An experimental investigation of the pressure and concentration dependence of muonic Coulomb capture and cascade in gases

Muonic Coulomb capture ratios and x-ray intensity patterns in four binary mixtures of the gases N₂, Ne, Ar, Kr, and Xe have been measured at three atomic ratios. An influence of the concentration has been established. The Lyman series intensity patterns of pure N₂, Ne, Ar, Kr, and Xe were measured at pressures between 0.4 and 51 bar and found to depend on the pressure. Possible explanations are discussed.     

Nonvanishing theorems for L-functions of modular forms and their derivatives

Inventiones mathematicae -     

Comparison theorems for weak splittings of bounded operators

Summary Comparison theorems for weak splittings of bounded operators are presented. These theorems extend the classical comparison theorem for regular splittings of matrices by Varga, the less known result by Wonicki, and the recent results for regular and weak regular splittings of matrices by Neumann and Plemmons, Elsner, and Lanzkron, Rose and Szyld. The hypotheses of the theorems presented here are weaker and the theorems hold for general Banach spaces and rather general cones. Hypotheses are given which provide strict inequalities for the comparisons. It is also shown that the comparison theorem by Alefeld and Volkmann applies exclusively to monotone sequences of iterates and is not equivalent to the comparison of the spectral radius of the iteration operators.This work was supported by the National Science Foundation grants DMS-8807338 and INT-8918502     

First passage percolation: The stationary case

Summary If the passage time of the edges of the ^d lattice are stationary, ergodic and have finite moment of orderp>d, then a.s. the set of vertices that can be reached within timet, has an asymptotic shape ast.     

Differential Simplicity in Polynomial Rings and Algebraic Independence of Power Series

Let k be a field of characteristic zero, f(X,Y), g(X,Y)k[X,Y],g(X,Y) (X,Y) and d:=g(X,Y)/X + f(X,Y)/Y. A connection is establishedbetween the d-simplicity of the local ring k[X,Y]_(X,Y) and thetranscendency of the solution in tk[[t]] of the algebraic differentialequation g(t,y(t))·(/t)y(t)+f(t,y(t)). This connectionis used to obtain some interesting results in the theory ofthe formal power series and to construct new examples of differentiallysimple rings.     

A robust and efficient adaptive reweighted estimator of multivariate location and scatter

This article proposes a reweighted estimator of multivariate location and scatter, with weights adaptively computed from the data. Its breakdown point and asymptotic behavior under elliptical distributions are established. This adaptive estimator is able to attain simultaneously the maximum possible breakdown point for affine equivariant estimators and full asymptotic efficiency at the multivariate normal distribution. For the special case of hard-rejection weights and the MCD as initial estimator, it is shown to be more efficient than its non-adaptive counterpart for a broad range of heavy-tailed elliptical distributions. A Monte Carlo study shows that the adaptive estimator is as robust as its non-adaptive relative for several types of bias-inducing contaminations, while it is remarkably more efficient under normality for sample sizes as small as 200.     

Derivation of the k–ε model for locally homogeneous turbulence by homogenization techniques

We derive the incompressible and compressible k–ε model for locally homogeneous turbulence. The model is rigorously derived on formal mathematical grounds using the MPP modelling technique. This lets us calculate by either analytical or numerical means the closure constants of the model. To cite this article: T. Chacón Rebollo, D. Franco Coronil, C. R. Acad. Sci. Paris, Ser. I 337 (2003).