On the tensor product of supersingleton representations ofosp(1, 2n)

The tensor product of two supersingleton representations _n of the Lie superalgebraosp (1, 2n) is studied forn2. The main results are as follows: (a) anticommutators and commutators of the odd generators in _{n n} form a skew-symmetric representation of the Lie algebrau(n, n); (b) simple explicit form of all irreducible components of _{n n}, which are labelled by a single parameterJ=0, 1, ..., has been found. Each of them is a^*-representation ofosp (1, 2n) for which assertion (a) is valid. The dimension of its vacuum subspace equals , i.e., the nondegenerate vacuum occurs for J=0 only. Basic property of this family of irreducible^*-representations of osp(1, 2n) are analogous to those of massless representations of osp(1, 4).Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.     

Quantitative characterization of chaotic instabilities in semiconductors

A method for quantitative characterization of chaotic dynamical systems is discussed. An electronic instrument for determining the number of independent variablesk ^*, involved in the motion, is described. It allows one to obtain these in real time from a single observable. The suggested technique has been applied to quantification of strange attractors underlying chaotic instabilities in semi-insulating GaAsCr, and n-Ge, irradiated with high energy electrons. In n-Ge, for instance, the measured numbersk ^* range from 2 to 4 depending on control parameters. These measurements reveal the highly deterministic nature of the observed chaotic oscillations. The physical mechanisms responsible for the current instabilities and chaotic behaviour are discussed.     

Encapsulation of magnetite in vesicles

The encapsulation of fine magnetite particles of 10 nm size and marker ANS within asolectin vesicles has been made by sonication of the mixture in water. For the proof of encapsulation of magnetite in vesicles the electron microscope and spectrofluoriphotometer technique were used. The theory for the calculation of the magnetic force acting on the system consisted of non-capsulated magnetic particles dispersed in water and magnetic vesicles was developed.This work was supported by the Slovak Academy of Sciences within the framework of Project GAV No. 1361.     

On the critical regimes in the theory of randomly forced magnetohydrodynamic turbulence

In this paper large-scale properties of developed magnetohydrodynamic turbulence have been investigated by using double expansion method in the frame of quantum field renormalization group. It has been shown that universal kinetic scaling regime exists, but the double expansion in general leads to qualitatively different results than those provided by the usual -expansion treatment.This work was supported by Slovak Grant Agency for Science.     

Polypropylene/Poly (Trimethylene Terephthalate)–Blend Fibers

Polypropylene (PP)/polyester (PES)–blend fibers were prepared by extruder melt spinning. The polymer blend consisted of PP and a “master batch” (MB) based on polytrimethylene terephthalate (PTT) or polyethylene terephthalate (PET), binary PTT/PET or PP/PTT blends, and also on a ternary PP/(PTT/PET) blend. The phase structure of PP/PES–blend fibers was examined. PES microfibers showed separation from the PP matrix in blend fibers. The impact of MB composition and rheological characteristics on phase structure parameters indicate a significant contribution of the PTT in the binary MB on the length of dispersed PES microfibers in the PP matrix. However, the blends of PP and ternary MB (PP/PTT/PET) have a lower diameter and length of the PES microfibers. The presence of PTT/PET (PES) enhances the structural and mechanical properties of the blend PP/PES fibers. In addition, PTT increases the tensile strength of the PP/PES–blend fibers if a binary MB is used, while the fiber nonuniformity is reduced in the presence of a ternary MB.     

Primary isotopic effect on the magnetic shielding of tin nuclei (117Sn and 119Sn)

The Kirkwood-Buff statistical mechanical theory of surface tension γ for monatomic fluids is extended to molecular fluids. A rigorous expression for γ is derived in terms of the angular pair distribution function f(z ₁ R ₁₂θ₁θ₂) of an equilibrium fluid-fluid system (liquid-gas, liquid-liquid, or gas-gas). The Fowler approximation is applied for the liquid-gas case, and a simple expression for γ is derived in terms of the bulk liquid angular pair correlation function g(R ₁₂θ₁θ₂). Thermodynamic perturbation theory for g(R ₁₂θ₁θ₂) is also used to calculate γ theoretically. The theoretical results are compared with experimental values.     

On the Validity of Entropy Production Principles for Linear Electrical Circuits

We explain the (non-)validity of close-to-equilibrium entropy production principles in the context of linear electrical circuits. Both the minimum and the maximum entropy production principles are understood within dynamical fluctuation theory. The starting point are Langevin equations obtained by combining Kirchoff’s laws with a Johnson-Nyquist noise at each dissipative element in the circuit. The main observation is that the fluctuation functional for time averages, that can be read off from the path-space action, is in first order around equilibrium given by an entropy production rate. That allows to understand beyond the schemes of irreversible thermodynamics (1) the validity of the least dissipation, the minimum entropy production, and the maximum entropy production principles close to equilibrium; (2) the role of the observables’ parity under time-reversal and, in particular, the origin of Landauer’s counterexample (1975) from the fact that the fluctuating observable there is odd under time-reversal; (3) the critical remark of Jaynes (1980) concerning the apparent inappropriateness of entropy production principles in temperature-inhomogeneous circuits.     

Sufficiency in Quantum Statistical Inference

This paper attempts to develop a theory of sufficiency in the setting of non-commutative algebras parallel to the ideas in classical mathematical statistics. Sufficiency of a coarse-graining means that all information is extracted about the mutual relation of a given family of states. In the paper sufficient coarse-grainings are characterized in several equivalent ways and the non-commutative analogue of the factorization theorem is obtained. As an application we discuss exponential families. Our factorization theorem also implies two further important results, previously known only in finite Hilbert space dimension, but proved here in generality: the Koashi-Imoto theorem on maps leaving a family of states invariant, and the characterization of the general form of states in the equality case of strong subadditivity. Supported by the EU Research Training Network Quantum Probability with Applications to Physics, Information Theory and Biology and Center of Excellence SAS Physics of Information I/2/2005. Supported by the Hungarian grant OTKA T032662     

Multicomponental Fluorimetric Determination of Aluminium, Gallium and Indium

For the fast characteristics of mixtures of Aluminium, Gallium and Indium the fluorimetric evaluation in the form of complexes with 8-Hydroxyquinoline-5-sulphonic acid is described at selected pH. The highly collinear correlated fluorescent spectra and their first derivation were evaluated under various experimental conditions with the Multiple Linear Regression (MLR), Partial Least Squares (PLS) methods and Kalman filtering. When comparing the results, the PLS gives the least relative prediction errors under optimal conditions, 5.6–15.9% for the concentration range of Al 0.025–0.2 μg cm⁻³, Ga 0.1–0.8 μg cm⁻³ and In 0.1–0.8 μg cm⁻³ in the mixture.     

Parallel receivers and sparse sampling in multidimensional NMR

The recent introduction of NMR spectrometers with multiple receivers permits spectra from several different nuclear species to be recorded in parallel, and several standard pulse sequences to be combined into a single entity. It is shown how these improvements in the flow and quality of spectral information can be significantly augmented by compressive sensing techniques--controlled aliasing, Hadamard spectroscopy, single-point evaluation of evolution space (SPEED), random sampling, projection-reconstruction, and hyperdimensional NMR. Future developments of these techniques are confidently expected to mitigate one of the most serious limitations in multidimensional NMR--the excessive duration of the measurements.