Mappings of Finite Distortion:¶Discreteness and Openness

We establish a sharp integrability condition on the partial derivatives of a mapping with L ^p -integrable distortion for some p>n? 1 to guarantee discreteness and openness. We also show that a mapping with exponentially integrable distortion and integrable Jacobian determinant is either constant or both discrete and open. We give an example demonstrating the preciseness of our criterion.     

X-ray diffraction study of TiO2 thin films on mica

Thin layers of polycrystalline TiO₂ were deposited on flaky muscovite and phlogopite particles. Deposition was performed in water slurry using aqueous TiCl₄ as titanium source. The effect of heat treatments on the structure of TiO₂ thin films was investigated at different layer thicknesses. On muscovite mica the films crystallized as anatase TiO₂. On phlogopite mica the increasing layer thickness favored partial rutile formation at higher calcination temperatures, although the films could not be converted to pure rutile. The preferred orientation of the TiO₂ films was evident. The most intense reflections were measured from (004) and (105) planes. The crystallite size of TiO₂ was strongly dependent on calcination temperature and TiO₂ layer thickness. It varied between 15 and 47 nm for films deposited on phlogopite, and 15 and 57 nm for films deposited on muscovite.     

Synthetic studies in the alkaloid field-IX: Stereospecific total synthesis of (±)-19,20-dihydro-20-desformyl-20-methoxycarbonyl-vallesiachotamine and its 20-desethyl analogue

The stereospecific total synthesis of (±) - 19,20 - dihydro - 20 - desformyl - 20 - methoxycarbonyl-vallesiachotamine and its 20-desethyl analogue has been carried out by sodium dithionite reduction of appropriate 1-[2-(3-indolyl)ethyl]-3-methoxycarbonyl pyridinium salts to the corresponding 1,4-dihydropyridine derivatives, followed by acid-induced cyclization.     

A CASSCF study on the lowest π→π* excitation of urocanic acid

The photochemical cis/trans isomerization of urocanic acid (UCA, (E)‐3‐(1′H‐imidazol‐4′‐yl)propenoic acid) was investigated using complete active space SCF (CASSCF) ab initio calculations. The singlet ground state and the triplet and the singlet manifolds of the lowest‐lying π→π* (HOMO→LUMO) excitation of the neutral and the anionic UCA were calculated using the 6‐31G* and the 6‐31+G* basis sets, respectively. The torsional barrier of the double bond of the propenoic acid moiety in UCA is observed to be considerably lower in the T₁ and S₁ excited states of the neutral UCA and in the T₁ but not in the S₁ excited state of the anionic UCA, as compared to the S₀ state of the respective protonation form. The cis‐isomer of both the neutral and the anionic UCA is lower in energy than the trans‐isomer in the S₀, T₁, and S₁ states. This energy difference is larger in the excited states than in the ground state, probably due to strengthening of the intramolecular hydrogen bond of cis‐UCA as the molecule is excited. The results of the calculations, interpreted in terms of the idea that UCA is deprotonated upon electronic excitation, led to construction of a new model for the photoisomerization mechanisms of UCA. According to this model, the trans‐to‐cis isomerization proceeds via both the triplet and the singlet manifolds in the deprotonated form of UCA. This isomerization may occur in the S₀ state of the neutral UCA as well. The cis‐to‐trans isomerization is suggested to proceed only in the S₀ state of the neutral UCA. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 25–37, 1999     

Ab initio study of bonding trends for f0 actinide oxyfluoride species

 Fully relativistic, four-component Dirac–Fock calculations and quasirelativistic pseudopotential calculations at different ab initio levels are used to study the bonding trends among the naked, triatomic [OAnO] ^q+ groups or the oxyfluorides [AnO _n F _m ] ^q with f ⁰ configurations. The triatomic f ⁰ series is suggested to range from the bent ThO₂ via the linear OPaO⁺ to at least NpO₂ ³⁺, a possible new gas-phase species. The neutral oxyfluoride molecules include the experimentally unknown NpO₂F₃ and PuO₂F₄. The latter is a candidate for the so far unknown oxidation state Pu(VIII), which is found to lie considerably above Pu(VI), but to be locally stable. Their all-oxygen isoelectronic analogues are NpO₅ ³⁻, known in the solid state, and the unknown PuO₆ ⁴⁻. Further possible candidates for Pu(VIII) are PuO₄(D _4h ) and the cube-shaped PuF₈(O _h ). Isoelectronic UF₈ ²⁻ is calculated to be D _4d , in agreement with experiment. Received: 18 May 2001 / Accepted: 21 June 2001 / Published online: 11 October 2001     

Determination of Stoichiometric Dissociation Constants of Benzoic Acid in Aqueous Sodium or Potassium Chloride Solutions at 25°C

Equations were determined for the calculation of the stoichiometric (molality scale) dissociation constant K_m of benzoic acid in dilute aqueous NaCl and KCl solutions at 25°C from the thermodynamic dissociation constant K_a of this acid and from the ionic strength I_m of the solution. The salt alone determines mostly the ionic strength of the solutions considered in this study and the equations for K_m were based on the single-ion activity coefficient equations of the Hückel type. The existing literature data obtained by conductance measurements and by electromotive force (EMF) measurements on Harned cells were first used to revise the thermodynamic value of the dissociation constant of benzoic acid. A value of K_a = (6.326 ± 0.005) × 10^-5 was obtained from the most precise conductivity set [Brockman and Kilpatrick] and this value is supported within their precisions by the less precise conductivity set of Dippy and Williams and by the EMF data set measured by Jones and Parton with quinhydrone electrodes. The new data measured by potentiometric titrations in a glass electrode cell were then used for the estimation of the parameters of the Hückel equations of benzoate ions. The resulting parameters were also tested with the existing literature data measured by cells with and without a liquid junction. The Hückel parameters suggested here are close to those determined previously for anions resulting from aromatic and aliphatic carboxylic acids. By means of the calculation method based on the Hückel equations, K_m can be obtained almost within experimental error at least up to I_m of about 0.5 mol-kg_-1 for benzoic acid in NaCl and KCl solutions.     

On functions with derivatives in a Lorentz space

We establish a sharp integrability condition on the partial derivatives of a Sobolev mapping to guarantee that sets of measure zero get mapped to sets of measure zero. This condition is sharp also for continuity and differentiability almost everywhere. Received: 6 January 1999 / Revised version: 5 May 1999     

Syntheses of new poly (arylene vinylene) analogues: Poly (4,7-benzofuran vinylene) and poly (4,7-benzothiophene vinylene)

The reaction of bis(4,7-tetrahydrothiopheniomethyl) benzofuran dibromide with aqueous tetramethylammonium hydroxide leads to a water-soluble polyelectrolyte which can be film cast and thermolytically eliminated to give poly(4,7-benzofuran vinylene) (PBFV). Subjection of bis(4,7-tetrahydrothiopheniomethyl) benzothiophene dibromide to the same reaction sequence gives poly(4,7-benzothiophene vinylene) (PBTV). UV-VIS studies show that PBFV has a band gap of 2.76 eV, while PBTV has a band gap of 2.92 eV. These polymers are members of a new class of conjugated poly (arylene vinylene)s, in which heterocyclic pseudoaromatic rings are fused onto a poly(1,4-phenylene vinylene) backbone. © 1994 John Wiley & Sons, Inc.