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     

ANALYSIS OF PHOTOTRANSFORMATION INTERMEDIATES IN THE PATHWAY FROM THE RED-ABSORBING TO THE FAR-RED-ABSORBING FORM OF AVENA PHYTOCHROME BY A MULTICHANNEL TRANSIENT SPECTRUM ANALYZER

Phototransformation of the red-absorbing form of phytochrome (Pr) to the far-red-absorbing form (Pfr) was followed with a custom-built transient spectrum analyzer. Large phytochrome, which consisted of approximately 120000-dalton monomers, was immunopurified or conventionally purified from etiolated oat (Avena sativa L., cv. Garry) shoots. Phototransformation was initiated by exciting Pr with a 115-mJ, 600-ns half-width, 655-nm laser pulse. Absorption spectra were recorded on a microsecond time scale at predetermined times after the flash. It has been reported earlier that flash excitation of large oat Pr produces a transformation intermediate with maximum absorbance near 700 nm in a difference spectrum and that this intermediate decays by two kinetically distinct reactions. Difference spectra for these two reactions are indistinguishable. Both show bleaching centered at 690 nm with no detectable associated absorbance increase between 570 and 830 nm. Subsequent appearance of absorbance at 724 nm, which presumably but not necessarily represents the appearance of Pfr, had earlier been shown to occur by two kinetically distinct reactions for large oat phytochrome. Data presented here indicate in addition the occurrence of a third, slower reaction. Difference spectra for the two faster reactions are indistinguishable, both with maxima near 728 nm and minima near 650 nm. The difference spectrum for the slowest component, however, was qualitatively different exhibiting a maximum near 722 nm with no corresponding minimum. About 15-20% of the absorbance increase at 724 nm occurred by this slowest reaction, which exhibited a half-life of 3 s at 25°C and a Q₁₀ of 1.2 for immunopurified and 1.5 for conventionally purified phytochrome. The percentage occurring by this reaction was independent of temperature over the range studied (1-25dEC). For immunopurified phytochrome the enthalpy of activation, Gibbs free energy of activation, and entropy of activation of this slowest reaction were found to be about lOkJ-mol^-1, 75kJ.mol^-1, and -220 J.mol^-1 K^-1, respectively, and for conventionally purified phytochrome 25kJ.mol^-1, 75kJ.mol^-1and —170 J.mol^-1 K^-1, respectively. The thermodynamic characteristics of this reaction indicate that it may involve a significant ordering of the protein moiety as it transforms to Pfr.     

Fabrication of polymer Langmuir-Blodgett films containing regioregular poly(3-hexylthiophene) for application to field-effect transistor

Semiconducting thin films consisting of regioregular poly(3-hexylthiophene) (RR-PHT) and poly(N-dodecylacrylamide) (pDDA) were constructed by the Langmuir-Blodgett (LB) technique. A mixture of RR-PHT and pDDA spread from a chloroform solution on a water surface forms a stable monolayer, which can be transferred onto solid substrates by the LB method, yielding a well-defined polymer LB film. Surface morphology studies of the LB film indicate that the RR-PHT is dispersed uniformly throughout the surface. The polymer thin film was chemically doped by contacting with FeCl3 acetonitrile solution, and a conductivity of 5.6 S/cm was achieved. Further, the LB film was utilized as the semiconducting film in the field-effect transistor (FET), and mobilities of 2.2 x 10(-4) and 4.4 x 10(-4) cm2 V(-1) s(-1) were obtained by analyzing the saturated and linear regions of the current-voltage characteristic, respectively.     

Application of solvent extraction and synchronous spectrofluorimetry to the determination of the formation constant for a 1:1 complex of carbazole withβ-cyclodextrin in water-dimethyl sulfoxide medium

Extraction of carbazole in heptane was performed at 25±1°C with an aqueous dimethyl sulfoxide (DMSO) medium containing -cyclodextrin (CD) at consecutive concentrations in the range of 0–10 mM. The fluorescence intensity of carbazole remaining in the heptane phase was measured by synchronous scanning fluorimetry. The apparent formation constant (K _f) for a 1:1 carbazole: CD inclusion complex in water-DMSO medium was determined by using a linear plot of the distribution ratio calculated from the fluorescence intensities vs. the -CD concentration. The values thus obtained ranged from 477 M^–1 in a 10% v/v DMSO medium to 12.1 M^–1 in a 60% v/v medium. Good linear relationships were observed between logK _f and the DMSO concentration ([DMSO]), and also between logK _f and the logarithm of the distribution coefficient (K _d) for carbazole. The formation constant in 100% water was estimated to be approximately 1.0×10³ M^–1 on the basis of the logK _f vs. [DMSO] and the logK _f vs. logK _d correlations.     

1-D cobalt(II) spin transition compound with strong interchain interaction: [Co(pyterpy)Cl(2)].X

Cobalt(II) compounds [Co(pyterpy)Cl(2)].MeOH (1.(MeOH)) and [Co(pyterpy)Cl(2)].2H(2)O (1.(2H(2)O)) were synthesized. The compound 1.(MeOH) forms the quasi 3-D networks by making pi-pi stacking between the 1-D chains. The methanol molecules from 1.(MeOH) can be removed by heating, and substituted by absorption of water molecules. The MeOH molecules in 1.(MeOH) are removed by heating at 410 K, and they are substituted by water molecules to form 1.(2H(2)O). 1.(2H(2)O) exhibits a S = (3)/(2) (HS) left arrow over right arrow S = (1)/(2) (LS) spin transition with a thermal hysteresis. We have succeeded in constructing a guest dependent 1-D spin-crossover cobalt(II) compound.     

Ethylene and propylene polymerization behavior of a series of bis(phenoxy–imine)titanium complexes

This contribution reports ethylene and propylene polymerization behavior of a series of Ti complexes bearing a pair of phenoxy–imine chelate ligands. The bis(phenoxy–imine)Ti complexes in conjunction with methylalumoxane (MAO) can be active catalysts for the polymerization of ethylene. Unexpectedly, this C₂ symmetric catalyst produces syndiotactic polypropylene. ¹³C NMR spectroscopy has revealed that the syndiotacticity arises from a chain-end control mechanism. Substitutions on the phenoxy–imine ligands have substantial effects on both ethylene and propylene polymerization behavior of the complexes. In particular, the steric bulk of the substituent ortho to the phenoxy–oxygen is fundamental to obtaining high activity and high molecular weight for ethylene polymerization and high syndioselectivity for the chain-end controlled propylene polymerization. The highest ethylene polymerization activity, 3240 kg/mol-cat h, exhibited by a complex having a t-butyl group ortho to the phenoxy–oxygen, represents one of the highest reported to date for Ti-based non-metallocene catalysts. Additionally, the polypropylene produced exhibits a T_m, 140 °C, and syndioselectivity, rrrr 83.7% (achieved by a complex bearing a trimethylsilyl group ortho to the phenoxy–oxygen) that are among the highest for polypropylenes produced via a chain-end control mechanism. Hence, the bis(phenoxy–imine)Ti complexes are rare examples of non-metallocene catalysts that are useful for the polymerization of not only ethylene but also propylene.     

A novel synthesis of amino acid derivatives of phospholene oxides

A convenient synthetic approach is established to prepare a new class of 1-l-α-amino acid derivatives of phospholene oxides by amination of (±)-1-chloro-2-phospholene-1-oxides with several optically pure l-α-amino acid esters. All compounds obtained as a diastereomeric mixture in good to high yields. The two diastereomers were successfully separated by column chromatography and structurally identified by their spectral analyses.     

Crystal structure of the parent misfit-layered cobalt oxide [Sr2O2]qCoO2

The crystal structure of our newly discovered Sr-Co-O phase is investigated in detail through high-resolution electron microscopy (HREM) techniques. Electron diffraction (ED) measurement together with energy dispersive X-ray spectroscopy (EDS) analysis show that an ampoule-synthesized sample contains an unknown Sr-Co-O ternary phase with monoclinic symmetry and the cation ratio of Sr/Co=1. From HREM images a layered structure with a regular stacking of a CdI₂-type CoO₂ sheet and a rock-salt-type Sr₂O₂ double-layered block is observed, which confirms that the phase is the parent of the more complex “misfit-layered (ML)” cobalt oxides of [M_mA₂O_m+2]_qCoO₂ with the formula of [Sr₂O₂]_qCoO₂, i.e. m=0. It is revealed that the misfit parameter q is 0.5, i.e. the two sublattices of the CoO₂ sheet and the Sr₂O₂ block coexist to form a commensurate composite structure. We propose a structural model with monoclinic P2₁/m symmetry, which is supported by simulations of ED patterns and HREM images based on dynamical diffraction theory.     

Photoreactive polyamides having m- or 1-type dimer moiety derived from 4-(3-oxo-3-phenyl-1-propenyl)benzoic acid derivatives

Photoreactive polyamides having m- or 1 -type cyclobutane moiety were prepared via a topochemical photodimerization of 4-(3-oxo-3-phenyl-1-propenyl)benzoic derivatives,⁴ followed by polycondensation of cyclobutane dicarboxylate derivatives with diamines. From the spectral studies of resulted polyamides compared with the corresponding reference diamides, it was concluded that both types of polyamides were depolymerized photochemically to give the same type of amide derivative having chalcone moiety with a small amount of undefined side reaction. The cyclobutane ring of the m-dimer from 4-(3-oxo-3-phenyl-1-propenyl)benzoic acid in crystal is severely twisted presumably because of the enhanced steric repulsions between two pairs of adjacent substituents. The higher quantum yield of the m-dimer for the photocleavege, compared with that of the 1 -dimer, has been interpreted in terms of such steric repulsions by the strained structure of the m-dimer.     

Molecular orientation of azobenzene chromophores in ultrathin polymer nanosheets studied by attenuated total reflection spectroscopy

This paper describes characterization of molecular orientation for azobenzene moieties in a polymer nanosheet. Copolymers of N-[4-(phenylazo)phenyl] acrylamide (PAZoA) with tert-pentyl acrylamide (tPA) were synthesized and the monolayers deposited on tapered quartz waveguides by Langmuir–Blodgett (LB) technique. Spectroscopic properties of the copolymer (p(tPA/PAZoA)) monolayers were monitored by integrated optical waveguide technique on the molecular level. Molecular orientation of the azobenzene was precisely determined by polarized absorption spectra. It was found that the azobenzene groups took a horizontal orientation and distributed uniformly in the p(tPA/PAZoA) monolayer without significant PAZoA aggregation. Photoisomerization process from trans to cis form was also investigated. More than half of the trans form (60–70%) was photoisomerized under unpolarized light irradiation, and the photoisomerization rate was independent on the PAZoA contents. This implies that the microenvironment of PAZoA moieties was almost the same in three different p(tPA/PAZoA) monolayers.