Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Projected gradient approach to the numerical solution of the SCoTLASS

The SCoTLASS problem-principal component analysis modified so that the components satisfy the Least Absolute Shrinkage and Selection Operator (LASSO) constraint-is reformulated as a dynamical system on the unit sphere. The LASSO inequality constraint is tackled by exterior penalty function. A globally convergent algorithm is developed based on the projected gradient approach. The algorithm is illustrated numerically and discussed on a well-known data set. (c) 2004 Elsevier B.V. All rights reserved.

The promotion of grassland forb abundance: A chemical or biological solution?

Techniques that increase the biodiversity value of species-poor grassland are required if conservation targets aimed at reversing the decline in species-rich grassland are to be met. This study investigated the diversification of swards dominated by Lolium perenne by testing the efficacies of two treatments applied to reduce competitive exclusion of species introduced as seed. The 'biological' treatment was the addition of the hemiparasitic plant species introduced as seed. The 'biological' treatment was the application of a selective graminicide, fluazifop-P-butyl (Fusilade 250EW). Changes in plant community composition were monitored for a period of 2 years. Values of plant species richness increased significantly between years regardless of treatment, but to a greater extent in plots sown with R. minor. The number of established sown species and their richness and tended to promote unsown species rather than those introduced as seed. Overall, the R. minor treatment was associated with the greatest impact on sward composition, facilitating establishment and development of the introduced species and promoting forb abundance. (c) 2007 Gessellschaft fur Okologie. Published by Elsevier GmbH. All rights reserved.

Metal complexes of a tetraazacyclophane: solution and molecular modelling studies

An alternative synthetic approach to yield the compound 2,3,5,6,8,9,11,14-octahydrobenzo[1][ 1,4,7,10]tetraazacyclotetradecine (bz[14]N-4) is presented. The protonation constants of bz[14]N-4 and the stability constants of its complexes with Ni2+, Cu2+, Zn2+, Cd2+, Pb2+ were determined in H2O at 25degreesC with ionic strength 0.10 mol dm(-3) in KNO3 and they were compared with structurally related macrocycles cyclam (1,4,8,11-tetraazacyclotetradecane) and cyclen (1,4,7,10-tetraazacyclododecane). These studies indicate that only 1 : 1 ( M : L) species are formed in solution, and the ligand exhibits a high affinity for larger ions such as Cd2+ and Pb2+. The X-ray study of [bz[14]N4H3](3+) shows that an inclusion compound with a chloride counter-anion is formed through NH...Cl hydrogen bonds. Spectroscopic data in solution ( electronic and NMR spectra) showed that the macrocycle adopts a planar arrangement upon metal complexation. Molecular mechanics calculations reveal that in spite of the presence of the benzene ring in the macrocyclic framework this ligand can encapsulate metal ions with different stereo-electronic sizes in square planar arrangements. Our results indicate that the presence of the benzene ring in the backbone of the bz[14]N-4 confers a coordination behaviour intermediate between that of cyclam and cyclen.

Direct detection of dimethylstannylene and tetramethyldistannene in solution and the gas phase by laser flash photolysis of 1,1-dimethylstannacyclopent-3-enes

The photochemistry of 1,1-dimethyl- and 1,1,3,4-tetramethylstannacyclopent-3-ene (4a and 4b,respectively) has been studied in the gas phase and in hexane solution by steady-state and 193-nm laser flash photolysis methods. Photolysis of the two compounds results in the formation of 1,3-butadiene (from 4a) and 2,3-dimethyl-1,3-butadiene (from 4b) as the major products, suggesting that cycloreversion to yield dimethylstannylene (SnMe2) is the main photodecomposition pathway of these molecules. Indeed, the stannylene has been trapped as the Sn-H insertion product upon photolysis of 4a in hexane containing trimethylstannane. Flash photolysis of 4a in the gas phase affords a transient absorbing in the 450-520nm range that is assigned to SnMe2 by comparison of its spectrum and reactivity to those previously reported from other precursors. Flash photolysis of 4b in hexane solution affords results consistent with the initial formation of SnMe2 (lambda(max) approximate to 500 nm), which decays over similar to 10 mu s to form tetramethyldistannene (5b; lambda(max) approximate to 470 nm). The distannene decays over the next ca. 50 mu s to form at least two other longer-lived species, which are assigned to higher SnMe2 oligomers. Time-dependent DFT calculations support the spectral assignments for SnMe2 and Sn2Me4, and calculations examining the variation in bond dissociation energy with substituent (H, Me, and Ph) in disilenes, digermenes, and distannenes rule out the possibility that dimerization of SnMe2 proceeds reversibly. Addition of methanol leads to reversible reaction with SnMe2 to form a transient absorbing at lambda(max) approximate to 360 nm, which is assigned to the Lewis acid-base complex between SnMe2 and the alcohol.