Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (a.k.a. Kullback-Leibler divergence). The processes considered are general time evolutions both in classical and quantum mechanics, and the initial state is sometimes therm...

Numerical investigations have been carried out on 35% scaled down model of PGT10 gas turbine exhaust diffuser under the condition of with inlet guidevanes and without struts. Numerical simulations were carried out to determine the static pressure development and pressure recovery, by varying the area ratio and divergence angles varying from θ = 7 to 13 by keeping the diffusion length constant. ...

Evanescent operators such as the Gauss-Bonnet term have vanishing perturbative matrix elements in exactly D=4 dimensions. Similarly, evanescent fields do not propagate in D=4; a three-form field is in this class, since it is dual to a cosmological-constant contribution. In this Letter, we show that evanescent operators and fields modify the leading ultraviolet divergence in pure gravity. To ana...

In this paper we propose a new motion estimator for image sequences depicting fluid flows. The proposed estimator is based on the Helmholtz decomposition of vector fields. This decomposition consists in representing the velocity field as a sum of a divergence free component and a curl free component. The objective is to provide a low-dimensional parametric representation of optical flows by dep...

The focus of this work is on using texture information for searching, browsing and retrieving images from a large database. In the wavelet approaches, texture is characterized by its energy distribution in the decomposed subbands. However it is unclear on how to define similarity functions on extracted features; usually simple norm-based distances together with heuristic normalization are emplo...

Lagrangian GPS drifter experiments, carried out in the surface layer of stratified Lake Kinneret (Israel), are presented. Differential kinematic properties and Lagrangian statistics were calculated and used to estimate the dominant mechanisms for horizontal dispersion. On time scales smaller than a few internal wave periods, internal waves lead to strong divergence and convergence events, causi...

We consider the learning coefficients in learning theory and give two newmethods for obtaining these coefficients in a homogeneous case: a method for finding a deepest singular point and a method to add variables. In application to Vandermonde matrix-type singularities, we show that these methods are effective. The learning coefficient of the generalization error in Bayesian estimation serves t...

Nearest neighbor cells in Rd are used to define coefficients of divergence (φ-divergences) between continuous multivariate samples. For large sample sizes, such distances are shown to be asymptotically normal with a variance depending on the underlying point density. The finite-dimensional distributions of the point measures induced by the coefficients of divergence converge to those of a gener...

This paper gives out the general solutions of variable coefficients Linear ODE and Riccati equation by way of integral series E(X) and F (X). Such kinds of integral series are the generalized form of exponential function, and keep the properties of convergent and reversible.

We give a simple proof of Jackson’s terminating q-analogue of Dixon’s identity. In the last twenty years several short proofs of Dixon’s identity have been published [3–5]. However, there are not so many proofs of Jackson’s terminating q-analogue of Dixon’s identity [2, 6]: ∑ k (−1)kq(3k2+k)/2 [ a+ b a+ k ][ a+ c c+ k ][ b+ c b+ k ] = [a+ b+ c]! [a]![b]![c]! , (1) where [n]! = ∏n i=1 1−qi 1−q a...