Samarium Based High Surface Area Perovskite Type Oxides SmFe1-XAlXO3 (X=0.00, 0.50, 0.95). Part II, Catalytic Combustion of CH4

The catalytic combustion of methane with stoichiometric amounts of oxygen to CO₂ and H₂O has been studied over samarium based high surface area perovskite type oxides SmFe_1-xAl_xO₃ (x=0.00, 0.50 0.95) prepared via a new sol-gel method. A comparison to other lanthanum perovskites prepared by the ceramic method shows higher catalytic activity for SmFeO₃ and SmFe_0.5Al_0.5O₃ samples.     

On the Residual Finiteness of Outer Automorphisms of Hyperbolic Groups

We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable hyperbolic group is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated Fuchsian group and of every free-by-finite group is residually finite.     

Bi-complement Reducible Graphs

We introduce a new family of bipartite graphs which is the bipartite analogue of the class ofcomplement reduciblegraphs orcographs. Abi-complement reduciblegraph orbi-cographis a bipartite graphG = (W ∪ B, E) that can be reduced to single vertices by recursively bi-complementing the edge set of all connected bipartite subgraphs. Thebi-complementedgraphofGis the graph having the same vertex setW ∪ BasG, while its edge set is equal toW × B − E. The aim of this paper is to show that there exists an equivalent definition of bi-cographs by three forbidden configurations. We also propose a tree representation for this class of graphs.     

Synthesis of 6,7,8,9-tetrahydro-N,N-di-n-propyl-1H-benz[g] indol-7-amine,a potential dopamine receptor agonist

In this work, the synthesis of 6,7,8,9-tetrahydro-N,N-di -n-propyl-1H-benz[g]indol-7-amine (1) is described. This compound was designed as an indole bioisostere to the known dopamine receptor agonist 5-OH-aminotetraline 2 . The key step of the synthesis was a Mukaiyama type aldol condensation between the dimethyl acetal of 1-(p-toluenesulfonyl)pyrrole-3-acetaldehyde ( 4 ) and 4-di-n-propylamino-1-trimethylsilyloxycyclohexene ( 8 ) followed by cycloaromatization to afford 1-p-toluenesulfonyl-6,7,8,9-tetrahydro-N,N-di-n- propyl-1H-benz[g]indol-7-amine ( 10 ). Scission of the sulfonamide bond in 10 gave the target compound 1 . A byproduct which was isolated was assigned to the structure of 1-(p-toluenesul-fonyl)-6-[3-[1-(p-toluenesulfonyl)]pyrrolyl]indole ( 11 ). This compound was also synthesized in good yield by an acid catalyzed dimerization of the dimethyl acetal of 1-(p-toluenesulfonyl)pyrrole-3-acetaldehyde ( 4 ). Preliminary screening of 1 indicated that it possesses central dopamine receptor agonist properties.     

On the birth of stall cells on airfoils

Critical point theory asserts that two-dimensional topologies are defined as degeneracies and any three-dimensional disturbance of a two-dimensional flow will lead to a new three-dimensional flowfield topology, regardless of the disturbance amplitude. Here, the topology of the composite flowfields reconstructed by linear superposition of the two-dimensional flow around a stalled airfoil and the leading stationary three-dimensional global eigenmode has been studied. In the conditions monitored the two-dimensional flow is steady and laminar and is separated over a fraction of the suction side, while the amplitudes considered in the linear superposition are small enough for the linearization assumption to be valid. The multiple topological bifurcations resulting have been analysed in detail; the surface streamlines generated by the leading stationary global mode of the separated flow have been found to be strongly reminiscent of the characteristic stall cells, observed experimentally on airfoils just beyond stall in both laminar and turbulent flow.     

A density version of the Halpern–Läuchli theorem

We prove a density version of the Halpern–Läuchli Theorem. This settles in the affirmative a conjecture of R. Laver.     

Low‐frequency scattering by a penetrable body with an eccentric soft or hard core

A plane wave is scattered by an acoustically soft or hard sphere, covered by a penetrable non‐concentric spherical lossless shell that disturbs the propagation of the incident wave field. The dimensions of the coated sphere are much smaller than the wavelength of the incident field. Low‐frequency theory reduces this scattering problem to a sequence of potential problems, which can be solved iteratively. Exactly one bispherical coordinate system exists that fits the given geometry of the obstacle. For the case of a soft and hard core, the exact low‐frequency coefficients of the zeroth and the first‐order for the near field as well as the first‐ and second‐order coefficients for the normalized scattering amplitude are obtained and the cross sections are calculated. Discussion of the results and their physical meaning is included. Copyright © 2009 John Wiley & Sons, Ltd.     

Coordination-driven self assembly of a brilliantly fluorescent rhomboid cavitand composed of bodipy-dye subunits

The two sp(3) hybridized fluorine atoms of a Bodipy dye have been synthetically replaced with the linear donor ligand 4-ethynylpyridine (-C≡C-Py) to form a rigid and highly symmetrical 109.5° building block in which the fluorophore subunit is vertically aligned to the plane formed by the -C≡C-Py donors. Upon reaction of the above tecton with a 90° organoplatinum acceptor unit, an intensely fluorescent rhomboid cavitand was manifested in solution. In contrast to the vast majority of coordination-driven self-assembled chromophoric systems, the present one fully conserves the excellent photophysical properties of the parent Bodipy dye. These unique features of the present metallosupramolecular entity constitute a fascinating metal-to-ligand self-assembled prototype for building compact and intensely luminescent materials with host-guest capabilities.     

Fundamental Solutions of Linear Differential Equations in the Sense of Mnemofunctions

In this paper we discuss the definition and construction of the fundamental solution of a linear differential equation with constant coefficients in the algebra of mnemofunctions. This algebra contains the tempered distributions. We also present some examples including a physical illustration of our results for the equation u = .