On the weakened Siegel’s conjecture

In the paper, we prove that two definitions of E-functions present in mathematics are equivalent if E-functions satisfy second-order linear differential equations. For this set of functions, a weakened variant of the well-known Siegel conjecture about representability of any E-function by a polynomial of hypergeometric functions is also proved. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 33–39, 2005.     

Motivic Serre invariants of curves

In this article, we generalize the theory of motivic integration on formal schemes topologically of finite type and the notion of motivic Serre invariant, to a relative point of view. We compute the relative motivic Serre invariant for curves defined over the field of fractions of a complete discrete valuation ring R of equicharacteristic zero. One aim of this study is to understand the behavior of motivic Serre invariants under ramified extension of the ring R. Thanks to our constructions, we obtain, in particular, an expression for the generating power series, whose coefficients are the motivic Serre invariant associated to a curve, computed on a tower of ramified extensions of R. We give an interpretation of this series in terms of the motivic zeta function of Denef and Loeser.     

On Linear-Time Algorithms for the Continuous Quadratic Knapsack Problem

We give a linear time algorithm for the continuous quadratic knapsack problem which is simpler than existing methods and competitive in practice. Encouraging computational results are presented for large-scale problems. The author thanks the Associate Editor and an anonymous referee for their helpful comments.     

The σ<Emphasis Type="Italic">g</Emphasis>-Drazin Inverse and the Generalized Mbekhta Decomposition

In this paper we define and study an extension of the g-Drazin for elements of a Banach algebra and for bounded linear operators based on an isolated spectral set rather than on an isolated spectral point. We investigate salient properties of the new inverse and its continuity, and illustrate its usefulness with an application to differential equations. Generalized Mbekhta subspaces are introduced and the corresponding extended Mbekhta decomposition gives a characterization of circularly isolated spectral sets.     

Regularization of singular systems of linear algebraic equations by shifts

Regularization of singular systems of linear algebraic equations by shifts is examined. New equivalent conditions for the shift regularizability of such systems are derived.     

Impact of two mass scale oscillations on the analysis of atmospheric and reactor neutrino data

We study the stability of the results of the three-neutrino oscillation analysis of atmospheric and reactor neutrino data under departures of the one dominant mass scale approximation. In order to do so we perform the analysis of atmospheric and reactor neutrino data in terms of three-neutrino oscillations where the effect of both mass differences is explicitly considered. We study the allowed parameter space resulting from this analysis as a function of the mass splitting hierarchy parameter which parameterizes the departure from the one dominant mass scale approximation. We consider schemes with both direct and inverted mass ordering. Our results show that in the analysis of the atmospheric data the derived range of the largest mass splitting, , is stable, while the allowed ranges of mixing angles and are wider than those obtained in the one dominant mass scale approximation. Inclusion of the CHOOZ reactor data in the analysis results in the reduction of the parameter space in particular for the mixing angles. As a consequence the final allowed ranges of the parameters from the combined analysis are only slightly broader than when obtained in the one dominant mass scale approximation. Received: 31 May 2002 / Revised version: 10 July 2002 / Published online: 31 October 2002