Magnetic-Field-Dependent Electronic Relaxation of Gd3+ in Aqueous Solutions of the Complexes [Gd(H2O)8]3+, [Gd(propane-1,3-diamine-N,N,N′,N′-tetraacetate)(H2O)2]−, and [Gd(N,N′-bis[(N-methylcarbamoyl)methyl]-3-azapentane-1,5-diamine-3,N,N′-triacetate)(H2O)] of interest in magnetic-resonance imaging

EPR Spectra have been measured for aqueous solutions of a series of Gd³⁺ complexes at variable temperature and a range of magnetic fields; S-band (0.14 T), X-band (0.34 T), Q-band (1.2 T), and 2-mm-band (5.0 T). The major contribution to the observed line widths is magnetic-field-dependent and is interpreted as being due to the modulation of the zero-field splitting produced by distortion of the complexes from perfect symmetry. The transverse and longitudinal relaxation matrices for an ⁸S ion with such an interaction have been calculated using Redfield theory with vector-coupling methods, and diagonalised numerically to obtain relaxation rates and intensities for the degenerate transitions which contribute to the multiplet. The observed line width, which is inversely proportional to the magnetic field at low temperatures, is best described by the intensity-weighted mean transverse relaxation time for the four transitions with non-zero intensity. A least-squares fit of the data yields the square of the zero-field splitting tensor, Δ², and a correlation time, τ_v, with activation energy, E_v. The physical significance of these parameters and the extent of validity of the theoretical approach are considered. The parameters are used to predict the magnetic-field dependence of the longitudinal and transverse electronic relaxation times, which are discussed in the context of their relevance to ¹H-NMR relaxivity.     

Kinetic features of ethylene polymerization over supported catalysts [2,6‐bis(imino)pyridyl iron dichloride/magnesium dichloride] with AlR3 as an activator

The effects of polymerization temperature, polymerization time, ethylene and hydrogen concentration, and effect of comonomers (hexene‐1, propylene) on the activity of supported catalyst of composition LFeCl₂/MgCl₂‐Al(i‐Bu)₃ (L = 2,6‐bis[1‐(2,6‐dimethylphenylimino)ethyl] pyridyl) and polymer characteristics (molecular weight (MW), molecular‐weight distribution (MWD), molecular structure) have been studied. Effective activation energy of ethylene polymerization over LFeCl₂/MgCl₂‐Al(i‐Bu)₃ has a value typical of supported Ziegler–Natta catalysts (11.9 kcal/mol). The polymerization reaction is of the first order with respect to monomer at the ethylene concentration >0.2 mol/L. Addition of small amounts of hydrogen (9–17%) significantly increases the activity; however, further increase in hydrogen concentration decreases the activity. The IRS and DSC analysis of PE indicates that catalyst LFeCl₂/MgCl₂‐Al(i‐Bu)₃ has a very low copolymerizing ability toward propylene and hexene‐1. MW and MWD of PE produced over these catalysts depend on the polymerization time, ethylene and hexene‐1 concentration. The activation effect of hydrogen and other kinetic features of ethylene polymerization over supported catalysts based on the Fe (II) complexes are discussed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5057–5066, 2007     

Squeezed states and uncertainty relations since 1991

A brief review of the history of ten workshops/conferences on “Squeezed States and Uncertainty Relations” and main achievements in the related fields of quantum physics for the period from 1991 to 2007 are presented.     

The nucleon and Δ-resonance masses in relativistic chiral effective-field theory

We study the chiral behavior of the nucleon and Δ-isobar masses within a manifestly covariant chiral effective-field theory, consistent with the analyticity principle. We compute the πN and πΔ one-loop contributions to the mass and field-normalization constant, and find that they can be described in terms of universal relativistic loop functions, multiplied by appropriate spin, isospin and coupling constants. We show that these manifestly relativistic one-loop corrections, when properly renormalized, obey the chiral power-counting and vanish in the chiral limit. The results including only the πN-loop corrections compare favorably with the lattice QCD data for the pion-mass dependence of the nucleon and Δ masses, while inclusion of the πΔ loops tends to spoil this agreement.     

Characterization of spherical particles using high-order neural networks and scanning flow cytometry

We retrieve the radius R, real n and imaginary k parts of the refractive index of homogeneous spherical particles using angular distribution of the light-scattering intensity. To solve the inverse light-scattering problem we use a high-order neural-network technique. The effect of network parameters on optimization is examined. The technique is evaluated for noise-corrupted input data at 0.6 μm<R<10.6 μm, 1.02<n<1.38, and 0<k<0.03. The errors of retrieval for nonabsorbing particles do not exceed 0.05 μm for radius and 0.015 for refractive index. The experimental verification is fulfilled by experimental data retrieved by means of a scanning flow cytometer. The light-scattering profiles of polystyrene beads and spherized red blood cells are processed with the high-order neural networks and a non-linear regression at Mie theory. The parameters retrieved by the high-order neural networks correlate well with the parameters retrieved by the least-square method.     

Stationary Mode and Binomial Moments for Networks of the Type [SM|GI|∞] r

By using methods of the Markov renewal theory, we find conditions for the existence of a stationary mode for multichannel networks with semi-Markov input stream. As a tool of stationary distribution analysis, we introduce multivariate binomial moments and investigate their asymptotic properties. For a multichannel queuing system with periodic input stream, we construct the generating function of the stationary distribution in explicit form in terms of the parameters of the system under consideration.     

Modeling the interaction of a wave front with a forest

We investigate the processes that arise when a wave front hits a natural obstacle in the form of a forest. The modeling is carried out in the framework of a single methodological approach that uses the Euler equation to describe the motion of the air mass both over an open area and inside the forest. In the latter case the equations include mass forces associated with the vegetation. The numerical solution is obtained by Godunov’s method using parallel programming techniques. Two types of incident wave front are investigated: a plane shockwave and a nonlinear acoustic impulse modeling a spherical explosion wave at a large distance from the source. The specific features of the interaction process, including penetration of the wave front into the forest, partial reflection from the near boundary, and diffraction above the top boundary, are investigated for different types of vegetation (coniferous and deciduous forests). The numerical results reveal the formation of a pair of ascending and descending currents in the upper part of the forest (inside the tree crowns). The existence of this structure is confirmed by experimental findings. __________ Translated from Prikladnaya Matematika i Informatika, No. 21, pp. 48–71, 2005.