Application of a separating transformation to estimates of inner radii of open sets

We obtain solutions of new extremal problems of the geometric theory of functions of a complex variable related to estimates for the inner radii of nonoverlapping domains. Some known results are generalized to the case of open sets. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1313–1321, October, 2007.     

When is a Riemannian submersion homogeneous?

We study the structure of the most common type of Riemannian submersions, namely those whose fibers are given by the orbits of an isometric group action on a Riemannian manifold. Special emphasis is given to the case where the ambient space has nonnegative curvature. The first author was supported by research grant MTM2004-04794-MEC. Most of this work was done during a visit of the second author to Madrid, financed in part by funds of the aforementioned grant.     

Differential Conditions for Constrained Nonlinear Programming via Pareto Optimization

We deal with the differential conditions for local optimality. The conditions that we derive for inequality constrained problems do not require constraint qualifications and are the broadest conditions based on only first-order and second-order derivatives. A similar result is proved for equality constrained problems, although the necessary conditions require the regularity of the equality constraints.     

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.     

AI and OR in management of operations: history and trends

The last decade has seen a considerable growth in the use of Artificial Intelligence (AI) for operations management with the aim of finding solutions to problems that are increasing in complexity and scale. This paper begins by setting the context for the survey through a historical perspective of OR and AI. An extensive survey of applications of AI techniques for operations management, covering a total of over 1200 papers published from 1995 to 2004 is then presented. The survey utilizes Elsevier's ScienceDirect database as a source. Hence, the survey may not cover all the relevant journals but includes a sufficiently wide range of publications to make it representative of the research in the field. The papers are categorized into four areas of operations management: (a) design, (b) scheduling, (c) process planning and control and (d) quality, maintenance and fault diagnosis. Each of the four areas is categorized in terms of the AI techniques used: genetic algorithms, case-based reasoning, knowledge-based systems, fuzzy logic and hybrid techniques. The trends over the last decade are identified, discussed with respect to expected trends and directions for future work suggested.     

Convergence of generalized conjugate partial Fourier integrals

Generalized conjugate partial Fourier integrals are used to find jumps of functions. The rate of convergence is studied and sharp results are obtained.     

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.