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.

     

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.     

Primitive ideals of locally C*-algebras

This paper is concerned with the connection between the structure space of a locally C*-algebra and the set of its continuous topologically irreducible *-representations. Properties of primitive ideals in such algebras are further investigated, for instance, closed ideals are expressed as intersections of primitive ideals, by using that the Jacobson radical reduces to 0.     

Multi-Regge cluster model versus multiparticle experimental data

Zeitschrift für Physik C Particles and Fields - We perform an analysis of predictions of the multi-Regge cluster model and compare them with available longitudinal and transverse data. We show...     

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.     

Thermal and Emission Properties of a Series of Lanthanides Complexes with N-Biphenyl-Alkylated-4-Pyridone Ligands: Crystal Structure of a Terbium Complex with N-Benzyl-4-Pyridone

This work focuses on the investigation of the liquid crystalline behavior and luminescence properties of the lanthanide complexes of Eu(III), Sm(III) and Tb(III) with N-biphenyl-alkylated-4-pyridone ligands. The organic ligands having a biphenyl group attached via a long flexible spacer with either 9 or 10 carbon atoms were synthesized by the reaction between 4-hydroxypyridine and the corresponding bromide compounds. The chemical structures of the organic and lanthanide complexes were assigned based on elemental analysis, single-crystal X-ray diffraction, ¹H, ¹³C NMR and IR spectroscopies, and thermogravimetric analysis (TGA). The X-ray diffraction analysis of a parent compound shows that the lanthanide ions are surrounded by three monodentate pyridone ligands and three bidentate nitrate ions, giving a 9-coordinate environment. The mesogenic behavior and the type of liquid crystalline phases exhibited by the new complexes were analyzed by differential scanning calorimetry (DSC) and polarizing optical microscopy (POM), and powder X-ray diffraction (XRD) studies. Only the lanthanide complexes with longer spacer (10) display a monotropic SmA phase, typically on a short thermal range (less than 10 °C). The complexes with shorter flexible chains (9) show no liquid crystalline properties with melting temperatures lower than their analogs with longer spacers. The emission spectra recorded in solid state at room temperatures show typical emission bands for each lanthanide ion employed (Eu(III), Tb(III) and Sm(III)).