Convergence to equilibrium of critical branching particle systems and superprocesses,and related nonlinear partial differential equations

We consider a class of multitype particle systems in ^d undergoing spatial diffusion and critical stable multitype branching, and their limits known as critical stable multitype Dawson-Watanabe processes, or superprocesses. We show that for large classes of initial states, the particle process and the superprocess converge in distribution towards known equilibrium states as time tends to infinity. As an application we obtain the asymptotic behavior of a system of nonlinear partial differential equations whose solution is related to the distribution of both the particle process and the superprocess.Research partially supported by CONACyT (Mexico), CNRS (France) and BMfWuF (Austria).     

Boundaries for algebras of holomorphic functions

Let A_u(B_G) be the Banach algebra of all complex valued functions defined on the closed unit ball B_G of a complex Banach space G which are uniformly continuous on B_G and holomorphic in the interior of B_G, endowed with the sup norm. A characterization of the boundaries for A_u(B_G) is given in case G belongs to a class of Banach spaces that includes the pre-dual of a Lorentz sequence space studied by Gowers in Israel J. Math. 69 (1990) 129-151. The non-existence of the Shilov boundary for A_u(B_G) is also proved.     

FRACTIONAL DIFFUSION EQUATIONS WITH INTERNAL DEGREES OF FREEDOM

We present a generalization of the linear one-dimensional diffusion equation by com-bining the fractional derivatives and the internal degrees of freedom. The solutions areconstructed from those of the scalar fractional diffusion equation. We analyze the in-terpolation between the standard diffusion and wave equations defined by the fractionalderivatives. Our main result is that we can define a diffusion process depending on theinternal degrees of freedom associated to the system.     

<Emphasis FontCategory="NonProportional">L</Emphasis>-Matrices and solvability of linear complementarity problems by a linear program-Matrices and solvability of linear complementarity problems by a linear program

The classes ofL ₁-matrices,L ₂-matrices,L ₃-matrices andW-matrices are introduced to study solvability of a linear complementarity problem via solving a linear program. Three sufficient conditions are presented to guarantee that a linear complementarity problem is solvable via a linear program. The new sufficient conditions are weaker than the ones introduced by Mangasarian. This fact is also illustrated by an example. Partially supported by NSFC. This author is also with College of Business Administration of Human University as a Lotus chair professor.     

Multiple solutions of boundary value problems: an elementary approach via the shooting method

In this paper we derive the existence of multiple solutions for boundary value problems of the type $$u\prime \prime + f\left( {t,u} \right) = 0,u\left( 0 \right) = 0,u\left( \pi \right) = 0$$ , in terms of the behaviour of the ratiof(t,u)/u nearu=0 and near infinity. The nonlinear termf is assumed to be locally Lipschitz inu, so that the shooting method can be used. (AMS Subject Classification: 34B15).     

MS-Xα study of the KCl: Cu− spectrum

We have interpreted the KCl:Cu^? spectrum in the context of the MS-X_α method. The results, considering only allowed electric-dipole transitions, are in good agreement with the experimental data. Four new absorption bands, peaking at 573, 390, ～324 and ～310nm, at room temperature, are reported.     

Identification of phototransformation products of sildenafil (Viagra) and its N-demethylated human metabolite under simulated sunlight

Recent publications on pharmaceutical monitoring are increasingly covering the field of illicit drugs and lately the forensic evaluation of designing illegal analogs of lifestyle drugs like the phosphodiesterase type 5 (PDE-5) inhibitors Viagra (sildenafil), Levitra (vardenafil) and Cialis (tadalafil). Recently, the presence of all three erectile dysfunction treatment drugs has been reported in wastewaters at very low concentrations. In the environment, contaminants undergo various physical or chemical processes classified into abiotic (photolysis, hydrolysis) and biotic (biodegradation) reactions. Thus, changes in the chemical structure lead to the formation of new transformation products, which may persist in the environment or be further degraded. This study describes the photolysis of sildenafil (SDF) and its human metabolite N-demethylsildenafil (DM-SDF) under simulated solar radiation (Xenon lamp). Following chromatographic separation of the irradiated samples, eight photoproducts in the SDF samples and six photoproducts for DM-SDF were detected and characterized. The combination of ultra performance liquid chromatography-electrospray ionization-quadrupole time-of-flight-mass spectrometry (UPLC-ESI-QToF-MS), liquid chromatography-atmospheric pressure chemical ionization-triple quadrupole mass spectrometry (LC-APCI-QqQ-MS) and hydrogen/deuterium-exchange experiments allowed to propose plausible chemical structures for the photoproducts, taking into account the characteristic fragmentation patterns and the accurate mass measurements. These mass spectral data provided sound evidence for the susceptibility of the piperazine ring toward photodegradation. A gradual breakdown of this heterocyclic structure gave rise to a series of products, which in part were identical for SDF and DM-SDF. The sulfonic acid, as the formal product of sulfonamide hydrolysis, was identified as key intermediate in the photolysis pathway. In both drug/metabolite molecules, phototransformation processes taking place beyond the sulfonamide group were deemed to be of minor relevance.     

A simple polymer electrolyte membrane system for enrichment of low-level tritium (3H) in environmental water samples

Tritium (³H) is an essential tracer of the Earth's water cycle; yet widespread adoption of tritium in hydrologic studies remains a challenge because of analytical barriers to quantification and detection of ³H by electrolytic pre-concentration. Here, we propose a simple tritium electrolytic enrichment system based on the use of solid polymer electrolyte membranes (PEMs) that can be used to enrich ³H in 250–3000?mL environmental water samples to a 10-mL final volume. The IAEA PEM-³H system reported here can produce high enrichment factors (>70-fold) and, importantly, removes some of the deterrents to conventional ³H enrichments methods, including the use of toxic electrolysis and neutralization chemicals, spike standards, a complex electrolysis apparatus that requires extensive cooling and temperature controls, and improves precision by eliminating the need for tracking recovery gravimetrics. Preliminary results with varying operating conditions show ³H enrichments to 70-fold and higher are feasible, spanning a wide range of tritium activities from 5 to 150 TU with a precision of ～4.5?%. Further work is needed to quantify inter-sample memory and to establish lower ³H detection limits. The IAEA PEM-³H system is open source, with 3-D CAD and design files made freely available for adoption and improvement by others.     

Simplification and analysis of a model of social interaction in voting

A recently proposed model of social interaction in voting is investigated by simplifyingit down into a version that is more analytically tractable and which allows a mathematicalanalysis to be performed. This analysis clarifies the interplay of the different elementspresent in the system – social influence, heterogeneity and noise – and leads to a betterunderstanding of its properties. The origin of a regime of bistability is identified. Theinsight gained in this way gives further intuition into the behaviour of the originalmodel.