Necessary and sufficient conditions of extremum for polynomials and power series in the case of two variables

The present paper is a continuation of the author's previous works, in which necessary and sufficient local extrema at a stationary point of a polynomial or a power series (and thus of an analytic function) are given. It is known that for the case of one variable, the necessary and sufficient conditions of the extremum are closing, i.e., they can be formulated as a single condition. The next most complicated case is the case with two variables, which is the one considered in this paper. In this case, many procedures, to which the verification of necessary and sufficient conditions is reduced, are based on the computation of real roots of a polynomial from one variable, as well as on the solution of some other rather simple practically realizable problems. An algorithm based on these procedures is described. Nevertheless, there are still cases where this algorithm "doesn't work". For such cases we propose the method of "substitution of polynomials with uncertain coefficients", using which, in particular, we have described an algorithm that allows us to unambiguously answer the question about the presence of a local minimum at a stationary point for a polynomial that is the sum of two A-quasi-homogeneous forms, where A - is a two-dimensional vector, whose components are natural numbers.Comment: 30 pages, 2 figure

Seismic Vibration of Nuclear Power Station Building

Reactor Building is considered as a system with concentrated masses. The movement of the system is described with account of elastic component, shear and rotation of the base relatively foundation. Seismic excitation is described by set of accelerogramms. The equations of movement are solved using complex modal analysis. Natural frequencies are acceleration functions for masses of the system are defined

Modeling of radiative - conductive heat transfer in compositing materials

A layer of composite material is investigated, which is heated one-sidedly with one-dimensional energy transfer accounting for thermal conductivity and radiation. A mathematical model is suggested for non-stationary coefficient thermophysical problem under radiative-conductive heat transfer in a material layer. Temperature dependencies of thermal capacity and thermal conductivity coefficient of composite radio-transparent material have been determined through numerical modeling by solving the coefficient reverse problem of thermal conductivity

Effects of dimephosphone on skin survival in conditions of reduced blood circulation

The search for and creation of drugs with dermatoprotective and metabotropic activity is one of the priorities of modern diabetology. Synthetic organophosphorus compounds with no anticholinesterase activity, to which dimephosphone belongs to, deserve great attention in this respec

Аделаида Борисовна Васильева (к девяностолетию со дня рождения)

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Measurement of trapped proton fluences in main stack of P0006 experiment

We have measured directional distribution and Eastward directed mission fluence of trapped protons at two different energies with plastic nuclear track detectors (CR-39 with DOP) in the main stack of the P0006 experiment on LDEF. Results show arriving directions of trapped protons have very high anisotropy with most protons arriving from the West direction. Selecting these particles we have determined the mission fluence of Eastward directed trapped protons. We found experimental fluences are slightly higher than results of the model calculations of Armstrong and Colborn

Rare earth elements materials production from apatite ores

The paper deals with the study of processing apatite ores with nitric acid and extraction of the rare earth elements. The rare earth elements can be successfully separated and recovered by extraction from the nitrate- phosphate solution, being an tributyl phosphate as extraction agent. The developed scheme of the processing apatite concentrate provides obtaining rare earth concentrates with high qualitative characteristics

Multiplicities of secondaries in interactions of 1.8 GeV/nucleon Fe-56 nuclei with photoemulsion and the cascade evaporation model

A nuclear photographic emulsion method was used to study the charge-state, ionization, and angular characteristics of secondaries produced in inelastic interactions of Fe-56 nuclei at 1.8 GeV/nucleon with H, CNO, and AgBr nuclei. The data obtained are compared with the results of calculations made in terms of the Dubna version of the cascade evaporation model (DCM). The DCM has been shown to satisfactorily describe most of the interaction characteristics for two nuclei in the studied reactions. At the same time, quantitative differences are observed in some cases

Extraction of rare earth elements from hydrate-phosphate precipitates of apatite processing

The features of extraction of rare earth elements (REE) were considered from hydrate-phosphate precipitates of REE of apatite processing by nitric acid technology. The preliminary purification of nitrate solution of REE from impurities of titanium, aluminum, iron, uranium and thorium was suggested to obtain stable solutions not forming precipitates. Washing the extract was recommended with the evaporated reextract that allows to obtain directly on the cascade of REE extraction the concentrated solutions suitable for the separation into groups by the extraction method. Technical decisions were suggested for the separation of REE in groups without the use of salting-out agent

Target fragments in collisions of 1.8 GeV/nucleon Fe-56 nuclei with photoemulsion nuclei, and the cascade-evaporation model

Nuclear photographic emulsion is used to study the dependence of the characteristics of target-nucleus fragments on the masses and impact parameters of interacting nuclei. The data obtained are compared in all details with the calculation results made in terms of the Dubna version of the cascade-evaporation model (DCM)