Interpolation with lagrange polynomials a simple proof of Markov inequality and some of its generalizations

The following theorem is provedTheorem 1.Let q be a polynomial of degree n(qP_n)with n distinct zeroes lying inthe interval[-1,1] and△'_q={-1}∪{τ_i:q'(τ_i)=0,i=1,n-1}∪{1}.If polynomial pP_n satisfies the inequalitythen for each k=1,n and any x[-1,1]its k-th derivative satisfies the inequality丨p~(k)(x)丨≤max{丨q~((k))(x)丨,丨1/k(x~2-1)q~(k+1)(x)+xq~((k))(x)丨}.This estimate leads to the Markov inequality for the higher order derivatives ofpolynomials if we set q=T_n,where Tn is Chebyshev polynomial least deviated from zero.Some other results are established which gives evidence to the conjecture that under theconditions of Theorem 1 the inequality ‖p~((k))‖≤‖q~(k)‖holds.     

Electron-electron correlations in Raman spectra of VO2

Physics of the Solid State - It has been shown that, in single crystals and films of a strongly correlated material, namely, vanadium dioxide, upon a thermally stimulated phase transition from the...     

2-Allyloxy/propargyloxypyridines: synthesis,structure, and biological activity

The alkylation (allylation and propargylation) of 3-cyano-6-dialkylamino-2-pyridones containing a d-annulated ring occurs at the oxygen atom. The structures of the starting compounds and their alkylation products were determined by X-ray diffraction. The neurotropic and antimicrobial activity of alkylation products was examined.     

Energy spectrum and optical properties of infinite carbon nanotubes in the Hubbard model

Physics of the Solid State - The energy spectra of carbon nanotubes with chiralities (5, 5) and (10, 0) have been calculated in terms of the Schubin-Wonsowskii-Hubbard model. It has been shown...     

Dielectric Spectroscopy as a Method for Testing Thin Vanadium Dioxide Films

Technical Physics - We have analyzed the dielectric spectra of thin (1200 Å) films of vanadium dioxide, a material with strong electron–electron correlations. We have tested both undoped...     

UO2, NpO2 and PuO2 preparation in aqueous nitrate solutions in the presence of hydrazine hydrate

It was established that heating to 90 °C of nitrate solutions of U, Np and Pu in the presence of hydrazine hydrate results in the formation of hydrated dioxides of these elements. On ignition under inert or reducing conditions in the temperature range of 280–800 °C hydrated uranium dioxide transmogrify into crystalline UO₂. On ignition in air atmosphere UO₂·nH₂O turns into UO₃ at 440 °C and into U₃O₈ at 570–800 °C. It was shown that thermolysis of the solution containing a mixture of uranium, neptunium and plutonium nitrates at 90 °C in the presence of hydrazine hydrate allows one to prepare hydrated dioxides (U, Np, Pu)O₂·nH₂O which on heating to ~300 °C transmogrify into crystalline product of UO₂, NpO₂ and PuO₂ solid solution. The technique of preparation of solid solutions of U and Pu dioxides is very promising as simple and effective method of production of MOX-fuel for.     

Chamber behavior of double Hurwitz numbers in genus 0

We study double Hurwitz numbers in genus zero counting the number of covers CP¹→CP¹ with two branching points with a given branching behavior. By the recent result due to Goulden, Jackson and Vakil, these numbers are piecewise polynomials in the multiplicities of the preimages of the branching points. We describe the partition of the parameter space into polynomiality domains, called chambers, and provide an expression for the difference of two such polynomials for two neighboring chambers. Besides, we provide an explicit formula for the polynomial in a certain chamber called totally negative, which enables us to calculate double Hurwitz numbers in any given chamber as the polynomial for the totally negative chamber plus the sum of the differences between the neighboring polynomials along a path connecting the totally negative chamber with the given one.     

Electron transport in hybrid superconductor heterostructures with manganite interlayers

Hybrid herostructures comprising an YBa₂Cu₃O _x (YBCO) high-temperature superconductor (HTS) layer and Nb/Au low-temperature superconductor (LTS) bilayer (with critical HTS and LTS temperatures T _c and T′_c, respectively), separated by a thin (d _M = 5–20 nm) interlayer of LaMnO₃, La_0.7Ca_0.3MnO₃, or La_0.7Sr_0.3MnO₃ manganite have been studied. The electric resistance and magnetic properties of individual (evaporated directly onto the substrate) manganite films and related hybrid herostructures have been measured. Based on quasi-classical equations, analytical expressions for the conductivity of herostructures at T ≤ T′_c are obtained in the case of a low-transparency superconductor/manganite interface. It is established that the conductivity of heterostructures is determined by the proximity effect (related to the penetration of a condensate wavefunction from the Nb/Au bilayer to manganite) and depends strongly on interface transparency. At low temperatures (T ≪ T _c′), the conductivity peaks are found at voltages determined by the exchange field of the manganite interlayer. At T _c′ < T < T _c, conductivity features at nearly zero bias voltages are observed, which are related to the superconductivity of the YBCO electrode.