Brieskorn modules and Gauss Manin systems for non-isolated hypersurface singularities

We study the Brieskorn modules associated to a germ of a holomorphicfunction with non-isolated singularities and show that the Brieskornmodule has naturally the structure of a module over the ringof microdifferential operators of non-positive degree, and thatthe kernel of the morphism to the Gauss–Manin system coincideswith the torsion part for the action of t and also with thatfor the action of the inverse of the Gauss–Manin connection.This torsion part is not finitely generated in general, anda sufficient condition for the finiteness is given here. A Thom–Sebastiani-typetheorem for the sheaf of Brieskorn modules is also proved whenone of two functions has an isolated singularity.     

Momentum and heat transfers from fully developed turbulent flow in an eccentric annulus to inner and outer tube walls

An analysis and measurement were made of momentum and heat transfers from fully developed turbulent flow in an eccentric annulus to inner and outer tube walls. The eddy diffusivities of momentum and heat obtained in the turbulent flow in a circular tube were applied to the annular flow in the analysis. The result indicates that the calculated friction factor and average Nusselt numbers on the inner and outer tube walls are in fairly good agreement with the measurements.     

Jumping coefficients and spectrum of a hyperplane arrangement

In an earlier version of this paper written by the second named author, we showed that the jumping coefficients of a hyperplane arrangement depend only on the combinatorial data of the arrangement as conjectured by Mustaţǎ. For this we proved a similar assertion on the spectrum. After this first proof was written, the first named author found a more conceptual proof using the Hirzebruch–Riemann–Roch theorem where the assertion on the jumping numbers was proved without reducing to that for the spectrum. In this paper we improve these methods and show that the jumping numbers and the spectrum are calculable in low dimensions without using a computer. In the reduced case we show that these depend only on fewer combinatorial data, and give completely explicit combinatorial formulas for the jumping coefficients and (part of) the spectrum in the case the ambient dimension is 3 or 4. We also give an analogue of Mustaţǎ’s formula for the spectrum.     

Preparation and electrochemical properties of SAM of alkanethiols functionalized with 2-aza[3]ferrocenophane on gold electrode

Thiols functionalized with N-aryl[3]azaferrocenophane formulated as HS-(CH₂)_n-N(CH₂Cp)₂Fe (1: n = 6, 2: n = 8, 3: n = 10, 4: n = 12) and disulfide obtained by oxidation of 4 (5) were synthesized via three or four steps reactions starting from 1,1′-ferrocenedimethanol, 4-aminophenol, and α,ω-aklanedithiol. Self-assembled monolayers (SAMs) of these thiols and disulfide on gold electrode were prepared by immersing the electrode in MeCN solutions of the compounds. Cyclic voltammograms of the SAM of 1 (n = 6) exhibited reversible redox of the Fe center at E_1/2 = 0.26 V (vs. Ag⁺/Ag) in the presence of Et₄NBF₄ in MeCN and at E_1/2 = 0.40 V (vs. AgCl/Ag) in the presence of NaClO₄ in H₂O. Addition of HClO₄ to the solutions shifted the redox peaks to higher potentials, E_1/2 = 0.51 V (vs. Ag⁺/Ag) in MeCN and E_1/2 = 0.48 V (vs. AgCl/Ag) in H₂O, respectively, which was ascribed to positive charge of tertiary ammonium group formed by protonation of the amino group of the azaferrocenophane. E_1/2 of SAM of 1 in H₂O solution varies depending on the anion contained in the electrolyte, NaClO₄ (0.40 V), NaBF₄ (0.46 V), Na₂SO₄ (0.53 V), and NaCl (0.55 V). Kinetic data of electron transfer between the Fe center and the gold surface of the SAM of 2-4 were obtained with variable scanning rate. Laviron’s analysis provided tunneling constant β, 0.05 Å⁻¹, suggesting that the structural changes in the SAMs on oxidation/reduction undergoes the insignificant change of the kinetic constants of the electron transfer depending on the range of the spacer length. In the acidic aqueous media, the kinetic parameters indicated that the imbalanced electron transfer between oxidized and reduced states of the Fe center was caused by the protonation of bridged amine group of azaferrocenophane.     

Structure and properties of protonated N-alkyl-2-aza[3]ferrocenophanes

Protonation of N-alkyl-2-aza[3]ferrocenophanes by HCl and NH₄PF₆ affords hexafluorophosphate salts having a trialkylammonium group. Structures of the protonated and unprotonated N-(p-methylbezyl)-2-aza[3]ferrocenophanes were determined by X-ray crystallography. Variable temperature ¹³C{¹H} NMR spectra of the N-protonated N-hexyl-2-aza[3]ferrocenophane revealed inversion of the nitrogen of the 2-aza[3]ferrocenophane on the NMR time scale probably via partial deprotonation of the nitrogen atom. Cyclic voltammograms of the N-protonated compounds exhibited reversible redox peaks at higher potentials than those of the corresponding neutral ferrocenophanes.     

Dual-phase solid polymer electrolytes prepared from styrene–butadiene copolymer latices

A new dual-phase solid polymer electrolyte system has been proposed. In this system, a network of ion pathways is formed in a low-polarity, host polymer matrix. A series of electrolytes were prepared from styrene-butadiene copolymer latices with dissolved lithium salts. Polymer films were formed from these latices, and then impregnated with γ-butyrolactone (γ-BL) or γ-butyrolactone/dimethoxyethane mixture (γ-BL/DME), giving latex polymer electrolytes. The ionic conductivity of the polymer electrolyte system increased with increasing solvent content, although a distinct percolation threshold was not measured. Ionic conductivity also increased with the use of DME cosolvent, with the highest conductivity being 1.4 × 10^?4S/cm. Complex impedance diagrams are discussed. The diagrams show significant deviations from the ideal. TEM/SEM observations are consistent with the desired dual-phase morphology. © 1993 John Wiley & Sons, Inc.