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).     

Nontrivial periodic solutions of a nonlinear beam equation

We consider the existence of a nontrivial solution of the following equation: where g is a nondecreasing function defined on R¹, satisfies g(O) = O, and some other additional conditions. Our results and methods are quite similar to those associated with recent work on the nonlinear wave equation [1]-[8]: .     

Mass spectral behavior of some homoleptic and mixed aryldichalcogenide bis(diphenylphosphino)ferrocenenickel(II), palladium(II), and platinum(II), and bis(diisopropylphosphino)ferrocenepalladium(II) complexes

The mass spectral behavior of a number of organometallic complexes containing the Group 10 metals Ni, Pd, and Pt, together with various thiolate ligands were studied. For Pd, two main types of complexes, differing by the substituents on the phosphorus atom were studied. Types I and II were substituted with bis(diphenylphosphino)ferrocene and bis(diisopropylphosphino)ferrocene ligands, respectively. The Ni complexes, except for one, and the Pd Type I complexes had no molecular radical cations (M(+.)) in their EI spectra. On the other hand, all the Pt complexes showed intense M(+.) ions in their EI spectra indicating that these complexes were more stable as radical cations than those of Ni and Pd. The FAB and MALDI spectra of all the complexes displayed intense quasi-molecular ions (MH(+)) and the fragmentations in both modes were similar. The MALDI spectra of several complexes displayed only M(+.) ions while one gave evidence of both MH(+) and M(+.) ions. Several Pd Type II complexes yielded intense M(+.) in their EI spectra.     

Gelation of β-lactoglobulin in the presence of propylene glycol alginate: kinetics and gel properties

The role of the non-gelling polysaccharide, propyleneglycol alginate (PGA), on the dynamics of gelation and gel properties of β-lactoglobulin (β-lg) under conditions where the protein alone does not gel (6%) was analyzed. To this end, the kinetics of gelation, aggregation and denaturation of β-lg in the mixed systems (pH 7) were studied at different temperatures (64–88 °C). The presence of PGA increased thermal stability of β-lg. The rate of β-lg denaturation was decreased and the onset and peak denaturation temperatures increased by 2.2–2.4 °C. PGA promoted the formation of larger aggregates that continued to grow in time. An average aggregate diameter of approximately 300 nm is reached at the gel point in the mixed β-lg+PGA systems, irrespective of the heating temperature. Comparing the activation energies for the aggregation (193 kJ/mol), denaturation (422 kJ/mol) and formation of the primary gel structure (1/t_gel) (256 kJ/mol) processes in the mixed protein–polysaccharide system, it can be concluded that the rate determining step in the formation of the primary gel structure would be the aggregation of protein. E_a values for the processes after the gel point (solid phase gelation) suggest a diffusion limited process because of the high viscosity of the solid gelling matrix. The characteristics of the mixed β-lg+PGA gels in terms of rheological and textural parameters, water loss and microstructure were studied as a function of heating temperature and time. The extent of aggregation and the type of interactions involved, prior to denaturation seem to be very important in determining the gel structure and its properties.     

Mono- and beta,beta-double-Heck reactions of alpha,beta-unsaturated carbonyl compounds in aqueous media

Optimized reaction conditions for the mono- and beta,beta-diarylation of electron-deficient alkenes in aqueous media catalyzed either by a p-hydroxyacetophenone oxime-derived palladacycle or by palladium(II) acetate under phosphine-free conditions and in the presence of (dicyclohexyl)methylamine as base are described. Regioselective monoarylation of unsubstituted and substituted alpha,beta-unsaturated carbonyl compounds takes place with aryl iodides at 120 degrees C in water. Aqueous N,N-dimethylacetamide (DMA), tetra-n-butylammonium bromide (TBAB) as additive, and the palladacycle as catalyst are the most efficient conditions for the coupling with aryl bromides, good stereoselectivities being also obtained in the arylation of crotonates and itaconates, whereas cinnamic derivatives afford lower steroselectivity, with the exception of cinnamic acid and nitrile. beta,beta-Diarylation of unsubstituted alpha,beta-unsaturated carbonyl compounds can be controlled by using higher loading of the palladacycle and can be performed in refluxing water for aryl iodides, whereas DMA must be used for aryl bromides. Microwave irradiation can be used in the monoarylation of tert-butyl acrylate with aryl iodides in water or the coupling between ethyl cinnamate and aryl bromides in aqueous DMA.     

New strategy for the asymmetric synthesis of phenyl ketone cyanohydrins: quaternization of cyanohydrins derived from 2-p-tolylsulfinyl benzaldehyde

[reaction: see text] Optically pure functionalized cyanohydrins derived from 1-[2-(p-tolylsulfinyl)phenyl] ethanone can be obtained by the reaction of 2-p-tolylsulfinyl benzaldehyde derived cyanohydrins with bases and further treatment with suitable electrophiles. High yields and excellent stereoselectivities (up to de >98%) were obtained for these remote 1,4-asymmetric induction processes controlled by a sulfinyl chiral inductor.     

Effects of temperature and anion type on the two-dimensional condensation of the 4,4′-bipyridine cation radical on mercury

The reduction of 4,4′-bipyridine (BPH²⁺₂) on mercury in an acid medium gives a very narrow sharp tail-less reversible voltammetric peak that can be ascribed to the formation of a two-dimensional (2D) phase of the cation radical BPH^·+₂ at the electrode according to the reaction

BPH²⁺₂ + e⁻ |BPH^·+₂|_2D

The corresponding oxidation peak possesses similar properties and arises from the destruction (fusion) of the 2D phase.In this work we studied the influence of some experimental variables, namely the type of anion present in the medium, the concentration of 4,4′-bipyridine and temperature on the 2D phase transition peaks. Also, we tested various analytical criteria to validate this assignation and fitted both voltammetric peaks numerically to the theoretical model developed for this purpose.