On collinear Griffiths points

J. Tabov has proved [1] that four Griffiths points are collinear if the vertices of a given quadrangle are on a circle. In this article we prove some generalization of this result in a very simple geometrical way (based on Desargues theorem). Received 9 July 1999; revised 13 December 1999.     

On stochastic processes with linear conditional moments

In the paper, we show that a stochastic process with linear regression and linear conditional variance must be either a Gaussian process or a Poisson-type process. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I.     

MCSCF calculation of response properties of Argon

Summary Analytic equations of the multiconfigurational SCF (MCSCF) response theory are combined with the finite-field (FF) approach to compute static and frequency dependent electric and magnetic properties of the Argon atom. A complete active space (CAS SCF) function including the 3s, 3p, 3d, 4s and 4p orbitals in the active space and a large (17s 13p 7d 5f 3g) basis set are employed. This permits an accurate determination of various linear and non-linear response properties such as e.g. electric dipole polarisability and second hyperpolarisability, Verdet constant, magnetisability and second hyperpolarisability. The results, both for the static values and for the frequency dependence of these properties, compare well with other most recent experimental and theoretical data.Dedicated to Jan Linderberg on the occasion of his 60th birthday     

Highly conducting solid electrolytes based on poly (ethylene oxide-co-propylene oxide)

The conducting properties of solid electrolytes comprising random poly(ethylene oxide-co-propylene oxide) (of 84 : 16 monomer units mole ratio) and lithium, sodium, potassium, cesium, and rubidium salts have been studied. The systems containing some lithium or sodium salts achieved conductivity levels as high as 10^?5–10^?4 S/cm at ambient temperature and greater than 10^?3 S/cm at 100°C. However, the systems with rubidium and cesium salts exhibit conductivities a few orders of magnitude smaller. DSC studies show that the electrolytes studied are characterized by a high content of an amorphous phase (95–100%). It is suggested that the copolymer exhibits lower complexing abilities than that of poly(ethylene oxide), which results in a higher flexibility of electrolytes containing small cations and poor dissociation of the salts having large cations. © 1995 John Wiley & Sons, Inc.     

Investigation of muonic hydrogen isotopes scattering from H2 molecule

Hyperfine Interactions - Knowledge of the cross sections for scattering of µp, µd and µt on molecules of hydrogen isotopes is necessary not only for checking the algorithmic solution...     

Acid-catalyzed Hydrolysis of the cis-[Cr(1,10-phenanthroline)2(O2CO)]+ Ion Studied by the u.v.–vis Stopped Flow Method

The cis-[Cr(phen)₂(O₂CO)]⁺ ion was prepared through the displacement of two molecules of water from the cis-[Cr(phen)₂(OH₂)₂]³⁺ by the bidentate carbonate anion. It underwent two-phase hydrolysis reactions under acidic conditions (0.1 < [H⁺] < 2.7 m) at 5, 10, 15, 20 and 25 °C. Via slow carbonato chelate ring opening (first step k₁^slow) and a second fast decarboxylation(k₂^fast value). The first step was preceded by protonation of the coordinate bidentate carbonate ligand. The second step exhibited no pH dependence, while k₁^slow values increased with acid concentration that suggested the presence of both protonated and deprotonated reactant species. Based on these observations we have proposed a hydrolysis mechanism featuring H₂O-induced ring-opening of the coordinate CO₃²⁻ group in the first step k₁^slow followed by loss of CO₃²⁻ from two intermediates, [Cr(phen)₂(O₂COH)]²⁺ (k₁^slow) and [Cr(phen)₂(OH₂)(O₂COH)]²⁺ (k₂^fast).     

Set-valued dynamic systems and random iterations of set-valued weaker contractions in uniform spaces

Set-valued weaker contractions in uniform, locally convex and metric spaces are defined and dynamic systems of such weaker contractions are studied. Conditions guaranteeing the convergence of generalized sequences of random iterations and iterations and the existence and uniqueness of endpoints of set-valued weaker contractions are established. Our definitions and results are new for set-valued maps in uniform, locally convex and metric spaces and even for single-valued maps.     

Liquid-fog and liquid-gas phase transitions in hot nuclei

Thermal multifragmentation of hot nuclei is interpreted as the nuclear liquid-fog phase transition inside the spinodal region. The exclusive data for p(8.1 GeV) + Au collisions are analyzed within the framework of the statistical model SMM. It is found that the partition of hot nuclei is specified after expansion to a volume equal to V _t = (2.6 ± 0.3)V ₀. The freeze-out volume is found to be twice as large: V _f = (5 ± 1)V ₀. The similarity between multifragmentation and ordinary fission is discussed. The text was submitted by the authors in English.     

Electrospray ionization mass spectrometric study of 1,3,4-oxadiazole–copper complexes

The complexes of 2,5-disubstituted-1,3,4-oxadiazoles, namely 2,5-diphenyl-1,3,4-oxadiazole (1), 2,5-bis(2-pyridyl)-1,3,4-oxadiazole (2) and 2,5-bis(4-pyridyl)-1,3,4-oxadiazole (3), with copper cation were studied by electrospray ionization mass spectrometry (ESI-MS). The ability of the compounds studied to form complexes with copper (under the ESI conditions) can be ordered as 2 > 1 > 3. The compounds studied tend to form both 1 : 1 and 2 : 1 chelate complexes with both copper(II) and copper(I). The complexes with copper(I) are formed in the ESI process. The influence of solvent polarity, solution flow-rate, counter ions (Cl⁻, NO₃⁻, CH₃COO⁻, SO₄²⁻, acetylacetonates) on the type of the ions observed was studied. Copyright © 2004 John Wiley & Sons, Ltd.     

An approximate Newton method for non-smooth equations with finite max functions

A new version of finite difference approximation of the generalized Jacobian for a finite max function is constructed. Numerical results are reported for the generalized Newton methods using this approximation.