The first <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>-cohomology of some groups with one end

Let p be a real number greater than one. In this paper we study the vanishing and nonvanishing of the first L ^p -cohomology space of some groups that have one end. We also make a connection between the first L ^p -cohomolgy space and the Floyd boundary of the Cayley graph of a group. We apply the result about Floyd boundaries to show that there exists a real number p such that the first L ^p -cohomology space of a nonelementary hyperbolic group does not vanish. Received: 4 August 2006 Revised: 2 November 2006     

Two methods for semi-automated quantification of changes in ventricular volume and their use in schizophrenia

Two semi-automated methods for quantification of ventricular volume change from baseline and follow-up magnetic resonance imaging scans have been developed. Technique 1 employs direct segmentation of the ventricles from both the scans using thresholding and contour extraction. Technique 2 operates on difference images produced by voxel based intensity subtraction of the baseline from the registered follow-up images. Here, all voxels with intensities above a noise threshold and in a restricted area are monitored to compute volumetric changes. In phantom measurements the first technique was accurate to 0.0046%, the second to 0.167% of the phantom volume. Results from normal volunteers was that the average ventricular volume changed by 1.52% and 1.54% for images acquired within 9 months using techniques 1 and 2, respectively. With schizophrenic patients mean change of 10.78% and 9.43% were found employing the first and second procedures, respectively. All measurements agreed with a radiologist’s visual grading of the changes. Robust, objective, fast, easy-to-use, and fairly accurate procedures have been developed and validated to quantify volumetric changes.     

Proper holomorphic maps between Reinhardt domains and strictly pseudoconvex domains

LetR be a Reinhardt domain andD a bounded simply connected strictly pseudoconvex domain withC ^∞ boundary. We prove that any proper holomorphic mapF:R →D is, up to biholomorphism ofD, of the form \((z_1^{d_1 } , z_2^{d_2 } , \ldots , z_n^{d_n } )\) withd ₁,d ₂,…,d _n ∈ IN.     

Exciton-related optical nonlinearities in semiconductors and semiconductor microcrystallites

We report on large optical nonlinearities due to specific many-body effects in high-density electron-hole pair systems. On bulk CdS we study the effect of free-carrier screening on the absorption and refraction in the vicinity of the band-gap at room temperature. Steady-state saturable absorption at mW-power levels and four-wave mixing with first-order efficiencies as large as 2% of the incoming light are demonstrated on a 1m slab. On CuBr microcrystallites embedded in glass we investigate the changes of the exciton absorption caused by many-exciton effects both at cryo and room temperature. In contrast to bulk semiconductors, we observe a blue shift of the exciton peak at resonant optical excitation. In addition, strong saturation of absorption with very large contrast shows up. We find Lorentzian saturation intensities in the 100 kW/cm² range.     

The preparation of 4-oxo-N-aryl-4H-1-benzopyran-2-acetamides by the condensation/cyclization of trilithiated acetoacetanilides with lithiated methyl salicylates

Several acetoacetanilides were trilithiated in excess lithium diisopropylamide, and the resulting polylithiated intermediates were regioselectively condensed with lithiated methyl salicylates followed by acid cyclization to substituted 4-oxo-N-aryl-4H-1-benzopyran-2-acetamides (benzopyranone-2-acetamides).     

Reactions of Molecules with Two Equivalent Functional Groups. 5. Anomalous Reactivity of 1,10-Cyclooctadecanedione. Crystal and Molecular Structures of cis,cis-1,10-Diphenyl-1,10-cyclooctadiene and the Stereoisomers of 1,10-Diphenyl-1,10-cyclooctadecanediol(1)

The reaction of the title diketone (3) with phenyl Grignard produces (with rate constant k(1)) the conjugate base (6-M) of 10-hydroxy-10-phenylcyclooctadecanone (6), which is subsequently converted (with rate constant k(2)) to the conjugate base of the title diol, as a mixture of the cis (7, 55%) and trans (8, 45%) isomers. The ratio k(2)/k(1), 2.2 +/- 0.4, indicates that the carbonyl group in 6-M is 4.4 times as reactive as each carbonyl in 3. Competition experiments further demonstrate that the relative rates (per carbonyl) for addition of phenylmagnesium bromide to 3, 10-methylenecyclooctadecanone (11), and cyclopentadecanone (12) are 1.0:0.60:1.92. Possible reasons for this order of reactivity are discussed. Diols 7 and 8 undergo facile double dehydration to form the title diene 13, which is predicted by molecular mechanics calculations to be the most stable of the four possible symmetrical diene isomers. The structures of 7, 8, and 13 were secured by single-crystal X-ray studies.     

HPLC determination of 2-furaldehyde and 5-hydroxymethyl-2-furaldehyde in alcoholic beverages

A method for the determination of 2-furaldehyde (F) and 5-hydroxymethyl-2-furaldehyde (HMF) in alcoholic beverages by high performance liquid chromatography (HPLC) is described. A C-18 column and an acetonitrile-water mobile phase with isocratic elution were used. UV detection at 280 nm was carried out. The method was validated according to the EURACHEM guidelines. The procedure offers a high specificity and detection limits of the order of 0.005 μg mL^− 1. Recoveries of 94-103% were obtained from spiked samples at different levels with both analytes. Intermediate precision calculated for a period of 2 months was + 0.8% for HMF and + 0.4% for F. The method was applied to the analysis of alcoholic beverages like bourbon, rum, brandy, liquors and aperitif wines.     

5-vinylisoxazole

Cycloaddition of fulminic acid to 1-butyn-3-ol gave a mixture of 5-α-hydroxyethylisoxazole (I) and 4-α-hydroxyethylisoxazole (II) in the ratio 9:1. By the dehydration of 1, 5-vinylisoxazole (III) was obtained. Compound III has also been prepared by cyclization of 4-penten-2-ynal as well as its diethylacetal with hydroxylamine hydrochloride; in both instances no isomers have been obtained. Compound III spontaneously polymerizes even at room temperature yielding a polymer still containing isoxazole rings.     

Synthesis of some 4-substituted-2-(o-halogenophenyl)-1,2,3-triazoles

Mesoaldehyde 1,3-dioxime was treated with either 2,4,6-trichlorophenyl- (a), o-fluorophenyl- (b), or o-bromophenyl- (c) hydrazine to give the corresponding mesoaldehyde 1,3-dioxime-2-halogenophenylhydrazones (1a,b,c). The latter were O-acetylated with acetic anhydride, and cyclized to triazole 4-oximes (3b, c) or triazole 4-O-acetyloximes ( 6a,b,c ) with cesium carbonate, then converted to nitriles ( 7a,b,c ) by refluxing with acetic anhydride followed by pyrolysis, or to aldehydes ( 4a,b,c ) by hydrolysis. The nitriles ( 7a,b,c ) were also converted to acids ( 9a,b,c ), esters ( 10a,b,c ), amides ( 8a,c ), an alcohol (11a), and an amine ( 12a ). In addition, tetrazoles of two types were prepared. The first ( 13d,e ) were obtained from the acid chlorides by the action of 5-aminotetrazole, whereas the second ( 14f ) was produced from the respective nitrile by the action of ammonium azide.     

Addition reaction of azido-exTTFs to C60: synthesis of fullerotriazoline and azafulleroid electroactive dyads

[structure: see text] The addition reaction of azido-exTTFs to C(60) affords electroactive fullerotriazoline and azafulleroid dyads, which behave as amphoteric redox systems. Fluorescence experiments and transient absorption spectroscopy reveal that excitation of the fullerene moiety leads to radical pair lifetimes that are 2 orders of magnitude higher than those previously reported for related fullerotriazolines.