Some existence results for quasilinear elliptic equations in a finite cylinder

We study the existence of solutionsu in the finite cylinderS _a=(?a, a)×ω of the quasilinear elliptic equation $$\sum\limits_{i,j = 1}^n {a_{i,j} (x)\partial _{i,j} u + f(x,u,\nabla u) = 0} $$ with Dirichlet boundary condition on flat parts of σS _a and Neumann condition on the curved parts. In this paper, we focus on the technicality caused by the “corners” ofS _a. We prove the existence of such solutions provided that suitable sub and super solutions are known and under the condition that the coefficientsa _1,i,i#1 vanish on the corners. We also prove a more general result in ?².     

Synthesis of Enantiopure Primary Amines by Stereoselective Ring Opening of Chiral Octahydro-1,3-benzoxazines by Grignard and Organoaluminum Reagents

Chiral 1,3-perhydrobenzoxazines 1, 2, and 9-14, prepared by condensation of 8-(benzylamino)menthol with different aldehydes, react with alkylmagnesium bromides and trimethylaluminum leading to the open amino alcohols 3a-d, 4a-d, and 15-20 in excellent chemical yields and good to excellent diastereomeric excess. The sequential elimination of the menthol appendage by heating with P(2)O(5) and the benzyl group by hydrogenolysis lead to primary amines 7a-d, 8a-d, and 27-30 in excellent chemical yields and ee. The addition of the alkyl group from the Grignard derivatives and the methyl group from the trimethylaluminum occurs from opposite sides of the heterocycle, yielding the final primary amines with the same stereochemistry.     

FeCp]+-induced hexafunctionalization of hexamethylbenzene with dendrons for the direct synthesis of redox-active iron-centered metallodendrimers

Phenol tri- and nonaallyl dendrons (3 and 7, respectively) were functionalized at the focal position to give the new triallyl dendrons 4 and 6 and the nonaallyl dendrons 11 and 13 that contain a iodoalkyl or a bromobenzyl termini. All these dendrons were used for the [FeCp]+-induced hexafunctionalization of hexamethylbenzene in [FeCp(eta6-C6Me6)][PF6] (1) under mild conditions in the presence of KOH. These reactions directly yielded the 18-allyl and 54-allyl dendrimers 9, 10, and 14 with a [FeCp(eta6-arene)]+ unit located at the dendrimer core. Cyclic voltammetry studies were recorded in THF and DMF with these metallodendrimers and compared with those of analogous dendrimers or complexes of smaller size that contain a [FeCp(eta6-arene)]+ unit at the core. The decreased rate of heterogeneous electron transfer when the dendritic size increases first disclosed by Diederich and Gross is confirmed. The variation of the redox potential of the Fe(II/I) redox system with increasing dendritic size is negligible even in a solvent of high dielectric constant such as DMF. This trend is attributed to fact that the involved "redox" orbital is buried on the metal center, well protected by the shell of alkyl chains (electron-reservoir nature), unlike in ferrocene. The chemical irreversibility increases in THF as the dendrimer size increases, due to more facile ligand substitution with THF at the 19-electron level when the chain bulk increases.     

Preparation and characterization of bolaform surfactant vesicles

Vesicular formulations (liposomes and niosomes) play an increasingly important role since they can be used as drug delivery and targeting systems. We described the formation of two niosomal systems based on synthetic bolaform surfactants (4,7,10,13-pentaoxa-16-aza-cyclooctadecane)-hexadecanedioc acid diamide (BD-16) and alpha,omega-(4,7,10,13-pentaoxa-16-aza-cyclooctadecane)-hexadecane (BC-16). Systems containing BD-16 or BC-16 and different amount of cholesterol (CH) were prepared by aqueous dispersion of films, followed by examination of methylene blue (MB) entrapment, particle size and morphology. Indeed, we also studied the hydration in the distilled water and physiological solution, in order to investigate the complexing ability on vesicle formation. The results obtained in this study show a high encapsulation capacity and this ability and the size depends on cholesterol content.     

A new synthetic route to bulky "second generation" tris(imidazol-2-ylidene)borate ligands: synthesis of a four coordinate iron(II) complex

A bulky tripodal tris(carbene)borate ligand, prepared from 1-tert-butylimidazole, is cleanly transferred to iron(II) by a magnesium reagent.     

Fluoride-induced coupling of perfluoroketene dithioacetals with silyl alkynes: A way towards new polyfunctionalized trifluoromethyl building blocks

Under fluoride activation, the vinyl fluorine of perfluoroketene dithioacetal may be substituted by silylated nucleophiles. Using silyl alkynes, a formal transition metal free sila-Sonogashira cross-coupling reaction occurred. The resulting enynes were hydrolyzed giving new polyfunctional trifluoromethyl building blocks.     

Cyclopentathiadiazines, new heterocyclic materials from cyclic enaminonitriles

Indene and cyclopentene enaminonitriles were reacted with SCl2, iBu3N and NCS to give the first cyclopenta[1,2,6]thiadiazines that showed unusual characteristics, one as a NIR dye and another as a liquid crystal.