Geometric method for a global repellor in competitive Lotka-Volterra systems

The geometric method of involving the relative positions of the nullcline planes is used to analyze the global asymptotic behavior of solutions of autonomous Lotka-Volterra competitive systems. Some observations about limit sets are made and, based on these observations, new criteria are established for the system to have a single point global repellor. Clearly, these criteria can be used to preclude the existence of nonconstant periodic solutions.     

Field Theoretic Cogalois Theory via Abstract Cogalois Theory

Abstract Cogalois Theory for arbitrary profinite groups was initiated by T. Albu and ?.A. Basarab [An Abstract Cogalois Theory for profinite groups, J. Pure. Appl. Algebra 200 (2005) 227-250]. The aim of this paper is twofold: firstly, to present the abstract group theoretic versions of various types of Kummer field extensions, and secondly, to show how some basic results of the (Field Theoretic) Cogalois Theory can be very easily deduced from their abstract versions.     

A multiwave approximate Riemann solver for ideal MHD based on relaxation. I: theoretical framework

We present a relaxation system for ideal magnetohydrodynamics (MHD) that is an extension of the Suliciu relaxation system for the Euler equations of gas dynamics. From it one can derive approximate Riemann solvers with three or seven waves, that generalize the HLLC solver for gas dynamics. Under some subcharacteristic conditions, the solvers satisfy discrete entropy inequalities, and preserve positivity of density and internal energy. The subcharacteristic conditions are nonlinear constraints on the relaxation parameters relating them to the initial states and the intermediate states of the approximate Riemann solver itself. The 7-wave version of the solver is able to resolve exactly all material and Alfven isolated contact discontinuities. Practical considerations and numerical results will be provided in another paper.     

Dualisability versus residual character: A theorem and a counterexample

We show that a finite algebra must be inherently non-dualisable if the variety that it generates is both residually large and congruence meet-semidistributive. We also give the first example of a finite dualisable algebra that generates a variety that is residually large.     

Fast computation of adaptive wavelet expansions

In this paper we describe and analyze an algorithm for the fast computation of sparse wavelet coefficient arrays typically arising in adaptive wavelet solvers. The scheme improves on an earlier version from Dahmen et al. (Numer. Math. 86, 49–101, 2000) in several respects motivated by recent developments of adaptive wavelet schemes. The new structure of the scheme is shown to enhance its performance while a completely different approach to the error analysis accommodates the needs put forward by the above mentioned context of adaptive solvers. The results are illustrated by numerical experiments for one and two dimensional examples.     

Three characteristic reactions of organocobalt compounds in organic synthesis

Organocobalt compounds in organic synthesis have three characteristic reactions. The first occurs because cobalt has a high affinity to carbon–carbon π‐bonds or carbon–nitrogen π‐bonds. The second occurs because cobalt has a high affinity to carbonyl groups. The third is due to cobalt easily tending to form square‐planar bipyramidal six‐coordination structures with four nitrogen atoms or two nitrogen atoms and two oxygen atoms at the square‐planar position, and to bond with one or two carbon atoms at the axial position. The first characteristic reactions are the representative reactions of organocobalt compounds with a mutually bridged bond between the two π‐bonds of acetylene and the cobalt–cobalt bond of hexacarbonyldicobalt. These are reactions with a Co₂(CO)₆ protecting group to reactive acetylene bond, the Nicholas reactions, the Pauson–Khand reactions ([2 + 2 + 1] cyclizations), [2 + 2 + 2] cyclizations, etc. These reactions are applied for the syntheses of many kinds of pharmaceutically useful compounds. The second reactions are carbonylations that have been used or developed as industrial processes such as hydroformylation for the manufacture of isononylaldehyde, and carbonylation for the production of phenylacetic acid from benzyl chloride. The third reactions are those reactions with the B₁₂‐type catalysts, and they have recently been used in organic syntheses and are utilized as catalysts for stereoselective syntheses. These reactions have been used as new applications for organic syntheses. Copyright © 2007 John Wiley & Sons, Ltd.     

π‐conjugated polymers having diaza[12]annulene rings and aminopenta‐2,4‐dienylidene groups generated by the ring opening of pyridinium rings

Reactions of N‐(2,4‐dinitrophenyl)pyridinium chloride with 2,5‐dimethyl‐1,4‐phenylenediamine in 1:2, 1:1.5, 1:1, and 2:1 molar ratios caused the ring opening of the pyridinium ring and thereby yielded polymers ( P1 – P4 ) consisting of 5‐(2,5‐dimethyl‐1,4‐phenylene)penta‐2,4‐dienylideneammonium chloride (unit A) and N‐2,5‐dimethyl‐1,4‐phenylene diaza[12]annulenium dichloride (unit B). The ¹H NMR spectra suggested that the composition ratios of unit A to unit B in P1 – P4 were 0.98:0.02, 0.94:0.06, 0.81:0.19, and 0.79:0.21, respectively. P1 – P4 showed an absorption maximum (λ_max) at a longer wavelength than the monomers because of the expansion of the π‐conjugation system. Films of P3 and P4 showed λ_max at a considerably longer wavelength than those in solution, and this was attributable to the ordered structures of the polymers in the solid state. Powder X‐ray diffraction analysis supported the ordered structures of P3 and P4 . Pellets molded from P3 and P4 exhibited a metallic luster, whereas those from P1 and P2 did not show such a luster. Cyclic voltammetry measurements indicated that P1 – P4 were electrochemically active in films. The thermal stability of the polymers depended on the composition ratios of unit A to unit B. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1507–1514, 2007     

A modified Weiszfeld algorithm for the Fermat-Weber location problem

This paper gives a new, simple, monotonically convergent, algorithm for the Fermat-Weber location problem, with extensions covering more general cost functions. Received: September 1999 / Accepted: January 2001?Published online April 12, 2001     

Melt properties and crystal morphology of polydodecamide plasticized by benzenesulfonamides

The melt of polydodecamide (PA‐12) shows a significant viscosity decrease upon incorporation of benzenesulfonamide plasticizers (BSAs), this effect being maximum for a monofunctional BSA with a 12‐carbon‐atom‐long alkyl chain. Nonexhaustive X‐ray diffraction analysis developed on isothermally crystallized samples validated a two‐phase model for describing PA‐12 plasticized by N‐(n‐butyl)benzenesulfonamide (BBSA). The massive presence of BBSA between the lamellar crystals was established, and lamellar fragmentation was also observed. Further, a steady increase in PA‐12 crystallinity with an increasing BBSA content was evident (and confirmed by DSC) and is consistent with the plasticizer easing the mobility of polymer chains during crystallization. Large melting point depressions resulting from both polymer–plasticizer miscibility and lamellar fragmentation were observed with several mono‐ and bifunctional BSA plasticizers. Phase separation in PA‐12 solid state was only observed at 20 mol % of ?SO₂NH₂, alhough miscibility occurred in the melt. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2022–2034, 2001