Constructing one-parameter transformations on white noise functions in terms of equicontinuous generators

Let be a barreled locally convex space. A continuous operator on is called anequicontinuous generator if { ⁿ /n!;n=0,1,2,...} is an equicontinuous family of operators. For each equicontinuous generator a one-parameter group of operators is constructed by means of power series. There is a one-to-one correspondence between the equicontinuous generators and the locally equicontinuous holomorphic one-parameter groups of operators. If two equicontinuous generators ₁, ₂ satisfy [₁,₂]=₂ for some thena₁+b₂ is also an equicontinuous generator for anya, b. These general results are applied to a study of operators on white noise functions. In particular, a linear combination of the number operator and the Gross Laplacian, which are natural infinite dimensional analogues of a finite dimensional Laplacian, is always an equicontinuous generator. This result contributes to the Cauchy problems in white noise (Gaussian) space.Work supported by Alexander von Humboldt-Stiftung and Japan Society for Promotion of Sciences     

Stereoselective synthesis of methyl (Z)-(4,4-difluoro-2,3,4,5-tetrahydro-1H-1-benzazepin-5-ylidene)acetate using a dianion Horner-Wadsworth-Emmons reagent

Stereoselective synthesis of methyl (Z)-(4,4-difluoro-2,3,4,5-tetrahydro-1H-1-benzazepin-5-ylidene)acetate (1a) is described. Z-selectivity of the Horner-Wadsworth-Emmons (HWE) reaction was obtained based on an investigation of the reaction conditions for introduction of a methylidene group onto the 5-position of benzazepine.     

Palladium-catalyzed dimerization disilylation of 1,3-butadiene with chlorosilanes

[reaction: see text] 1,3-Butadiene reacted with chlorosilanes and Grignard reagents at 20 degrees C in the presence of a catalytic amount of Pd(acac)(2) to give disilylated dimers 2 regioselectively, which have two silyl groups (R(3)Si) at the 3- and 8-positions of a 1,6-octadiene skeleton. When phenyl- or allyl-substituted chlorosilanes were used, coupling product was obtained stereo- as well as regioselectively, giving rise to only (E)-olefins. It is proposed that Pd-ate complexes play important roles in both C-Si bond-forming processes.     

155Gd Mössbauer spectra of some Gd(III)-b-diketonato complexes

¹⁵⁵Gd Mössbauer spectra of some Gd(III)-b-diketonato complexes are reported. All of their ¹⁵⁵Gd Mössbauer isomer shift (d) values fall in a narrow range of +0.55-+0.65 mm^.s^-1, and are between those of GdF₃ and the cubic form of Gd₂O₃. This indicates that their Gd-O bonds have small covalent character. The value for quadrupole coupling constant (e²qQ) spread out from 1.67 to 7.56 mm^.s^-1 and reflects the difference well in symmetry of the coordination polyhedron around Gd(III) ions for those Gd(III)-b-diketonato complexes.     

Reaction between rare earth elements and HFNO2 solution

Rare earth elements react with HFNO₂ solution to produce nitrosylium fluorometallates (NO)_xLnF_x+3. The value of x is 1.0 or 1.5 for light rare earth elements and 0.5 or 1.0 for heavy rare earths. Nitrosylium fluorometallates of rare earth elements can be decomposed into the simple fluoride and nitrosyl fluoride at low temperatures (46–68°C).     

Carbonylation of lithium enolates with carbon monoxide mediated by selenium

[reaction: see text] Lithium enolates of ketones and aldehydes undergo carbonylation with carbon monoxide with the aid of selenium under mild conditions to yield beta-keto and beta-formyl selenol esters after trapping with alkyl iodides. This reaction proceeds via a unique carbonylation mechanism comprised of O-carbonylation and subsequent migration of the SeCO moiety to the alpha-carbon.     

Chemiluminescence sequential injection immunoassay for vitellogenin using magnetic microbeads

A rapid and sensitive immunoassay for the determination of carp vitellogenin (Vg) is described. The method involves a sequential injection analysis (SIA) system equipped with a chemiluminescence detector and a samarium-cobalt magnet. An anti-Vg monoclonal antibody, immobilized on magnetic beads, was used as a solid support for the immunoassay. The introduction, trapping and release of the magnetic beads in the flow cell were controlled by a samarium-cobalt magnet and the flow of the carrier solution. The immunoassay was based on a sandwich immunoreaction of anti-Vg monoclonal antibody (primary antibody) on the magnetic beads, Vg, and the anti-Vg antibody labeled with horseradish peroxidase (HRP) (secondary antibody), and was based on a subsequent chemiluminescence reaction of HRP with hydrogen peroxide and p-iodophenol, in a luminol solution. The magnetic beads to which the primary antibody was immobilized were prepared by coupling the primary antibody with the magnetic beads after an agarose-layer on the surface of the magnetic beads was epoxidized. The primary antibody-immobilized magnetic beads were introduced, and trapped in the flow cell equipped with the samarium-cobalt magnet, a Vg sample solution, an HRP-labeled secondary antibody solution and the luminol solution were sequentially introduced into the flow cell based on an SIA programmed sequence. Chemiluminescence emission was monitored by means of a photomultiplier located at the upper side of the flow cell. The optimal incubation times both for the first and second immunoreactions were determined to be 20 min. A concave calibration curve was obtained between Vg concentration and chemiluminescence intensity when various concentrations of standard Vg samples (2–100 ng mL⁻¹) were applied to the SIA system under optimal conditions. In spite of a narrow working range, the lower detection limit of the immunoassay was about 2 ng mL⁻¹.     

Ni- or Cu-catalyzed cross-coupling reaction of alkyl fluorides with Grignard reagents

n-Octyl fluoride underwent a cross-coupling reaction with n-propylmagnesium bromide in the presence of 1,3-butadiene using NiCl2 as a catalyst at room temperature to give undecane in moderate yields. This alkyl-alkyl cross-coupling proceeded more efficiently when CuCl2 was employed instead of NiCl2. Addition of 1,3-butadiene dramatically improved the yields of the coupling products from primary alkyl Grignard reagents in both Ni- and Cu-catalyzed reactions. Alkyl fluorides efficiently reacted with tertiary alkyl and phenyl Grignard reagents using CuCl2 in the absence of 1,3-butadiene to afford the coupling products in high yields. The competitive reaction of a mixture of alkyl halides (R-X; X = F, Cl, Br) with nC5H11MgBr showed that the reactivities of the halides increase in the order R-Cl < R-F < R-Br. In contrast, in the Cu-catalyzed reaction with PhMgBr, the reactivities increase in the order R-Cl < R-Br < R-F.     

Analytical application of second-harmonic a.c. polarography

Phase-selective second-harmonic a.c. polarography can be used to distinguish two different species having similar reduction potentials. Because each species has a different phase angle depending on the electrode kinetics, a certain phase angle can be chosen to detect only one component in the mixture. In 1 M potassium chloride solution, indium-(III) at the 4 × 10^-6 M level can be determined in the presence of 50-fold amounts of cadmium(II), and zinc(II) at the 2 × 10^-5 M level in the presence of 100-fold amounts of nickel(II).