Stable in situ sorting and minimum data movement

In this paper, we describe an algorithm to stably sort an array ofn elements using only a linear number of data movements and constant extra space, albeit in quadratic time. It was not known previously whether such an algorithm existed. When the input contains only a constant number of distinct values, we present a sequence ofin situ stable sorting algorithms makingO(n lg^(k+1) n+kn) comparisons (lg^(K) means lg iteratedk times and lg* the number of times the logarithm must be taken to give a result 0) andO(kn) data movements for any fixed valuek, culminating in one that makesO(n lg*n) comparisons and data movements. Stable versions of quicksort follow from these algorithms.Research supported by Natural Sciences and Engineering Research Council of Canada grant No.A-8237 and the Information Technology Research Centre of Ontario.Supported in part by a Research Initiation Grant from the Virginia Engineering Foundation.     

An STO-3G investigation of barriers to rotation in model systems for aromatic polycarbonates

Non-empirical, STO-3G, and semi-empirical, MNDO, calculations have been performed to investigate the rigid rotation of the phenyl group in phenyl carbonic acid, as a model for Bisphenol A polycarbonate. The MNDO results predict a barrier to rotation of ～55 kcal mole^?1, a factor of ～2 greater than that for the STO-3G computations. Analysis of the relevant orbital energies dictates that the lowest excited state of phenyl carbonic acid is $\text{π → π}{}^1$.     

Bupropion hydrochloride: the development of a chiral separation using an ovomucoid column

The separation of bupropion enantiomers on an ovomucoid stationary phase was investigated. The mobile- and stationary-phase parameters that may influence the separation were identified. The parameters that were studied include: type and concentration of organic modifier, mobile phase pH, ionic strength, type of buffer, and column temperature, as well as the effect that the amount of sample injected had on the separation. The optimized chiral separation baseline-resolved the enantiomers in less than 10 min. Calibration curves for a standard were linear over a range of 0.27-53.0 microg/g (ppm) with a correlation coefficient of 0.999 for both enantiomers. A detection limit of 0.13 microg/g and a quantitation limit of 0.27 microg/g were also found. The system precision of the method was 0.2%.     

A preliminary investigation of the thermal and X-ray induced degradation of cellulose nitrates by FAB/SIMS and 13C NMR

Some surface aspects of the thermal and X-ray induced degradation of a cellulose nitrate have been studied by FAB/SIMS.The pristine material gives peaks at 30 and 46 amu, indicative of NO⁺ and NO₂⁺ originating from the nitrate ester groups. The thermally degraded material indicates these peaks at slightly lower intensities, whereas the X-ray degraded material shows little evidence for their appearance. These data complement recent ESCA data on the same systems.¹The conclusion is that electromagnetic degradation is predominantly a surface effect, whereas thermal degradation is a bulk oriented phenomenon. ¹³C nmr has been used to add further evidence for this last point.     

Three-dimensional blow-up solutions of the Navier-Stokes equations

In this paper we extend the plane blow-up results of Grundy& McLaughlin (1997) to the three-dimensional Navier-Stokes equations.Using a solution structure originally due to Lin we first providenumerical evidence for the existence of blow-up solutions on- < x, z < , 0 y 1 with boundary conditions on y = 0and y = 1 involving derivatives of the velocity components.The formulation enables us to consider plane and radial flowas special cases. Various features of the computations are isolatedand are used to construct a formal asymptotic solution closeto blow-up. We show that the numerical and asymptotic analysesprovide a mutually consistent global picture which supportsthe conclusion that, for the family of problems we considerhere, blow-up in fact can take place in three dimensions butat an inverse linear rate rather than the faster inverse squareof the plane case.     

The analysis of a fringe heuristic for binary search trees

A detailed analysis is presented for the behaviour of binary search trees built by using a heuristic that performs only local reorganizations at the bottom of the tree.