The exterior Dirichlet problem for quasi-linear elliptic equations with small boundary data

It is shown that if the order of non-uniformity of a quasi-linear elliptic equation is h,10,2(h–1)/h norm. For 0h1,existence of a bounded solution is guaranteed without any smallness assumption on the given boundary data.More precise information is given for the special case of the minimal surface equation.     

Synthesis of gramicidin S and its analogues via an on-resin macrolactamization assisted by a predisposed conformation of the linear precursors

A simple and efficient preparation of gramicidin S and its analogues is described. It involves solid-phase peptide synthesis and on-resin macrolactamization without side chain protection, affording cyclic products in high yield and high purity. The high specificity of the cyclization reaction was shown to originate in the formation of a pre-organized conformation of the linear biosynthetic precursor of gramicidin S. This facile method will provide convenient access to the analogues of the natural product for functional optimization to counter microbial resistance.     

Half-sandwich titanium(IV) complexes with Kläui's tripod ligand

Treatment of [Ti(O-i-Pr)(2)Cl(2)] with NaL(OEt) (L(OEt)(-) = [CpCo[P(O)(OEt)(2)](3)](-), Cp = eta(5)-C(5)H(5)) afforded [L(OEt)Ti(O-i-Pr)(2)Cl] that reacted with HCl in ether to give [L(OEt)TiCl(3)] (1). The average Ti-O and Ti-Cl distances in 1 are 1.975 and 2.293 A, respectively. Reaction of titanyl sulfate with NaL(OEt) in water followed by addition of HBF(4) afforded [L(OEt)TiF(3)] (2), the Ti-O and Ti-F distances of which are 2.020(2) and 1.792(2) A, respectively. The Zr(IV) analogue [L(OEt)ZrF(3)] (3) was prepared similarly from zirconyl nitrate, NaL(Oet), and HBF(4) in water. The Zr-O and average Zr-F distances in 3 are 2.139(2) and 1.938(2) A, respectively. Treatment of 1 with tetrachlorocatechol (H(2)Cl(4)cat) afforded [L(OEt)Ti(Cl(4)cat)Cl] (4). The average Ti-O(P), Ti-O(C), and Ti-Cl distances in 4 are 1.972, 1.926, and 2.334 A, respectively. Hydrolysis of 4 in the presence of Et(3)N yielded the mu-oxo dimer [(L(OEt))(2)Ti(2)(Cl(4)cat)(2)(mu-O)] (5). The average Ti-O(P), Ti-O(C), and Ti-O(Ti) distances in 5 are 2.027, 1.926, and 1.7977(9) A. Treatment of 1 with 1,1'-binaphthol (BINOLH(2)) in the presence of Et(3)N afforded [(L(OEt))(2)Ti(2)(mu-O)(2)(mu-BINOL)] x 2BINOLH(2) (6.2BINOLH(2)). Complex 1 is capable of catalyzing ring opening of epoxides with Me(3)SiN(3) under solvent-free conditions presumably via a Ti-azide intermediate.     

INFLUENCE OF BACKBONE RIGIDITY ON THE LIQUID CRYSTALLINITY OF MESOGEN-CONTAINING POLYACETYLENES

Two acetylene polymers containing cyanobiphenyl-based mesogens,poly { 10-[ ((4'- cyano-4-biphenylyl ) oxy ) carbonyl] - 1 -decyne } (PA8CN ), which has a relativelyfiexible polyalkyne backbone, and poly {[4-(((12-((4'-cyano-4-biphenylyl)oxy)dodecyl)oxy)carbonyl) phenyl]-acetylene} (PB12CN), which has a fairly rigid poly (phenylacetylene )backbone, were synthesized using respectively WCl_6 and [Rh(nbd)Cl]_2 as the catalysts.PA8CN exhibits enantiotropic interdigitated smectic A phase (S_(Ad)) over a temperaturerange as wide as ca. 100℃, whereas PB12CN is non-mesomorphic, demonstrating thatthe backbone rigidity plays an important role in determining the liquid crystallinity of thepolyacetylenes.     

Chips and Qi: microcomponent-based analysis in traditional Chinese medicine

Over the last 50 years or so Traditional Chinese medicine (TCM) has been subject to intensive basic and clinical research. Although the effectiveness and remarkable safety of TCM have been documented after controlled clinical studies, there are several herbal and animal parts that are toxic or difficult to identify. DNA polymorphism-based assays have recently been developed for the identification of herbal medicines. In this approach, small amounts of DNA are amplified by the polymerase chain reaction and the reactions products are analyzed by gel electrophoresis, sequencing, or hybridization with species-specific probes. With the DNA based identification of TCM materials as an example, chip-based analytical micro devices were developed with the goal of fabricating an integrated device that will enable sample preparation, amplification, and analysis on a single microchip-based device ("lab-on-a-chip"). The application of a silicon-based polymerase chain reaction microreactor and a DNA microarray for the DNA sequence-based identification of toxic medicinal plants is reported here.     

Equilibrium studies of the sorption of Cu(II) ions onto chitosan

Chitosan is a polymer that can be obtained from the shells of seafood such as prawns, crabs, and lobsters. Chitosan has free amino groups, which can attract metal ions, and has been used as an adsorbent for the removal of metal ions from effluents. In this research, the sorption of copper ions from solution onto chitosan at two pHs has been investigated. DSC, TGA, surface area, SEM, and NMR studies have been used to report the pure physical states of chitosan and the chitosan-copper complex. The experimental isotherm data were analyzed using the Langmuir, Freundlich, and Redlich-Peterson equations. Correlation coefficients were determined for each isotherm analysis. Error functions have been used to determine the alternative single component parameters by nonlinear regression due to the inherent bias in using the correlation coefficient resulting from linearization. The error function method provided the best parameters for the isotherm equations in this system and is demonstrated for error comparison purposes.     

A Density Functional Study of Substituent Effects on the O-H and O-CH(3) Bond Dissociation Energies in Phenol and Anisole

The substituent effects on O-H and O-CH(3) bond dissociation energies for a series of 18 para-substituted phenols (p-XC(6)H(4)OH) and 11 para-substituted anisoles have been studied using the density functional method in order to understand the origin of these effects. The calculated substituent effects agree well with experimental measurements for phenols but are substantially larger than the reported values for anisoles. Both ground-state effect and radical effect contribute significantly to the overall substituent effect. An electron-donating group causes a destabilization in phenols or anisoles (ground-state effect) but a stabilization in the phenoxy radicals (radical effect), resulting in reduced O-R bond dissociation energy. An electron-withdrawing group has the opposite effect. In most cases, the radical effect is more important than the ground-state effect. There is a good correlation between the calculated radical effects and calculated variations in charge and spin density on the phenoxy oxygen. This supports the concept that both polar and spin delocalization effects influence the stability of the phenoxy radical. While almost every para-substituent causes a stabilization of the phenoxy radical by spin delocalization, electron-donating groups stabilize and electron-withdrawing groups destabilize the phenoxy radical by the polar effect.     

Stoichiometric and catalytic oxidations of alkanes and alcohols mediated by highly oxidizing ruthenium-Oxo complexes bearing 6, 6'-dichloro-2,2'-bipyridine

The ruthenium(II) complex cis-[Ru(6, 6'-Cl(2)bpy)(2)(OH(2))(2)](CF(3)SO(3))(2) (1) is a robust catalyst for C-H bond oxidations of hydrocarbons, including linear alkanes, using tert-butyl hydroperoxide (TBHP) as terminal oxidant. Alcohols can be oxidized by the "1 + TBHP" protocol to the corresponding aldehydes/ketones with high product yields at ambient temperature. Oxidation of 1 with Ce(IV) in aqueous solution affords cis-[Ru(VI)(6, 6'-Cl(2)bpy)(2)O(2)](2+), which is isolated as a green/yellow perchlorate salt (2). Complex 2 is a powerful stoichiometric oxidant for cycloalkane oxidations under mild conditions. Oxidation of cis-decalin is highly stereoretentive; cis-decalinol is obtained in high yield, and formation of trans-decalinol is not observed. Mechanistic studies showing a large primary kinetic isotope effect suggest a hydrogen-atom abstraction pathway. The relative reactivities of cycloalkanes toward oxidation by 2 have been examined through competitive experiments, and comparisons with Gif-type processes are presented.     

Synthesis and red luminescence of Pr-doped CaTiO3 nanophosphor from polymer precursor

Uniform and sphere-like nanoparticles of crystalline Pr³⁺-doped CaTiO₃ have been prepared from complex polymer precursor at 600°C, in which, metal atoms are previously dispersed by citric acid in ethylene glycol solvent. The decomposition process of the precursor, crystallization, and particle sizes of CaTiO₃ have been investigated by using thermal analysis, powder X-ray diffraction and transmission electron microscopy. Diffuse reflectance spectra, photoluminescence and decay curve indicate that a strong red emission located at the nearly NTCS “ideal red” site is deduced from the energy transfer from the band gap absorption to doping Pr³⁺ ions. The thermoluminescence curves exhibit that a potential long phosphorescent material based on Pr³⁺-doped CaTiO₃ will be explored in future.     

Structural and bonding characteristics in transition metal-silane complexes

Transition metal-silane complexes containing metal-eta 2-H-Si coordination display different structural and bonding characteristics in comparison to other sigma-complexes, such as dihydrogen and alkane (agostic) complexes. The different characteristics can be related to the strong sigma*-accepting properties of the eta 2-silane ligand(s) because of the weaker H-Si sigma bond. Various examples of metal-silane complexes have been reviewed and their structural stabilities have been systematically discussed. Silyl-hydride complexes having substantial silyl-hydrido interactions have also been emphasized.