[en] Precise characterizations of an admissible rate of decrease of a non-trivial function having zero integrals over all balls of fixed radius are established. The case of an essentially anisotropic behaviour of the function at infinity is considered for the first time. In particular, the function is even allowed to grow exponentially in one variable, which is compensated in a certain sense by its rapid decrease in other variables. Bibliography: 17 titles

No abstract available

[en] Quite diverse observations of quasars, galaxies, blackbody radiation, made in most regions of the sky indicate a possibility of general stratification in all of the universe, geometrically and kinematically

[en] The imaginary potential and entropic force are two important different mechanisms to characterize the dissociation of heavy quarkonia. In this paper, we calculate these two quantities in strongly coupled theories with anisotropic Lifshitz scaling and hyperscaling violation exponent using holographic methods. We study how the results are affected by the hyperscaling violation parameter $\mathrm{\theta <!--\; ??\; -->}$ and the dynamical exponent z at finite temperature and chemical potential. Also, we investigate the effect of the chemical potential on these quantities. As a result, we find that both mechanisms show the same results: the thermal width and the dissociation length decrease as the dynamical exponent and chemical potential increase or as the hyperscaling violating parameter decreases.

[en] Published in summary form only

[en] We have fabricated oxide-based spin-filter junctions in which we demonstrate that magnetic anisotropy can be used to tune the transport behavior of spin-filter junctions. We have demonstrated spin-filtering behavior in La_0.7Sr_0.3MnO₃/CoCr₂O₄/Fe₃O₄ and La_0.7Sr_0.3MnO₃/MnCr₂O₄/Fe₃O₄ junctions where the interface anisotropy plays a significant role in determining transport behavior. Detailed studies of chemical and magnetic structure at the interfaces indicate that abrupt changes in magnetic anisotropy across the non-isostructural interface is the cause of the significant suppression of junction magnetoresistance in junctions with MnCr₂O₄ barrier layers.

[en] Using a statistical approach, the magnetization and the initial susceptibility for a one - dimensional chain of a dilute ferromagnetic fluid have been investigated. Our assembly consisted of an N - partcle chain with N/3 non - interacting systems. We have studied three distinct cases: case 1 with randomly oriented easy axis of the particle assembly and the applied magnetic field is parallel to the chain. We found that the initial susceptility follows Curie - Weiss hehavior with posittive ordering temerature T_degree that does not depend on the anisotropy constant K of the particles. In case 2, the applied field is perpendicular to the chain with radomly orient easy zxis In this case, we found an prependicular to the chain with randomly priented easy axis. In this case, we found an antiferromagnetic transition with no dependence on K. In case 3, when the easy axis is fixed at an angle ζ relative to H, we found that whether H paralled or perpendicular to the chain threr is an interplay between ferromagnetic - like and antiferromagnetic - like behavior, depending on K, particle separtion within the system and the angle ζ. (authors)

[en] The original version of this article unfortunately contained mistakes.

No abstract available

[en] The compressibility properties of systems consisting of generic rotating rigid triangles are analyzed and discussed. It is shown that these systems which are usually associated with auxeticity can exhibit strongly anisotropic properties for certain conformations, which may give rise to the anomalous property of negative linear compressibility (NLC), that is, the system with particular geometry will expand along one direction when loaded hydrostatically. It is also shown that through carefully choosing the geometric features (i.e. the dimensions and the alignment of the rotating triangles as well as the angles between them) and the direction along which the linear compressibility is measured, one may control the magnitude and range of the NLC. All this provides a novel but effective method of manufacturing the systems which can be tailored to achieve particular values of NLC to fit particular practical applications. (paper)