Rational Krylov methods for fractional diffusion problems on graphs

BIT Numerical Mathematics - In this paper we propose a method to compute the solution to the fractional diffusion equation on directed networks, which can be expressed in terms of the graph...     

Triazene proton affinities: A comparison between density functional,Hartree–Fock,and post-Hartree–Fock methods

The consistency of three density functional computational implementations (DMol, DGauss, and deMon) are compared with high-level Hartree–Fock and Møller–Plesset (MP) calculations for triazene (HN?NNH₂) and formyl triazene (HN?NNHCOH). Proton affinities on all electronegative sites are investigated as well as the geometries of the neutral and protonated species. Density functional calculations employing the nonlocal gradient corrections show agreement with MP calculations for both proton affinities and geometries of neutral and protonated triazenes. Local spin density approximation DMol calculations using numerical basis sets must employ an extended basis to agree with other density functional codes using analytic Gaussian basis sets. The lowest energy conformation of triazene was found to be nonplanar; however, the degree of nonplanarity, as well as some bond lengths, is dependent on the basis set, electron correlation treatment, and methods used for the calculation. © 1994 by John Wiley & Sons, Inc.

1 This article is a U.S. Government work and, as such, is in the public domain in the United States of America.

     

Two-point Padé approximants for formal Stieltjes series

We prove that certain two-point Padé approximants occupying the diagonal of the Padé table form monotone sequences of lower and upper bounds uniformly converging to a Stieltjes function. The results can be applied to the theory of inhomogeneous media for the calculation of the bounds on the effective transport coefficients of heterogeneous materials.     

Isomorphism of two realizations of quantum affine algebraU_q (\widehat{\mathfrak{g}\mathfrak{l}{\text{(}}n{\text{)}}})

We establish an explicit isomorphism between two realizations of the quantum affine algebra given previously by Drinfeld and Reshetikhin-Semenov-Tian-Shansky. Our result can be considered as an affine version of the isomorphism between the Drinfield/Jimbo and the Faddeev-Reshetikhin-Takhtajan constructions of the quantum algebra .     

Grain Boundary Wetting in Polycrystals: 1. Probability of Wetting of Structural Elements

A model describing the wetting of structural elements in polycrystals such as grain boundaries (faces), triple lines (edges), and quaternary nodes (vertices) is proposed. It is assumed that the only driving force during wetting is the tendency of a system to the energy minimization due to the substitution of low-energy liquid–solid interfaces for high-energy grain boundaries. In this case, the anisotropy of grain boundary energy caused by the differences in misorientation of adjacent grains is taken into account, whereas the liquid–solid interface energy is assumed to be independent of the orientation. The well-known condition of grain boundary wetting (the Gibbs–Smith condition) is extended to the triple lines and quaternary nodes by introducing parameters determined as characteristic free energy of these elements.     

LiNa2AlF6: a powder structure solution

Lithium sodium aluminium fluoride was obtained as a white powder by melting a stoichiometric mixture of AlF₃, NaF and LiF at 1223 K, and then cooling to 923 K and sintering at this temperature for 4 h. The ab initio crystal structure determination was carried out using X‐ray powder diffraction techniques. The monoclinic structure of LiNa₂AlF₆ can be related to cubic elpasolite. The Li and Al atoms lie on inversion centres. The main octahedral AlF₆ structural elements are not deformed, but are rotated slightly with respect to the unit‐cell axes. The Li atoms have octahedral coordinations, whereas the Na atoms have cubo‐octahedral coordinations. The Na coordination polyhedron is distorted in comparison with that of elpasolite.     

Synthesis and properties of monodisperse oligofluorene-functionalized truxenes: highly fluorescent star-shaped architectures

This paper describes the strategy toward novel monodisperse, well-defined, star-shaped oligofluorenes with a central truxene core and from monofluorene to quaterfluorene arms. Introduction of solubilizing n-hexyl groups at both fluorene and truxene moieties results in highly soluble, intrinsically two-dimensional nanosized macromolecules T1-T4. The radius for the largest oligomer of ca. 3.9 nm represents one of the largest known star-shaped conjugated systems. Cyclic voltammetry experiments reveal reversible or quasi-reversible oxidation and reduction processes (Eox = +0.74 to 0.80 V, Ered = -2.66 to 2.80 eV vs Fc/Fc+), demonstrating excellent electrochemical stability toward both p- and n-doping, while the band gaps of the oligomers are quite high (EgCV = 3.20-3.40 eV). Close band gaps of 3.05-3.29 eV have been estimated from the electron absorption spectra. These star-shaped macromolecules demonstrate good thermal stability (up to 400-420 degrees C) and improved glass transition temperatures with an increase in length of the oligofluorene arms (from Tg = 63 degrees C for T1 to 116 degrees C for T4) and show very efficient blue photoluminescence (lambdaPL = 398-422 nm) in both solution (PhiPL = 70-86%) and solid state (PhiPL = 43-60%). Spectroelectrochemical experiments reveal that compounds T1-T4 are stable electrochromic systems which change their color reversibly from colorless in the neutral state (approximately 340-400 nm) to colored (from red to purple color; approximately 500-600 nm) in the oxidized state.     

Dissolution of gold in the DMSO—RX systems. The concept of a donor-acceptor electron transport system

Summary The liquid phase oxidation of gold in donor-acceptor organic and aqueous-organic media has been studied. The compounds [AuCl(Me₂S)], [AuBr(Me₂S)], [AuBr₃(Me₂S)], [Me₃S][AuBr₄], [Me₃S][AuBr₄(Me₂S)]·H₂O, [Me₃SO]-[AuBr₄]·H₂O, [Me₃S][Au₂Br₇(Me₂S)₂]·3H₂O, [Me₃S]₂-[Au₂Br₈]·2DMSO·H₂O, [Me₂(Bu)SO][AuBr₄]·H₂O and [Me₃S]Br were isolated by dissolution of Au⁰ in DMSO-RX mixtures (R = H or Bu; X = Cl or Br). The products were characterized by elemental analysis and i.r. spectroscopy. The nature of the Au⁰-DMSO-RX systems and the oxidant species are discussed in terms of a newly-developed concept of donor-acceptor electron transport (DAET) systems.     

Detection of explosives on solid surfaces by thermal desorption and ambient ion/molecule reactions

A simple, fast and direct method is presented for detecting traces of solid explosives on cotton swabs or in particulate samples: ions are transferred into a mass spectrometer after thermal desorption and corona discharge chemical ionization in ambient air; specificity is enhanced using ambient ion/molecule reactions or by conventional tandem mass spectrometry.     

STUDY OF LUMINESCENT FORMS OF THE URANYL ION

Luminescence spectra and luminescence decay kinetics of uranyl sulphate water and uranyl nitrate acetone solutions of different concentrations have been studied. Similar experiments have been done with uranyl sulphate powder under vacuum. It has been experimentally shown that the hydrolysis of uranyl sulphate in water takes place, and under low salt concentrations (0.1-4.0 times 10^-4 M) a luminescence of a basic form of the photoexcited ion with a tentative structure of UO₂OH⁺* has been observed. The luminescence of the acidic form UO⁺* has been observed under higher salt concentrations (1–4 times 10^-2 M) in water and under any salt concentration in acetone. The acidic form has the characteristic emission spectrum possessing vibrational structure. The luminescence concentrational quenching of both photoexcited uranyl forms and exciplex emission have not been observed. The effect of a number of organic quenchers and molecular oxygen on uranyl luminescence has been studied. There is no luminescence quenching by O₂ up to 2 times 10⁶ Pa (20 atm) pressure. The low effectiveness of energy transfer from the photoexcited uranyl forms has been explained in terms of strong steric screening of 5f-uranium (VI) orbital by oxygen atoms and by external filled up uranium electronic shells.