arXiv subjects
Publications and source records attributed to D. B. Baranov.
Differentiable real function reproducing primes up to a given number and having a differentiable inverse function is constructed. This inverse function is compared with the Riemann-Von Mangoldt exact expression for the number of primes not exceeding a given value. Software for computation of the direct and inverse functions and their derivatives is developed. Examples of approximate solution of Diophantine equations on the primes are given.
The new interatomic potential g(r), providing the tunnelling of atoms, is suggested for calculating HFB phonon-roton spectrum E(p) of liquid He-4. The tunnelling enables the calculations to reproduce the experimental dependence of shifts E(p) on pressure P induced by He-3 admixture in the constant total density and volume.
A formula for potential U of the He-4--He-4 interaction in the liquid state is obtained by the direct electromagnetic computation as a function of the interatomic distance R. The potential decreases exponentially at large R. The further development and application of the result are discussed.
The 1D and 2D Bose-condensation of trapped atoms in a gravitational field are considered. The deformation of the finite parabolic potential in this field is modeling via the combination of two rectangular 1D and 2D traps, for which the cut-off and the re-definition of spectrum are taken into account. A Bose-condensation T_c shift by the gravity is calculated. A sign and a magnitude of it in a deformed trap depends on the order of including the gravitational field. The special choice of this order may describe three consistent Bose-condensations with different temperatures. These transitions may be associated with a transportation of a trap on the cycle (I) Earth-(II) Space-(III) Earth.