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.     

Numerical Simulation of Free Surface-Structure-Interaction with Multi-Regional Mesh Deformation

The Fluid-Structure-Interactions (FSI) for technological constructions on sea are becoming nowadays very important in view of growing consumption of renewable energy sources. Exceptionally the offshore wind farms are exposed to extreme weather conditions due to breaking and non-breaking wave loads. This work presents numerical Finite-Volume-Method (FVM) analysis of fluid and structure interactions with water waves impact on elastic solid structures. We develop a Free Surface-Structure-Interaction (FSSI) solver in OpenFAOM [1] with multi-regional mesh deformation. A two dimensional numerical water impact model on a damping element prototype of an offshore wind turbin tower is investigated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quantitation of glucosamine sulfate in plasma by HPLC-MS/MS after administration of powder for oral solution formulation

A rapid method for the quantification of glucosamine in human plasma using high‐performance liquid chromatography coupled to tandem mass spectrometry was developed and validated. The sample preparation includes a simple deproteinization step, using d ‐[1‐¹³C] glucosamine hydrochloride as an internal standard. Chromatographic separation was performed on an ACE Ciano column using isocratic elution with acetonitrile and aqueous 2 mm ammonium acetate containing 0.025% formic acid (80:20). Selected reaction monitoring was performed using the transitions m/z 180.1 → m/z 72.1 and m/z 181.0 → m/z 74.6 to quantify glucosamine and internal standard, respectively. The method was validated and proved to be linear, accurate and precise over the range 50–5000 ng/mL of glucosamine. Recovery rates higher than 90% were obtained for both glucosamine and internal standard. No matrix effect was detected in the samples. The validated method was successfully applied to a pharmacokinetic study after oral administration of a powder for oral solution formulation containing glucosamine sulfate. Copyright © 2011 John Wiley & Sons, Ltd.     

Zur Untersuchung von Drogen und daraus dargestellten Pr?paraten

Ohne Zusammenfassung     

Maximality of the signless Laplacian energy

We study the problem of determining the graph with $n$ vertices having largest signless Laplacian energy. We conjecture it is the complete split graph whose independent set has (roughly) $2n∕3$ vertices. We show that the conjecture is true for several classes of graphs. In particular, the conjecture holds for the set of all complete split graphs of order $n$, for trees, for unicyclic and bicyclic graphs. We also give conditions on the number of edges, number of cycles and number of small eigenvalues so the graph satisfies the conjecture.     

Effective operators for magic ±2 nuclei

Using the many-body Green function technique effective operators for magix ±2 nuclei are derived. Our formulation allows a microscopic proof of the heuristically found additivity of anomalous moments. Possible deviations of the rule are quantitatively discussed. The theory is applied to²⁰⁶Pb,²¹⁰Pb and²¹⁰Po. The theoretical results are in good agreement with experiment.     

On the distribution of Laplacian eigenvalues of trees

For a tree T$T$ with n$n$ vertices, we apply an algorithm due to Jacobs and Trevisan (2011) to study how the number of small Laplacian eigenvalues behaves when the tree is transformed by a transformation defined by Mohar (2007). This allows us to obtain a new bound for the number of eigenvalues that are smaller than 2. We also report our progress towards a conjecture on the number of eigenvalues that are smaller than the average degree.