The correlations of finite Desarguesian planes, Part II: The classification (I)

This paper continues the classification of the correlations of planes of odd nonsquare order. Part I (Generalities) – see reference [1]-included introductory definitions and results (Section 1), algebraic preliminaries (Section 2), as well as a discussion of equivalent correlations (Section 3) and of their general properties (Section 4). The classification proper revolves around a special polynomial which can have one, two, or q + 1 zeros, or no zeros at all, and each of these four possibilities leads to different families of correlations. The present article contains Section 5, devoted to the cases in which the correlation is defined by a diagonal matrix (Subsection 5.1) or the polynomial in the preceding paragraph possesses q + 1 zeros (Subsection 5.2), one zero (Subsection 5.3) and two zeros (Subsection 5.4). Subsection 5.5 presents certain results to be used in the subsequent sections.     

On nonlinear wave equations with degenerate damping and source terms

In this article we focus on the global well-posedness of the differential equation , where is a sub-differential of a continuous convex function . Under some conditions on and the parameters in the equations, we obtain several results on the existence of global solutions, uniqueness, nonexistence and propagation of regularity. Under nominal assumptions on the parameters we establish the existence of global generalized solutions. With further restrictions on the parameters we prove the existence and uniqueness of a global weak solution. In addition, we obtain a result on the nonexistence of global weak solutions to the equation whenever the exponent is greater than the critical value , and the initial energy is negative. We also address the issue of propagation of regularity. Specifically, under some restriction on the parameters, we prove that solutions that correspond to any regular initial data such that , are indeed strong solutions.

     

Stable Transitivity of Certain Noncompact Extensions of Hyperbolic Systems

Let be the restriction to a hyperbolic basic set of a smooth diffeomorphism. We find several criteria for transitivity of noncompact connected Lie group extensions. As a consequence, we find transitive extensions for any finite-dimensional connected Lie group extension. If, in addition, the group is perfect and has an open set of elements that generate a compact subgroup, we find open sets of stably transitive extensions. In particular, we find stably transitive -extensions. More generally, we find stably transitive -extensions for all n ≥ 1. For the Euclidean groups SE(n) with n ≥ 4 even, we obtain a new proof of a result of Melbourne and Nicol stating that there is an open and dense set of extensions that are transitive.For groups of the form where K is compact, a separation condition is necessary for transitivity. Provided X is a hyperbolic attractor, we show that an open and dense set of extensions satisfying the separation condition are transitive. This generalizes a result of Niţică and Pollicott for -extensions.Communicated by Viviane Baladisubmitted 24/05/04, accepted 11/10/04     

Canonical Ensemble with Temperature Limitation

Ideal Bose and Fermi systems are studied on the basis of a canonical ensemble, subject to the condition that their temperature is less than a given temperature T_max. A single new parameter (the tau-parameter, τ) is needed to keep account of the new constraint. The parameter τ is shown to be the exponential of a pseudo-chemical potential that is linearly dependent on temperature. The inclusion of the τ- parameter leads to generalizations of usual thermodynamic quantities (internal energy, heat capacity and entropy) and various particular cases are discussed. The heat capacity of a Bose system can exhibit a maximum at a temperature less than the maximum temperature T_max. The number of micro-states in the canonical ensemble is found to increase with τ. The heat capacity c_V of a Fermi system of non-interacting spins exhibits a Schottky anomaly. The peak depends on τ, and for some cases c_V/k can significantly exceed unity. The influence of τ on the entropy of the Fermi system and on the number of micro-states in the canonical ensemble is significant but not spectacular.     

Partitions of finite affine geometries into caps

In a finite geometry of order q² we define a (q^mq^r)-affine cap to be a set of cardinality q^m which is a disjoint union ot q^m affine subgeometrics AG(r,q). such that no three points are coliinear unless contained in the same AG(r,q).

Given a PG(n,q²), where n = 2t + 1 or 2t + 2, and an n + 1 by n + 1 Hermitian matrix H over Gh(q²) with minimal polynomial (x - λ)^{n + 1}. we show that H induces a partition of the AG(n, q²) obtained by deleting a distinguished hyperplane from the PG, into (qⁿ,q^{l + 1})-affine caps; these caps can be viewed as the "large points" of an AG (n,q) with a natural incidence relation. It is also shown that H induces another partition of AG(n,q²), into q^{n - l 1}-caps, constituting the "large points" of an affine geometry AG(n + t + 1,q).

Also, the collineation C of PG(n, q²) given by x^c = H^Tx induces collineations on the AG(n,q) and AG(n + t + 1,q).     

Thermal degradation of vinyl alcohol/vinyl acetate copolymers. III. Study of the reaction products

The thermal decomposition of vinyl alcohol/vinyl acetate copolymers have been studied at p = 10⁻²–10⁻⁴ Torr and T = 0–600°C. The decomposition products (solids, liquids, and gases) have been characterized by infrared (IR) and ultraviolet (UV) spectroscopy, gas chromatography, vapor pressure osmometry, and elemental analysis. It has been ascertained on the basis of the obtained data that the decomposition mechanism of the vinyl alcohol/vinyl acetate copolymers depends on the chemical composition and sequence distribution of comonomers.     

Combining unsupervised and supervised artificial neural networks to predictaquatic toxicity

Most quantitative structure-activity relationship (QSAR) models are linear relationships and significant for only a limited domain of compounds. Here we propose a data-driven approach with a flexible combination of unsupervised and supervised neural networks able to predict the toxicity of a large set of different chemicals while still respecting the QSAR postulates. Since QSAR is applicable only to similar compounds, which have similar biological and physicochemical properties, large numbers of compounds are clustered before building local models, and local models are ensembled to obtain the final result. The approach has been used to develop models to predict the fish toxicity of Pimephales promelas and Tetrahymena pyriformis, a protozoan.     

7,8,9,10-Tetrahydropyrrolo[2,1-a]isoquinolines in the search for new indolizine derivatives

7,8,9,10-Tetrahydropyrrolo[2,1-a]isoquinolines were obtained by 1,3-dipolar cycloaddition reactions of their corresponding N-ylides with olefinic (acrylonitrile) and symmetrical or non-symmetrical acetylenic dipolarophiles (methyl/ethyl propiolate, dimethyl acetylenedicarboxylate). Also, stable 5,6,7,8-tetrahydroisoquinolinium dicyanomethylide was isolated and characterized by X-ray diffraction analysis.