Rhodium(I) catalyzed four-component reaction of Fischer alkenyl carbene complexes and 1,1-diphenylallene

Alkyl substituted chromium Fischer carbene complexes react with 1,1-diphenylallene in the presence of rhodium(I) catalysts (10 mol%) to yield highly substituted dienyl indenone derivatives. In this process a catalytic chromium(0)-rhodium(I) exchange occurs, four new C-C bonds are created, and four-components (two allenes, the carbene ligand and one CO ligand) are joined in a chemo- and regioselective manner.     

Control of the Diels-Alder-Addition Regioselectivity by Remote Olefins. Syntheses and Cycloadditions of 2,3,5-Trimethylidenebicyclo[2.2.1]heptane and 2,3,5,6,7-Pentamethylidenebicyclo[2.2.2]octane

The syntheses of 2,3,5-trimethylidenebicyclo[2.2.1]heptane ( 1 ) and 2,3,5,6,7-pentamethylidenebicyclo[2.2.2]-octane ( 2 ) are reported. The Diels-Alder additions of the diene moieties of these polyenes can be regioselective, probably because of a possible transannular interaction between the homoconjugated methylidene and s-cis-buta-diene groups.     

[M(bpy)3] (M = Fe,Ru, Os): New Crystalline Materials from the reductive electrocrystallization of [M(bpy)3](PF6)2

Reductive electrocrystallization at a constant current density (11.0–11.5 μA/cm²) of millimolar solutions of [M(bpy)₃](PF₆)₂, where M = Fe, Ru, or Os, and bpy = 2,2′-bipyridine in acetonitrile containing 0.1M Bu₄NPF₆ results in the formation of dark crystals on the Pt cathode. The crystals grow as long, thin, and shiny needles having a hexagonal cross section of 0.1–0.5 mm in diameter. Combustion microanalyses results are consistent with the composition for [Fe(bpy)₃], [Ru(bpy)₃], and [Os(bpy)₃]. In addition, the chromophores are conserved, as confirmed by recording both the electronic and the ¹H-NMR spectra after reoxidation of the electrocrystals in humid air. The spectra are identical to those for authentic samples of [Fe(bpy)₃]²⁺, [Ru(bpy)₃]²⁺, and [Os(bpy)₃]²⁺. A ratio of 2.0 ± 0.1 e^?/molecule is observed upon completion of the controlled potential electrolysis of a solution of [M(bpy)₃]²⁺, which results in the precipitation of a dark solid and the almost complete fading of the color of the original solution. Unexpectedly, the crystals do not exhibit an ESR signal. These data indicate the formation of novel materials, crystalline [Fe(bpy)₃], [Ru(bpy)₃], and [Os(bpy)₃].     

Regularity of solutions and interfaces of a generalized porous medium equation inR N

Summary We consider the Cauchy problem for the generalized porous medium equation u_t=(u) where u=u(x, t), xRⁿ and t>0, and the initial datum u(x, 0) is assumed to be nonnegative, integrable mid to nave compact support. The nonlinearity (u) is a C¹ function defined for uO which grows like a power of u. Our assumptions generalize the porous medium case, (u)=u^m, m>1, and also include the equation of the Marshak waves. This problem has finite speed of propagation. We estimate the rate of growth of the support of the solution with precise estimates for t 0 and t. Our main result deals with the regularity of the solutions. We show that after a certain time t₀ the pressure, defined by v=(u), with (u)=(u)/u and (0)=0, is a Lipschitz-continuous function of x and t and the interface is a Lipschitz-continuous surface in R^N+1; the solution u is Hölder continuous for all times t> 0.Both authors partially supported by CAICYT, Project 2805-83. The second author also supported by USA-Spain Joint Research Grant CCB-8402023.     

Harmonic maps from compact Kähler manifolds to exceptional hyperbolic spaces

It has been conjectured that a lattice in a noncompact group of real rank one, other than SU(1,n), cannot be isomorphic to the fundamental group of a compact Kähler manifold; moreover, it is known to be true for SO(1,n). In this note it is shown that this conjecture also holds for the case of uniform lattices in F_4(?20), the group of isometries of the Cayley hyperbolic plane. The result is a consequence of a classification theorem for harmonic maps between Kähler and Cayley hyperbolic manifolds.     

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.