The Rayleigh criterion (which measures the correlation between pressure and heat release) is the standard tool used to investigate and predict combustion instabilities both in experimental and numerical studies. However, the Rayleigh term is just one of the terms appearing in the acoustic energy equation. The recent development of Large Eddy Simulations (LES) for combustion chambers allows to c...

In this paper we study the problem of linearly equalizing the Multiple Input Multiple Output (MIMO) communications channels from an H∞ point of view. H∞ estimation theory has been recently introduced as a method for designing filters that have acceptable performance in the face of model uncertainty and lack of statistical information on the exogenous signals. In this paper we obtain a closed-fo...

In this paper we deduce a lower bound for the rank of a family of p vectors in Rk (considered as a vector space over the rationals) from the existence of a sequence of linear forms on Rp, with integer coefficients, which are small at k points. This is a generalization to vectors of Nesterenko’s linear independence criterion (which corresponds to k = 1). It enables one to make use of some known ...

The conceptual predictive statistic, Cp, is a widely used criterion for model selection in linear regression. Cp serves as an estimator of a discrepancy, a measure that reflects the disparity between the generating model and a fitted candidate model. This discrepancy, based on scaled squared error loss, is asymmetric: an alternate measure is obtained by reversing the roles of the two models in ...

P-wave velocity is regularly proposed as a proxy for water saturation when studying quasisaturated soils. However, several authors have underlined that this can only be reliably correlated to if the pore fluid “ homogeneous ”. Using bender elements measure compression wave in quasi-saturated Fontainebleau sand, we show it highly sensitive both and frequency. The characteristic length of pressur...

Assume (1) asset returns follow a stochastic multi-factor process with time-varying conditional expectations; (2) investments are linear functions of factors. This paper calculates asymptotic joint moments of the logarithm of investor’s wealth and the factors. These formulas enable fast computation of a wide range of investment criteria. The results are illustrated by a numerical example that s...