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The behaviors of resistance, magnetoresistance (up to 5 T), and Hall electromotive force (EMF) with varying temperature (from 10 to 300 K) and measuring current (from 10 mkA to 10 mA) are studied for the Si sample with CrSi2 nanocrystallites (NC) in the plane (111). The conduction in such heterostructure proceeds in the plane with the NC and is the conduction of a two-dimensional system of charge carriers that shows some unusual effects. The temperature variation of resistivitymaybe treated as the result of the effect of thermal activation but in this case it is characterized by a low activation energy different in value in different temperature ranges. This suggests that the mechanism of conduction is more complex. It is found that the conduction is determined by the effect of temperature variation not only on carrier concentration but also on its mobility. Magnetoresistivity is also of different shape in different temperature ranges. All the above features are treated in terms of the proposed model of electron hopping through the conduction band (or hole hopping through the valence band). A peculiar effect of giant reduction in resistivity with increasing the measuring current has been revealed. Discussed are some possible factors responsible for this effect., Comment: 9 pages, 7 figures

The estimates of the uniform norm of the Chebyshev polynomial associated with a compact set $K$ consisting of a finite number of continua in the complex plane are established. These estimates are exact (up to a constant factor) in the case where the components of $K$ are either quasismooth (in the sense of Lavrentiev) arcs or closed Jordan domains bounded by a quasismooth curve.

We construct polynomial approximations of Dzjadyk type (in terms of the k-th modulus of continuity, $k \ge 1$) for analytic functions defined on a continuum E in the complex plane, which simultaneously interpolate at given points of E. Furthermore, the error in this approximation is decaying as $e^{-cn^\alpha}$ strictly inside E, where c and $\alpha$ are positive constants independent of the degree n of the approximating polynomial., Comment: 21 page; submitted to J. Math. Pures Appl

We establish a discrepancy theorem for signed measures, with a given positive part, which are supported on an arbitrary convex curve. As a main application, we obtain a result concerning the distribution of zeros of polynomials orthogonal on a convex domain., Comment: 24 pages; to appear in Constr. Approx

We extend the results on the uniform convergence of Bieberbach polynomials to domains with certain interior zero angles (outward pointing cusps), and show that they play a special role in the problem. Namely, we construct a Keldysh-type example on the divergence of Bieberbach polynomials at an outward pointing cusp and discuss the critical order of tangency at this interior zero angle, separating the convergent behavior of Bieberbach polynomials from the divergent one for sufficiently thin cusps., Comment: 18 pages, AMS-LaTeX, to appear in J. d'Analyse Math