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.