Geometric properties of F-normed Orlicz spaces

Aequationes mathematicae - The paper deals with F-normed functions and sequence spaces. First, some general results on such spaces are presented. But most of the results in this paper concern...     

First-order interaction energies and the basis set truncation effects

The basis set superposition error is investigated in terms of the first-order symmetry adapted perturbation theory (SAPT). The analysis of the first-order SAPT contribution to the interaction energy reveals the origin of the basis set truncation effects at both the one-electron and many-electron levels of approximation. This helps to formulate the necessary conditions which ensure that the calculated interaction energy is free of the basis set superposition contributions. At the level of the one-electron approximation used for both the interacting system and its subsystems a part of the basis set truncation errors can be eliminated by using what is called the dimer-centred basis set. In order to remove all contributions which arise from the symmetrization of the product of wave functions of the subsystems one needs to redefine their reference states. This means that for the interacting system represented by a single HF determinant, the subsystems must be considered at the level of full CI in the orbital space spanned by all occupied orbitals used to describe the dimer. Then, the interaction energy becomes completely free of the basis set superposition contributions. These general considerations are exemplified by calculations of the first-order SAPT interaction energy in helium and H₂ dimers at different levels of approximation for monomers. Also the convergence of the calculated energies to the complete basis set limit is investigated.     

First order phase change detection using planar waveguide Bragg grating refractometer

Solid-to-liquid and gas-to-liquid phase changes in water and ordered-to-isotropic phase changes in a nematic liquid crystal are detected with an optical sensor. A planar Bragg grating defined purely by refractive index modulation is covered with a water or liquid crystal overcladding and the temperature is controlled to trigger phase changes. Measurement of the Bragg wavelength allows changes of effective refractive index to be detected and discontinuities in behaviour caused by phase transitions can be clearly identified.     

On the Uniqueness of the Density for the Invariant Measure in an Infinite Hyperbolic Iterated Function System

Periodica Mathematica Hungarica - We consider a regular infinite hyperbolic iterated function satisfying a property which guarantees that the associated Frobenius-Perron operator ? is almost...     

Geometry and ergodic theory of non-recurrent elliptic functions

We explore the class of elliptic functions whose critical points all contained in the Julia set are non-recurrent and whose ω-limit sets form compact subsets of the complex plane. In particular, this class comprises hyperbolic, subhyperbolic and parabolic elliptic maps. Leth be the Hausdorff dimension of the Julia set of such an elliptic functionf. We construct an atomlessh-conformal measurem and show that theh-dimensional Hausdorff measure of the Julia set off vanishes unless the Julia set is equal to the entire complex plane ℂ. Theh-dimensional packing measure is positive and is finite if and only if there are no rationally indifferent periodic points. Furthermore, we prove the existence of a (unique up to a multiplicative constant) σ-finitef-invariant measure μ equivalent tom. The measure μ is shown to be ergodic and conservative, and we identify the set of points whose open neighborhoods all have infinite measure μ. In particular, we show that ∞ is not among them. The research of the first author was supported in part by the Foundation for Polish Science, the Polish KBN Grant No 2 PO3A 034 25 and TUW Grant no 503G 112000442200. She also wishes to thank the University of North Texas where this research was conducted. The research of the second author was supported in part by the NSF Grant DMS 0100078. Both authors were supported in part by the NSF/PAN grant INT-0306004.     

Microwave-assisted synthesis of spherical monodispersed magnesium fluoride

Spherical monodispersed magnesium fluoride has been obtained using the microwave-assisted precipitation technique from magnesium nitrate and ammonium fluoride solutions. Studies aimed at optimizing synthesis conditions from the point of view of preparing spherical MgF₂ particles of possibly high monodispersity were performed. Spherical MgF₂ particles of 0.25-0.36 μm in diameter have been obtained with relative standard deviation from the average value ranging from 7 to 15%. It has been established that a certain optimal range of Mg(NO₃)₂ and NH₄F concentrations exists that enables a highly monodispersed MgF₂ to be prepared. The range is narrow (0.01-0.03 mol dm⁻³) for both precursors. Spherical MgF₂ particles have been characterized by SEM, XRD, DTG/DTA and FTIR techniques.     

Laser properties of praseodymium pentaphosphate single crystals

PrP₅O₁₄, Pr_xLa_1−xP₅O₁₄, and Pr_xY_1−xP₅O₁₄ (0≦x≦1) single crystals of laser quality were synthesized and their crystallographic and optical parameters measured. Laser emissions in the visible (λ=637.4 nm) with no mirrors in place (superradiance) and also in various optical resonators have been observed.     

Photochemical reduction of transition metal substituted heteropoly anions in nonpolar solutions

Photochromism of [SiW11O39Ni(X)]6- as a tetraheptylammonium salt in various solvents under broadband UV light is observed in the presence of alcohols. The reaction proceeds faster with benzyl alcohol than with ethanol. Benzaldehyde is identified as the oxidized product of benzyl alcohol. Photochemistry is a reliable means to produce stable reduced transition metal substituted heteropoly tungstates in nonpolar media, where they hold promise as multielectron reduction catalysts. Preliminary reactivity toward CO2 reduction is demonstrated.     

How Points Escape to Infinity Under Exponential Maps

We investigate the finer fractal structure of the set of pointsescaping to infinity under iteration of an arbitrary exponentialmap. Providing exact formulas, we show how sensitively the Hausdorffdimension depends on the rate of growth of canonical Devaney–Krychcodes.     

Estimates of the energy of intramolecular hydrogen bonds

A method for the estimation of the energy of intramolecular hydrogen bonds in conjugated systems existing in a variety of conformations is presented. The method is applied to determine the intramolecular hydrogen bond energy in 3-aminopropenal and 3-aminopropenthial. According to the proposed estimation scheme, the intramolecular H-bond energies are found to be of the order of 5-7 kcal/mol. These results are compared with those obtained by using other estimation schemes as well as with the recent results by other authors. Also, the H-bond energies in dimers and trimers of the two molecules are calculated and compared with the corresponding data for internally hydrogen-bonded monomers. This comparison shows that the bond equalization effect is primarily due to proton donor-proton acceptor proximity. In comparison with intermolecular hydrogen bonds, the rigidity of the chelate skeleton enhances this proximity effect. The same effect can be seen in systems with intermolecular hydrogen bonds, although its magnitude is diminished because of the absence of additional forces which pull the proton donor and proton acceptor groups toward each other. No specific resonance-assisted origin of the intramolecular hydrogen bond energy seems to be needed to elucidate the energetics of these bonds.