A closed-form representation of mixed-integer program value functions

We identify a class of formulas computable in polynomial time such that the functions defined by these formulas are precisely the value functions of mixed-integer programs with rational constraint coefficients.     

Dynamic supercoiling bifurcations of growing elastic filaments

Certain bacteria form filamentous colonies when the cells fail to separate after dividing. In Bacillus subtilis, Bacillus thermus, and Cyanobacteria, the filaments can wrap into complex supercoiled structures as the cells grow. The structures may be solenoids or plectonemes, with or without branches in the latter case. Any microscopic theory of these morphological instabilities must address the nature of pattern selection in the presence of growth, for growth renders the problem nonautonomous and the bifurcations dynamic. To gain insight into these phenomena, we formulate a general theory for growing elastic filaments with bending and twisting resistance in a viscous medium, and study an illustrative model problem: a growing filament with preferred twist, closed into a loop. Growth depletes the twist, inducing a twist strain. The closure of the loop prevents the filament from unwinding back to the preferred twist; instead, twist relaxation is accomplished by the formation of supercoils. Growth also produces viscous stresses on the filament which even in the absence of twist produce buckling instabilities. Our linear stability analysis and numerical studies reveal two dynamic regimes. For small intrinsic twist the instability is akin to Euler buckling, leading to solenoidal structures, while for large twist it is like the classic writhing of a twisted filament, producing plectonemic windings. This model may apply to situations in which supercoils form only, or more readily, when axial rotation of filaments is blocked. Applications to specific biological systems are proposed.     

Task Specific Onium Salts and Ionic Liquids as Soluble Supports in Grieco ’s Multicomponent Synthesis of Tetrahydroquinolines

In this work was presented an application of the use of task specific onium salts (TSOSs) as soluble supports in Grieco’s multicomponent synthesis of tetrahydroquinolines. These soluble supports are of wide applicability and combine advantages of solid phase synthesis without its limitations with those of solution phase chemistry. After a simple washing step, products were cleaved from the supports and obtained in pure form and good yields.     

A large deviation principle for 2D stochastic Navier–Stokes equation

In this paper one specifies the ergodic behavior of the 2D-stochastic Navier–Stokes equation by giving a Large Deviation Principle for the occupation measure for large time. It describes the exact rate of exponential convergence. The considered random force is non-degenerate and compatible with the strong Feller property.     

Critical percolation exploration path and SLE 6: a proof of convergence

It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE ₆. We provide here a detailed proof, which relies on Smirnov’s theorem that crossing probabilities have a conformally invariant scaling limit (given by Cardy’s formula). The version of convergence to SLE ₆ that we prove suffices for the Smirnov–Werner derivation of certain critical percolation crossing exponents and for our analysis of the critical percolation full scaling limit as a process of continuum nonsimple loops. Research of Charles M.Newman was partially supported by the US NSF under grants DMS-01-04278 and DMS-06-06696.     

General Aspects and Optimization of Enantioselective Biocatalysis in Organic Solvents: The Use of Lipases [New Synthetic Methods (76)]

Enantioselective biocatalysis in nonaqueous media is becoming increasingly important in preparative synthetic chemistry. This article discusses (1) the general catalytic properties of enzymes in nonaqueous environments, (2) the basic principles that govern lipase-catalyzed enantioselective esterification and transesterification reactions in organic media for the preparation of optically active acids and alcohols, (3) the determination of kinetic and thermodynamic parameters, and (4) the quantitative analysis of published data.     

Autour du théorème de Ferrand–Obata (Concerning the Theorem of Ferrand–Obata)

The aim of this article is to give a new dynamical proof of the Ferrand–Obata theorem when the manifold is compact. This will give us a generalisation of this theorem to transversally conformal foliations ofcodimension greater than three and constant basic functions.