We consider an M/M/∞ service system in which an arriving customer is served by the first idle server in an infinite sequence S 1 , S 2 ,. .. of servers. We determine the first two terms in the asymptotic expansions of the moments of L as λ → ∞, where L is the index of the server S L serving a newly arriving customer in equilibrium, and λ is the ratio of the arrival rate to the service rate. The...

Let X; X 1 ; : : : ; X k be i.i.d. random variables, and for k 2 IN let D k (X) = E(X 1 _ _ X k+1) ? EX be the k-th centralized maximal moment. A sharp lower bound is given for D 1 (X) in terms of the L evy concentration Q l (X) = sup x2IR P (X 2 x; x + l]). This inequality, which is analogous to P. L evy's concentration-variance inequality, illustrates the fact that maximal moments are a gauge...

We introduce a new micro/macro decomposition of collisional kinetic equations which naturally incorporates the exact space boundary conditions. The idea is to write the distribution fonction f in all its domain as the sum of a Maxwellian adapted to the boundary (which is not the usual Maxwellian associated with f) and a reminder kinetic part. This Maxwellian is defined such that its ’incoming’ ...

Understanding moments of families of L-functions has long been an important subject with many number theoretic applications. Quite often, the application is to bound the error term in an asymptotic expression of the average of an arithmetic function. Also, a good bound for a moments can be used to obtain a point-wise bound for an individual L-function in the family; strong enough bounds of this...

In 1972, H.L. Montgomery and F. Dyson uncovered a surprising connection between the Theory of the Riemann Zeta function and Random Matrix Theory. For the next few decades, the major developments in the area were the numerical calculations of Odlyzko and conjectures for the moments of the Riemann Zeta function (and other L-functions) found by Conrey, Ghosh, Gonek, Heath-Brown, Hejhal and Sarnak....

Hybrid Euler-Hadamard products have previously been studied for the Riemann zeta function on its critical line and for Dirichlet Lfunctions in the context of the calculation of moments and connections with Random Matrix Theory. According to the Katz-Sarnak classification, these are believed to represent families of L-function with unitary symmetry. We here extend the formalism to families with ...

In this paper, we describe a class of Wiener functionals that are ‘indeterminate by their moments’, that is, whose distributions are not uniquely determined by their moments. In particular, it is proved that the integral of a geometric Brownian motion is indeterminate by its moments and, moreover, shown that previous proofs of this result are incorrect. The main result of this paper is based on...

knowledge about low flow statistics is essential for effective water resource planning and management in ungauged orpoorly gauged catchment areas, especially in arid and semi-arid regions such as iran. we employed a data set of 20 riverflow time-series from the iranian central plateau river basin, iran to evaluate the low-flow series using several frequencyanalysis methods and compared the resu...