PDE with Random Coefficients and Euclidean Field Theory

In this paper a new proof of an identity of Giacomin, Olla, and Spohn is given. The identity relates the 2 point correlation function of a Euclidean field theory to the expectation of the Green's function for a pde with random coefficients. The Euclidean field theory is assumed to have convex potential. An inequality of Brascamp and Lieb therefore implies Gaussian bounds on the Fourier transform of the 2 point correlation function. By an application of results from random pde, the previously mentioned identity implies pointwise Gaussian bounds on the 2 point correlation function.     

Site-directed photochemical disruption of the actin cytoskeleton by actin-binding Rose Bengal-conjugates

The in situ light-induced, non-enzymatic digestion of cytoskeletal actin by a xanthene dye conjugated to heavy meromyosin, anti-actin antibodies and/or anti-myosin antibodies is reported. The dye Rose Bengal was conjugated to either anti-actin antibodies, anti-myosin antibodies or heavy meromyosin. Under our experimental conditions, visible light induced the non-enzymatic breakdown of cytoskeletal actin when mammalian tissue culture cells were probed either with Rose Bengal-conjugated anti-actin and/or anti-myosin antibodies. Similar results were obtained when tissue culture cells were probed with Rose Bengal-conjugated heavy meromyosin before irradiation with visible light. The in situ photochemical reaction depended on the presence of actin-binding Rose Bengal-conjugates.     

The ground state energy of a Bose gas with Coulomb interaction

LetH _N be the 2N particle Hamiltonian $$\begin{array}{*{20}c} {H_N = \sum\limits_{i = 1}^{2N} {( - \Delta _\iota ) + \sum\limits_{i< j = 1}^N {\left| {x_i - x_j } \right|^{ - 1} + } \sum\limits_{i< j = 1}^N {\left| {x_{i + N} - x_{j + N} } \right|^{ - 1} } } } \\ { - \sum\limits_{i,j< j = 1}^N {\left| {x_i - x_{j + N} } \right|^{ - 1} ,} } \\ \end{array} $$ whereΔ _i is the Laplacian in the variablex _i ∈?³, 1≦i≦2N. The operatorH _N is assumed to act on wave functionsΨ(x ₁, ...,x _N ;x _N+1, ...,x _2N ) which are symmetric in the variables (x ₁, ...,x _N ) and (x _N+1, ...,x _2N ). SupposeΨ is supported in a setΛ ^2N , whereΛ is a cube in ?³. It is shown that if a normalized wave functionΨ can be written as a product of two wave functions $$\psi (x_1 ,...,x_N ;x_{N + 1} ,...,x_{2N} ) = \psi _1 (x_2 ,...,x_N )\psi _2 (x_{N + 1} ,...,x_{2N} ),$$ and the density of particles inΛ is constant, then 〈Ψ|H _N |Ψ〉≧?CN ^7/5 for some universal constantC.     

Synthesis and characterization of photosensitive polyimides

All aromatic polyimides bearing diarylsulfide linkages in the main chain were prepared either by condensation of a sulfur containing dianhydride with an aromatic diamine or the condensation of a sulfur containing aromatic diamine with a dianhydride. Phenylation with diphenyl iodonium salts was then used to convert the diarylsulfide groups to triarylsulfonium salts. The resulting photosensitive polyimides were shown to undergo main chain cleavage during photolysis using UV irradiation. These new polyimides are candidates for positive working, high temperature photoresist materials.     

Synthesis,characterization, and properties of novel aromatic bispropenyl ethers

Aromatic bispropenyl ethers are a new class of highly reactive thermosetting monomers that have been prepared and characterized. Two synthetic routes to their preparation have been developed. The first of these involves the base-catalyzed isomerization of bisallyl ether precursors that gives predominantly the Z bispropenyl ether isomers. The second method employs tris(triphenylphosphine)ruthenium(II) dichloride as an isomerization catalyst and produces predominantly the E isomers. Using these methods, a number of bispropenyl ether monomers containing different aromatic groups have been synthesized. The cationic polymerization of these novel monomers to give crosslinked network polymers using diaryliodonium salts as photo and thermal initiators has been studied.     

Estimates on the solution of a schrödinger equation and some applications

Dedicated to Elliott Lieb on the occasion of his 60th birthday.     

Financial Modelling in a Banking Environment

The Bank of Ireland undertakes financial modelling for strategic planning purposes. The work was previously undertaken by a time-sharing bureau but is now performed on microcomputers. The paper briefly describes the modelling process and gives some points on the use of microcomputers.     

Energy dependence of the optical model parameters for 3He ions scattered from 40Ca and 58Ni

The differential cross sections for the elastic scattering of ³He ions on targets of ⁴⁰Ca and ⁵⁸Ni have been measured at incident energies of 27.7, 51.4, 73.2 and 83.5 MeV. The results of optical model analyses showed that only one unique potential (J_R ≈ 330 MeV · fm³) with a surface absorptive term can provide acceptable fits to the large angle elastic scattering cross sections at 83.5 MeV. The particular geometrical set found at 83.5 MeV could not, however, give an adequate fit to the data with energy less than 40 MeV. Subsequent analyses indicated that a break in the energy dependence of the real potential is observed for the low energy data. Explicit energy dependent terms were obtained by fitting all the data simultaneously. These phenomenological potentials were also compared with the folded nucleon-nucleus potential. The influence of the α-particle channels on the elastic scattering of ³He ions at 83.5 MeV was also examined.     

Investigation of the pyrolysis products of methionine-enkephalin-Arg-Gly-Leu using liquid chromatography-tandem mass spectrometry

Low-temperature pyrolysis of methionine-enkephalin-Arg-Gly-Leu has been carried out and the non-volatile residues have been analyzed. The fragments were separated and characterized by LC-UV/Vis-MS/MS. Two major types of pyrolysis products were identified by matching the experimental results with a theoretical list that contains the expected fragments. These products were mainly composed of cyclic oligopeptides and linear fragments produced from the peptide backbone. These fragments have preserved the sequence of amino acids in the peptide. In some cases, a complete or partial loss of an amino-acid side group was observed. Tandem mass spectrometry and cyanogen bromide cleavage experiments were used to confirm the nature of the cyclic and linear pyrolysates, in addition to chromatographic and mass spectrometric data of actual standard synthetic cyclic peptides.