Singular numbers of the monodromy operator and sufficient conditions of the asymptotic stability of periodic system of differential equations with fixed delay

To obtain sufficient conditions for the asymptotic stability of linear periodic systems with fixed delay commensurable with the period of coefficients, singular numbers of the monodromy operator are used. To find these numbers, a self-adjoint boundary value problem for ordinary differential equations is applied. We study the motion of eigenvalues of this boundary value problem under a variation of a parameter. Obtaining sufficient conditions for the asymptotic stability is reduced to finding the bifurcation value of the parameter for the boundary value problem.     

Banach-Saks property in Marcinkiewicz spaces

We catalogue all Marcinkiewicz function and sequence spaces with the Banach-Saks property and present necessary and sufficient conditions for a wide subclass of spaces to possess the p-Banach-Saks property, 1<p<∞. We apply our results to several open problems.     

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.     

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.     

A perturbation-based heuristic for the capacitated multisource Weber problem

This paper proposes a perturbation-based heuristic for the capacitated multisource Weber problem. This procedure is based on an effective use of borderline customers. Several implementations are considered and the two most appropriate are then computationally enhanced by using a reduced neighbourhood when solving the transportation problem. Computational results are presented using data sets from the literature, originally used for the uncapacitated case, with encouraging results.     

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     

Monstrous Branes

 We study D-branes in the bosonic closed string theory whose automorphism group is the Bimonster group (the wreath product of the Monster simple group with ℤ₂). We give a complete classification of D-branes preserving the chiral subalgebra of Monster invariants and show that they transform in a representation of the Bimonster. Our results apply more generally to self-dual conformal field theories which admit the action of a compact Lie group on both the left- and right-moving sectors. Received: 20 February 2002 / Accepted: 17 August 2002 Published online: 19 December 2002 Communicated by R.H. Dijkgraaf