Lines of curvature near umbilical points on surfaces immersed in R4

LetM be a compact orientable surface,I:M R⁴ an immersion of classC ^r and a normal unitary smooth vector field. We prove that in the space of pairs (I, ) the family of pairs all whose umbilical points are Darbouxian is generic.     

Energy functional depending on elastic strain and chemical composition

In this paper we deal with energy functionals depending on elastic strain and chemical composition and we obtain lower semicontinuity results, existence theorems and relaxation in the spacesH ^1,p(; ⁿ)×L ^q (; ^d) with respect to weak convergence. Our proofs use parametrized measures associated with weakly converging sequences.The research was partially supported by the National Science Foundation under Grants No. DMS-9000133 and DMS-9201215 and also by the Army Research Office and the National Science Foundation through the Center for Nonlinear Analysis.The research was partially supported by the National Science Foundation uncer Grants No. DMs 911572, the AFOSR 91 0301, the ARO DAAL03 92 G 003 and also by the ARO and the NSF through the Center for Nonlinear Analysis.The research was supported by DGICYT (Spain) through Programa de Perfeccionamiento y Movilidad del Personal Investigador and through grant PB90-0245, by the Army Research Office and the National Science Foundation through the Center for Nonlinear Analysis and also by the project EurHomogenization SC1-CT91-0732 of the European Comunity.     

Construction of functional porphyrin polystyrene nano-architectures by ATRP

A series of mono-functionalized metallo-porphyrin polystyrenes have been synthesized using atom transfer radical polymerization and their self-assembling behavior was studied by electron microscopy showing that the polystyrene tail-length influences the aggregate architecture.     

A new color of the synthetic chameleon methoxyallene: synthesis of trifluoromethyl-substituted pyridinol derivatives: an unusual reaction mechanism, a remarkable crystal packing, and first palladium-catalyzed coupling reactions

Addition of lithiated methoxyallene to pivalonitrile afforded after aqueous workup the expected iminoallene 1 in excellent yield. Treatment of this intermediate with silver nitrate accomplished the desired cyclization to the electron-rich pyrrole derivative 2 in moderate yield. Surprisingly, trifluoroacetic acid converted iminoallene 1 to a mixture of enamide 3 and trifluoromethyl-substituted pyridinol 4 (together with its tautomer 5). A plausible mechanism proposed for this intriguing transformation involves addition of trifluoroacetate to the central allene carbon atom of an allenyl iminium intermediate as crucial step. Enamide 3 is converted to pyridinol 4 by an intramolecular aldol-type process. A practical direct synthesis of trifluoromethyl-substituted pyridinols 4, 10, 11, and 12 starting from typical nitriles and methoxyallene was established. Pyridinol 10 shows an interesting crystal packing with three molecules in the elementary cell and a remarkable helical supramolecular arrangement. Trifluoromethyl-substituted pyridinol 4 was converted to the corresponding pyridyl nonaflate 13, which is an excellent precursor for palladium-catalyzed reactions leading to pyridine derivatives 14-16 in good to excellent yields. The new synthesis of trifluoromethyl-substituted pyridines disclosed here demonstrates a novel reactivity pattern of lithiated methoxyallene which is incorporated into the products as the unusual tripolar synthon B.     

Rotational fluctuations of water inside the nanopores of SBA-type molecular sieves

The rotational molecular dynamics of water confined to nanoporous molecular sieves of a regular hexagonal (SBA-15) and of a foamlike pore structure was studied by dielectric spectroscopy in the frequency range from 10(-2) to 10(9) Hz and in a broad temperature interval. Two relaxation processes were observed: the process at lower frequencies is related to water molecules forming a layer, which is strongly adsorbed at the pore surface, whereas the relaxation process at higher frequencies is assigned to fluctuations of water molecules situated close to the center of the pore. The relaxation times of the low-frequency process for both materials and of the high-frequency process for the SBA-15 material have an unusual saddlelike temperature dependence, reported here for the first time. To describe this temperature dependence, a model developed for water confined to nanoporous glasses by Ryabov et al. [J. Phys. Chem. B 2001, 105, 1845] was applied, which considers two competing effects. The characteristic features of these two competing processes were compared with those reported for other porous systems.     

Complex strict convexity of certain Banach spaces

Istratescu's characterization of complex strict convex (csc) Banach spaces is used to show that a modulared sum of a sequence ofcsc Banach spaces is again acsc Banach space. The equivalence of the Strong Maximum Modulus Property and complex strict convexity is used to show thatL ¹(,X) iscsc whenX is (real) strictly convex and thatl ¹(X _n) iscsc if and only if eachX _n iscsc.     

Time evolution studies of the H2O/quartz interface using sum frequency generation, atomic force microscopy, and molecular dynamics

Many interfacial studies on solid surfaces, for example, quartz/water, assume that a standard cleaning procedure regenerates the surface reproducibly. In the reported work, the results of two surface specific techniques, sum frequency generation (SFG) spectroscopy and atomic force microscopy, show that the effects of prolonged exposure to Nanopure water and to pH 10 NaOH are distinctly different. In conjunction with the experimental data, molecular mechanics is used to correlate the SFG spectral frequencies to the hydrogen stretching vibrations of the surface-bound water molecules. It is found that after 17 days of soaking in water, water molecules penetrate into the SiO2 matrix to produce a swollen and amorphous layer; it is likely that broken Si-O bonds from the polishing process serve as nucleation sites for hydration and swelling. Disorder introduced in the interfacial water layer is detected by the rising intensity of the weakly hydrogen-bonded SFG peak at 3450 cm(-1). Dominance of the 3450 cm(-1) is absent in a pH 10, NaOH-soaked quartz disk, indicating that the strong hydrogen-bonded network in water remains intact.     

Propylene oxidation by palladium nitro and nitrato complexes: in situ NMR and IR studies

The mechanism of the propylene oxidation by Pd(NO_n)Cl_2 − m(CH₃CN)₂ complexes (n = 2, 3; m = 0, 1, 2) in chloroform solutions has been studied by ¹H NMR and IR spectroscopy. The main reaction products are acetone and 2-nitropropylene, with their ratio depending on the equilibrium existing in the reaction solutions between palladium complexes containing NO_n ligands bonded to a palladium atom via either an oxygen or a nitrogen atom. Reactivities of the oxygen bonded nitrato and nitrito complexes are significantly higher than that of the nitrogen bonded nitro complex. Various new organopalladium intermediates have been observed and monitored in situ. A reversible insertion of the coordinated propylene into the Pd-O or Pd-N bonds results in nitrato-, nitrito- and nitropalladation intermediates, which then decompose via a β-hydrogen elimination. Two isomers of the nitritopalladation intermediate have been detected, i.e., a palladium metallacycle and an open ring complex, with the latter being much more reactive towards the β-hydrogen elimination than the former. The decomposition of the nitrato- and nitritopalladation intermediates results in the organometallic precursor of acetone, i.e., an acetonylpalladium complex, and then in acetone itself. On the other hand, the nitropalladation intermediate originates 2-nitropropylene. In the presence of dioxygen, which re-oxidizes the nitrosyl groups, the acetone formation becomes a catalytic reaction with respect to both palladium and nitrogen.