Remark on pathwise uniqueness of stochastic differential equations driven by Lévy processes

Consider real-valued processes determined by stochastic differential equations driven by Lévy processes. The jump parts of the driving Lévy process are not always α-stable ones, nor symmetric ones. In the present article, we shall study the pathwise uniqueness of the solutions to the stochastic differential equations under the conditions on the coefficients that the diffusion and the jump terms are Hölder continuous, while the drift one is monotonic. Our approach is based on Gronwall’s inequality.     

A new method for generation of non-stabilized α-amino-substituted carbanions by the reaction of magnesium carbenoids with N-lithio arylamines: their reactivity and a new synthesis of α-amino acid derivatives

Magnesium carbenoids were generated from aryl 1-chloroalkyl sulfoxides with i-PrMgCl in THF at low temperature in quantitative yields. The magnesium carbenoids were found to be reactive with N-lithio alkylamines to afford an olefin, which was derived from dimerization of the magnesium carbenoid, in moderate yield. On the other hand, reaction of the magnesium carbenoids with N-substituted N-lithio arylamines gave non-stabilized α-amino-substituted carbanions in good yields. Reactivity of the α-amino-substituted carbanions with some electrophiles was investigated and it was found that ethyl chloroformate reacted to give α-amino acid derivatives in good yields. As a whole, a new method for one-pot, three-component combined synthesis of α-amino acid derivatives from aryl 1-chloroalkyl sulfoxides was realized.     

Preparation of the enantiopure 1,2-diamine monomer and its polymerization: The efficient polymeric chiral ligand of an asymmetric hydrogenation catalyst

An enantiopure 1,2-diamine monomer possessing a p-vinylbenzyl group as a polymerizable group was synthesized from chiral 1,2-bis(p-hydroxyphenyl)-N,N′-bis(tert-butoxycarbonyl)-1,2-diaminoethane. The chiral monomer was copolymerized with styrene, and this was followed by the deprotection of the tert-butoxycarbonyl group, which yielded the polymer-supported chiral 1,2-diamine. The polymeric catalyst system was established with the polymeric chiral 1,2-diamine complexed with 2,2′-bis(diphenylphosphino)-1,1′-binaphthyl/RuCl₂. In the presence of potassium tert-butoxide (t-BuOK), the polymeric catalyst system worked well in the asymmetric hydrogenation of aromatic ketones. The corresponding chiral secondary alcohols were obtained in quantitative yields with a high level of enantioselectivity. The insolubility of the catalyst, caused by the crosslinked structure of the polymer, made it recyclable. The polymeric catalyst was reused several times without a loss of catalytic activity. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4556–4562, 2004     

Spatially defined silver mirror reaction on a micropatterned aldehyde-terminated self-assembled monolayer

A simple microfabrication technique for silver (Ag) based on spatially defined silver mirror reaction using a photolithographically micropatterned aldehyde (CHO)-terminated self-assembled monolayer (SAM) is proposed. First, both a Si substrate covered with native oxide and a quartz glass plate were exposed to a vapor of triethoxysilylundecanal (TESUD) diluted with absolute toluene for 3 h at 403 K. This vapor phase treatment produced a 1.2-nm-thick TESUD-SAM with a flat, homogeneous surface. Several samples were then photolithographically micropatterned using an excimer lamp radiating 172 nm vacuum ultraviolet light, and subsequently employed as templates for area-selective electroless Ag plating. Optical microscopy, atomic force microscopy (AFM) and X-ray photoelectron spectroscopy (XPS) confirmed that Ag metal was preferentially deposited on the CHO-terminated regions, resulting in the formation of well-ordered Ag microstructures composed of rectangular 5 μm × 25 μm features. The CHO terminal groups of the TESUD-SAM were found to be effective in reducing Ag ionic species at the solid/liquid interface.     

Visual colorimetry for trace antimony(V) by ion-pair solid-phase extraction with bis[2-(5-chloro-2-pyridylazo)-5-diethylaminophenolato]cobalt(III) on a PTFE type membrane filter.

A new visual colorimetry for trace antimony(V) based on ion-pair solid-phase extraction to a PTFE-type membrane filter with bis[2-(5-chloro-2-pyridylazo)-5-diethylaminophenolato]cobalt(III) ion ([Co(5-Cl-PADAP)(2)](+)) has been developed. Experiments showed that hexachloroantimonate(V) ion (SbCl(6)(-)) was adsorbed with [Co(5-Cl-PADAP)(2)](+) to the front surface of the PTFE filter. The adsorption of antimony(V) ion was promoted by the addition of lithium chloride as a source of chloride ion. The excess reagent of [Co(5-Cl-PADAP)(2)](+) was eluted by rinsing with a 10 wt% methanol aqueous solution. In this case, the slow rate of the hydrolysis reaction of SbCl(6)(-) and the difference of the hydrophobicity of the ion pairs were important for adsorption and separation with a PTFE-type membrane filter. The antimony(V) concentration was determined through a visual comparison with a standard series. The visual detection limit was 0.10 microg. The calibration curve assessed with the reflection spectrometric responses at 580 nm was linear in the concentration range of 0.10 - 1.2 microg (r = 0.996). The proposed method has been applied to the determination of sub-microgram levels of antimony(V) ion in water samples.     

Selective oxidation of n-butane over Fe-promoted vanadyl pyrophosphate prepared from modification of nano-sized interlayer of lamellar vanadyl benzylphosphate

A novel approach for the preparation of promoted vanadyl pyrophosphate in well-defined structure was examined. Lamellar vanadyl benzylphosphate (LVBP) was used as a host material and iron acetylacetonate as a guest. It was found that iron acetylacetonate was successfully inserted into the interlayer of LVBP by heating of LVBP and iron acetylacetonate in toluene solution. Calcination of this in tercalated material resulted in a well-crystallized vanadyl pyrophosphate phase with uniform dispersion of Fe in bulk and surface. The obtained Fe-promoted vanadyl pyrophosphate showed an enhancement in the activity for selective oxidation of n-butane, especially at high temperature and long contact time.     

Samarium enolate on crosslinked polystyrene beads. II. An anionic initiator for the well‐defined synthesis of poly(allyl methacrylate) on a solid support

A samarium enolate, supported on a crosslinked polystyrene resin, successfully initiated the living anionic polymerization of allyl methacrylate (AMA) to afford the corresponding poly(AMA) with well‐controlled molecular weights. Diblock, triblock, and tetrablock copolymerizations with methyl methacrylate (MMA) were also successfully performed. The formed polymers, supported on the resin by a benzyl ester linker, were quantitatively isolated from the resin by selective cleavage of the linker with trifluoroacetic acid (TFA). Allyl ester in the side chain was not affected by this isolation step. The allyl group of the immobilized poly(AMA‐b‐MMA) on the resin was transformed into a 2,3‐dihydroxypropyl group by osmium oxidation. The resulting copolymer was isolated by TFA treatment of the resin, and it showed amphiphilicity. In both the polymerization and side‐chain modification, the formed polymers were easily washed from excess reagents only by filtration, and this demonstrated the feasibility of the automated synthesis of functional polymers based on this solid‐supported polymerization technique. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 853–860, 2003     

Optical Design of a Space Retroreflector Using a Hybrid Search

Retroreflectors on satellites are used as targets for laser ranging and laser long-path absorption measurements of atmospheric trace species. To compensate for the velocity aberration, slight tuning of the design is necessary. The curvatures of mirrors, the angles between mirrors, and the direction of the retroreflector on the satellite must be tuned to optimize the optical efficiency of the retroreflector. An enumerative scheme is not applicable when the number of parameters is large. We proposed earlier a technique using a genetic algorithm for the optical design of a space retroreflector.¹⁾ In this paper, we have improved the method introducing a hybrid technique that is a combination of a genetic algorithm and simulated annealing.     

New method for calculating reflected wave fronts of acute retroreflectors with tuned dihedral angle

An acute retroreflector having dihedral angles of 45, 60 and 90 deg exactly reflects incident rays in the opposite direction. Beam pattern or wave front of the reflected light of the acute retroreflector can be controlled by tuning dihedral angles. We present here a new method for calculating the reflected wave front of the acute retroreflector, in which the wave front is calculated with high accuracy and in a shorter calculation time than by the conventional ray trace method.