The notion of generalised exponential family is considered in the restricted context of nonextensive statistical physics. Examples are given of models belonging to this family. In particular, the q-Gaussians are discussed and it is shown that the configurational probability distributions of the microcanonical ensemble belong to the q-exponential family.

We obtain estimates for the multidimensional analogon of the exponential sum

Based on concentration probability of estimators about a true parameter, third-order asymptotic e ciency of the rst-order bias-adjusted MLE within the class of rst-order bias-adjusted estimators has been well established in a variety of probability models. In this paper we consider the class of second-order bias-adjusted Fisher consistent estimators of a structural parameter vector on the basis...

In this paper we prove, without assuming Schanuel’s conjecture, that the E-subring generated by a real number not definable without parameters in the real exponential field is freely generated. We also obtain a similar result for the complex exponential field.

We prove an existence of a unique solution of an exponential martingale equation in the class of BMO martingales. The solution is used to characterize optimal martingale measures.

Let f be an entire function of exponential type whose indicator diagram is contained in the segment [−iσ, iσ], σ > 0. Then the upper density of zeros of f is at most cσ where c ≈ 1.508879 is the positive solution of the equation log( √

We prove a Bombieri-Vinogradov type result for linear exponential sums over primes. Then we apply it to show that, for any irrational α and some θ > 0, there are infinitely many primes p such that p+ 2 has at most two prime factors and ‖αp+ β‖ < p−θ.

*Correspondence: [email protected] 1Department of Mathematics, Texas A&M University-Kingsville, Kingsville, 78363, USA Full list of author information is available at the end of the article Abstract Impulsive differential equations with impulses occurring at random times arise in the modeling of real world phenomena in which the state of the investigated process changes instantaneously at uncer...

In this paper, we present a variable structure control method that eliminates the reaching phase. The approach is based on modifying the sliding domain equations through the use of exponential functions. In addition, the proposed method insures optimal convergence parameters with respect to the tracking errors and control effort.

1. Introduction. The problem we address here arises in the study of the error function in the shifted circle problem (see [BCDL]). Let α = (α 1 , α 2) ∈ R