Unusual spin dynamics in topological insulators

The dynamic spin susceptibility (DSS) has a ubiquitous Lorentzian form in conventional materials with weak spin orbit coupling, whose spectral width characterizes the spin relaxation rate. We show that DSS has an unusual non-Lorentzian form in topological insulators, which are characterized by strong SOC. At zero temperature, the high frequency part of DSS is universal and increases in certain directions as $\omega^{d-1}$ with $d=2$ and 3 for surface states and Weyl semimetals, respectively, while for helical edge states, the interactions renormalize the exponent as $d=2K-1$ with $K$ the Luttinger-liquid parameter. As a result, spin relaxation rate cannot be deduced from the DSS in contrast to the case of usual metals, which follows from the strongly entangled spin and charge degrees of freedom in these systems. These parallel with the optical conductivity of neutral graphene.Comment: 5 pages, 3 figure

Slicing the Sierpi\'nski gasket

We investigate the dimension of intersections of the Sierpi\'nski gasket with lines. Our first main result describes a countable, dense set of angles that are exceptional for Marstrand's theorem. We then provide a multifractal analysis for the set of points in the projection for which the associated slice has a prescribed dimension.Comment: 19 pages, 4 figure

A Platform Independent Access Control Metamodel for Web Services

Web services provide platform independent communication through an XML-based standard family. The major software vendors released their own SOA products implementing these standards. However, the configuration of the WS-* protocols differs from product to product. Matching these configurations between different products can be a very tedious task. Security protocols are among the most complicated protocols to configure, especially if access control is also required. Although the XACML standard aims to solve this task, its rules and policies described in XML are not very user friendly, and XACML has a very poor support in the major SOA products. Therefore, we have developed a platform independent metamodel for describing distributed systems of web services. From models described in this metamodel the platform specific configurations and program codes can be easily generated for the various SOA products, increasing the productivity of the development. This article introduces an access control extension to this metamodel

Convex Hull Thrackles

A \emph{thrackle} is a graph drawn in the plane so that every pair of its edges meet exactly once, either at a common end vertex or in a proper crossing. Conway's thrackle conjecture states that the number of edges is at most the number of vertices. It is known that this conjecture holds for linear thrackles, i.e., when the edges are drawn as straight line segments. We consider \emph{convex hull thrackles}, a recent generalization of linear thrackles from segments to convex hulls of subsets of points. We prove that if the points are in convex position then the number of convex hulls is at most the number of vertices, but in general there is a construction with one more convex hull. On the other hand, we prove that the number of convex hulls is always at most twice the number of vertices

Unusual hyperfine interaction of Dirac electrons and NMR spectroscopy in graphene

Theory of nuclear magnetic resonance (NMR) in graphene is presented. The canonical form of the electron-nucleus hyperfine interaction is strongly modified by the linear electronic dispersion. The NMR shift and spin-lattice relaxation time are calculated as function of temperature, chemical potential, and magnetic field and three distinct regimes are identified: Fermi-, Dirac-gas, and extreme quantum limit behaviors. A critical spectrometer assessment shows that NMR is within reach for fully 13C enriched graphene of reasonable size.Comment: 5 pages, 3 figure

Adapted physical education in the Hungarian educational system: a conceptual framework

Declining health status of youth assumes considerable proportions. The continuously growing number of children with bad body positions, overweight and obesity, diabetes and asthma has been subject to several national or international publications. The number of state surveys, assessments of the situation and action plans has been arising, but real action has been keeping us waiting. Hungary, as a unique country among the neighboring countries, has realized the school-integrated rehabilitation of children suffering from internal and locomotor disorders. Schools in Hungary the Adapted Physical Education (APE), as a part of Physical Education (PE) have been helping disabled children finding their way back to their healthy fellows. In this case study we would like to present the interpretation of the definition, the goals and tasks of APE how and in what way they differ from the European approach and also introduce the definitions are used in Hungarian educational terminology (Physiotherapy, PE, Light Physical Education – as LPE and APE). We consider it to be important to show those substantial points which fundamentally differentiate Physiotherapy, APE and LPE. With setting the goals and tasks we would like to make it clear, that APE is an integral part of PE as a school subject in Hungary. That is the reason why with setting the fundamental goals and tasks, the goals and tasks of PE have to be considered as a starting-point. Compared to international publications a wider interpretation of APE in our study also provides an opportunity to establish an integral European way of thinking

The algebraic difference of two random Cantor sets: The Larsson family

In this paper, we consider a family of random Cantor sets on the line and consider the question of whether the condition that the sum of the Hausdorff dimensions is larger than one implies the existence of interior points in the difference set of two independent copies. We give a new and complete proof that this is the case for the random Cantor sets introduced by Per Larsson.Comment: Published in at http://dx.doi.org/10.1214/10-AOP558 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the dimension of triangular self-affine sets

As a continuation of a recent work [Bárány et al, On the dimension of self-affine sets and measures with overlaps. Proc. Amer. Math. Soc. 144 (2016) 4427–4440] of the same authors, in this note we study the dimension theory of diagonally homogeneous triangular planar self-affine iterated function systems