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     

Plutonium-244 fission xenon in carbonaceous inclusions of primitive meteorites

A total of 13 samples of diamond separates studied so far, all contain excess ²⁴⁴Pu fission xenon. On the other hand, none of the SiC separates contains excess ²⁴⁴Pu fission xenon, while 5 out of 10 samples of graphite separates studied so far contain excess ²⁴⁴Pu fission xenon.     

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.     

Plutonium-244 dating

Re-calculation of the²⁴⁴Pu ages of lunar rocks 10057 and 12013 indicates that, while the former started to retain its xenon (4,189 _?74 ⁺⁴⁵ ) million years ago, the latter was formed at a much later time, after the extinct nuclide²⁴⁴Pu had essentially decayed away.     

Anisotropic contributions in the ligand polarization model for the f-f transition probabilities of Eu(III) complexes

The intensities of the ΔM = ± 1 component of the ⁷f_o→ ⁵D₂ transition in D₃ complexes containing the [ EuO₉] cluster, and of other d-d or f-f transitions in D₃ complexes with the yz- and xz-components of the electric quadrupole as the leading moment, are found to be dependent upon the polarizability anisotropy of the ligands. The expectation is supported by determinations of the single-crystal absorption intensities of Na₃ [Eu(diglycollate)₃]·2NaClO₄·6H₂O and [Eu(H₂O)₉] (C₂H₅SO₄)₃.     

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.     

Alternating copolymer of thiophene andN‐(phenylethynyl)pyrrole. New π‐conjugated alternating five‐membered ring copolymer and its packing structure

An alternating copolymer, Copoly‐1 , of thiophene and N‐(phenylethynyl)pyrrole was prepared by palladium‐catalyzed polycondensation. Powder X‐ray diffraction (XRD) analysis indicated that Copoly‐1 formed a stacked packing structure with doubly‐running polymer main chains. Optical data support the molecular and packing structures of Copoly‐1 . © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2219–2224, 2005     

Formation of a new crystalline silicate structure by grafting dialkoxysilyl groups on layered octosilicate

Dialkoxydichlorosilanes ((RO)2SiCl2, R = alkyl) react almost completely with interlayer silanol groups in a layered silicate octosilicate to create a new crystalline silicate structure consisting of new five-membered rings arranged regularly on both sides of the silicate layers. The introduction of dialkoxysilyl groups to the interlamellar region of layered silicates with regular reaction sites provides a new methodology for the design and construction of novel crystalline silicate frameworks by a soft chemical route.     

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.