Radial subspaces of Besov and Lizorkin-Triebel classes: Extended strauss lemma and compactness of embeddings

In this article, subspaces of radial distributions of Besov-Lizorkin-Triebel type are investigated. We give sufficient and necessary conditions for the compactness of the Sobolev-type embeddings. It is also proved that smoothness of the radial function implies decay of the function at infinity. This extends the classical Strauss lemma. The main tool in our investigations consists of an adapted atomic decomposition.     

Analysis of stress and strain in tension cylindrical sample

One of the basic engineering problem occurring during the numerical analysis is to define the function of yield stress of material in the real conditions of a technological process. These properties are necessary to calculate the deformation and the state of stress and strain in the surface layer of an object. An inappropriate selection of the mechanical properties of the material is the reason of the occurrence of errors in numerical calculations of a continuous object, considered as a boundary and initial problem. Scientific investigations are being conducted with the aim to develop a database concerning yield stresses for different metals, depends on complex conditions of thermo-dynamical loads, e.g. temperature, the equivalent of the strain and the strain rate. The article presents a method of the determination of this dependence while using an experimental and numerical analysis. During the model investigations on the INSTRON testing machine, the force of elongation of the sample is measured and then calculations are made of the displacement of nodes of finite elements, plotted on outside surface of sample. The process is considered as a multi nonlinear problem. For this reason, an incremental method of motion and deformation of solid in an updated Lagrange formulation is used. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Convergence theorems for adapted sequences of random sets

We consider random sets with values in a separable Banach space. We study set-valued amarts, L¹-amarts, uniform amarts and submartingales. For all these classes of random sets, we prove convergence theorems in all main modes of set convergence (weak, Wijsman, Mosco, and Hausdorff). We also prove new convergence theorems for vector-valued subpramarts and pramarts.     

Nonlinear massive spin-2 field generated by higher derivative gravity

We present a systematic exposition of the Lagrangian field theory for the massive spin-2 field generated in higher-derivative gravity upon reduction to a second-order theory by means of the appropriate Legendre transformation. It has been noticed by various authors that this nonlinear field overcomes the well-known inconsistency of the theory for a linear massive spin-2 field interacting with Einstein’s gravity. Starting from a Lagrangian quadratically depending on the Ricci tensor of the metric, we explore the two possible second-order pictures usually called “(Helmholtz-)Jordan frame” and “Einstein frame.” In spite of their mathematical equivalence, the two frames have different structural properties: in Einstein frame, the spin-2 field is minimally coupled to gravity, while in the other frame it is necessarily coupled to the curvature, without a separate kinetic term. We prove that the theory admits a unique and linearly stable ground state solution, and that the equations of motion are consistent, showing that these results can be obtained independently in either frame (each frame therefore provides a self-contained theory). The full equations of motion and the (variational) energy-momentum tensor for the spin-2 field in Einstein frame are given, and a simple but non-trivial exact solution to these equations is found. The comparison of the energy-momentum tensors for the spin-2 field in the two frames suggests that the Einstein frame is physically more acceptable. We point out that the energy-momentum tensor generated by the Lagrangian of the linearized theory is unrelated to the corresponding tensor of the full theory. It is then argued that the ghost-like nature of the nonlinear spin-2 field, found long ago in the linear approximation, may not be so harmful to classical stability issues, as has been expected.     

Evaluation by means of magneto-acoustic emission and Barkhausen effect of time and space distribution of magnetic flux density in ferromagnetic plate magnetized by a C-core

Experimental results are shown of magneto-acoustic emission (MAE) and Barkhausen effect (BE) for two ferritic steel plates of different dimensions. The paper presents preliminary results of modelling the MAE, based on the finite element method (FEM), taking into account the key role of the eddy currents. Explanations are suggested as to the effects of MAE peak maximum growth, shift, as well as the characteristic BE profiles at the bottom of the large plates.     

Evanescent light–atom interaction detected by optogalvanic effect

An evanescent light penetrating an atomic vapour near a dielectric surface could be a probe for many atom-boundary phenomena. We show the possibility of very sensitive detection of the resonant atom–light interaction near the surface by using the optogalvanic effect for an evanescent wave. We observe a narrowing of the profile of the detected atomic line, and we point out some properties of the optogalvanic effect in the evanescent wave.     

Multiplicity of nontrivial solutions for elliptic equations with nonsmooth potential and resonance at higher eigenvalues

We consider a semilinear elliptic equation with a nonsmooth, locally Lipschitz potential function (hemivariational inequality). Our hypotheses permit double resonance at infinity and at zero (double-double resonance situation). Our approach is based on the nonsmooth critical point theory for locally Lipschitz functionals and uses an abstract multiplicity result under local linking and an extension of the Castro-Lazer-Thews reduction method to a nonsmooth setting, which we develop here using tools from nonsmooth analysis.     

Reductive carbonylation of nitrobenzene over Pd/Fe/I2/Py and Pd/C/Fe/I2/Py catalytic systems

A simple catalytic system containing metallic palladium, iron and iodine has been shown to be very active in the carbonylation of nitrobenzene to carbamate. The influence of the components of the catalytic system studied on its selectivity and activity has been established. It has been found that the catalytic activity of palladium supported on carbon (using both lignite coal and bituminous coal) was not lower than the activity of metallic palladium. This revised version was published online in August 2006 with corrections to the Cover Date.     

Direct and reverse energy transport in systems of monomers and imperfect traps: Monte Carlo simulations

A Monte Carlo simulation of the concentration dependence of the fluorescence quantum yield _M and emission anisotropyr _M of a system containing dye molecules in the form of monomers M and clusters T (statistical pairs and trimers) playing the role of the imperfect traps for nonradiative excitation energy transfer (NET) has been carried out. The simulation has been made for determined values of Förster critical distancesR ₀ ^MM andR ₀ ^MT and for several values ofR ₀ ^TM andR ₀ ^TT , assuming that the energy may be transferred from M^* to T as well as from T^* to M (reverse nonradiative energy transfer, RNET). It was shown that the RNET process in the range of high concentrations may strongly change the values ofr _M as well as those of _M. For emission anisotropyr _M an effect of repolarization was observed which decreases rapidly with increasingR ₀ ^TM andR ₀ ^TT . A very good agreement between the simulation results of _M and the theoretical model with no adjustable parameters was found. In the model, the RNET process and influence of correlation between active molecules on energy migration among monomers were taken into account.