On the Vinogradov additive problem

Let us state the main result of the paper. Suppose that the collection N ₁, ..., N _n is admissible. Then, in the representation $$ \left\{ \begin{gathered} p_1 + p_2 + \cdots + p_k = N_1 , \hfill \\ \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \hfill \\ p_1^n + p_2^n + \cdots + p_k^n = N_n , \hfill \\ \end{gathered} \right. $$ where the unknowns p ₁, p ₂, ..., p _k take prime values under the condition p _s > n+ 1, s = 1, ..., k, the number k is of the form $$ k = k_0 + b\left( n \right)s, $$ where s is a nonnegative integer. Further, if k ₀ ≥ a, then, in the representation for k, we can set s = 0, but if k ₀ ≤ a ? 1, then, for a given k ₀ there exist admissible collections (N ₁, ..., N _n ) that cannot be expressed as k ₀ summands of the required form, but can be expressed as k ₀ + b(n) summands.     

Chemistry of modified flavonoids

2,4-Dihydroxyphenoxyacetophenones were obtained by the reaction of resorcinol with phenoxyacetonitrile under the conditions of the Houben-Hoesch reaction. Their cyclization under the conditions of acid and alkaline catalysis gave new derivatives of 3-phenoxychromone.For Communication 18, see [1].Chemical Faculty, Taras Shevchenko Kiev University, Kiev 252033. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 598–603, May, 1997.     

Unitarity bounds for multiparticle interaction amplitudes

A regular method of asymptotical estimations for multiparticle interaction amplitudes is constructed. The method gives a generalization of the well-known Froissart result to the multiparticle case.     

Defect of total nuclear scattering cross sections: Fifty years of the Glauber diffraction theory

In this mini survey, a historical excursus into theoretical investigations on the diffraction theory of fundamental nuclear processes, the origins of which go back to work by Glauber (1955), is presented with an emphasis on recent achievements in the field.     

Three-dimensional numerical simulation of the plasma plume from a stationary plasma thruster

A numerical method is proposed for simulating the low-density plasma plume exhausted from a stationary plasma thruster in a three-dimensional setting. In contrast to the axisymmetric approximation, the problem is formulated so as to determine the effect of the backflow on the upstream region and the thruster walls, which are of finite size. The numerical method is a generalization of rarefied gas numerical methods to the case when the force field is not specified analytically. The method takes into account the delta-function character of the boundary ion distribution function and the considerable difference between the velocity scales of ions and neutral atoms, which transform into each other. Numerical results are presented that demonstrate the effect of some factors on the plasma plume.     

Tomography for Several Particles with One Random Variable

The tomographic map of the quantum state of a system with several degrees of freedom, which depends on one random variable, analogous to the rotated and scaled center-of-mass of the system, is constructed. The time-evolution equation of the tomogram for this map is given in the explicit form. The properties of the map such as the transition probabilities between different states and relation to the star-product formalism are elucidated. An example of a multimode oscillator is considered in detail. Identical particles are discussed within the framework of the proposed tomography scheme.     

Quantum tomography as a new approach to simulating quantum processes

A new method is proposed for ab initio calculations of nonstationary quantum processes on the basis of a probability representation of quantum mechanics with the help of a positive definite function (quantum tomogram). The essence of the method is that an ensemble of trajectories associated with the characteristics of the evolution equation for the quantum tomogram is considered in the space where the quantum tomogram is defined. The method is applied for detailed analysis of transient tunneling of a wave packet. The results are in good agreement with the exact numerical solution to the Schrödinger equation for this system. The probability density distributions are obtained in the coordinate and momentum spaces at consecutive instances. For transient tunneling of a wave packet, the probability of penetration behind the barrier and the time of tunneling are calculated as functions of the initial energy.     

Ferromagnetic superstructure of an La0.85Sr0.15MnO3 manganite single crystal

The elastic thermal-neutron scattering patterns of a La_0.85Sr_0.15MnO₃ manganite orthorhombic single crystal are investigated in the temperature range 4.2–300 K. It is found that, in addition to the known ferromagnetic ordering (T _C=240 K), this compound exhibits a ferromagnetic superstructure with the (010)2π/b wave vector (in the Pnma setting of the space group D _2h ¹⁶ ). The ferromagnetic superstructure is observed in the studied crystal at temperatures ranging from 4.2 to 200 K. It is shown that the formation of the ferromagnetic superstructure in this compound is directly associated with a 1/8-type charge ordering of Mn³⁺ and Mn⁴⁺ ions.