The Hankel operator of the system with single control input delay is established by using state-space formulation in this paper. In general, this type of operator is not a compact one. Singular values of this type of operator are studied. Two examples are used to illustrate the computation of Hankel singular value by the theoretical method proposed in this paper.

We derive a spectral method for unsupervised learning of Weighted Context Free Grammars. We frame WCFG induction as finding a Hankel matrix that has low rank and is linearly constrained to represent a function computed by inside-outside recursions. The proposed algorithm picks the grammar that agrees with a sample and is the simplest with respect to the nuclear norm of the Hankel matrix.

Abstract. In 1998, Allouche, Peyrière, Wen and Wen considered the Thue–Morse sequence, and proved that all the Hankel determinants of the period-doubling sequence are odd integers. We speak of t-extension when the entries along the diagonal in the Hankel determinant are all multiplied by t. We prove that the t-extension of each Hankel determinant of the period-doubling sequence is a polynomial ...

We obtain the rate of decay of the smallest eigenvalue of the Hankel matrices R I t j+kW 2 (t) dt n j;k=0 for a general class of even exponential weights W 2 = exp ( 2Q) on an interval I. More precise asymptotics for more special weights have been obtained by many authors. Remark 1 Running Title: Smallest Eigenvalues of Hankel Matrices

We study the Hankel determinant of the generalized Jacobi weight (x − t)x(1 − x) for x ∈ [0, 1] with α, β > 0, t < 0 and γ ∈ R. Based on the ladder operators for the corresponding monic orthogonal polynomials Pn(x), it is shown that the logarithmic derivative of Hankel determinant is characterized by a τ -function for the Painlevé VI system.

This paper presents an iterative two-step LMI method for improving the H 1 model error compared to Hankel norm reduction. The improvement of the Hankel norm reduced model is usually not signii-cant, typically a few percents only. For practical use the LMI reduction scheme is usually not worthwhile , but it can be interresting from the theoretical and principal point of view.

We consider a Hankel determinant formula for generic solutions of the Painlevé IV equation. We show that the generating functions for the entries of the Hankel determinants are related to the asymptotic solution at infinity of the isomonodromic problem. Summability of these generating functions is also discussed.

The calculation of the density matrix for fermions and bosons in the Grand Canonical Ensemble allows an efficient way for the inclusion of fermionic and bosonic statistics at all temperatures. It is shown that in a Path Integral Formulation fermionic density matrix can be expressed via an integration over a novel representation of the universal temperature dependent functional. While several re...

Tapan S. Mehta, Stanislav O. Zakharkin, Gary L. Gadbury, and David B. Allison Department of Biostatistics, Section on Statistical Genetics, University of Alabama at Birmingham, Birmingham, Alabama; Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, Missouri; Clinical Nutrition Research Center, University of Alabama at Birmingham; and Department of Genetics, Universit...

Let Ss*(ez) denote the class of starlike functions with respect to symmetric points subordinate exponential function, i.e., which satisfy in unit disk U condition 2zf′(z)f(z)−f(−z)≺ez(z∈U). We obtained sharp estimate second-order Hankel determinants H2,3(f) and improved third-order H3,1(f) for this Ss*(ez).