In this paper we investigate the normal and large fluctuations of additive functionals associated with a stochastic process under general non-Poissonian resetting mechanism. Cumulative regenerative processes are very close to renewal-reward inherit most properties latter. Here review use classical law numbers central limit theorem for obtain same theorems resetting. Then, establish deviation pr...

The aim of this paper is to present a simplified, yet rigorous, deduction the Boussinesq approximated governing equations for buoyant flows. In order carry out core procedure, simplified version manifold asymptotic analyses available in literature discussed. method adopted study focussed on local balance valid general, not necessarily Newtonian, fluid. analysis carried by demonstrating leading ...

Differential privacy provides a rigorous framework for privacy-preserving data analysis. This paper proposes the first differentially private procedure controlling false discovery rate (FDR) in multiple hypothesis testing. Inspired by Benjamini-Hochberg (BHq), our approach is to repeatedly add noise logarithms of p-values ensure differential and select an approximately smallest p-value serving ...

In this paper, some of the formal arguments given by Jones and Kline [J. Math. Phys., v. 37, 1958, pp. 1-28] are made rigorous. In particular, the reduction procedure of a multiple oscillatory integral to a one-dimensional Fourier transform is justified, and a Taylor-type theorem with remainder is proved for the Dirac 8-function. The analyticity condition of Jones and Kline is now replaced by i...

This note is devoted to the mathematical arguments proving that Lowe’s Scale-Invariant Feature Transform (SIFT [23]), a very successful image matching method, is indeed similarity invariant. The mathematical proof is given under the assumption that the gaussian smoothing performed by SIFT gives aliasing free sampling. The validity of this main assumption is confirmed by a rigorous experimental ...

Large-scale scientific computer models, such as operational weather predictions models, pose challenges on the applicability of AD tools. We report the application of TAF to the development of the adjoint model and tangent linear model of a complex atmospheric model, ARPS. Strategies to overcome the problems encountered during the development process are discussed. A rigorous verification proce...

A general design procedure of decoupling networks, between two coupled antennas, is proposed using a single transmission line connected between the input ports of the antennas at a specified distance. A rigorous analysis for the decoupling circuit is introduced considering the return loss of the antennas into calculations. Furthermore, using numerical optimization, enhancement of decoupling bet...

An original method for service life assessment of building products is proposed. In addition to a rigorous analysis and system modelling, "Evidence Theory" is adapted and used. Allowing the taking into account of uncertainty and ignorance, this tool has proved efficient in our service life assessment procedure. After a short presentation of the context, the concept of "fusion" is sketched; the ...

The Optimal Variational Method (OVM) is introduced and applied for calculating approximate periodic solutions of “truly nonlinear oscillators”.Themain advantage of this procedure consists in that it provides a convenient way to control the convergence of approximate solutions in a very rigorous way and allows adjustment of convergence regions where necessary.This approach does not depend upon a...

Abstract: Complex diffusion is a common and broadly used denoising procedure in image processing. The method is based on an explicit finite difference scheme applied to a diffusion equation with a proper complex diffusion parameter in order to preserve edges and the main features of the image, while eliminating noise. In this paper we present a rigorous proof for the stability condition of comp...