Approximations of almost periodic functions by entire ones

In this paper we propose a new proof of the well-known theorem by S. N. Bernstein, according to which among entire functions which give on (−∞,∞) the best uniform approximation of order σ of periodic functions there exists a trigonometric polynomial whose order does not exceed σ. We also prove an analog of this Bernstein theorem and an analog of the Jackson theorem for uniform almost periodic functions with an arbitrary spectrum.     

Aqueous vibromagnetic extraction of hydrophilic and hydrophobic biologically active substances from peloids of varied genesis

Aqueous vibromagnetic extraction of hydrophobic and hydrophilic biologically active substances from peloids of varied origin (sapropels, and sulfide-slime mud) was developed. Instrumental analytical techniques (GC/MS, TLS, IR spectroscopy), gravimetry, and other methods were used to determine polar and nonpolar lipids and saturated and unsaturated fatty carboxylic and humic acids in colloid systems.     

Crystal structure of the new organic conductor (TSeF)7[FeNO(CN)5]2 with unusual molecular packing of conducting layer

X-ray single crystal diffraction study of the new molecular conductor (TSeF)₇[FeNO(CN)₅]₂ has been carried out at room temperature and 130 K. The crystal structure is composed by layers of π-electron donors TSeF, separated by anion layers along the a-direction. The conducting organic layer has unusual for molecular conductors arrangement of neutral monomeric and charged hexameric TSeF units orthogonally packed with respect to each other. Another specific feature of the structure is fully ordered state of the nitroprusside anion and deep penetrating of its functional NO-group into the adjacent organic layer.     

Effect of pressure on the Ginzburg-Landau parameter kappa=lambda/xi in YB6

Measurements of the transition temperature Tc, the upper critical field Hc2, and the magnetic penetration depth lambda under hydrostatic pressure (up to approximately 9.2 kbar) in the YB6 superconductor were carried out. A pronounced and negative pressure effect (PE) on Tc and Hc2 with dTc/dp=-0.0547(4) K/kbar and micro0dHc2(0)/dp=-4.84(20) mT/kbar, and zero PE on lambda(0) were observed. The PE on the coherence length dxi(0)/dp=0.28(2) nm/kbar was calculated from the measured pressure dependence of Hc2(0). Together with the zero PE on the magnetic penetration depth lambda(0), our results imply that the Ginzburg-Landau parameter kappa(0)=xi(0)/lambda(0) depends on pressure and that pressure "softens" YB6, e.g., moves it to the type-I direction.     

On the sine-Gordon equation with a self-consistent source

We use the method of the inverse scattering problem to solve the sine-Gordon equation with a self-consistent source which corresponds to moving eigenvalues of the corresponding spectral problem.     

Visualization of super-compressibility in supersonic spiral-twisted jets

We have visualized first the super-compressibility and associated it phenomena in submerged under-expanded supersonic spiral-twisted gaseous jets during its flowing from the annular nozzle with a central cone. We have observed the regular unusual axial symmetric vortex structures of body rotation and chain structures of jets in argon, helium, nitrogen and air. The type of structure depends on geometry of nozzle and pressure in pre-chamber. Strong density gradient appears discretely in mentioned jets.     

Phase transitions and the structure of the C60 crystal doped with lithium by electrodiffusion

The structure and phase transitions of C₆₀ crystals doped with lithium by injecting metal ions from the superionic crystal-C₆₀ single crystal heterojunction under electrodiffusion conditions are reported. The sample experienced irreversible transitions resulting in the virtually complete disappearance of EPR signals and MW conduction in the temperature range 320–370 K. In this temperature interval, a new C₆₀ phase was formed; the phase contained polymeric chains of C₆₀ molecules along the crystallographic c axis and lithium clusters. The structure of this phase was determined. Annealing at 620 K restored the EPR signal and, according to the X-ray data, the initial cubic structure of pure C₆₀. The X-ray pattern, however, contained additional diffraction peaks, which was evidence of the presence of one more phase with a structure yet unknown.     

Stability of Filtration of a Gas—Liquid Mixture

The stability of steady regimes of filtration of a gas—liquid mixture at pressure lower than the saturation pressure is studied for the case of a nonmonotonic dependence of the relative phase permeability of the liquid on the gas saturation. It is shown that periodic self–oscillations can appear, and their evolution leads to deterministic chaos due to the appearance and destruction of quasiperiodic motions.