of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ADAPTIVE FILTERING IN REPRODUCING KERNEL HILBERT SPACES By Weifeng Liu December 2008 Chair: Jose C. Principe Major: Electrical and Computer Engineering The theory of linear adaptive filters has reached maturity, unlike the field of nonli...

In this paper we propose a relatively new semi-analytical technique to approximate the solution of nonlinear multi-order fractional differential equations (FDEs). We present some results concerning to the uniqueness of solution of nonlinear multi-order FDEs and discuss the existence of solution for nonlinear multi-order FDEs in reproducing kernel Hilbert space (RKHS). We further give an error a...

In this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the Hypercyclicity Criterion. We characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional Banach space .

Selective expansion and activation of a very small number of antigen-specific CD4(+) T cells is a remarkable and essential property of the adaptive immune response. Antigen-specific T cells were until recently identified only indirectly by functional assays, such as antigen-induced cytokine secretion and proliferation. The advent of MHC Class II tetramers has added a pivotal tool to our researc...

In this paper we characterize the left Jordan derivations on Banach algebras. Also, it is shown that every bounded linear map $d:mathcal Ato mathcal M$ from a von Neumann algebra $mathcal A$ into a Banach $mathcal A-$module $mathcal M$ with property that $d(p^2)=2pd(p)$ for every projection $p$ in $mathcal A$ is a left Jordan derivation.

Let H d (t ≥ −d, t > −3) be the reproducing kernel Hilbert space on the unit ball B d with kernel k(z, w) = 1 (1− 〈z, w〉)d+t+1 . We prove that if an ideal I ⊳ C [z1 , . . . , zd] (not necessarily homogeneous) has what we call the approximate stable division property, then the closure of I in H d is p-essentially normal for all p > d. We then show that all quasi homogeneous ideals in two variabl...