Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Link invariants associated with gauge equivalent solutions of the Yang-Baxter equation: The one-parameter family of minimal typical representations of Uq[gl(2|1)]

In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that it is possible to obtain invariants of regular isotopy (as defined by Kauffman) which may not be ambient isotopic. We illustrate our results with explicit computations using solutions of the trigonometric Yang-Baxter equation associated with the one-parameter family of minimal typical representations of the quantum superalgebra U-q,[gl(2/1)]. We have implemented MATHEMATICA code to evaluate the invariants for all prime knots up to 10 crossings.

Synthesis and characterization of mono- and bis-ligand zinc(II) and cadmium(II) complexes of the di-2-pyridylketone Schiff base of S-benzyl dithiocarbazate (Hdpksbz) and the X-ray crystal structures of the [Zn(dpksbz)2] and [Cd(dpksbz)NCS]2 complexes

New mono- and bis-chelated zinc(II) and cadmium(II) complexes of formula, [M(dpksbz)NCS] (dpksbz = anionic form of the di-2-pyridylketone Schiff base of S-benzyldithiocarbazate) and [M(dpksbz)(2)] (M = Zn-II, Cd-II) have been prepared and characterized. The structure of the bis-ligand complex, [Zn(dpksbZ)(2)] has been determined by X-ray diffraction. The complex has a distorted octahedral geometry in which the ligands are coordinated to the zinc(II) ion as uninegatively charged tridentate chelates via the thiolate sulfur atoms, the azomethine nitrogen atoms and the pyridine nitrogen atoms. The distortion from a regular octahedral geometry is attributed to the restricted bite angles of the Schiff base ligands. X-ray structural analysis shows that the [Cd(dpksbz)NCS](2) complex is a centrosymmetric dimer in which each of the cadmium(II) ions adopts a five-coordinate, approximately square-pyramidal configuration with the Schiff base acting as a tetradentate chelating agent coordinating a cadmium(II) ion via one of the pyridine nitrogen atoms, the azomethine nitrogen atom and the thiolate sulfur atom; the second pyridine nitrogen atom is coordinated to the other cadmium(II) ion of the dimer. The fifth coordination position around each cadmium(II) is occupied by an N-bonded thiocyanate ligand. (C) 2003 Elsevier Science Ltd. All rights reserved.

The preparation of zinc(II) and cadmium(II) complexes of the pentadentate N3S2 ligand formed from 2,6-diacetylpyridine and S-benzyldithiocarbazate (H2SNNNS) and the X-ray crystal structure of the novel dimeric [Zn2(SNNNS)2] complex

The pentadentate chelating agent, 2,6-diacetylpyridinebis(S-benzyldithiocarbazate) (H2SNNNS) reacts with zinc(II) and cadmium(II) ions forming stable complexes of empirical formula, [M(SNNNS)] (M=Zn2+, Cd2+; SNNNS2 =doubly deprotonated anionic form of the Schiff base). These complexes have been characterized by a variety of physico-chemical techniques. IR and H-1 NMR spectral evidence indicate that the Schiff base coordinates to the zinc(II) and cadmium(II) ions via the pyridine nitrogen atoms, the azomethine nitrogen atoms and the mercaptide sulfur atoms. The crystal and molecular structure of the zinc(II) complex has been determined by X-ray diffraction. The complex is a dimer in which the pyridine nitrogen atom,the azomethine nitrogen atom and the thiolate sulfur atom from one ligand coordinate to one of the zinc(II) ions whereas the azomethine and thiolate sulfur atoms from another ligand complete pentacoordination around the zinc(II) ion, the ligands being coordinated in their deprotonated forms. The coordination geometry about each zinc(II) can be considered as intermediate between a square-pyramid and trigonal-bipyramid. The cadmium(II) complex is also assigned with a dimeric structure. (C) 2003 Elsevier Ltd. All rights reserved.

Variation of the crystalline structure of coal char during gasification

The variation of the crystallite structure of several coal chars during gasification in air and carbon dioxide was studied by high-resolution transmission electron microscopy (HRTEM) and X-ray diffraction (XRD) techniques. The XRD analysis of the partially gasified coal chars, based on two approaches, Scherrer's equation and Alexander and Sommer's method, shows a contradictory trend of the variation of the crystallite height with carbon conversion, despite giving a similar trend for the crystallite width change. The HRTEM fringe images of the partially gasified coal chars indicate that large and highly ordered crystallites exist at conversion levels as high as 86%. It is also demonstrated that the crystalline structure of chars can be very different although their pore structures are similar, suggesting a combination of crystalline structure analysis with pore structure analysis in studies of carbon gasification.

The synthesis and X-ray crystal structure of 6-bromo-2,4,4-trimethyl-cyclohex-2-enone

Regiospecific bromination of 2,4,4-trimethyl-cyclohex-2-enone was achieved and the X-ray crystal structure of 6-bromo-2,4,4-trimethyl-cyclohex-2-enone is presented.

The synthesis and X-ray crystal structure of 9-carboxyhexahydro-7-methoxy-4a,7-ethano-benzopyran-5-en-1-one

9-Carboxyhexahydro-7-methoxy-4a,7-ethano-benzopyran-5-en-1-one (1) was prepared and examined by X-ray crystallography to probe its potential as a new peptide scaffold/template. The crystal structure of the anhydride precursor 7-(2-acetoxyethyl)-4-methoxy-3a,4,7,7a-tetrahydro-4,7-ethanoisobenzofuran-1,3-dione (6) is also reported.