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     

Effect of molecular dynamics and modulated structure on H NMR spectrum studied in [Mg(H2O)6][SiF6]

The spectrum of magnetic resonance is typically affected by a modulated structure in an incommensurate phase, resulting in the broadened spectrum characterized by ‘edge singularities’. We demonstrate that the modulated structure in the crystal where molecular motion exists is responsible for the narrowing of the spectrum in the fast motional region by means of the simulation of ²H NMR spectrum of [Mg(H₂O)₆][SiF₆]. The program developed by combining the theories of phase solitons in the incommensurate phase and motional change of ²H NMR spectrum was used for the simulation. We obtained a good agreement between the theoretical ²H NMR spectrum and experimental one for [Mg(H₂O)₆][SiF₆].     

Cross-chiral examinations of molecular enantioselective recognition by fast atom bombardment mass spectrometry: Host–guest complexations between chiral crown ethers and chiral organic ammonium ions

Using fast atom bombardment (FAB) mass spectrometry (MS), cross-chiral relationships were confirmed for the first time for the diasteromeric host-guest complexations between the chiral crown ether host (1) and the chiral organic ammonium ion guest (2) on the basis of the relative peak intensities (RPI). Both host–guest combinations (R, R, R, R) – 1, (R) – 2 and (S, S, S, S) – 1, (S) – 2 obviously provided larger RPI values than the combination of both (R, R, R, R) – 1, (S) – 2 and (S, S, S, S) – 1, (R) – 2 by a factor of 1.6 as an averaged value: 1.87 (n = 4)/1.16 (n = 4) = 1.6. These results are consistent with the expected stabilities of the host-guest complexations by CPK model examinations. Successfully observed cross-chiral examinations strongly suggest a potentially useful FABMS/RPI methodology for rapidly searching newly designed and synthesized crown ether-like host compounds with a higher degree of enantioselectivity.     

Synthesis and DNA binding properties of iminodiacetic acid-linked polyamides: characterization of cooperative extended 2:1 side-by-side parallel binding

A series of iminodiacetic acid (IDA)-linked polyamides (DpPyPyPy-IDA-PyPyPyDp) were prepared and constitute polyamides joined head-to-head by a functionalizable five-atom linker. It was found that the IDA linker exerts a unique influence over the DNA binding conformation differing from both the beta-alanine (extended) or gamma-aminobutyric acid (hairpin) linkers, resulting in cooperative parallel side-by-side 2:1 binding in an extended conformation most likely with a staggered versus stacked alignment. A generalized variant of a fluorescent intercalator displacement (FID) assay conducted on a series of hairpin deoxyoligonucleotides containing a systematically varied A/T-rich binding-site size was used to distinguish between the binding modes of the IDA-linked polyamides.     

Vibrational dephasing and hydrodynamic effects on vibrational relaxation rates in acetophenone: Raman bandshape analysis

The isotropic component of Raman band for C=O stretching mode of acetophenone in solution was analyzed by estimating the correlation coefficient with reference to Lorentzian lineshape. In the intermediate region of solute/solvent concentration there is a sharp decrease in the correlation coefficient and there appears to be a transition from non-Lorentzian to Lorentzian lineshape. The vibrational relaxation rates have been estimated from the isotropic component of Raman band in different solvents. The rate is shown to be dependent on several macroscopic as well as microscopic properties of the solute-solvent system and intermolecular interactions. The hydrodynamic and dispersion forces appear to play a major role in determining the vibrational relaxation rate and the broadening of the bands.     

Electrochemically driven clathration/declathration of ferrocene and its derivatives by a nanometer-sized coordination cage

The electrochemical, NMR, and crystallographic studies clearly indicate that the clathration and declathration of ferrocene and its derivatives in a self-assmbled Pd(II)-linked nanometer-sized cage can be controlled by the oxidation state of the guest. Namely, the guests are clathrated when they are reduced but declathrated when they are oxidized. The process is rapid on the NMR time scale but slow on the CV time scale.     

Direct synthesis of hetero-biaryl compounds containing an unprotected NH2 group via Suzuki-Miyaura reaction

Hetero-biaryl compounds were prepared via the Suzuki-Miyaura coupling reaction of hetero-aryl moieties containing an unprotected NH₂ group and arylboronic acids. D-t-BPF was found to be an efficient ligand for the cross-coupling of NH₂-unprotected hetero-aryl chlorides with phenylboronic acid.     

Fluoride-induced chemiluminescent decomposition of dioxetanes bearing a siloxyaryl moiety to produce an alkyl aryl ketone as an emitter

Tetrabutylammonium fluoride induces the decomposition of 1-tert-butyl-4,4-dimethyl-5-(3-siloxyphenyl)-2,6,7-trioxabicyclo[3.2.0]heptane (4a) in DMSO to form an oxyanion of aromatic ketone (14a) as an emitter with high singlet-chemiexcitation yield comparable with that for a chemically initiated electron exchange luminescence (CIEEL) active dioxetane producing an oxyanion of aromatic ester as an emitter. A 7-siloxynaphthalen-2-yl analog (4b) was found on similar treatment to emit light with the maximum wavelength the longest among CIEEL-active dioxetanes hitherto known.     

Quantification of clenbuterol in equine plasma,urine and tissue by liquid chromatography coupled on-line with quadrupole time-of-flight mass spectrometry

Clenbuterol (CBL) is a potent beta(2)-adrenoceptor agonist used for the management of respiratory disorders in the horse. The detection and quantification of CBL can pose a problem due to its potency, the relatively low dose administered to the horse, its slow clearance and low plasma concentrations. Thus, a sensitive method for the quantification and confirmation of CBL in racehorses is required to study its distribution and elimination. A sensitive and fast method was developed for quantification and confirmation of the presence of CBL in equine plasma, urine and tissue samples. The method involved liquid-liquid extraction (LLE), separation by liquid chromatography (LC) on a short cyano column, and pseudo multiple reaction monitoring (pseudo-MRM) by electrospray ionization quadrupole time-of-flight tandem mass spectrometry (ESI-QTOF-MS/MS). At very low concentrations (picograms of CBL/mL), LLE produced better extraction efficiency and calibration curves than solid-phase extraction (SPE). The operating parameters for electrospray QTOF and yield of the product ion in MRM were optimized to enhance sensitivity for the detection and quantification of CBL. The quantification range of the method was 0.013-10 ng of CBL/mL plasma, 0.05-20 ng/0.1 mL of urine, and 0.025-10 ng/g tissue. The detection limit of the method was 13 pg/mL of plasma, 50 pg/0.1 mL of urine, and 25 pg/g of tissue. The method was successfully applied to the analysis of CBL in plasma, urine and various tissue samples, and in pharmacokinetic (PK) studies of CBL in the horse. CBL was quantified for 96 h in plasma and 288 h in urine post-administration of CLB (1.6 micro g/kg, 2 x daily x 7 days). This method is useful for the detection and quantification of very low concentrations of CBL in urine, plasma and tissue samples.     

Efficient copper-catalyzed coupling of aryl iodides and thiobenzoic acid

A highly efficient copper-catalyzed coupling reaction of aryl iodides and thiobenzoic acid, using 10 mol % of copper iodide, 20 mol % of 1,10-phenanthroline, and ⁱPr₂NEt in toluene, was developed. This methodology is applicable to a variety of aryl iodides.