Affine-scaling for linear programs with free variables

The affine-scaling modification of Karmarkar's algorithm is extended to solve problems with free variables. This extended primal algorithm is used to prove two important results. First the geometrically elegant feasibility algorithm proposed by Chandru and Kochar is the same algorithm as the one obtained by appending a single column of residuals to the constraint matrix. Second the dual algorithm as first described by Adler et al., is the same as the extended primal algorithm applied to the dual.     

Geometrical method for determining the surface damage threshold for femtosecond laser pulses

A new geometrical method to determine the surface damage threshold for ultrashort pulses is presented. It consists in the formation of a surface damage profile by a movement of the sample across the laser beam focus. A single measurement of the maximum transversal dimension of this damage profile, which depends solely on the laser beam power, is used to calculate the local damage threshold intensity. It is also theoretically shown that the damage in the transverse dimension can be controlled under the diffraction-limited spot.     

A detailed study of the generation of optically detectable watermarks using the logistic map

A digital watermark is a visible, or preferably invisible, identification code that is permanently embedded in digital media, to prove owner authentication and provide protection for documents. Given the interest in watermark generation using chaotic functions a detailed study of one chaotic function for this purpose is performed. In this paper, we present an approach for the generation of watermarks using the logistic map. Using this function, in conjunction with seed management, it is possible to generate chaotic sequences that may be used to create highpass or lowpass digital watermarks. In this paper we provide a detailed study on the generation of optically detectable watermarks and we provide some guidelines on successful chaotic watermark generation using the logistic map, and show using a recently published scheme, how care must be taken in the selection of the function seed.     

Global stability of the Armstrong-Frederick model with periodic biaxial inputs

The paper is concerned with the study of plasticity models described by differential equations with stop and play operators. We suggest sufficient conditions for the global stability of a unique periodic solution for the scalar models and for the vector models with biaxial inputs of a particular form, namely the sum of a uniaxial function and a constant term. For another class of simple biaxial inputs, we present an example of the existence of unstable periodic solutions. The paper was written during the research stay of D. Rachinskii at the Technical University Munich supported by the research fellowship from the Alexander von Humboldt Foundation. His work was partially supported by the Russian Science Support Foundation, Russian Foundation for Basic Research (Grant No. 01-01-00146, 03-01-00258), and the Grants of the President of Russia (Grant No. MD-87.2003.01, NS-1532.2003.1). The support is gratefully acknowledged.     

Dependence of the H2-H2 Interaction on the Monomer Bond Lengths: Steps Toward an Accurate ab initio Estimate

We compute the vibrational coupling between two H₂ molecules from ab initio quantum chemical calculations of the H₂-H₂ potential carried out at the full configuration interaction level of theory using the atom-centered aug-cc-pVTZ basis set for hydrogen. We compare the full configuration interaction results with those obtained using two variants of coupled cluster theory and find that a fully iterative treatment of connected triples may be required to estimate the H₂-H₂ vibrational coupling accurately using coupled cluster theory.     

Sequential Importance Sampling Algorithms for Dynamic Stochastic Programming

This paper gives a comprehensive treatment of EVPI-based sequential importance sampling algorithms for dynamic (multistage) stochastic programming problems. Both theory and computational algorithms are discussed. Under general assumptions it is shown that both an expected value of perfect information (EVPI) process and the corresponding marginal EVPI process (the supremum norm of the conditional expectation of its generalized derivative) are nonanticipative nonnegative supermartingales. These processes are used as importance criteria in the class of sampling algorithms treated in the paper. When their values are negligible at a node of the current sample problem scenario tree, scenarios descending from the node are replaced by a single scenario at the next iteration. On the other hand, high values lead to increasing the number of scenarios descending from the node. Both the small sample and asymptotic properties of the sample problem estimates arising from the algorithms are established, and the former are evaluated numerically in the context of a financial planning problem. Finally, current and future research is described. Bibliography: 49 titles. __________ Published in Zapiski Nauchnykh Seminarov POMI, Vol. 312, 2004, pp. 94–129.     

Periodic Integrable Systems with Delta-Potentials

In this paper we study root system generalizations of the quantum Bose-gas on the circle with pair-wise delta-function interactions. The underlying symmetry structures are shown to be governed by the associated graded algebra of Cherednik's (suitably filtered) degenerate double affine Hecke algebra, acting by Dunkl-type differential-reflection operators. We use Gutkin's generalization of the equivalence between the impenetrable Bose-gas and the free Fermi-gas to derive the Bethe ansatz equations and the Bethe ansatz eigenfunctions.     

Interplay between four conjectures on certain zero-sum problems

In this paper, we explore the interplay of four different conjectures on certain zero-sum problems in Z_p Z_p. This study of the inter-relations between these conjectures leads to the conclusion that determining the structure of minimal zero sequences (see below for the precise definition) is crucial. Also, we study the analogous situation in Z_n.     

On f-injective modules

In this paper, the notions of f-injective and f^*-injective modules are introduced. Elementary properties of these modules are given. For instance, a ring R is coherent iff any ultraproduct of f-injective modules is absolutely pure. We prove that the class S^* \Sigma^* of f^*-injective modules is closed under ultraproducts. On the other hand, S^* \Sigma^* is not axiomatisable. For coherent rings R, S^* \Sigma^* is axiomatisable iff every c₀ \chi_0 -injective module is f^*-injective. Further, it is shown that the class S \Sigma of f-injective modules is axiomatisable iff R is coherent and every c₀ \chi_0 -injective module is f-injective. Finally, an f-injective module H, such that every module embeds in an ultraprower of H, is given.