Extended kac-akhiezer formulae and the fredholm determinant of finite section hilbert-schmidt kernels

This paper deals with some results (known as Kac-Akhiezer formulae) on generalized Fredholm determinants for Hilbert-Schmidt operators on L2-spaces, available in the literature for convolution kernels on intervals. The Kac-Akhiezer formulae have been obtained for kernels which are not necessarily of convolution nature and for domains in R(n).

Trace Formulae for Curvature of Jet Bundles over Planar Domains

For a domain Omega in C and an operator T in B-n(Omega), Cowen and Douglas construct a Hermitian holomorphic vector bundle E-T over Omega corresponding to T. The Hermitian holomorphic vector bundle E-T is obtained as a pull-back of the tautological bundle S(n, H) defined over by Gr(n, H) a nondegenerate holomorphic map z bar right arrow ker(T - z), z is an element of Omega. To find the answer to the converse, Cowen and Douglas studied the jet bundle in their foundational paper. The computations in this paper for the curvature of the jet bundle are rather intricate. They have given a set of invariants to determine if two rank n Hermitian holomorphic vector bundle are equivalent. These invariants are complicated and not easy to compute. It is natural to expect that the equivalence of Hermitian holomorphic jet bundles should be easier to characterize. In fact, in the case of the Hermitian holomorphic jet bundle J(k)(L-f), we have shown that the curvature of the line bundle L-f completely determines the class of J(k)(L-f). In case of rank Hermitian holomorphic vector bundle E-f, We have calculated the curvature of jet bundle J(k)(E-f) and also obtained a trace formula for jet bundle J(k)(E-f).

Trace Formulae in Operator Theory

In this article, we survey several kinds of trace formulas that one encounters in the theory of single and multi-variable operators. We give some sketches of the proofs, often based on the principle of finite-dimensional approximations to the objects at hand in the formulas.

A backward particle interpretation of Feynman-Kac formulae

We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals "on-the-fly" as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We provide uniform convergence results with respect to the time horizon parameter as well as functional central limit theorems and exponential concentration estimates. Our results have important consequences for online parameter estimation for non-linear non-Gaussian state-space models. We show how the forward filtering backward smoothing estimates of additive functionals can be computed using a forward only recursion.

Dirac spectra, summation formulae, and the spectral action

Noncommutative geometry is a source of particle physics models with matter Lagrangians coupled to gravity. One may associate to any noncommutative space (A, H, D) its spectral action, which is defined in terms of the Dirac spectrum of its Dirac operator D. When viewing a spin manifold as a noncommutative space, D is the usual Dirac operator. In this paper, we give nonperturbative computations of the spectral action for quotients of SU(2), Bieberbach manifolds, and SU(3) equipped with a variety of geometries. Along the way we will compute several Dirac spectra and refer to applications of this computation.

Simplified Formulae for the Estimation of Offshore Wind Turbines Clutter on Marine Radars

The potential impact that offshore wind farms may cause on nearby marine radars should be considered before the wind farm is installed. Strong radar echoes from the turbines may degrade radars' detection capability in the area around the wind farm. Although conventional computational methods provide accurate results of scattering by wind turbines, they are not directly implementable in software tools that can be used to conduct the impact studies. This paper proposes a simple model to assess the clutter that wind turbines may generate on marine radars. This method can be easily implemented in the system modeling software tools for the impact analysis of a wind farm in a real scenario.

Use of different glazes in frozen oil sardines

This paper reports on the relationship between the seasonal variations in the oil content of the Indian oil sardines (Sardinella longiceps) and their frozen storage life at -l8°C and on the use of various chemicals and coating materials to extent their storage life. It is observed that there is an inverse relationship between the oil content and the frozen storage life- oil content varying from 10.33 to 42.43% (MFB) and storage life from 2 to 5 months. Extension of storage life is achieved by dipping in hydroquinone solution prior to freezing or by coating with agar after freezing. Data on changes in peroxide value, free fatty acids, moisture, drip and organoleptic characteristics during frozen storage are presented.

Comparison between empirical formulae of intake vortices

The hydrodynamic properties of free surface vortices at hydraulic intakes were investigated. Based on the axisymmetric Navier-Stokes equations and empirical assumptions, two sets of formulations for the velocity distributions and the free surface profiles are proposed and validated against measurements available in the literature. Compared with previous formulae, the modifications based on Mih's formula are found to greatly improve the agreement with the experimental data. Physical model tests were also conducted to study the intake vortex of the Xiluodu hydroelectric project in China. The proposed velocity distribution formula was applied to the solid boundary as considered by the method of images. A good agreement was again observed between the prediction and the measurements. © 2011 International Association for Hydro-Environment Engineering and Research.

Technological aspects of preservation and processing of edible shell fishes IV. Comparative efficiency of different glazes in the preservation of frozen crab meat

The present work was undertaken to enlighten upon the comparative efficiency of different glazes in improving the quality of frozen crab meat (Scylla Serrata).