On depth first search strees inm-out digraphs

We consider depth first search (DFS for short) trees in a class of random digraphs: am-out model. Let _i be thei ^th vertex encountered by DFS andL(i, m, n) be the height of _i in the corresponding DFS tree. We show that ifi/n asn, then there exists a constanta(,m), to be defined later, such thatL(i, m, n)/n converges in probability toa(,m) asn. We also obtain results concerning the number of vertices and the number of leaves in a DFS tree.     

Some aspects of the dependence of solid-state structure on electron count

The method of moments is used to show how the structures of molecules and solids is sensitive to the number of valence electrons.     

Transport processes in the sorption of colored ions by peat particles

A three-step model has been proposed for the adsorption of Astrazone Blue dye (Basic Blue 69) on peat. The initial rate of uptake of dye ions due to physical adsorption and chemisorption (ion exchange) has been correlated using a surface mass transfer coefficient. These coefficients have been determined and expressed in the dimensionless mass transfer form, Sh/Sc^0.33, as a function of agitation, initial dye concentration, peat particle size range, dye solution temperature, and mass of peat.     

Preparation of some substituted imidazo[1,2-a]pyridine derivatives

2-Bromopyridine derivatives 2a-2c were prepared. Compounds 2b and 2c and ammonia yielded aminopyridines 3b and 3c which were converted to imidazo[1,2-a]pyridine derivatives 4b and 4c . Compound 4b was nitrated giving the analogue 5b of metronidazole 1 .     

Including correlation effects in an improved spreadsheet calculation of combined standard uncertainties

A spreadsheet method allowing rapid calculation of combined standard uncertainties is described. The model used allows explicitly for correlation effects, and requires a user to enter only the parameters, the calculation used to obtain the final result (including relevant influence factors), the individual standard uncertainties for the parameters, and estimates of correlation coefficients where necessary. The estimation of correlation coefficients in common cases is discussed, and it is shown that correlation is likely to be practically significant only when the correlated contribution to individual standard uncertainties is significantly over about 30% of the relevant standard uncertainty, leading to correlation coefficients |r| greater than 0.1. The implementation includes a more robust differentiation algorithm than previously reported for spreadsheet use, and initial preparation of the spreadsheets has been automated. The principle is illustrated with a simple example. Electronic Supplementary Material  Supplementary material is available in the online version of this article at and is accessible for authorized users.

Preprocessing of rotamers for protein design calculations

We have developed a process that significantly reduces the number of rotamers in computational protein design calculations. This process, which we call Vegas, results in dramatic computational performance increases when used with algorithms based on the dead-end elimination (DEE) theorem. Vegas estimates the energy of each rotamer at each position by fixing each rotamer in turn and utilizing various search algorithms to optimize the remaining positions. Algorithms used for this context specific optimization can include Monte Carlo, self-consistent mean field, and the evaluation of an expression that generates a lower bound energy for the fixed rotamer. Rotamers with energies above a user-defined cutoff value are eliminated. We found that using Vegas to preprocess rotamers significantly reduced the calculation time of subsequent DEE-based algorithms while retaining the global minimum energy conformation. For a full boundary design of a 51 amino acid fragment of engrailed homeodomain, the total calculation time was reduced by 12-fold.     

The stereochemistry of the hydroboration rearrangement.

Hydroboration of 1,2-dimethylcyclopentene with BH₃·THF affords a product in which boron migrates $\text{stereospecifically}$ at low temperature into the cyclopentane ring. At higher temperatures subsequent (non-stereospecific) isomerisation occurs via a competing reaction mechanism.     

Cyclic ketones and substituted α-keto acids as alternative substrates for novel Biginelli-like scaffold syntheses

The reactions of benzocyclic ketones and α-ketoacids as carbonyl components in the Biginelli reaction were investigated. These unusual Biginelli substrates furnished novel drug-like dihydropyrimidinone scaffolds suitable for further elaboration.