In this paper we study a Jacobi block matrix and the behavior of the limit of its entries when a perturbation of its spectral matrix measure by the addition of a Dirac delta matrix measure is introduced. © 2001 Elsevier Science Inc. All rights reserved.

We derive the asymptotic behavior of the occupation measure Z(B1) of the unit ball for super-Brownian motion started from the Dirac measure at a distant point x and conditioned to hit the unit ball. In the critical dimension d = 4, we obtain a limiting exponential distribution for the ratio Z(B1)/ log |x|.

We derive the asymptotic behavior of the occupation measure Z(B1) of the unit ball for superBrownian motion started from the Dirac measure at a distant point x and conditioned to hit the unit ball. In the critical dimension d = 4, we obtain a limiting exponential distribution for the ratio Z(B1)/ log |x|.

In a continuous-in-time model there is the important financial quantity called Loan which can not be determined directly in terms of Algebraic Spending but has a major impact on the financial strategy. In this paper, we use a mathematical framework to discuss an inverse problem of determining the implied Loan Measure from Algebraic Spending Measure when it is possible. In addition, we build a n...

We assume that each valence quark in a nucleon is in a phenomenological modified harmonic oscillator potential of the form: ( l+yo) (ar +br+cr +dr ), where a, b, c and d are constants and ? is one of the Dirac matrices. Then by making use of a suitable ansatz, the Dirac equation has a very simple solution which is exact. We then have calculated the static properties of the nucleon in the ...

This paper is concerned with the optimal approximation of a given multivariate Dirac mixture, i.e., a density comprising weighted Dirac distributions on a continuous domain, by an equally weighted Dirac mixture with a reduced number of components. The parameters of the approximating density are calculated by minimizing a smooth global distance measure, a generalization of the well-known Cramér-...

The Ginsparg-Wilson relation, if written in a suitable form, can be used as a condition for lattice Dirac operators of massless fermions also in odd dimensions. The fermion action with such a Dirac operator is invariant under a generalized parity transformation, which reduces to the ordinary parity transformation in the (naive) continuum limit. The fermion measure, however, transforms non-trivi...

This paper introduces a new approach to the recursive propagation of probability density functions through discrete-time stochastic nonlinear dynamic systems. An efficient recursive procedure is proposed that is based on the optimal approximation of the posterior densities after each prediction step by means of Dirac mixtures. The parameters of the individual components are selected by systemat...

This paper presents a filter approach for estimating the state of nonlinear dynamic systems based on recursive approximation of posterior densities by means of Dirac mixture functions. The filter consists of a prediction step and a filter step. The approximation approach is based on a systematic minimization of a distance measure and is hence optimal and deterministic. In contrast to non-determ...

The following two situations are shown to be equivalent. I. The commutation relation [A,A∗] = α holds on the span of excited states of the form (A∗)kζ. Here A is a Dirac operator acting in a weighted Hilbert space of sections of a Dirac bundle S over a Riemannian manifold M , ζ is a vacuum state, and α > 0 is a constant. II. There exists a scalar solution h on all of M to the simultaneous equat...