NEW WAVELET BASES FOR NON－HOMOGENEOUS SYMBOLIC SPACE OpS1,1^m AND RELATED KERNEL－DISTRIBUTION SPACES

This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.

Hausdorff measure of sets of finite type of one-sided symbolic space

Some estimation formulae and a computation formula for the hausdorff meausre fo the sets of finite type of the one-sided symbolic space are given

On new chaotic mappings in symbol space

A well known chaotic mapping in symbol space is a shift mapping.However,other chaotic mappings in symbol space exist too.The basic change is to consider the process not only at a set of times which are equally spaced,say at unit time apart（a shift mapping）,but at a set of times which are not equally spaced,say if the unit time can not be fixed.The increasing mapping as a generalization of the shift mapping and the k-switch mapping are introduced.The increasing and k-switch mappings are chaotic.

A SIMPLE PROOF OF THE CHAOTICITY OF SHIFT MAP UNDER A NEW DEFINITION OF CHAOS

Recently, Du has given a new strong definition of chaos by using the shift map. In this paper, we give a proof of the main theorem by constructing a dense uncountable invariant subset of the symbol space E2 containing transitive points in a simpler way with the help of a different metric. We also provide two examples, which support this new definition.

Chaos for Subshifts of Finite Type

This paper deals with chaos for subshifts of finite type. We show that for any subshift of finite type determined by an irreducible and aperiodic matrix, there is a finitely chaotic set with full Hausdorff dimension. Moreover, for any subshift of finite type determined by a matrix, we point out that the cases including positive topological entropy, distributional chaos, chaos and Devaney chaos are mutually equivalent.

Strong Mixing Subshift of Finite Type and Hausdorff Measure of Its Chaotic Set

We present a sufficient and necessary condition for the subshift of finite type to be a measure-preserving transformation or to be a strong mixing measure-preserving transformation with respect to the Hausdorff measure. It is proved that a strong mixing subshift of finite type has a chaotic set with full Hausdorff measure.

Single-User Blind Channel Equalization Using Modified Constant Modulus Algorithm

A modified constant modulus algorithm (MCMA) for blind channel equalization is proposed by modifying the constant modulus error function. The MCMA is compared with the conventional constant modulus algorithm (CMA) for symbol-spaced equalization of 4PSK signals. The result shows that the performance of the MCMA is superior to that of the CMA in both convergence rate and intersymbol interference for frequency selective channels in noisy environments. Simulation results using 8PSK signals also demonstrate that a fractionally spaced equalizer can preserve performance over variations in symbol-timing phase, whereas a baud-rate equalizer cannot.

EXTENSIONS OF HILBERT MODULES AND HANKEL OPERATORS

Extensions of the Hardy and the Bergman modules over the disc algebra are studied.The author relates extensions of these canonical modules to the symbol spaces of corresponding Hankel operators.In the context of function theory,an explicit formula of Ext(L^(2)_(a)(D),H^(2)(D))is obtained.Finally,it is also proved that Ext(L^(2)_(a)(D),L:(D))≠0.This may be the essential difference between the Hardy and the Bergman modules over the disk algebra.