Convexity properties of holomorphic mappings in

Not many convex mappings on the unit ball in for are known. We introduce two families of mappings, which we believe are actually identical, that both contain the convex mappings. These families which we have named the ``Quasi-Convex Mappings, Types A and B' seem to be natural generalizations of the convex mappings in the plane. It is much easier to check whether a function is in one of these classes than to check for convexity. We show that the upper and lower bounds on the growth rate of such mappings is the same as for the convex mappings.

     

Cationic cyclic carbene or carbon-bonded ylide complexes of iridium(III) and platinum(II)

2-Chloro-4-methylthiazole, 2-chlorobenzoxazole and 2-chlorobenzthiazole oxidatively add to both [IrCl(CO)(PMe₂Ph)₂] and [Pt(PhCHCHPh)(PEt₃)₂]; protonation of the products at nitrogen produces cationic carbene complexes.     

Alkoxide attack at carbonyl and hydrosulphide attack at isocyanide in the mixed carbonyl-isocyanide cation [OsCl(CO)2(CNR)(PPh3)2]+. A new synthesis of π-bound isothiocyanate (RNCS) complexes

[OsCl(CO)₂(CNR)(PPh₃)₂]⁺ (R = p-tolyl) reacts with OMe^? to give OsCl(CO₂Me)(CO)(CNR)(PPh₃)₂ but reaction with SH^? produces the π-bound p-tolylisothiocyanate complex, Os(η²-SCNR)(CO)₂(PPh₃)₂, which can be protonated or methylated at N to yield complexes containing bidentate thiocarboxamido-ligands.     

Flow and heat transfer in a second grade fluid over a stretching sheet

An analysis is carried out to study the flow and heat transfer characteristics in a second grade fluid over a stretching sheet with prescribed surface temperature including the effects of frictional heating, internal heat generation or absorption, and work due to deformation. In order to solve the fourth-order non-linear differential equation, associated with the flow problem, a fourth boundary condition is augmented and a proper sign for the normal stress modulus is used. It is observed that for a physical flow problem the solution is unique. The solutions for the temperature and the heat transfer characteristics are obtained numerically and presented by a table and graphs. Furthermore, it is shown that the heat flow is always from the stretching sheet to the fluid.     

Starch‐graft‐copolymer latexes initiated and stabilized by ozonolyzed amylopectin

A method is presented for synthesizing surfactant‐free latexes comprising a starch‐graft‐vinyl polymer, (1) starting with a suspension of the highly branched starch amylopectin, either native or degraded, (2) then using ozonolysis to create free‐radical initiation sites on this amylopectin scaffold, and (3) finally adding the monomer and inducing polymerization. The ozone simultaneously thins the starch and creates initiating/grafting sites on the starch, from which starch‐graft‐copolymer latexes can be grown. The encapsulation of starch inside the hydrophobic polymer particles created by a heterogeneous free‐radical polymerization process is demonstrated with energy‐dispersive spectroscopy; this is the first time that the particle morphology of such a latex has been so characterized. The data unambiguously prove that low‐molar‐mass degraded starch can be encapsulated within a latex particle. The underlying mechanisms have been explored, and data quantifying the rates of production of hydroperoxides by ozone, the thermal decomposition of the starch hydroperoxides so formed, and the degradation of amylopectin by ozone are reported. The activation energy for the thermal decomposition of the starch macroinitiator, determined in this work to be 125 ± 8 kJ mol⁻¹, is consistent with the proposition that the initiating species are mainly hydroperoxides. Colloidally stable poly(styrene‐co‐n‐butyl acrylate) latexes based on high‐molar‐mass amylopectin have been developed. These are stable against electrolytes (several months in 4 mol L⁻¹ NaCl), with 20% of the starch effectively grafted to the particles. Films cast from such latexes are more pliable than starch films and are readily redispersed in water. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5832–5845, 2006     

Synthesis of isomeric angularly annealed dinaphthoporphyrin systems: examination of the relative positioning and orientation of ring fusion as factors influencing the porphyrin chromophore

Porphyrins built up from two naphtho[1,2-c]pyrrole subunits and two beta-substituted pyrroles can produce five isomeric dinaphthoporphyrin systems. To gain insights into the effects of ring fusion on extended porphyrin chromophores, all five of these systems were synthesized in isomerically pure form. In four of these syntheses, dihydronaphthopyrroles were used to introduce one or both of the naphthalene subunits, and dehydrogenation with DDQ in refluxing toluene later produced the fully conjugated systems. Naphthopyrroles were also prepared by reacting isocyanoacetate esters with 1-nitronaphthalene in the presence of a phosphazene base. These compounds proved to be less stable than their dihydronaphthopyrrolic counterparts but could still be utilized in these synthetic studies. Three isomeric adj-dinaphthoporphyrin systems were prepared using the MacDonald "2 + 2" condensation or by the cyclization of a,c-biladiene intermediates with copper(II) chloride or AgIO(3)-Zn(OAc)(2). A dinaphthoporphyrin with two naphthalene units pointing toward one another could only be obtained in low yields due to a combination of stability and steric factors, but the other two adj-difused systems were isolated in good overall yields. However, the final dehydrogenation step occurred in moderate yields (50-60%) and could only be performed when the porphyrins bore propionate ester side chains that produced sufficient solubility in organic solvents. The two related opp-dinaphthoporphyrins were synthesized by a "head-to-tail" self-condensation of a dipyrrylmethane aldehyde, or a "3 + 1" synthesis using a tripyrrane intermediate bearing two fused dihydronaphthalene moieties, in excellent yields. In both cases, a final dehydrogenation step was required, but the opp-dinaphthoporphyrins were consistently formed in virtually quantitative yields. The opp-dinaphthoporphyrin series gave UV-vis spectra with relatively strong Soret bands at 425 nm, and the visible region was dominated by an unusually strong Q-band III. The adj-dinaphthoporphyrins produced broader less intense Soret bands and four well-defined Q-bands, including a relatively strong absorption at 645 nm. However, the relative orientation of the naphthalene rings had no significant effects on these spectra. On the other hand, the dications produced in TFA-chloroform solutions showed more discrimination between the individual porphyrin systems, and the metallo derivatives also displayed significant variations in their electronic absorption spectra.     

Direct observation of orbital ordering in La0.5Sr1.5MnO4 using soft x-ray diffraction

We report the first direct resonant soft x-ray scattering observations of orbital ordering. We have studied the low temperature phase of La0.5Sr1.5MnO4, a compound that displays charge and orbital ordering. Previous claims of orbital ordering in such materials have relied on observations at the manganese K edge. These claims have been questioned in several theoretical studies. Instead we have employed resonant soft x-ray scattering at the manganese L(III) and L(II) edges which probes the orbital ordering directly. Energy scans at constant wave vector are compared to theoretical predictions and suggest that at all temperatures there are two separate contributions to the scattering: direct orbital ordering and strong cooperative Jahn-Teller distortions of the Mn3+ ions.     

Vancomycin resistance in enterococci: reprogramming of the D-ala-D-Ala ligases in bacterial peptidoglycan biosynthesis

Vancomycin binds to bacterial cell-wall intermediates to achieve its antibiotic effect. Infections of vancomycin-resistant enterococci are, however, becoming an increasing problem; the bacteria are resistant because they synthesize different cell-wall intermediates. The enzymes involved in cell-wall biosynthesis, therefore, are potential targets for combating this resistance. Recent biochemical and crystallographic results are providing mechanistic and structural details about some of these targets.     

The X-ray structure of Os(CS)(PhCCPh)(PPh3)2, a complex containing a four-electron donor acetylene ligand

Os(CS)(PhC?CPh)(PPh₃)₂ is formed by the treatment of Os(CS)(CO)(PPh₃)₃ with diphenylacetylene and is an example of a complex containing a four-electron donor acetylene ligand. Os(CS)(PhC?CPh)(PPh₃)₂ crystallizes in the monoclinic space group P2₁/n with the cell dimensions a = 9.028(5), b = 25.256(2) and c = 19.22(2) Å with β = 103.8(7)°, V = 4260 ų, Z = 4 and d(calcd) = 1.461 g cm^?3 for mol.wt 937.09 g mol^?1. Diffraction data were collected with a Nonius CAD-4 diffractometer and refined to R = 4.05% and R_w = 4.19% for 1172 independent reflections. The structure can be described as a distorted trigonal bipyramid with the CS ligand occupying an axial position. The two cis-PPh₃ ligands are in equatorial sites with the acetylene occupying a position between the remaining axial and equatorial sites. The diphenylacetylene is symmetrically bound to the metal with an average Os? C distance of 2.04(3) Å. The Os? CS distance is unusually short at 1.79(2) Å.