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.     

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.     

Hirzebruch–Milnor classes of complete intersections

We prove a new formula for the Hirzebruch–Milnor classes of global complete intersections with arbitrary singularities describing the difference between the Hirzebruch classes and the virtual ones. This generalizes a formula for the Chern–Milnor classes in the hypersurface case that was conjectured by S. Yokura and was proved by A. Parusiński and P. Pragacz. It also generalizes a formula of J. Seade and T. Suwa for the Chern–Milnor classes of complete intersections with isolated singularities.     

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.