A subset X in the d-dimensional Euclidean space is called a k-distance set if there are exactly k distinct distances between two distinct points in X and a subset X is called a locally k-distance set if for any point x in X , there are at most k distinct distances between x and other points in X . Delsarte, Goethals, and Seidel gave the Fisher type upper bound for the cardinalities of k-distanc...

We study the role played by the indefinite weight function a(x) on the existence of positive solutions to the problem  −div (|∇u|∇u) = λa(x)|u|u+ b(x)|u|u, x ∈ Ω, ∂u ∂n = 0, x ∈ ∂Ω , where Ω is a smooth bounded domain in Rn, b changes sign, 1 < p < N , 1 < γ < Np/(N − p) and γ 6= p. We prove that (i) if ∫ Ω a(x) dx 6= 0 and b satisfies another integral condition, then there exists some λ∗ suc...

We consider error estimates for optimal and Gaussian quadrature for-mulae if the integrand is analytic and bounded in a certain complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented. This method is applied to Szegg o-type weight functions and ellipses as regions of analyticity. In this situation, the error constants for the Gau...

In this paper, we describe the Centre for Interactive Systems Research’s participation in the INEX 2006 adhoc track. Rather than using a fieldweighted BM25 model in INEX 2005, we revert back to using the traditional BM25 weighting function. Our main research aims in this year are to investigate the effects of document filtering by result record cut-off, element filtering by length cut-off and t...

We give a new Hilbert-type integral inequality with the best constant factor by estimating the weight function. And the equivalent form is considered.

This paper proposes a technique to estimate speakers’ perceptual age automatically only with acoustic information of their utterances. Firstly, we experimentally collected data of how old individual speakers in databases sound to listeners. Speech samples of approximately 500 male speakers with a very wide range of the real age were presented to listeners, who were asked to estimate the age onl...

A speaker adaptation scheme named maximum likelihood model interpolation (MLMI) is proposed. The basic idea of MLMI is to compute the speaker adapted (SA) model of a test speaker by a linear convex combination of a set of speaker dependent (SD) models. Given a set of training speakers, we first calculate the corresponding SD models for each training speaker as well as the speakerindependent (SI...

We show that the Lusin area integral or the square function on the unit ball of C, regarded as an operator in weighted space L(w) has a linear bound in terms of the invariant A2 characteristic of the weight. We show a dimension-free estimate for the “area-integral” associated to the weighted L(w) norm of the square function. We prove the equivalence of the classical and the invariant A2 classes.

In this paper, a speaker adaptation method is presented which computes the speaker adapted model by a weighted sum of a set of speaker dependent models. The set of weights are estimated to maximize the likelihood of the adaptation data. Then a linguistic tree is constructed to cluster the mean vectors. The means in the same linguistic class share the same weight set, while the means in differen...

The existence and uniqueness properties for extremal mappings with smallest weighted L distortion between annuli and the related Grötzsch type problems are discussed. An interesting critical phase type phenomena is observed. When p < 1, apart from the identity map, minimizers never exist. When p = 1 we observe Nitsche type phenomena; minimisers exist within a range of conformal moduli determine...