phys. Lett. B 447 (1999) 352, Addendum; Phys. Lett. B 467 (1999) 303, Erratum; Indian J. Phys. B 73 (1999) 377] show compact objects in the mass radius curve. We compare our calculations of incompressibility for this EOS with that of nuclear matter. One of the nuclear matter EOS has a continuous transition to ud-matter at about five times normal density. Another nuclear matter EOS incorporates density dependent coupling constants. From a look at the consequent velocity of sound, it is found that the transition to ud-matter seems necessary.     

I THE （μ＋ κ）oORBITS OF ESSENTIALLY NORMAL OPERATORS AND THEIR STRONG IRREDUCIBILITY

The authors characterize the (μ +κ)-orblts of a class essmntially normal operators and provethat some essentially normal operators with connected spectrum are strongly irreducible aftera small compact perturbation. This partially answers a question of Domigo A. Herrero.     

Minkowski空间中带超平面边界的紧致类空超曲面

In this paper, we study the relations between a compact spacelike hypersurface with hy-perplanar boundary in the (n 1)- dimensional Minkowski space-time L^n 1 being totally umbilicaland its hyperplanar boundary in a fixed hyperplane π of L^(n 1) being totally umbilical under certainconditions. We give the sufficient conditions for such hypersurface and its hyperplanar boundary tobe totally umbilical in their respective ambients.     

On dual and three space problems for the compact approximation property

We introduce the properties W^∗D and BW^∗D for the dual space of a Banach space. And then solve the dual problem for the compact approximation property (CAP): if X^∗ has the CAP and the W^∗D, then X has the CAP. Also, we solve the three space problem for the CAP: for example, if M is a closed subspace of a Banach space such that M^⊥ is complemented in X^∗ and X^∗ has the W^∗D, then X has the CAP whenever X/M has the CAP and M has the bounded CAP. Corresponding problems for the bounded compact approximation property are also addressed.     

Countably Compact Property of G（H∞）

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Optimal control of nonlinear evolution equations with nonmonotone nonlinearities

In this paper, we prove the existence of optimal admissible pairs for a large class of strongly nonlinear evolution equations, involving nonmonotone nonlinearities. An example of a nonlinear parabolic optimal control system is also worked out in detail.The author wishes to thank Professor T. S. Angell for useful comments and suggestions.This research was supported by NSF Grant No. DMS-88-02688.     

一类积——微分算子的占优本征值(Ⅱ)

本文研究的积—微分算子是以众多应用领域为背景的、无界非自伴线性算子。我们以泛函分析为工具,籍助L~2空间的线性算子理论,在较一般的条件下,证明了这类算子存在占优本征值(Dominant Eigenvalue)。