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.     

Deuteron NMR spin–lattice relaxation of NH3D ions in partially deuterated (NH4)2SnCl6 and NH4ClO4

Deuteron spin–lattice relaxation is studied in 5% and 100% deuterated ammonium hexachlorostannate and perchlorate. The relaxation rate is observed to be independent of deuteration down to temperatures slightly lower than that of the maximum. At lower temperatures the rate of the 5% deuterated sample exceeds that of the 100% deuterated sample by four and two orders of magnitude in ammonium hexachlorostannate and perchlorate, respectively. The angular dependence of the deuteron relaxation rate in 5% deuterated ammonium hexachlorostannate at 6 K is explained in terms of existing models on quadrupolar relaxation. In 5% ammonium perchlorate one hydrogen equilibrium position, which lies on the preferred axis for 120° rotations, has a larger probability to be occupied by the deuteron of NH₃D⁺ ions. The deuterons at the other positions are still performing rotational jumps about the preferred C₃ axis and also about the other threefold axes, although at a slower rate. Such observations require a reconsideration of the relaxation process. A somewhat more general expression is derived for the relaxation rate, which agrees with the experimentally observed angular dependence for 5% deuterated ammonium perchlorate at 60 K. At lower temperatures the quadrupole coupling of the deuterons at the preferred axis may become practically time-independent. Then a significant contribution to the relaxation rate can be provided by the deuteron–proton magnetic dipolar interaction, which is still fluctuating fast via the rotation of the three protons about the axis through the stationary deuteron.     

Sur une décomposition d'ensembles

Sans résumé     

Carbon-14 kinetic isotope effects in the debromination of p-methyldibromocinnamic acid

The kinetic isotope effect (KIE) was applied in the study of the mechanism of bromine elimination from p-methyl-erythro-a,b-dibromocinnamic acid, successively labeled at the a and b carbons. The large ¹⁴C KIE for the b-position and small KIE for the a one of side chain of p-methyl-erythro-a,b-dibromocinamic acid proves that elimination of bromine leading to the formation of (E)-p-methylcinnamic acid proceeds via the E1 mechanism.     

FTIR in situ transmission studies on the kinetics of paper degradation via hydrolytic and oxidative reaction paths

This study deals with the quantitative and qualitative interpretation of transmission FTIR spectra of aged model paper samples to prepare the basis for a kinetic model of cellulose degradation involving mixed hydrolytic and oxidative mechanism. The ageing experiments were performed in situ under various conditions (pure water vapour, dried air, 100, 150 °C) to discriminate between hydrolytic and oxidative paths. Our focus was on the spectra between 1500–1900 cm^-1, where the products of paper ageing appear in the form of various carbonyl groups. A procedure of spectra standardization was used to interpret the bands area in terms of the conversion of carbon atoms in cellulose. From the time evolution of the bands the overall kinetic curves were generated. The positions of the carbonyl bands were verified by independent experiments and theoretical calculations (DFT method). A simple model involving a hydrolytic reaction route and first order kinetics was positively tested on the available experimental basis. PACS 81.05.-t; 82.20.Wt; 87.15.Rn     

Mixed Norm and Multidimensional Lorentz Spaces

In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved ([16], [7]). However, the question for multidimensional Lorentz spaces is still open. In this paper, we consider weights of product type, and give necessary and sufficient conditions for the Lorentz spaces, defined with respect to the two-dimensional decreasing rearrangement, to be normable. To this end, it is also useful to study the mixed norm Lorentz spaces. Finally, we prove embeddings between all the classical, multidimensional, and mixed norm Lorentz spaces. Research partially supported by KAW 2000.0048 and STINT KU 2002-4025. Research partially supported by Grants MTM2004-02299, 2005SGR00556 and The Swedish Research Council no. 624-2003-571.