Lower bounds for blow-up time in a nonlinear parabolic problem

For a parabolic problem with a gradient nonlinearity which was introduced by Chipot and Weissler [M. Chipot, F.B. Weissler, Some blow up results for a nonlinear parabolic problem with a gradient term, SIAM J. Math. Anal. 20 (1989) 886-907] (see also [B. Kawohl, L.A. Peletier, Observations on blow up and dead cores for nonlinear parabolic equations, Math. Z. 202 (1989) 207-217]), the question of blow-up is investigated. Specifically, if the solution blows up, a lower bound for the time of blow-up is derived     

Isoperimetric inequalities for polarization and virtual mass

This paper is the continuation of a previous investigation. Here representations for the components of the virtual mass and polarization tensors in terms of boundary integrals are given and new isoperimetric inequalities for star-shaped bodies are derived. Research supported by NSF Grant, MCS 8300842. Research supported by Natural Sciences and Engineering Research Council Canada.     

(Benzo[4, 5]cyclohepta[l, 2-b]thiophen-4-ylidene)acetic Acids: Novel Non-ulcerogenic Antiinflammatory Agents

Compound (Z)- 8a has been found to display interesting antiinflammatory activity. In order to prepare derivatives with a wide variety of substituents in the aromatic part of the molecule, a new synthesis of the key intermediates 9a-g was developed starting from thiophene-3-carboxylic acid ( 11 ) and substituted benzyl bromides. The conversion of 9a-g to 10a-g follows a known procedure. Ketones 10a-g , on reaction with alkyl (dialkoxy-phosphoryl)acetate, followed by isomer separation and alkaline ester hydrolysis, yielded the desired derivatives (Z)- 8a-g and (E)- 8a-g . The biologically most interesting compound (Z)- 8a is currently undergoing clinical trials.     

On the geometric form of solutions of a free boundary problem involving galvanization

In [6], T. I. Vogel studied a free boundary problem originating in the galvanization process. He showed that if the given boundary Γ* is starlike or convex, then so is the free boundary solution Γ. Our purpose is to generalize Vogel's second result by showing (under certain assumptions) that Γ cannot have more (local) maxima or minima (relative to a given direction) than Γ*; also that Γ cannot have more inflection points or greater total curvature than Γ*. The author has already proven analogous results for the Bernoulli free boundary problem in [1], [2] and [3].     

Por?se Tonfilter

Ohne Zusammenfassung     

X‐ray photoelectron spectroscopic chemical state quantification of mixed nickel metal,oxide and hydroxide systems

Quantitative chemical state X‐ray photoelectron spectroscopic analysis of mixed nickel metal, oxide, hydroxide and oxyhydroxide systems is challenging due to the complexity of the Ni 2p peak shapes resulting from multiplet splitting, shake‐up and plasmon loss structures. Quantification of mixed nickel chemical states and the qualitative determination of low concentrations of Ni(III) species are demonstrated via an approach based on standard spectra from quality reference samples (Ni, NiO, Ni(OH)₂, NiOOH), subtraction of these spectra, and data analysis that integrates information from the Ni 2p spectrum and the O 1s spectra. Quantification of a commercial nickel powder and a thin nickel oxide film grown at 1‐Torr O₂ and 300 °C for 20 min is demonstrated. The effect of uncertain relative sensitivity factors (e.g. Ni 2.67 ± 0.54) is discussed, as is the depth of measurement for thin film analysis based on calculated inelastic mean free paths. Copyright © 2009 John Wiley & Sons, Ltd.     

Flashlamp-pumped laser performance of LiCaAIF6:Cr3+

The results of flashlamp pumping of the LiCaAIF₆:Cr³⁺ (Cr:LiCAF) laser crystal are reported. We have so far obtained slope efficiencies as high as 1.55% in a close-coupled, diffusely reflecting cavity. Based on the measured insertion loss of the presently available material, we predict that an efficiency of about 4% will be obtained when low-loss material becomes available. This extrapolated efficiency is comparable with the performance of a high-quality alexandrite laser rod in the same apparatus.     

Total synthesis and antimalarial activity of symplostatin 4

The first total synthesis of symplostatin 4, a marine cyanobacterium-derived natural product, is described. Notable features of the route include the efficient preparation of three key fragments and final assembly to the natural product via sequential imide and amide couplings. Symplostatin 4 was also demonstrated to possess significant antimalarial activity (ED(50) of 74 nM against Plasmodium falciparum, strain 3D7).     

N,N′‐Diethyl‐4‐nitrobenzene‐1,3‐diamine, 2,6‐bis(ethylamino)‐3‐nitrobenzonitrile and bis(4‐ethylamino‐3‐nitrophenyl) sulfone

N,N′‐Diethyl‐4‐nitrobenzene‐1,3‐diamine, C₁₀H₁₅N₃O₂, (I), crystallizes with two independent molecules in the asymmetric unit, both of which are nearly planar. The molecules differ in the conformation of the ethylamine group trans to the nitro group. Both molecules contain intramolecular N—H...O hydrogen bonds between the adjacent amine and nitro groups and are linked into one‐dimensional chains by intermolecular N—H...O hydrogen bonds. The chains are organized in layers parallel to (101) with separations of ca 3.4 Å between adjacent sheets. The packing is quite different from what was observed in isomeric 1,3‐bis(ethylamino)‐2‐nitrobenzene. 2,6‐Bis(ethylamino)‐3‐nitrobenzonitrile, C₁₁H₁₄N₄O₂, (II), differs from (I) only in the presence of the nitrile functionality between the two ethylamine groups. Compound (II) crystallizes with one unique molecule in the asymmetric unit. In contrast with (I), one of the ethylamine groups, which is disordered over two sites with occupancies of 0.75 and 0.25, is positioned so that the methyl group is directed out of the plane of the ring by approximately 85°. This ethylamine group forms an intramolecular N—H...O hydrogen bond with the adjacent nitro group. The packing in (II) is very different from that in (I). Molecules of (II) are linked by both intermolecular amine–nitro N—H...O and amine–nitrile N—H...N hydrogen bonds into a two‐dimensional network in the (10) plane. Alternating molecules are approximately orthogonal to one another, indicating that π–π interactions are not a significant factor in the packing. Bis(4‐ethylamino‐3‐nitrophenyl) sulfone, C₁₆H₁₈N₄O₆S, (III), contains the same ortho nitro/ethylamine pairing as in (I), with the position para to the nitro group occupied by the sulfone instead of a second ethylamine group. Each 4‐ethylamino‐3‐nitrobenzene moiety is nearly planar and contains the typical intramolecular N—H...O hydrogen bond. Due to the tetrahedral geometry about the S atom, the molecules of (III) adopt an overall V shape. There are no intermolecular amine–nitro hydrogen bonds. Rather, each amine H atom has a long (H...O ca 2.8 Å) interaction with one of the sulfone O atoms. Molecules of (III) are thus linked by amine–sulfone N—H...O hydrogen bonds into zigzag double chains running along [001]. Taken together, these structures demonstrate that small changes in the functionalization of ethylamine–nitroarenes cause significant differences in the intermolecular interactions and packing.