Completeness of indexed ε-calculus

Epsilon terms indexed by contexts were used by K. von Heusinger to represent definite and indefinite noun phrases as well as some other constructs of natural language. We provide a language and a complete first order system allowing to formalize basic aspects of this representation. The main axiom says that for any finite collection S ₁,,S _k of distinct definable sets and elements a ₁,,a _k of these sets there exists a choice function assigning a _i to S _i for all ik. We prove soundness and completeness theorems for this system S _i ^fin . Mathematics Subject Classification (2000): 03B10, 03B65     

Photolysis of 10,10-difluorophenanthren-9(10H)-one. Evidence for solvent-assisted α-cleavage

The photolysis of 10,10-difluorophenanthren-9(10H)-one 1 in different solvents shows that the major competing reaction of the diradical formed by α-cleavage: recombination and hydrogen atom abstraction depends on the hydrogen atom donating ability of the solvent. Photolysis of 1 in cyclohexane in the presence of air or oxygen leads mainly to α-cleavage while photoreduction with the formation of 10-fluoro-9-phenanthrol occurs when the solution is deaerated prior to irradiation. In acetonitrile, a poor hydrogen donor, recombination of the diradical back to starting compound 1 is the sole process.     

Generating Singularities of Solutions of Quasilinear Elliptic Equations Using Wolff's Potential

We consider a quasilinear elliptic problem whose left-hand side is a Leray-Lions operator of p-Laplacian type. If p < < N and the right-hand side is a Radon measure with singularity of order at x_0A , then any supersolution in W^1,p() has singularity of order at least (–p)/(p–1) at x₀. In the proof we exploit a pointwise estimate of A-superharmonic solutions, due to Kilpeläinen and Malý, which involves Wolff's potential of Radon's measure.     

EPMA and Microstructural Characterization of Yttrium Doped BaTiO3 Ceramics

 Yttrium-doped BaTiO₃ ceramics have been studied as a potential material for positive temperature coefficient resistors (PTCR). The mechanism of Y incorporation into BaTiO₃ plays an important role for displaying good electrical properties. Determination of the amount of yttrium in the BaTiO₃ as well as microstructure characterization of the samples were performed using SEM, EDS and WDS analysis. An optimized trace element WDS quantitative analysis was applied to determine elemental concentrations for Ba, Ti and Y in the samples as accurately as possible. BaTiO₃ and Y₂O₃ were used as standards. Analysis was undertaken using a JEOL JXA 840A electron probe microanalyzer. WDS X-ray intensity measurements were performed under 20 kV, 50 nA beam current and 0.2% preset standard counting deviation (σ_c) using a PET crystal. Measured k-ratios were quantified by ZAF matrix correction. Average results of WDS quantitative analysis showed 20.17 ± 0.08 at % Ti, 19.95 ± 0.09 at % Ba, 0.22 ± 0.03 at % Y, and 59.66 at % O. The results suggest incorporation of yttrium in the BaTiO₃ preferentially at the Ba-sites, however partial incorporation of Y at Ti-sites could not be excluded.     

Synthesis and characterisation of Pd(II) complexes with a derivative of aminoazobenzene: Dynamic H-NMR study of cyclopalladation reactions in DMF

Three new Pd(II) complexes, i.e. [PdCl₂L]₂ (A), PdCl₂L₂ (B) and [Pd(μ-Cl)(L-H)]₂ (C), each with two diethyl [α-(4-benzenazoanilino)-2-hydroxybenzyl]phosphonates (L) bound to either one or two palladium atoms, are synthesized and characterized by elemental analysis, by IR, UV-vis and solid-state ¹³C-NMR spectra. Complexes B and C are additionally characterized by ¹H-, ¹³C- and ³¹P-NMR and electrospray mass spectrometry (ESMS) studies using dimethylformamide (DMF) as a solvent. In DMF solution adducts A and B undergo spontaneous rearrangement into the cyclopalladated complex C. Dynamic ¹H-NMR study of this rearrangement as well as of the reactions of L with PdCl₂ and Na₂PdCl₄ revealed a complex equilibrium in DMF solutions and enabled the formation mechanism of all involved species to be resolved. The complex A is immediately solvolyzed producing two molecules of intermediate M [PdCl₂(L)(DMF)]. Complex M was also the first intermediate in the reaction of L with PdCl₂. Once present in concentration above 10⁻⁵ mol dm⁻³M dimerizes very fast into chloro-bridged dimer [PdCl(μ-Cl)(L)]₂ (D) which undergoes cyclopalladation and converts into the complex C. The formation of C from the intermediate D is clearly demonstrated by the concentration dependence of the cyclopalladation reaction which has order greater than one. Chloride ions, released by cyclopalladation, react with D by splitting chloro-bridge and binding to metal atoms to produce byproduct [PdCl₃(L)]⁻ (T). The same species T are formed in the reaction of L with Na₂PdCl₄ whereby a chloride ion is replaced by the ligand L. The complex B undergoes similar, but slower, solvolytic reaction producing M and L while further reaction steps are identical as in the solvolysis of A.     

Oscillatory and phase dimensions of solutions of some second-order differential equations

In order to measure fractal oscillatority of solutions at t=∞, we define oscillatory and phase dimensions of solutions of a class of second-order nonlinear differential equations. The relation between these two dimensions is found using formulas for box dimension of chirps and nonrectifiable spirals. Applications include the Liénard equation and weakly damped oscillators.