Hysteresis and Eddy-current Relaxation in SiFe Materials

The rate-dependent effects in metallic ferromagnetic materials with magnetization processes attributed to domain-walls motion were studied. The experimental method for eddy-current relaxation time determination was proposed. Some discrepancies between the data and theoretical predictions were observed and discussed. The origin of these discrepancies is accounted for by the decrease of viscous-type relaxation process as the rate of change of averaged magnetization is approaching zero.     

Feature of the magnetotransport of a quasi-one-dimensional electrons on the superfluid helium

The magnetotransport in a nondegenerate quasi-one-dimensional (Q1D) electron system over superfluid helium has been investigated experimentally. The measurements are performed in the presence of a perpendicular magnetic field B up to 2.6 T in the temperature range T=0.48–2.05 K in the system of conducting channels of 100–400 nm width. It is shown that the value of longitudinal magnetoresistance ρ_xx increases with B. In the electron-gas scattering region (T>0.9 ), the behaviour of ρ_xx agrees with classical Drude law. In the quantum transport regime, the self-consistent Born approximation (SCBA) theory for a 2D electron system over liquid helium describes the experimental data qualitatively. The deviation due to the difference of the experimentally studied Q1D system of the electrons in a parabolic potential well differs from theoretically analysed one. The experimental data agree with the theoretical calculation for the Q1D electron system at the weak magnetic field and the low temperature.

The negative magnetoresistance of the conducting channels has been observed in both the gas- and the ripplon-scattering region. These effects have been explained by weak carrier localization on the gas atoms at high temperature and by display of the quantum magnetotransport features in a mesoscopic system at low temperature.     

Effect of genesis on the properties and hydrogen reducibility of NiO-ZnO mixed oxides

The physico-chemical properties and reactivity tested by hydrogen reduction have been studied for two series of NiO-ZnO mixed oxides of various composition. The solid nickel oxide or zinc oxide in interaction with the solution of nitrate of the second component were used as the precursors in each series. The differences in some physico-chemical parameters of the samples in both series were correlated with their reduction behaviour, followed both in iso- and non-isothermal regime. Moreower, the influence of various factors modifying the reactivity of mixed oxides was also investigated and the results were compared with those obtained from earlier studied analogous systems of quite different origin.This revised version was published online in November 2005 with corrections to the Cover Date.     

Experimental and quantum chemical study of pyrrole self-association through N-H?π hydrogen bonding

An FT-IR study of pyrrole self-association in CCl₄ solutions was carried out. According to the IR measurements, pyrrole forms self-associated dimeric species via N-H?π hydrogen bonding. This was also confirmed by quantum chemical calculations for pyrrole monomer and dimer at B3LYP/6-31++G(d,p) level of theory. A T-shaped minimum was located on B3LYP/6-31++G(d,p) PES of pyrrole dimer characterized with a hydrogen bond of an N-H?π type, with centers-of-mass separation of monomeric units of 4.520 Å, H?π distance of 2.475 Å, the interplanar angle between the two monomeric units being 72.9°. The anharmonic vibrational frequency shift upon dimer formation calculated on the basis of 1D DFT vibrational potentials is in excellent agreement with the experimental data (84 vs. 87 cm⁻¹). Harmonic vibrational analysis predicts somewhat smaller shift (68 cm⁻¹). On the basis of NIR spectroscopic data, anharmonicity constants for the 2ν(N-H) and 2ν(N-H?π) vibrational transitions were calculated. The orientational dynamics of monomeric and self-associated pyrrole species was studied within the framework of the transition dipole moment time correlation function formalism. The period of essentially free rotation in the condensed phase reduces from 0.05 ps for the monomeric pyrrole to 0.02 ps for the proton-donor molecule within the dimer.     

On the vector field problem for O(n)/O(1)xO(1)xO(n-2)

We prove new results about the vector field problem on the real flag manifolds O(n)/O(1) x O(1) x O(n - 2). For some infinite families of these manifolds, we completely solve the vector field problem.     

Division and <Emphasis Type="Italic">k</Emphasis>-th root theorems for <Emphasis Type="Italic">Q</Emphasis>-manifolds

We prove that a locally compact ANR-space X is a Q-manifold if and only if it has the Disjoint Disk Property (DDP), all points of X are homological Z _∞-points and X has the countable-dimensional approximation property (cd-AP), which means that each map f: K → X of a compact polyhedron can be approximated by a map with the countable-dimensional image. As an application we prove that a space X with DDP and cd-AP is a Q-manifold if some finite power of X is a Q-manifold. If some finite power of a space X with cd-AP is a Q-manifold, then X ² and X × [0, 1] are Q-manifolds as well. We construct a countable family χ of spaces with DDP and cd-AP such that no space X ∈ χ is homeomorphic to the Hilbert cube Q whereas the product X × Y of any different spaces X, Y ∈ χ is homeomorphic to Q. We also show that no uncountable family χ with such properties exists. This work was supported by the Slovenian-Ukrainian (Grant No. SLO-UKR 04-06/07)     

Algorithms for ham-sandwich cuts

Given disjoint setsP ₁,P ₂, ...,P _d inR ^d withn points in total, ahamsandwich cut is a hyperplane that simultaneously bisects theP _i . We present algorithms for finding ham-sandwich cuts in every dimensiond>1. Whend=2, the algorithm is optimal, having complexityO(n). For dimensiond>2, the bound on the running time is proportional to the worst-case time needed for constructing a level in an arrangement ofn hyperplanes in dimensiond−1. This, in turn, is related to the number ofk-sets inR ^d−1 . With the current estimates, we get complexity close toO(n ^3/2 ) ford=3, roughlyO(n ^8/3 ) ford=4, andO(n ^d−1−a(d) ) for somea(d)>0 (going to zero asd increases) for largerd. We also give a linear-time algorithm for ham-sandwich cuts inR ³ when the three sets are suitably separated. A preliminary version of the results of this paper appeared in [16] and [17]. Part of this research by J. Matoušek was done while he was visiting the School of Mathematics, Georgia Institute of Technology, Atlanta, and part of his work on this paper was supported by a Humboldt Research Fellowship. W. Steiger expresses gratitude to the NSF DIMACS Center at Rutgers, and his research was supported in part by NSF Grants CCR-8902522 and CCR-9111491.