A scaling technique for finding the weighted analytic center of a polytope

Let a bounded full dimensional polytope be defined by the systemAx b whereA is anm × n matrix. Leta _i denote theith row of the matrixA, and define theweighted analytic center of the polytope to be the point that minimizes the strictly convex barrier function – _i=1 ^m w _i ln(a _i ^T x –b _i ). The proper selection of weightsw _i can make any desired point in the interior of the polytope become the weighted analytic center. As a result, the weighted analytic center has applications in both linear and general convex programming. For simplicity we assume that the weights are positive integers.If some of thew _i 's are much larger than others, then Newton's method for minimizing the resulting barrier function is very unstable and can be very slow. Previous methods for finding the weighted analytic center relied upon a rather direct application of Newton's method potentially resulting in very slow global convergence. We present a method for finding the weighted analytic center that is based on the scaling technique of Edmonds and Karp and is an enhancement of Newton's method. The scaling algorithm runs in iterations, wherem is the number of constraints defining the polytope andW is the largest weight given on any constraint. Each iteration involves taking a step in the Newton direction and its complexity is dominated by the time needed to solve a system of linear equations.Supported by the Campus Research Board, University of Illinois at Urbana-Champaign.Supported by the National Science Foundation under Grants CCR-9057481 and CCR-9007195.     

AnO(n logn) algorithm for the all-nearest-neighbors Problem

Given a setV ofn points ink-dimensional space, and anL _q -metric (Minkowski metric), the all-nearest-neighbors problem is defined as follows: for each pointp inV, find all those points inV–{p} that are closest top under the distance metricL _q . We give anO(n logn) algorithm for the all-nearest-neighbors problem, for fixed dimensionk and fixed metricL _q . Since there is an (n logn) lower bound, in the algebraic decision-tree model of computation, on the time complexity of any algorithm that solves the all-nearest-neighbors problem (fork=1), the running time of our algorithm is optimal up to a constant factor.This research was supported by a fellowship from the Shell Foundation. The author is currently at AT&T Bell Laboratories, Murray Hill, New Jersey, USA.     

Simple, facile and one-pot conversion of the Baylis-Hillman acetates into 3,5,6-trisubstituted-2-pyridones

A facile route for the synthesis of novel 3,5,6-trisubstituted-2-pyridones from the acetylated Baylis-Hillman esters with β-enamino esters or β-enamino nitriles in one pot with good yields is described.     

Status of sol–gel process for nuclear fuels

Sol–gel process provides an alternate route for fabrication of ceramic nuclear fuel. The sol–gel process provides several advantages over the conventional powder pellet fabrication process by eliminating handling of radioactive powders. The sol–gel process uses only fluids or fluid like materials, thus become amenable to remote handling. The sol–gel process has been developed for the production of coated particle fuels for High Temperature Gas Cooled Reactors (HTGRs), as sphere-pac fuel for Fast Breeder Reactors (FBRs) and as SGMP fuel for Thermal Reactors. Internal Gelation Process is one of the most important routes of the sol–gel process and has been accepted as the most promising process route globally. Several countries having plutonium or ²³³U based fuel program have developed sol–gel process for nuclear fuels. In India there is special interest for the development of the sol–gel process for the thorium–uranium fuels keeping in view the large resources of thorium in India. Sol–gel process for fuel fabrication is also very attractive route for closing the nuclear fuel cycle efficiently. Author is BRNS Raja Ramanna Fellow.     

Determination of bromide and nitrite by indirect redox titration using phenyl iodosoacetate

Bromide has been determined by its oxidation with an excess of phenyl iodosoacetate in the presence of acetanilide to give bromine which subsequently reacts with acetanilide to form 4-bromoacetanilide. The residual amount of phenyl iodosoacetate was evaluated iodometrically. Thus, for every mol of bromide one mol of phenyl iodosoacetate was consumed. For the determination of bromine in organic compounds, the test substance was decomposed by fusion with alkali peroxide to liberate bromide which was then evaluated by the phenyl iodosoacetate method. For its determination, nitrite has been reacted with an excess of isoniazid in acid medium to form isonicotinyl azide (which does not react with phenyl iodosoacetate) and the residual amount of isoniazid was titrated with phenyl iodosoacetate in the presence of acidified bromide and methyl red indicator (when isoniazid and phenyl iodosoacetate react in a 12 molar ratio). Each mol of nitrite is equivalent to 2 mol of phenyl iodosoacetate.     

Kinetics of Catalytic Hydrogenation of 5‐Hydroxymethylfurfural to 2,5‐bis‐Hydroxymethylfuran in Aqueous Solution over Ru/C

5‐Hydroxymethylfurfural (5‐HMF) is a cellulosic product of the hydrolysis of biomass, and it is widely considered for the production of several interesting chemicals and derivatives. In the present work, catalytic hydrogenation of 5‐hydroxymethylfurfural to 2,5‐bis‐hydroxymethylfuran was investigated using 5% Ru/C in the aqueous phase. Kinetic data were experimentally obtained over a wide range of temperatures (313–343 K), H₂ partial pressure (0.69–2.07 MPa), initial HMF concentration (19.8–59.5 mM), and catalyst loading (0.3–0.7 kg/m³) in a three‐phase slurry reactor. Disappearance of initial 5‐HMF concentrations was modeled using the power law and Langmuir–Hinshelwood–Hougen–Watson models. A model based on the competitive adsorption of molecular H₂ and HMF was proposed. It is presumed that surface reaction between nondissociatively chemisorbed H₂ and 5‐HMF was rate determining. This model provided the best fit for the kinetic data. From the Arrhenius equation, the activation energy for the surface reaction was found to be 104.9 kJ/mol.     

Pellet freezing of in vitro produced bovine embryos using dry ice

In vitro produced bovine embryos were frozen by pellet freezing or vitrification method. In the pellet freezing method, the embryos were cooled on the dry ice and then frozen as pellets. At warming, the pellets were immersed directly into 0.5 M sucrose. The survival rates of blastocysts frozen by the pellet freezing method were higher (P<0.01) in 40% ethylene glycol (EG) than those in the lower concentrations (20 and 30% EG). Higher survival rates of blastocysts frozen by the pellet freezing method were obtained but the development rates did not differ, as compared with those by the vitrification method. There were no significant differences between the pellet freezing and vitrification method in the frequencies of post-thaw survival of hatched blastocysts. These results demonstrate that the pellet freezing method using dry ice can be used successfully for the cryopreservation of blastocysts.