The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds—i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

Approximation algorithms

Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science.

Filamentary microstructure and linear temperature dependence of normal state transport in optimized high temperature superconductors

A filamentary model of “metallic” conduction in layered high temperature superconductive cuprates explains the concurrence of normal state resistivities (Hall mobilities) linear in T (T−2) with optimized superconductivity. The model predicts the lowest temperature T0 for which linearity holds and it also predicts the maximum superconductive transition temperature Tc. The theory abandons the effective medium approximation that includes Fermi liquid as well as all other nonpercolative models in favor of countable smart basis states.

Lamellar lipoproteins uniquely contribute to hyperlipidemia in mice doubly deficient in apolipoprotein E and hepatic lipase

Remnants of triglyceride-rich lipoproteins containing apolipoprotein (apo) B-48 accumulate in apo E-deficient mice, causing pronounced hypercholesterolemia. Mice doubly deficient in apo E and hepatic lipase have more pronounced hypercholesterolemia, even though remnants do not accumulate appreciably in mice deficient in hepatic lipase alone. Here we show that the doubly deficient mice manifest a unique lamellar hyperlipoproteinemia, characterized by vesicular particles 600 Å–1,300 Å in diameter. As seen by negative-staining electron microscopy, these lipoproteins also contain an electron-lucent region adjacent to the vesicle wall, similar to the core of typical lipoproteins. Correlative chemical analysis indicates that the vesicle wall is composed of a 1:1 molar mixture of cholesterol and phospholipids, whereas the electron-lucent region appears to be composed of cholesteryl esters (about 12% of the particle mass). Like the spherical lipoproteins of doubly deficient mice, the vesicular particles contain apo B-48, but they are particularly rich in apo A-IV. We propose that cholesteryl esters are removed from spherical lipoproteins of these mice by scavenger receptor B1, leaving behind polar lipid-rich particles that fuse to form vesicular lipoproteins. Hepatic lipase may prevent such vesicular lipoproteins from accumulating in apo E-deficient mice by hydrolyzing phosphatidyl choline as scavenger receptor B1 removes the cholesteryl esters and by gradual endocytosis of lipoproteins bound to hepatic lipase on the surface of hepatocytes.

Bcl-2 interacting protein, BAG-1, binds to and activates the kinase Raf-1.

The Bcl-2 protein blocks programmed cell death (apoptosis) through an unknown mechanism. Previously we identified a Bcl-2 interacting protein BAG-1 that enhances the anti-apoptotic effects of Bcl-2. Like BAG-1, the serine/threonine protein kinase Raf-1 also can functionally cooperate with Bcl-2 in suppressing apoptosis. Here we show that Raf-1 and BAG-1 specifically interact in vitro and in yeast two-hybrid assays. Raf-1 and BAG-1 can also be coimmunoprecipitated from mammalian cells and from insect cells infected with recombinant baculoviruses encoding these proteins. Furthermore, bacterially-produced BAG-1 protein can increase the kinase activity of Raf-1 in vitro. BAG-1 also activates this mammalian kinase in yeast. These observations suggest that the Bcl-2 binding protein BAG-1 joins Ras and 14-3-3 proteins as potential activators of the kinase Raf-1.