New parallel optimal‐parameter fast multipole method (OPFMM)

The three key translation equations of the fast multipole method (FMM) are deduced from the general polypolar expansions given earlier. Simplifications are introduced for the rotation‐based FMM that lead to a very compact FMM formalism. The optimum‐parameter searching procedure, a stable and efficient way of obtaining the optimum set of FMM parameters, is established with complete control over the tolerable error (ε). This new procedure optimizes the linear scaling with respect to the number of particles for a given ε. In addition, a new parallel FMM algorithm, which requires virtually no internode communication, is suggested that is suitable for the parallel construction of Fock matrices in electronic structure calculations. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1484–1501, 2001     

The Ramifications of the Centres: Quantised Function Algebras at Roots of Unity

This paper continues the study of quantised function algebrasO[G] of a semisimple group G at an lth root of unity . Thesealgebras were introduced by De Concini and Lyubashenko in 1994,and studied further by De Concini and Procesi and by Gordon,amongst others. Our main purpose here is to increase understandingof the finite-dimensional factor algebras O[G](g), for g G.We determine the representation type and block structure ofthese factors, and (for many g) describe them up to isomorphism.A series of parallel results is obtained for the quantised Borelalgebras and . 2000 Mathematical Subject Classification: 16W35,17B37.     

Construction of the Incipient Infinite Cluster for Spread-out Oriented Percolation Above 4 + 1 Dimensions

 We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ ^d × ℤ₊, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ ⁿ (E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n)  ℤ ^d × ℤ₊, summing this probability over x  ℤ ^d , and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ_∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n ⁻¹, we prove existence of a limiting measure ℚ_∞, with ℚ_∞ = ℙ_∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension of the cluster of the origin, under ℙ_∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented percolation to super-Brownian motion, for d+1 > 4+1. Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002 RID="*" ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl     

Photoinduced formation of a cryptand from a coronand: an unexpected switch in cation binding affinity

Aza-crown ethers 2 and 3 with anthracene-containing pendant arms have been synthesised and characterised. Both compounds bind Group 1 metal cations in solution, forming complexes of 1:1 stoichiometry. The properties of compound 2 and its complexes have been studied by a range of techniques, including NMR, UV and fluorescence spectroscopy and X-ray crystallography. The pendant arms can adopt either a cis or a trans geometry, the cis geometry favoured with larger cations. The geometry of the complex affects the fluorescence properties of the system, with larger cations giving higher excimer/monomer ratios. Upon irradiation at lambda>300 nm, coronand 2 forms the cryptand 5 through a reversible intramolecular [4pi+4pi] cycloaddition reaction. The rates of the forward and reverse reactions of this photochromic process are cation dependent; in particular the rate of the thermal reverse reaction is decreased by smaller cations and increased by larger cations, especially Rb(+). The metal binding constants in methanol for 2 and 5 have been determined, revealing that the cryptand 5 binds Na(+) and Rb(+) more weakly than crown ether 2 by over two orders of magnitude.     

Gene expression profiling using advanced mass spectrometric approaches

In the era of systems biology, computational and high-throughput experimental biological approaches are increasingly being combined to provide global snapshots of entire genomes and proteomes under tissue- and disease-specific conditions. The aim is to identify proteins changing in concentration and/or post-translational state and/or location, and develop a better molecular level understanding of the operation of biological systems. Here we describe an approach for comparative proteomics that builds upon the combination of high-performance nano-scale separations with the high-mass measurement accuracy, mass-resolving power and sensitivity of Fourier transform ion cyclotron resonance mass spectrometry to provide broad dynamic range, comprehensive and quantitative proteome measurements.     

High resolution spectrophotometry for identification of chlorine dioxide in concentrated chlorine solutions

Electrolyzed salt brine generators hold great promise for water disinfection in small communities and remote locations. Electrolysis cell liquors have been reported to contain chlorine, chlorine dioxide and ozone. High resolution spectrophotometry was used to observe the presence (or absence) of a unique spectral absorbance pattern present in solutions containing 1-2 mg/l chlorine dioxide.     

Structure of adamantan-1-ammonium 1-adamantanecarboxylate

Adamantan-1-ammonium 1-adamantanecarboxylate, C₂₁H₃₃NO₂ (I) is a novel dispiro-type compound. Aminoadamantane derivatives, in which the spiro carbon atoms are part of heterocyclic rings, are of potential interest as biological active substances and antiviral agents. Complex (I) crystallizes in the centrosymmetric space group C2/c (No. 15) with eight molecules in the unit cell with a = 25.227(4), b = 6.527(1), c = 22.489(4) Å, and = 90.75(1)°. The two spiro units are a 1-adamantylammonium cation and a 1-adamantane carbonyloxy anion. The complex units are stabilized by a network of intermolecular carbonyloxy-to-amine hydrogen bonding and van der Waals cohesive forces. Germane bond lengths are: C—N = 1.479(9) and C—O (mean) = 1.25(2) Å.     

On the Normal Subgroups of

We give a characterization theorem for the -normalized subgroups of , where is any commutative ring. This is the last of the simple Chevalley-Demazure group-schemes for which such a theorem is lacking.