Quantum States on Harmonic Lattices

We investigate bosonic Gaussian quantum states on an infinite cubic lattice in arbitrary spatial dimensions. We derive general properties of such states as ground states of quadratic Hamiltonians for both critical and non-critical cases. Tight analytic relations between the decay of the interaction and the correlation functions are proven and the dependence of the correlation length on band gap and effective mass is derived. We show that properties of critical ground states depend on the gap of the point-symmetrized rather than on that of the original Hamiltonian. For critical systems with polynomially decaying interactions logarithmic deviations from polynomially decaying correlation functions are found.     

Solvability of the Direct and Inverse Problems for the Nonlinear Schrödinger Equation

In this paper we study rigorous spectral theory and solvability for both the direct and inverse problems of the Dirac operator associated with the nonlinear Schrödinger equation. We review known results and techniques, as well as incorporating new ones, in a comprehensive, unified framework. We identify functional spaces in which both direct and inverse problems are well posed, have a unique solution and the corresponding direct and inverse maps are one to one.Mathematics Subject Classifications (2000) 34A55, 35Q55.     

Linear Key Predistribution Schemes

In a key predistribution scheme, some secret information is distributed among a set of users. For a given family of privileged groups, this secret information must enable every user in a privileged group to compute a common key associated with that group. Besides, this common key must remain unknown to some specified coalitions of users outside the privileged group. We present in this paper a new model, based on linear algebraic techniques, for the design of key predistribution schemes that unifies all previous proposals. This new model provides a common mathematical formulation and a better understanding of key predistribution schemes. Two new families of key predistribution schemes that are obtained by using this model are presented. Those families provide, for some specification structures, schemes that have better information rates than the ones given in previous proposals or fit in situations that have not been considered before.     

The gas-phase elimination kinetics of 3-buten-1-methanesulphonate and 3-methyl-3-buten-1-methanesulphonate

The elimination kinetics of the title compounds were carried out in a static system over the temperature range of 290–330°C and pressure range of 29.5–124 torr. The reactions, carried out in seasoned vessels with allyl bromide, obey first-order rate law, are homogeneous and unimolecular. The temperature dependence of the rate coefficients is given by the following Arrhenius equations: for 3-buten-1-methanesulphonate, log k₁(s^?1) = (12.95 ± 0.53) ? (175.3 ± 5.9)kJ mol^?1(2.303RT)^?1; and for 3-methyl-3-buten-1-methanesulphonate, log k₁(s^?1) = (12.98 ± 0.40) ? (174.7 ± 4.5)kJ mol^?1(2.303RT)^?1. The olefinic double bond appears to assist in the rate of pyrolysis. The mechanism is described in terms of an intimate ion-pair intermediate. © 1995 John Wiley & Sons, Inc.     

Germs of holomorphic vector fields in C3 without a separatrix

Oblatum 28-XII-1988 & 26-III-1990 & 10-X-1990 & 13-VI-1991 & 30-IX-1991     

Implementation of an algorithm for detecting patterns in defocused scenes using binary joint transform correlation

An original method to detect images in defocused scenes by means of a binary joint transform correlation is presented. Defocused images are described in frequency domain as the product between the Fourier transform of the in-focus scene by the optical transfer function of the imaging lens. This function, which presents positive and negative values, introduces sign errors in the joint power spectrum. The goal of this study is to detect the sign of the optical transfer function starting from the defocused image by means of a digital algorithm. Information provided by the algorithm allows to compensate the sign errors in the binary joint power spectrum and to obtain invariant correlations with respect to defocusing. Theoretical analysis and digital experiments to test the procedure are provided.     

Acoustic voice analysis in patients with essential tremor

To quantify several acoustic features of the voice in patients with essentialtremor (ET), 28 patients and 28 age- and sex-matched controls were studied. ET severity was assessed with the rating scale for tremor of Fahn, Tolosa, and Marín. The Computerized Speech Lab 4300 program (Kay Elemetrics) was used. Two-second samples of a sustained /a/ and a sentence were captured with a microphone and laryngograph equipment. Measures included fundamental frequency (F₀), frequency perturbation (fitter, Koike algorithm), intensity perturbation (shimmer, Horii algorithm), and harmonic-to-noise ratio (H/N, Yumoto algorithm) of the vowel /a/, and the frequency and intensity variability of the sentence, phonational range, and dynamic range at the natural frequency, maximum phonational time, and s/z ratio. All subjects underwent indirect laryngoscopy and/or laryngeal fibroscopy. When compared with controls, ET patients showed higher jitter, lower H/N ratio (the last one only with laryngographic signal), of the vowel /a/, lower frequency variability in the microphonc signal, lower intensity variability in the laryngographic signal of the sentence, and significantly lower dynamic range at natural frequency of phonation. ET patients reported higher frequency of the presence of high voice intensity, tremor, and struggle. Several acoustic parameters were influenced by the severity of the disease, including shimmer, jitter, H/N ratio, frequency variability of the sentence, and s/z ratio, although neither of the acoustic analysis values or the phonetometric measurements were affected by the presence of voice tremor or by a successful pharmacological treatment of ET.     

Anchimeric assistance in the gas phase dehydrohalogenation of 5-chloro-2-methylpent-2-ene

5-Chloro-2-methylpent-2-ene decomposes at temperatures of 370–420°C with initial pressures from 61to 158 torr to yield hydrogen chloride and a mixture of methylpentadiene isomers. In a static system, with seasoned vessel and propene inhibitor, the reaction is homogeneous, unimolecular, and of the first order. The rate coefficient is expressed by the following Arrhenius equation: log k (sec^?1) = (13.43 ± 0.30) ? (215.0 ± 3.7) kJ/mol/2.303RT. The result ofthe present work additionally supports the participation of the neighboringaliphatic olefinic double bond in the rate of HCl elimination of alkenyl chlorides in the gas phase. Moreover, it also confirms the three-membered conformation as the most favored structure for anchimeric assistance.