Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

Every 8-uniform 8-regular hypergraph is 2-colorable

As is well known, Lovász Local Lemma implies that everyd-uniformd-regular hypergraph is 2-colorable, providedd 9. We present a different proof of a slightly stronger result; everyd-uniformd-regular hypergraph is 2-colorable, providedd 8.Research supported in part by Allon Fellowship and by a grant from the United States Israel Binational Science Foundation.     

An organometallic inhibitor for glycogen synthase kinase 3

Replacing natural products with kinetically inert metal complexes may lead to a new class of therapeutics in which a metal center plays the role of an innocent bystander, organizing the orientation of the organic ligands in the receptor space. As an example of this approach, a ruthenium complex is described that copies the binding mode of indolocarbazole protein kinase inhibitors and serves as a reversible, low-nanomolar inhibitor for glycogen synthase kinase 3 (GSK-3).     

A Heuristic for the Control of Inventory in a Multi-echelon Environment with Transportation Costs and Capacity Limitations

This paper develops, demonstrates and tests a heuristic procedure for controlling finished goods in a multi-echelon environment where there are significant transportation costs and capacity limitations on storage and transportation resources. This overall problem can be formulated as a large, mixed-integer linear programme (MILP), but solving such a model for practical-sized problems is costly and time-consuming, or even impossible, given computer systems typically used by businesses. Instead, the MILP formulation is used to both motivate and provide a benchmark for testing the performance of the heuristic procedure developed in this paper. When compared to the optimal results from the MILP, the cost performance of the heuristic procedure is found to be excellent.     

Thermal stresses in a solid containing parallel circular cracks

This paper presents an analysis of the steady-state thermal stresses and displacements in an infinite elastic medium containing two or more parallel coaxial circular cracks. A “perturbation” technique is employed to reduce the problem of finding the temperature and the induced stresses to integral equations of Fredholm type which may be solved by numerical means or iterations. Two types of prescribed thermal conditions are considered. The first is concerned with a uniform flow of heat disturbed by insulated cracks and the second deals with stress-free cracks whose surfaces are exposed to identical amounts of heat. The details of the analysis are illustrated by considering the case of two cracks symmetrically located about the mid plane of the solid. When the cracks are of equal radii, iterative solutions of the governing integral equations are derived and used to determine expressions for the stress-intensity factors (opening and edge-sliding modes), displacements of crack surfaces and other quantities of physical interest which are valid for widely spaced cracks.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.