Fractional Fokker-Planck equation for fractal media

We consider the fractional generalizations of equation that defines the medium mass. We prove that the fractional integrals can be used to describe the media with noninteger mass dimensions. Using fractional integrals, we derive the fractional generalization of the Chapman-Kolmogorov equation (Smolukhovski equation). In this paper fractional Fokker-Planck equation for fractal media is derived from the fractional Chapman-Kolmogorov equation. Using the Fourier transform, we get the Fokker-Planck-Zaslavsky equations that have fractional coordinate derivatives. The Fokker-Planck equation for the fractal media is an equation with fractional derivatives in the dual space.     

Anomalous Hall effect and ferromagnetism in the new diluted magnetic semiconductor Sb<Subscript>2−<Emphasis Type="Italic">x</Emphasis></Subscript>Cr<Subscript>x</Subscript>Te<Subscript>3</Subscript>

The magnetic and galvanomagnetic properties of single crystals of the new diluted magnetic semiconductor p-Sb_2?xCr_xTe₃ (0 ≤ x ≤ 0.02) have been studied in the temperature range 1.7–300 K. A ferromagnetic phase with the Curie temperature T_c ≈ 5.8 K and the maximum Cr content x = 0.0215 has been revealed. The easy magnetization axis is parallel to the C₃ crystallographic axis. In the presence of strong magnetic fields, the Shubnikov-de Haas effect has been observed. Analysis of this effect shows that doping with chrome reduces the concentration of holes. Negative magnetoresistance and the anomalous Hall effect are observed at liquid helium temperature.     

Selberg-Type Integrals Associated with SL3

We present several formulae for Selberg-type integrals associated with the Lie algebra .