Almost Periodic and Asymptotically Almost Periodic Solutions of Liénard Equations

The aim of this paper is to study the almost periodic and asymptotically almost periodic solutions on (0,+1) of the Li´enard equation x′′ + f(x)x′ + g(x) = F(t), where F : T ! R (T = R+ or R) is an almost periodic or asymptotically almost periodic function and g : (a, b) ! R is a strictly decreasing function. We study also this problem for the vectorial Li´enard equation. We analyze this problem in the framework of general non-autonomous dynamical systems (cocycles). We apply the general results obtained in our early papers [3, 7] to prove the existence of almost periodic (almost automorphic, recurrent, pseudo recurrent) and asymptotically almost periodic (asymptotically almost automorphic, asymptotically recurrent, asymptotically pseudo recurrent) solutions of Li´enard equations (both scalar and vectorial)

A model for the distribution of aftershock waiting times

In this work the distribution of inter-occurrence times between earthquakes in aftershock sequences is analyzed and a model based on a non-homogeneous Poisson (NHP) process is proposed to quantify the observed scaling. In this model the generalized Omori's law for the decay of aftershocks is used as a time-dependent rate in the NHP process. The analytically derived distribution of inter-occurrence times is applied to several major aftershock sequences in California to confirm the validity of the proposed hypothesis.Comment: 4 pages, 3 figure

Stabilization of Disintegrating Ferroalloy and Steelmaking Slags

High-basic refinery slags are susceptible to silicate disintegration and turn into powder at cooling, and it is the cause of a negative impact of slag disintegration products on the environment. An applied method of slag disintegration preventing is the stabilization of its structure in the process of formation or cooling. The crystallographic method of stabilization of disintegrating slags lies in introducing micro additives into the slag composition. To realize the thermal method of slag stabilization, a rotor-type installation with a ball piece is proposed. Approbation of the applied methods of disintegrating slag stabilization showed their efficiency for producing a material with a number of new technological properties and uses. Keywords: disintegrating slags, stabilization, micro additives, rotor-type installatio

Contribution of the magnetic resonance to the third harmonic generation from a fishnet metamaterial

We investigate experimentally and theoretically the third harmonic generated by a double-layer fishnet metamaterial. To unambiguously disclose most notably the influence of the magnetic resonance, the generated third harmonic was measured as a function of the angle of incidence. It is shown experimentally and numerically that when the magnetic resonance is excited by pump beam, the angular dependence of the third harmonic signal has a local maximum at an incidence angle of {\theta} \simeq 20{\deg}. This maximum is shown to be a fingerprint of the antisymmetric distribution of currents in the gold layers. An analytical model based on the nonlinear dynamics of the electrons inside the gold shows excellent agreement with experimental and numerical results. This clearly indicates the difference in the third harmonic angular pattern at electric and magnetic resonances of the metamaterial.Comment: 7 pages, 5 figure

Theoretical analysis of flux amplification by soft magnetic material in a putative biological magnetic-field receptor

Birds are endowed with a magnetic sense that allows them to detectEarth’s magnetic field and to use it for orientation. Physiological andbehavioral experiments have shown the upper beak to host amagnetoreceptor. Putative magnetoreceptive structures in the beak arenerve terminals that each contain a dozen or so of micrometer-sizedclusters of superparamagnetic nanocrystals made of magnetite/maghemiteand numerous electron-opaque platelets filled with a so farunidentified, amorphous ferric iron compound. The platelets typicallyform chainlike structures, which have been proposed to function asmagnetic flux focusers for detecting the intensity of the geomagneticfield. Here, we test that proposition from first principles and developan unconstrained model to determine the equilibrium distribution ofmagnetization along a linear chain of platelets which we assume tobehave magnetically soft and to have no magnetic remanence. Ouranalysis, which is valid for arbitrary values of the intrinsic magneticsusceptibility chi, shows that chi needs to be much greater than unityto amplify the external field by two orders of magnitude in a chain ofplatelets. However, the high amplification is confined to the centralregion of the chain and subsides quadratically toward the ends of thechain. For large values of chi, the possibility opens up of realizingmagnetoreceptor mechanisms on the basis of attraction forces betweenadjacent platelets in a linear chain. The force in the central region ofthe chain may amount to several pN, which would be sufficient to convertmagnetic input energy into mechanical output energy. The strikingfeature of an ensemble of platelets is its ability to organize intotightly spaced chains under the action of an external field of givenstrength. We discuss how this property can be exploited for amagnetoreception mechanism

Black hole entropy, flat directions and higher derivatives

Higher order derivative corrections to the Einstein--Maxwell action are considered and an explicit form is found for the corrections to the entropy of extremal black holes. We speculate on the properties of these corrections from the point of view of small black holes and in the case when the classical black hole potential exhibits flat directions. A particular attention is paid to the issue of stability of several solutions, including large and small black holes by using properties of the Hessian matrix of the effective black hole potential. This is done by using a model independent expression for such matrix derived within the entropy function formalism.Comment: 21 pages, PACS numbers: 04.50.Gh, 04.70.Dy, 04.65.+

Critical Dynamics of Self-Organizing Eulerian Walkers

The model of self-organizing Eulerian walkers is numerically investigated on the square lattice. The critical exponents for the distribution of a number of steps ($\tau_l$) and visited sites ($\tau_s$) characterizing the process of transformation from one recurrent configuration to another are calculated using the finite-size scaling analysis. Two different kinds of dynamical rules are considered. The results of simulations show that both the versions of the model belong to the same class of universality with the critical exponents $\tau_l=\tau_s=1.75\pm 0.1$.Comment: 3 pages, 4 Postscript figures, RevTeX, additional information available at http://thsun1.jinr.dubna.su/~shche

The Problems of the Replacement of Alternative Penalties Taking into Account the Implementation of International Standards: Case of Some Post-Soviet Countries

International standards for the treatment of convicts without isolation from society contain the world experience of humanism in the execution of punishments and the development of the correctional system of all the countries in the world, concerning Russia and the countries of the former Soviet Union, they are adopted and implemented relatively recently. Today not all international standards have found their consolidation in the sectoral legislation of Russia and the CIS and Baltic countries. The execution of punishments is one of the most detailed regulated processes from the point of view of international regulation, as for the classification of the state as democratic, largely affects the compliance of its sectoral legislation in the penitentiary sphere with international standards. The aim of the study is to determine the features of the procedure for the replacement of alternative penalties, taking into account the implementation of international standards in some post-Soviet countries.     Keywords: international standards; alternative punishments; court; Prosecutor’s office; replacement of punishments

Pathological features of the lungs and liver of piglets under conditions of constant vaccination of livestock against circovirus infection

The pathogenicity of PCV 2 in the body of vaccinated piglets was studied based on the results of pathomorphological changes in the lungs and liver of animals. The work was carried out on commercial piglets vaccinated with the vaccine Ingelvak CircoFLEX (Germany) against circovirus. The work used clinical, zootechnical, enzyme immunoassay and pathomorphological research methods. It has been established that under the conditions of ongoing vaccination of piglets against PCV2, 30.3% of piglets still do not have virus-neutralizing antibodies. The main reason for the culling of animals are circovirus diseases that have respiratory clinical signs, as well as signs of multisystem wasting syndrome, determining the safety of the livestock at the level of 68.05%, the average live weight of 1 head at the moment of its transfer for fattening is 40.44±0.78 kg, and the average daily gain in live weight is 346.00±9.18 g. At autopsy, sick piglets reveal an increase in the lungs and liver, and the signs of inflammation in them, as a result of circulatory disorders, damage to the lymphoid tissue, the development of dystrophic and necrotic changes. The results of the research suggest that in order to increase the efficiency of the formation of post-vaccination immunity, specific medical preparations can be used to stimulate the immune response of the body, as well as to enhance the resistance of the lymphoid tissue of the lungs and liver in animals.The pathogenicity of PCV 2 in the body of vaccinated piglets was studied based on the results of pathomorphological changes in the lungs and liver of animals. The work was carried out on commercial piglets vaccinated with the vaccine Ingelvak CircoFLEX (Germany) against circovirus. The work used clinical, zootechnical, enzyme immunoassay and pathomorphological research methods. It has been established that under the conditions of ongoing vaccination of piglets against PCV2, 30.3% of piglets still do not have virus-neutralizing antibodies. The main reason for the culling of animals are circovirus diseases that have respiratory clinical signs, as well as signs of multisystem wasting syndrome, determining the safety of the livestock at the level of 68.05%, the average live weight of 1 head at the moment of its transfer for fattening is 40.44±0.78 kg, and the average daily gain in live weight is 346.00±9.18 g. At autopsy, sick piglets reveal an increase in the lungs and liver, and the signs of inflammation in them, as a result of circulatory disorders, damage to the lymphoid tissue, the development of dystrophic and necrotic changes. The results of the research suggest that in order to increase the efficiency of the formation of post-vaccination immunity, specific medical preparations can be used to stimulate the immune response of the body, as well as to enhance the resistance of the lymphoid tissue of the lungs and liver in animals