Clarkson's algorithm for violator spaces

Clarkson's algorithm is a three-staged randomized algorithm for solving linear programs. This algorithm has been simplified and adapted to fit the framework of LP-type problems. In this framework we can tackle a number of non-linear problems such as computing the smallest enclosing ball of a set of points in Rd. In 2006, it has been shown that the algorithm in its original form works for violator spaces too, which are a proper generalization of LP-type problems. It was not clear, however, whether previous simplifications of the algorithm carry over to the new setting.In this paper we show the following theoretical results: (a) It is shown, for the first time, that Clarkson's second stage can be simplified. (b) The previous simplifications of Clarkson's first stage carry over to the violator space setting. (c) The equivalence of violator spaces and partitions of the hypercube by hypercubes.     

Synthesis of Primary Amines by One-Pot Reductive Amination of Aldehydes

We report here a novel, one-pot, two-step reductive amination of aldehydes for the atom-economical synthesis of primary amines. The amination step has been carried out with hydroxylammonium chloride and does not require the use of a base. In the subsequent reduction step, a metal zinc/hydrochloride acid system has been used. This method is applicable to both aliphatic and aromatic aldehydes. The operational simplicity, the short reaction times, and the mild reaction conditions add to the value of this method as a practical alternative to the reductive amination of aldehydes.

Supplemental materials are available for this article. Go to the publisher's online edition of Synthetic Communications® to view the free supplemental file.     

Synthesis of Furoates and Furfurylic Alcohol Esters Under Very Mild Conditions Using Supported Base Catalysis

Sym-phthaloyl chloride under controlled cathodic reduction is converted into trans-[1(3H)-isobenzofuranone, 3-(3-oxo-1(3H)-isobenzofuranylidene)]: trans-biphthalyl in 65% yield.     

Attractors for a deconvolution model of turbulence

We consider a deconvolution model for 3D periodic flows. We show the existence of a global attractor for the model.     

Reynolds-averaged modeling of polymer drag reduction in turbulent flows

A novel eddy viscosity model for predicting friction drag reduction induced by polymers in turbulent wall-bounded flows is presented. The approach is based on the elliptic relaxation model modified to account for the modified Reynolds-stress equilibrium established by the presence of elastic polymer chains in the fluid. The increased wall damping of the turbulent fluctuations is obtained by modifying the pressure–strain redistribution term. Polymer solutions are represented using the Finite Extensibility Non-linear elastic FENE-P dumbbell model; only one transport equation for the elongation of the polymer chains is considered. The model reproduces the level of drag reduction observed over a wide range of rheological parameters. In addition, both the mean velocity and the turbulent fluctuations are predicted with good accuracy. The approach is computationally attractive because of its limited increase in computational cost in comparison with its Newtonian counterpart.