Jacobi elliptic functions and change of variable in a convolution

We solve the functional equation

Wiener-Hopf factorisation of Brownian motion

Summary We study how Brownian motion behaves under time change by a fluctuating additive functionalA _t , in particular letting be the first passage time ofA _t to zero we computeP _–x[B dy] explicitly in certain cases. The calculation is not an easy one, our method uses the Désiré André relation for the overshoot of a Lévy process and depends on some elliptic function identities. This paper only considers the one boundary case whereA _t is increasing (resp. decreasing) on the positive (resp. negative) half line.     

Rational materials design of sorbent coatings for explosives: applications with chemical sensors

A series of chemoselective polymers had been designed and synthesized to enhance the sorption properties of polymer coated chemical sensors for polynitroaromatic analytes. To evaluate the effectiveness of the chemoselective coatings, a polynitroaromatic vapor test bed was utilized to challenge polymer coated surface acoustic wave (SAW) devices with different explosive vapors. Dinitrotoluene detection limits were determined to be in the <100 parts per trillion ranges. ATR-FTIR studies were used to determine the nature of the polymer-polynitroaromatic analyte interactions, and confirm the presence of hydrogen-bonding between polymer pendant groups and the nitro functional groups of polynitroaromatic explosive materials.     

Substituent effects on monoboronic acid sensors for saccharides based on N-phenyl-1,8-naphthalenedicarboximides

In the course of our investigations on new monoboronic acid saccharide sensors with C(0) spacers, a series of probes 1-6 based on 1,8-naphthalenedicarboximide were synthesized. Sensor 1 displays features typical of PET monoboronic acid sensors and shows high selectivity to fructose. Sensor 2 exhibits a novel dual emission and remarkable sensitivity for glucose relative to fructose and galactose through subtle changes in pH. Sensor 3 displays significantly enhanced fluorescence in the presence of galactose at low pH. Although probes 4-6 exhibit unique properties such as high quantum yield (Phi(F) = 0.407) and excellent solubility in water, they did not show significant change in fluorescence intensity in the presence of monosaccharides. The effects of substituent on all six probes lend support to the proposed photoelectrochemical model.     

Neighboring Group Participation in Glycosylation Reactions by 2,6-Disubstituted 2-O-Benzoyl groups: A Mechanistic Investigation

Variable yields and glycosylation stereoselectivity were obtained for NIS/TfOH-medi- ated reaction of 4-methoxyphenyl 2,4,6-tetra-O-acetyl-β-D-galactopyranoside and thiogalactosides bearing acetyl, benzoyl, 2,6-dimethoxylbenzoyl, 2,4,6-trimethylbenzoyl, or 2,6-dichlorobenzoyl groups at the 2-positions and acetyl at the remainder. X-ray structures of 4-methylphenyl 2,3,4,6-tetra-O-(2,4,6-trimethylbenzoyl)-1-thio-β-D-galactopyr anoside and 4-methylphenyl 3,4-O-isopropylidene-2,6-di-O-(2,4,6-trimethylbenzoyl)-1-thio-β-D-galactopyranoside revealed slightly distorted ⁴ C ₁ chair conformations. Variable temperature NMR revealed that activation of 4-methylphenyl 2,3,4,6-tetra-O-(2,4,6-trimethylbenzoyl)-1-thio-β-D-galactopyranoside afforded only dioxolenium ion, whereas 4-methylphenyl 3,4,6-tri-O-acetyl-2-O-(2,4,6-trimethylbenzoyl)-1-thio-β-D-galactopyranoside gave a 1:1 mixture of dioxolenium ion and glycosyl triflate. However, the reaction intermediates formed from these deactivated donors do not influence the glycosylation stereoselectivity; instead, it is influenced by steric and electronic interactions at the transition states.     

Observation of nanometer-scale optical property discrimination by use of a near-field scanning apertureless microscope

We examine fundamental issues related to discriminating structural and optical features in near-field scanning apertureless microscopy. We report a series of controlled experiments with nanosphere-sized standard spheres in which we observed significant differences in resolution and structure between an atomic-force microscope image and a simultaneously acquired near-field optical (NFO) image. Further, in experiments that employed a mix of dyed and undyed nanospheres we found that we can observe differences in the same NFO image for adjacent nanospheres. Therefore we conclude that near-field scanning apertureless microscopy not only meets the criteria for a NFO image but also is capable of measuring optical properties below the diffraction limit. The two-point resolution was at least 200 nm when we were detecting optical phase and 50 nm when we were detecting optical intensity. The edge response was typically 15 nm, and the minimum observable features were of the order of 3 nm.     

Thin-layer chromatography of phenolic compounds

Summary Seventeen phenolic compounds, including phenol and the isomers of cresol, have been completely separated by thin-layer chromatography with a series of solvent/support systems.

---

Zusammenfassung 17 Phenolverbindungen, darunter Phenol und die isomeren Kresole, werden dünnschichtchromatographisch mit einer Reihe von Lösungsmittel-systemen vollständig getrennt.

---

Résumé On a réalisé la séparation complète de 17 composés phénoliques, y compris le phénol et les isomères du crésol, par chromatographie en couche mince, grâce à l'emploi de différents systèmes solvant/support.

     

Electron hole condensate radiation from Ge double injection devices between 1.5° and 4.2°

Carrier injection in Ge at helium temperatures produces radiation characteristic of the electron hole condensate. Time resolved spectra are used to analyze the presence of both condensate and free exciton radiation at high power levels. Device heating is indicated.