A study of Feynman integrals by micro-differential equations

We use the holonomic character of Feynman integrals to describe their singularity structure explicitly in some simple cases. The results in §1 show that under moderate conditions Feynman amplitudes can be locally expressed essentially in terms of Legendre functions near the points where two positive- Landau-Nakanishi surfaces meet. Related topics such as hierarchical principle in perturbation theory are also discussed in terms of holonomic systems involved. In §4 we use the concrete expressions for Feynman amplitudes obtained in §1 to discuss the validity of Sato's conjecture.Supported in part by NSF MCS 75-2333Supported in part by NSF GP 36269     

Time correlation functions of a one-dimensional infinite system

We investigate the time evolution of a simple one-dimensional system with an infinite number of particles. We calculate some time correlation functions and show that they behave asymptotically as 1/t.     

Polymerization of silylacetylenes by W and Mo catalysts

Polymerization of HC?CSiMe₃ homologues (HC?CSiMe₂R; R = n-C₆H₁₃, CH₂CH₂Ph, CH₂Ph, Ph, and t-Bu) was studied by use of W and Mo catalysts. W catalysts provided polymers in good yields from all these monomers. Mo catalysts gave mainly a polymer from HC?CSiMe₂–t-Bu, but virturally only cyclotrimers from sterically less croweded monomers (R = n-C₆H₁₃, CH₂CH₂Ph, CH₂Ph, and Ph). Polymers with flexible R groups (n-C₆H₁₃, CH₂CH₂Ph, and CH₂Ph) were totally soluble, their number-average molecular weights being 7000–18,000. Polymers with inflexible R groups (Ph and t-Bu) were partly insoluble. Every polymer was a yellow rubber or powder, and had the structure, \documentclass{article}\pagestyle{empty}\begin{document}$ \rlap{--} [{\rm CH} = {\rm C}\left( {{\rm SiMe}_{\rm 2} {\rm R}} \right)\rlap{--} ]_n $\end{document}. The results were compared with the polymerization and polymer of HC?CSiMe₃.     

Theoretical calculation of the steric effects of ortho substituents by the AM1 method

The AM1 calculation was done for ortho-substituted toluenes (o-X-C₆H₄-CH₃) and ortho-substituted tert-butylbenzenes (o-X-C₆H₄-t-Bu). The difference in the calculated heat of formation between o-X-C₆H₄-CH₃ and o-X-C₆H₄-t-Bu was used as a theoretical steric index for ortho-X. The correlation of this theoretical steric index with the empirical steric parameter sets such as our recently defined E_s(AMD) and the Taft–Kutter–Hansch (TKH) E_s was examined. In spite of the simplicity of the model system, the theoretical index was linear with the E_s(AMD) constant with a correlation coefficient of r = 0.972 for 17 substituents of various structures. Including the phenyl group, the correlation with the TKH E_s constant was r = 0.948. The theoretically calculated index was shown to serve as a measure of the ortho steric effect.     

ESTABLISHMENT and CHARACTERIZATION OF A MONOCLONAL ANTIBODY RECOGNIZING THE DEWAR ISOMERS OF(6–4)PHOTOPRODUCTS

Abstract— We established a monoclonal antibody(DEM–1) that recognizes UV-induced DNA damage other than cyclobutane pyrimidine dimers or(6–4)photoproducts. The binding ofDEM–1 antibody to 254 nm UV-irradiated DNA increased with subsequent exposure to UV wavelengths longer than 310 nm, whereas that of the 64M-2 antibody specific for the(6–4)photoproduct decreased with this treatment. Furthermore, the increase inDEM–1 binding was inhibited by the presence of the 64M-2 antibody during the exposure. We concluded that theDEM–1 antibody specifically recognized the Dewar photoproduct, which is the isomeric form of the(6–4)photoproduct. TheDEM–1 antibody, however, also bound to DNA irradiated with high fluences of 254 nm UV, suggesting that 254 nm UV could induce Dewar photoproducts without subsequent exposure to longer wavelengths of UV. Furthermore, an action spectral study demonstrated that 254 nm was the most efficient wavelength for Dewar photoproduct induction in the region from 254 to 365 nm, as well as cyclobutane dimers and(6–4)photoproducts, although the action spectrum values in the U V-B region were significantly higher compared with those for cyclobutane dimer and(6–4)photoproduct induction.     

Polymerization of (o-methylphenyl)acetylene and polymer characterization

(o-Methylphenyl)acetylene polymerized with high yields in the presence of W and Mo catalysts. W catalysts were more active than the corresponding Mo catalysts. The weight-average molecular weight of the polymer formed with W(CO)₆–CCl₄–hv reached 8 × 10⁵, being higher than the maximum value (ca. 2 × 10⁵) for poly(phenylacetylene). The polymer had the structure $\rlap{--} [{\rm CH} \hbox{=\hskip-1pt=} {\rm C}(o - {\rm CH}_3 {\rm C}_6 {\rm H}_4 )\rlap{--} ]_n $. The stereochemical structure of the main chain could be determined by ¹³C-NMR; the cis content varied in a range of 41–61% depending on the polymerization conditions. The present polymer was thermally more stable than poly(phenylacetylene) according to thermogravimetric analysis. Interestingly, this polymer possessed deeper color than poly(phenylacetylene), and showed a fairly strong absorption in the visible region.     

An efficient synthesis of the orally-active GpIIb/IIIa antagonist FR184764

An efficient synthesis of the orally-active GpIIb/IIIa antagonist FR184764 was achieved. The key intermediate, an optically active ethynyl β-amino ester, was synthesized efficiently by utilizing a lipase catalyzed kinetic resolution step.     

Separation of stereoisomers of some terpene derivatives by capillary gas chromatography-mass spectrometry and high-performance liquid chromatography using beta-cyclodextrin derivative columns

Gas chromatographic separations of the stereoisomers of menthol derivatives, important intermediates in the synthesis of physiologically active natural products, were carried out on several substituted beta-cyclodextrin (CD) columns, including per-O-methyl-beta-cyclodextrin (PME-beta-CD), heptakis(2,3-di-O-acetyl-6-tert-butyldimethylsilyl)-beta-CD (DIAC-6-TBDS-beta-CD), and heptakis(2,3-di-O-methyl-6-tert-butyldimethylsilyl)-beta-CD (DIME-6-TBDS-beta-CD) as chiral stationary phases (CSPs). With the DIME-6-TBDS-beta-CD column, a separation of the Z- and E-isomers of methylidenementhol was accomplished; no separation was achieved with the other columns. The stereoisomers of methylidenementhol and the corresponding tert-butyldimethylsilyl (TBS) ether were separated on both the beta-CD and the heptakis(2,3,6-tri-O-methyl)-beta-cyclodextrin (TME-beta-CD) columns by high-performance liquid chromatography (HPLC) with a mobile phase involving acetonitrile and H(2)O. For the separation of the Z- and E-isomers of methylidenementhol, the TME-beta-CD column was superior. In contrast, the beta-CD column was preferable in the case of the corresponding TBS ether.     

Rapid and sensitive determination of pertechnetate in99Mo/99mTc generator eluates by reversed-phase high-performance liquid chromatography

Reversed-phase high-performance liquid chromatography with u.v. detection was applied for rapid and sensitive determination of pertechnetate in⁹⁹Mo/^99mTc generator eluates, using a mixture solvent of acetonitrile and 0.04M aqueous acetate buffer (1/1) containing a few volume percentage of 0.5 M tetra-n-butylammonium hydroxide as the mobile phase. Employing a -bondapak C₁₃ column, the TcO ₄ ^– species was separated, monitored with absorbance at 254 nm, and observed at the retention time of 3.5 min. The detection limit was found to be 5.2·10^–10 g of Tc for each injection. Total Tc contents in the^99mTc eluates from clinically-used⁹⁹Mo/^99mTc generator were analyzed by this technique. The^99mTc (⁹⁹Tc) species was separated from the contaminant⁹⁹Mo. This method was found to be useful for the purification of^99mTc (⁹⁹Tc) as well as the determination of total Tc content.     

A synthesis, including asymmetric synthesis, of α-quaternary α-amino aldehydes from ketones and chloromethyl p-tolyl sulfoxide via sulfinylaziridines

Treatment of 1-chlorovinyl p-tolyl sulfoxides, prepared from ketones and chloromethyl p-tolyl sulfoxide, with N-lithio arylamines resulted in the formation of sulfinylaziridines in good to high yields. The sulfinylaziridines were treated with N-lithio aniline or N-lithio p-chloroaniline to afford α-quaternary α-amino aldehydes in good yields. From α-quaternary α-amino aldehydes, α-quaternary α-amino acid esters and β-quaternary β-amino alcohols were obtained. When optically active chloromethyl p-tolyl sulfoxide was used in this procedure, a method for the synthesis of optically active α-quaternary α-amino aldehydes was realized. The reaction mechanism, including asymmetric induction, for the formation of the sulfinylaziridines is described.