A modular integer GCD algorithm

This paper describes the first algorithm to compute the greatest common divisor (GCD) of two n-bit integers using a modular representation for intermediate values U, V and also for the result. It is based on a reduction step, similar to one used in the accelerated algorithm [T. Jebelean, A generalization of the binary GCD algorithm, in: ISSAC '93: International Symposium on Symbolic and Algebraic Computation, Kiev, Ukraine, 1993, pp. 111–116; K. Weber, The accelerated integer GCD algorithm, ACM Trans. Math. Softw. 21 (1995) 111–122] when U and V are close to the same size, that replaces U by (U−bV)/p, where p is one of the prime moduli and b is the unique integer in the interval (−p/2,p/2) such that . When the algorithm is executed on a bit common CRCW PRAM with O(nlognlogloglogn) processors, it takes O(n) time in the worst case. A heuristic model of the average case yields O(n/logn) time on the same number of processors.     

Aqueous solution and solid state interactions of lanthanide ions with a methacrylic ester polymer bearing pendant 15‐crown‐5 moieties

The interaction between trivalent lanthanide ions and poly(1,4,7,10,13‐pentaoxacyclopentadecan‐2‐yl‐methyl methacrylate), PCR5, in aqueous solution and in the solid state have been studied. In aqueous solution, evidence of a weak interaction between the lanthanides and PCR5 comes from the small red shift of the Ce(III) emission spectra and the slight broadening of the Gd(III) EPR spectra. From the Tb(III) lifetimes in the presence of H₂O and D₂O the loss of one or two water coordinated molecules is confirmed when Tb(III) is bound to PCR5. An association constant of the order of 200 M^?1 was obtained for a 1:1 (lanthanide:15‐crown‐5) complex from the shift of the polymer NMR signals induced by Tb(III). A similar association constant is obtained from the differences of the molar conductivity of Ce(III) solution at various concentrations in presence and absence of PCR5. When Tb(III) is adsorbed on PCR5 membranes, lifetime experiments in H₂O and D₂O confirm the loss of 5 or 6 water coordinated molecules indicating that in solid state the lanthanide(III)‐PCR5 interaction is stronger than in solution. The adsorption of Ce(III) in PCR5 membranes shows a Langmuir type isotherm, from which an equilibrium constant of 39 M^?1 has been calculated. SEM shows that the membrane morphology is not much affected by lanthanide adsorption. Support for lanthanide ion–crown interactions comes from ab initio calculations on 15‐crown‐5/La(III) complex. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1788–1799, 2007     

R-Matrices for Leibniz Algebras

Leibniz agebras are a generalization of Lie algebras, where no symmetry properties of the bracket are required. In this Letter we introduce a notion of R-matrices for this structure and the related Yang–Baxter equations, and discuss some of their basic properties.     

Modeling Language Evolution

We describe a model for the evolution of the languages used by the agents of a society. Our main result proves convergence of these languages to a common one under certain conditions. A few special cases are elaborated in more depth.     

Studies on quinones. XIV1. Oxidative demethylation of hydroquinones dimethylethers with nitric acid- impregnated manganese dioxide

The oxidative cleavage of several hydroquinones dimethylethers with nitric acid- impregnated manganese dioxide, in methylene chloride solution at room temperature, gave the corresponding quinones in 76–95% yield.     

Pretreatment of sugarcane bagasse hemicellulose hydrolysate for xylitol production byCandida guilliermondii

Applied Biochemistry and Biotechnology - In order to remove or reduce the concentrations of toxic substances present in the sugarcane bagasse hemicellulose hydrolysate for xyloseto-xylitol...     

On the theory of solvent effects

A simple electrostatic analysis is given of the virtual charge (solvaton) model to represent the environment effect on the electronic wave function of a solute immersed in a polarizable surrounding. New features of this model are found. The classical aspects are discussed and secondly the quantal implications are considered. A correct Hartree-Fock-like operator is derived which represents an electron in a molecular orbital subjected to the average effect of the other electrons and to the reaction field produced by the virtual charges on the atomic centers.A general formalism based on the preceding model is presented in appendix. The final equations have a form similar to Newton's equation to represent a solvated electron. Unlike some other theories in this field, there is no cut-off involved in the evaluation of the molecular integrals.     

Unusually high phosphodiesterolytic activity of La(III) hydroxide complexes stabilized by glycine derivatives

Glycine and N,N-dimethylglycine stabilize La(III) hydroxide complexes of the type La2L2(OH)4 which possess phosphodiesterolytic activity close to that observed with most active tetravalent cations like Ce(IV).     

Maximizing the xylitol production from sugar cane bagasse hydrolysate by controlling the aeration rate

Batch fermentations of sugar cane bagasse hemicellulosic hydrolysate treated for removing the inhibitors of the fermentation were performed byCandida guilliermondii FTI20037 for xylitol production. The fermentative parameters agitation and aeration rate were studied aiming the maximization of xylitol production from this agroindustrial residue. The maximal xylitol volumetric productivity (0.87 g/L h) and yield (0.67 g/g) were attained at 400/min and 0.45 v.v.m. (K_La 27/h). According to the results, a suitable control of the oxygen input permitting the xylitol formation from sugar cane bagasse hydrolysate is required for the development of an efficient fermentation process for large-scale applications.     

An ab-initio study of the molecular structure and properties of HPO

An ab-initio gaussian lobe function study of the structure and some molecular properties of the HPO molecule is reported. By a partial optimization of the geometrical structure the following equilibrium structure parameters are found: r_PO = 1.536 Å; r_PH = 1.475 Å; the bond angle is found to be close to 102° with a bending force constant of 0.58 mdyne/Å. The dipole moment, effective charges and quadrupole term components at various bond angles are reported. The wavefunction of the equilibrium geometry is available from the authors upon request.