Padé approximation in time-domain boundary conditions of porous surfaces

Formulation and implementation of time-domain boundary conditions (TDBCs) at the surface of a reactive porous material are made challenging by the slow decay, complexity, or noncausal nature of many commonly used models of porous materials. In this paper, approaches are described that improve computational efficiency and enforce causality. One approach involves approximating the known TDBC for the modified Zwikker-Kosten impedance model as a summation of decaying exponential functions. A second approach, which can be applied to any impedance model, involves replacing the characteristic admittance with its Padé approximation. Then, approximating fractional derivatives with decaying exponentials, a causal and recursive TDBC is formulated.     

Matrix Lax Polynomials, Geometry of Prym Varieties and Systems of Hess–Appel’rot Type

We consider a four-dimensional generalization of Hess–Appel’rot system and costruct its Lax pair. Both classical and algebro-geometric integration procedure are proceeded. The algebro-geometric integration is based on deep facts from geometry of Prym varieties such as the Mumford relation and Mumford-Dalalyan theory. The integration is similar to the integration of Lagrange bitop which has recetly been performed by the authors.     

Universal quadratures for boundary integral equations on two-dimensional domains with corners

We describe the construction of a collection of quadrature formulae suitable for the efficient discretization of certain boundary integral equations on a very general class of two-dimensional domains with corner points. The resulting quadrature rules allow for the rapid high-accuracy solution of Dirichlet boundary value problems for Laplace’s equation and the Helmholtz equation on such domains under a mild assumption on the boundary data. Our approach can be adapted to other boundary value problems and certain aspects of our scheme generalize to the case of surfaces with singularities in three dimensions. The performance of the quadrature rules is illustrated with several numerical examples.     

Exoelectron emission from solid nitrogen

Solid nitrogen was investigated by activation spectroscopy methods – thermally stimulated luminescence and thermally stimulated exoelectron emission (TSL and TSEE) in combination with luminescence analysis. TSEE from solid nitrogen pre-irradiated by an electron beam was measured and investigated for the first time. A set of peaks both in TSL and TSEE were observed. It was found that one of the peaks in the TSEE curve is caused by release of electrons in the course of the α-β phase transition of solid nitrogen. The corresponding activation energy was estimated.     

Entanglement and Density Matrix of a Block of Spins in AKLT Model

We study a 1-dimensional AKLT spin chain, consisting of spins S in the bulk and S/2 at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension . This subspace is described by non-zero eigenvalues and corresponding eigenvectors of the density matrix. We prove that for large block the von Neumann entropy coincides with Renyi entropy and is equal to . NSF Grant DMS-0503712.     

Recent Results on Fast Flow Gas-Phase Partial Oxidation of Lower Alkanes

Recent experimental results and kinetic modeling of fast flow gas-phase oxidation of methane and other lower alkanes to methanol and other oxygenates are discussed,alongside with prospects and possible areas for applications of the processes.     

Tetragonal polymorphic modification of tetrakis­(N,N‐diethyl­di­thio­carbam­ato‐S,S′)­tellurium(IV)

During an investigation of the W/Te/Br₂ system, we prepared crystals of the title compound, C₂₀H₄₀N₄S₈Te, from aceto­nitrile solution by slow addition of diethyl ether. It appeared to be a new tetragonal modification. The calculated density of the tetragonal modification (1.513 Mg m^?3) is slightly greater than found for the known orthorhombic modification (1.46 Mg m^?3). The bond distances and angles are practically the same.     

Antimony(III) fluoride: inclusion complexes with crown ethers

Four crystalline molecular complexes between antimony(III) fluoride and 18-membered crown ethers have been obtained and their structures investigated by single crystal X-ray diffraction techniques: [18-crown-6·SbF₃], C₁₂H₂₄F₃O₆Sb,P2₁2₁2₁,a=8.328(4),b=11.573(4),c=18.094(4),V=1744(1)³,Z=4; [benzo-18-crown-6·SbF₃], C₁₆H₂₄F₃O₆Sb,P2₁/n,a=10.490(2),b=13.714(1),c=13.442(2), =101.94(1)°,V=1892(1)³,Z=4; [cis-syn-cis-dicyclohexano-18-crown-6·SbF₃·CH₃OH], C₂₁H₄₀F₃O₇Sb,P2₁/n,a=8.270(4),b=23.386(3),c=12.772(1), =96.31(2)°,V=2455(1)³,Z=4; [cis-anti-cis-dicyclohexano-18-crown-6·SbF₃], C₂₀H₃₆F₃O₆Sb,Pna2₁,a=21.091(8),b=12.829(5),c=8.437(3),V=2283(2)³,Z=4. All species are the perching-type complexes with the antimony fluoride above the cavity and the metal lone pair pointed toward the center of the crown ring. The antimony atom interacts with all six crown oxygen atoms with Sb–O distances of 2.837(2)–3.344(2) . The antimony atom is displaced from the least square plane of the crown oxygen atoms at the distances of 1.288–1.383 .     

Novel and elegant modes of SbF3 coordination in the complexes with azacrown ethers

Synthesis and single-crystal X-ray structures are recorded for three adducts of SbF₃ with different azacrown ethers. [SbF₃·H₂O·L₁], 1, (L₁ = 12,13-benz-1,10-di(azamethyl)-4,7-dioxacyclotetradecane-1,14-dione), triclinic, , a = 11.234(2), b = 11.691(2), c = 8.869(2) Å, = 94.66(3), = 113.12(3), = 67.82(3)°, Z = 2. [SbF₃Cl·H₂O·(HL₂)], 2, (L₂ = monoaza-18-crown-6), orthorhombic, P2₁2₁2₁, a = 8.763(2), b = 13.003(3), a = 16.836(3) Å, Z = 4. [(SbF₃)₂Cl₂·(H₂L₃)], 3, (L₃ = 1,10-diaza-18-crown-6), triclinic, , a = 8.284(2), b = 9.016(2), c = 9.134(2) Å, = 82.92(3), = 65.24(3), = 63.38(3)°, Z = 1. All three structures include SbF₃ neutral molecules in the pyramidal mode and the antimony second coordination sphere is completed up to six in different fashions. In 1 the dimeric (SbF₃)₂ adducts are made up due to the involvement of the symmetry-related fluorine atom in coordination. The distorted octahedron is then completed by water molecule and carbonyl oxygen of L₁. The neutral molecules are joined by coordination and hydrogen bonds in the infinite ribbons. 2 and 3 are both comprised of neutral and charged species also bounded via coordination and hydrogen bonds. L₂ and L₃ in the complexes adopt the form of single and double-charged cations, respectively. The inorganic backbone unites the neutral SbF₃ molecules and chloride anions in the alternative mode. The sixth coordination site in the antimony polyhedron is completed by the water molecule in 2 and the ethereal oxygen atom in 3. Alignment of the inorganic entities within the structures of 2 and 3 is strikingly similar. Hydrogen bonding patterns are discussed.     

Synthesis and Crystal Structure of (<Emphasis Type="Italic">S</Emphasis>)-2-((<Emphasis Type="Italic">S</Emphasis>)-2-(<Emphasis Type="Italic">N</Emphasis>-Ts-Amino)-3-methylbutanoyl)-3-(1H-indol-3-yl)-6-phenyl-3,4-dihydro-1,2,4-triazin-5(2H)-one

Abstract  

The diastereoselective synthesis, NMR and X-ray structure of (S)-2-((S)-2-(N-Ts-amino)-3-methylbutanoyl)-3-(1H-indol-3-yl)-6-phenyl-3,4-dihydro-1,2,4-triazin-5(2H)-one—a potential antivirus agent are reported. The compound crystallizes in the triclinic space group P1 with unit cell parameters: a = 5.9259(6) ?, b = 9.6370(12) ?, c = 12.9541(9) ?, α = 109.210(9)°, β = 90.804(7)°, γ = 105.074(10)° and Z = 1.