Collective motion of magnetization in two-dimensional arrays of square elements

The resonance in a two-dimensional array of square ferromagnetic elements has been experimentally investigated. The magnetization of the elements is shown to be in the vortex state. The resonance peak splitting in the array with increasing density of the elements has been established. The explanation of this phenomenon is proposed and eigenfrequencies of the collective modes are theoretically estimated. Different combinations of polarities and chiralities of the nearest elements in the array are examined.     

Isobaric heating of polystyrene and evaluation of the Narayanaswamy parameter x from volume recovery data

Structure parameter x, defining the relative contributions of temperature and structure to the relaxation times, which is applied in Tool-Narayanaswamy-Moynihan (TNM) equation, was evaluated from volume heating isobars for polystyrene (PS) applying the peak shift method. The peak shifted with changing structural state of PS prior heating, which was reached by different period of aging time at 89 °C < T_g up to 2544 h. In this novelized procedure for volume data, originally tested only for enthalpic measurements, high sensitivity of peak temperature (position of inflection point of the heating isobar) was shown, together with high linearity of data. This allows to directly and sensitively calculate the shift and consequently structure parameter x. The value found in the research, x = 0.40 ± 0.02, is in good agreement with published results obtained by the peak-shift method from enthalpy data of PS.     

Numerical solution of turbulent jet flows

The work deals with numerical modelling of several turbulent 3D jet flows: steady impinging jet, steady free jet in cross–flow, synthetic free jet (unsteady) and synthetic impinging jet (unsteady). The numerical method is based on artificial compressibility method with dual time extension for unsteady cases. Space discretization uses cell–centered finite volume method with third order accurate upwind approximation for convection, the time discretisations are implicit. Turbulence is modelled using two–equation eddy viscosity models and by explicit algebraic Reynolds stress model (EARSM by Wallin and Hellsten). The results of first three cases are compared with measurements. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Biodegradation of Blown Films Based on Poly(lactic acid) under Natural Conditions

Summary: Commercially available polymer Bioflex® 219F, blend of polylactic acid and biodegradable co-polyester, was used for film preparation, performed on mono-extrusion blown moulding machine. Resulting thin film was investigated on biodegradability in composting conditions for 6 weeks. The influence of microbial attack on mechanical, physico-chemical properties, weight loss and surface morphology was tested weekly. The results obtained during 6 weeks of composting indicate relatively good accessibility to biological degradation. Moreover, the time course of studied properties was observed through the test period.     

Nucleophilicity of metal carbonyl anions in vinylic substitution reactions

Second order rate constants are reported for the reactions of metal carbonyl anions ([M(CO)_nL]^?) with several vinyl halides: PhCCl?C(CN)₂, Z‐ and E‐Ph(CN)C?CHHal (Hal = Cl, Br) which follow the addition–elimination (Ad_NE) substitution mechanism. The obtained data show that the nucleophilic reactivity of [M(CO)_nL]^? anions towards vinyl halides increases in the same order as in aliphatic S_N2 reactions, but much more steeply, by 14 orders of magnitude in the row log{ }: [CpFe(CO)₂]^? (～14), [Re(CO)₅]^? (7.8), [Mn(CO)₅]^? 2.1, [CpW(CO)₃]^? (0.7) > [CpMo(CO)₃]^? (0). A good correlation exists between nucleophilicities of [M(CO)_nL]^? anions towards vinyl (sp²‐carbon) and alkyl halides (sp³‐carbon) with slope 2.7. The reactivity of [M(CO)_nL]^? in a halogen–metal exchange process (with Z‐PhC(CN)?CHI) follows a similar ‘large’ scale as in the Ad_NE process. The nucleophilicity of [M(CO)_nL]^? anions correlates better with their one‐electron oxidation potentials (E_ox) than with their basicity (pK_a of [M(CO)_nL]H). Copyright © 2008 John Wiley & Sons, Ltd.     

Simple measure of similarity for the market graph construction

A simple measure of similarity for the construction of the market graph is proposed. The measure is based on the probability of the coincidence of the signs of the stock returns. This measure is robust, has a simple interpretation, is easy to calculate and can be used as measure of similarity between any number of random variables. For the case of pairwise similarity the connection of this measure with the sign correlation of Fechner is noted. The properties of the proposed measure of pairwise similarity in comparison with the classic Pearson correlation are studied. The simple measure of pairwise similarity is applied (in parallel with the classic correlation) for the study of Russian and Swedish market graphs. The new measure of similarity for more than two random variables is introduced and applied to the additional deeper analysis of Russian and Swedish markets. Some interesting phenomena for the cliques and independent sets of the obtained market graphs are observed.     

Critical higher order Sturm–Liouville difference operators

We investigate the so-called critical 2nth-order Sturm–Liouville difference operators and associated symmetric banded matrices. We show that arbitrarily small (in a certain sense) negative perturbation of a non-negative critical operator leads to an operator which is no longer non-negative.     

Weyl–Titchmarsh theory for discrete symplectic systems with general linear dependence on spectral parameter

In this paper we develop the Weyl–Titchmarsh theory for discrete symplectic systems with general linear dependence on the spectral parameter. We generalize and complete several recent results concerning these systems, which have the spectral parameter only in the second equation. Our new theory includes characterizations of the Weyl discs and Weyl circles, their limiting behaviour, properties of square summable solutions including the analysis of the exact number of linearly independent square summable solutions and limit point/circle criteria. Some illustrative examples are also provided.     

Preservation of completeness by some continuous maps

We show that a metrizable space Y is completely metrizable if there is a continuous surjection f:X→Y such that the images of open (clopen) subsets of the (0-dimensional paracompact) ?ech-complete space X are resolvable subsets of Y (in particular, e.g., the elements of the smallest algebra generated by open sets in Y).     

Numerical treatment of a free surface problem in ferrohydrodynamics

The interactions between a ferrofluid with a free surface and an immersed permanent magnet are studied. We consider a strategy for the computation of equilibrium positions of the free surface for various geometric positions of the magnet. It will be used for the numerical simulation of devices that are used in spacecraft technology to damp oscillations of satellites. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)