in this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.

The main objective of this paper is to propose a feasible, model free estimator of the predictive density of integrated volatility. In this sense, we extend recent papers by Andersen, Bollerslev, Diebold and Labys (2003), and by Andersen, Bollerslev and Meddahi (2004, 2005), who address the issue of pointwise prediction of volatility via ARMA models, based on the use of realized volatility. Our...

It is well known that phonemcs have different acoustic/phonetic realizations depending on the context. Fur example, the p h o n e m e / t / is typically realized with a different allophone (phonetic variant) in syllable initial position than in syllable final position. In syllable initial position (e.g., Tom),/ t / is almost always released (with a strong burst of energy) and aspirated (with h-...

This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance. The contraction property determines the asymptotic behavior of the network, which is either finite-time synchronization or asymptotic convergence to a splay state.

The Japanese Antarctic Research Expedition has conducted geomagnetic observations at Syowa Station, Antarctica, since 1966. Geomagnetic variation data measured with a fluxgate magnetometer are not absolute but are relative to a baseline and show drift. To enhance the importance of the geomagnetic data at Syowa station, therefore, it is necessary to correct the continuous variation data by using...

Abstract. Let dμ be a probability measure on the unit circle and dν be the measure formed by adding a pure point to dμ. We give a simple formula for the Verblunsky coefficients of dν based on a result of Simon. Then we consider dμ0, a probability measure on the unit circle with l Verblunsky coefficients (αn(dμ0)) ∞ n=0 of bounded variation. We insert m pure points to dμ, rescale, and form the p...

Let K n be the cone of positive semideenite n n matrices and let A be an aane subspace of the space of symmetric matrices such that the intersection K n \ A is non-empty and bounded. Suppose that n 3 and that codim A = ? r+2 2 for some 1 r n?2. Then there is a matrix X 2 K n \A such that rank X r. We give a short geometric proof of this result, use it to improve a bound on realizability of weig...

An identity for the Chebychev functional is presented in which a Riemann-Stieltjes integral is involved. This allows bounds for the functional to be obtained for functions that are of bounded variation, Lipschitzian and monotone. Some applications are presented to produce bounds for moments of functions about a general point γ and for moment generating functions.

We consider the Cauchy problem u t + F(u) x = 0; u(0; x) = u(x) () for a nonlinear n n system of conservation laws with coinciding shock and rarefaction curves. Assuming the existence of a coordinates system made of Riemann invariants, we prove the existence of a weak solution of () that depends in a lipschitz continuous way on the initial data, in the class of functions with arbitrarily large ...

Increasingly the problems of recognising faces under a variety of viewing conditions, including depth rotations , is being considered in the eld. The concept of norm-based coding in face recognition is not new but has been little investigated in machine models. Here we describe a norm-based face recognition system which is capable of generalising from a single training view to recognise novel v...