Functions of ann-dimensional Brownian motion that are Markovian

Letf be a continuous function fromR ⁿ toR and letX(t)=(X ₁ (t), …, X _n (t)) be a Brownian motion onR ⁿ . The explicit form off necessary in order to makef(X(t)) a Markov process is determined.     

Ferrimagnetic damping of epitaxial garnet film Yb1.7Eu1.3Ga0.5Fe4.5O12

The criterion for selecting rare-earth ions in iron garnet to achieve low damping and high magnetic mobility is established using the slow ferrimagnetic relaxation theory of Van Vleck and Orbach. Ytterbium and europium are excellent candidates to form mixed rare-earth iron garnet for magnetic bubble applications. An epitaxial film of Yb_1.7Eu_1.3Ga_0.5Fe_4.5O₁₂ was grown on a {111} gadolinium gallium substrate, and its low Landau-Lifshitz damping parameter λ/γ² = 1.1 × 10^?7 oe²-sec-rad^?1 was demonstrated by measuring the ferrimagnetic resonance line width.     

Syntheses of 1,5-dideoxy-1,5-imino-D-mannitol from D-mannose and from D-glucose

Unambiguous enantiospecific syntheses of 1,5-dideoxy-1,5-imino-D-mannitol (LU1, 1-deoxy-mannojirimycin) are reported (i) from D-mannose via hydrogenation of a 5-azido-5-deoxy mannose, and (ii) from D-glucose, in which the key step involves nucleophilic substitution of a trifluoromethanesulphonyl group from C-2 of D-glucose.     

Studies towards simalikalactone D and quassimarin: construction of an advanced pentacyclic intermediate

An advanced pentacyclic intermediate, amenable to further elaboration into the target molecules simalikalactone D and quassimarin, has been synthesized from (S)-(+)-carvone in 21 steps and with an overall yield of 12 %. The synthesis is efficient, stereocontrolled, enantiospecific, and chirality productive, creating eight new chiral centres in pentacycle, and should provide opportunities for rapid access to simalikalactone D analogues and other bioactive quassinoids. The reaction sequence involves a regioselective bishydroxylmethylation, a stereocontrolled epoxidation, an epoxymethano-bridge formation, a 1,3-sigmatropic rearrangement and an intramolecular Diels-Alder reaction as the key steps.     

Effect of reaction conditions on the grafting of 2-(dimethylamino)ethyl methacrylate onto hydrocarbon substrates

The grafting of 2-(dimethylamino)ethyl methacrylate (DMAEMA) onto two model hydrocarbons, squalane and n-eicosane, and to linear low density polyethylene (LLDPE) has been investigated. The results of the study indicate that a high reaction temperature, 160°C, and a low concentration of monomer, less than 0.3 M, are optimum conditions for the grafting reaction. Reaction products, which consisted of grafted hydrocarbons and poly(DMAEMA), were separated by solvent extraction and vacuum distillation; samples were then analyzed by NMR and FTIR spectroscopy and size exclusion chromatography. ¹H-NMR spectroscopy indicates that grafted squalane contained approximately 6 DMAEMA units per squalane residue. ¹H- and ¹³C-NMR and molecular weight studies strongly suggest that the grafts onto the model hydrocarbons consist of single DMAEMA units. Results of the melt grafting of DMAEMA onto LLDPE show that the grafting efficiency and degree of grafting are substantially lower than were expected from the model system. © 1994 John Wiley & Sons, Inc.     

Benzohydrazides,benzothiohydrazides, and benzamidrazones as sources of 1,3,4(2H)-oxadiazolenones, 1,3,4(2H)-thiadiazolenones,and 1,2,4(5H)-triazolenones

Benzohydrazides, benzothiohydrazides, and benzamidrazones have been converted to 1,3,4(2H)-oxadiazolenones, 1,3,4(2H)-thiadiazolenenones, and 1,2,4(5H)-triazolenones respectively by reaction with ethyl chloroformate, with ethyl thiolchloroformate, and with phenyl isocyanate. In some reactions, a carbamate or urea has been isolated as intermediate.     

Synthesis and Nucleophilic Addition Reactions of Tricarbonyl[η5‐2‐(phenylthio)hexadienyl]iron Hexafluorophosphate

3‐Phenylthio‐3‐sulfolene ( 1 ) was readily converted to a C‐5 substituted product 2 , which upon thermolysis and complexation with Fe₂(CO)₉ gave (η⁴‐diene)iron complexes 3a and 3b . Treatment of 3a and 3b with aq. HPF₆ and Ac₂O provided the title compound 5 , which reacted regio‐ and stereospecifically with some nucleophiles to give the addition products 3b and 7 .     

Time-resolved resonance Raman spectroscopy and density functional study of 2-fluorenylnitrene and its dehydroazepine products

We report time-resolved resonance Raman spectra for 2-fluorenylnitrene and its dehydroazepine products acquired after photolysis of 2-fluorenylnitrene in acetonitrile. The experimental Raman band frequencies exhibit good agreement with the calculated vibrational frequencies from UBPW91/cc-PVDZ density functional calculations for the singlet and triplet states of the 2-fluorenylnitrene as well as BPW91/cc-PVDZ calculations for the two dehydroazepine ring-expansion product species. The decay of the 2-fluorenylnitrene Raman signal and the appearance of the dehydroazepine products suggest the presence of an intermediate species (probably an azirine) that does not absorb very much at the 416 nm probe wavelength used in the time-resolved resonance Raman experiments. Comparison of the singlet 2-fluorenylnitrene species with the singlet 2-fluorenylnitrenium ion species indicates that protonation of the nitrene to give the nitrenium ion leads to a significant enhancement of the cyclohexadienyl character of the phenyl rings without much change of the C-N bond length.     

Synthesis and fluorescence enhancement of oligophenylene-substituted calix[4]arene assemblies

Tetra-oligophenylene substituted calix[4]arene assemblies containing up to three phenylene units have been synthesized by a convergent approach using Suzuki cross-coupling and their optical properties were investigated and compared with the corresponding monomer.     

Synthesis and functional properties of strongly luminescent diphenylamino end-capped oligophenylenes

Two novel homologous series of oligophenylenes (OPPs) symmetrically end-capped with diphenylamino groups and asymmetrically end-capped with anthryldiphenylamino groups were successfully synthesized by a convergent approach with use of palladium-catalyzed homo- and cross-coupling of arylboronic acids. The absorption maxima of both diphenylamino end-capped OPP series do not vary with the chain length although the molar absorptivities increase sequentially. On the other hand, the emission maxima slightly shift to longer wavelengths when the phenylene unit increases in the series. All the diphenylamino end-capped oligomers exhibit very large fluorescence quantum yields (81-89%). They also exhibit low first ionization potentials, corresponding to the oxidation of the triarylamino moiety, which are essentially unaffected by the oligomeric length extension. The good thermal stabilities of these oligomers allowed the fabrication of multilayer light-emitting devices and their investigations.