An algorithm for the numerical solution of the problem for eigenvalues in a waveguide in the complete vector statement using the finite-element method and the Bunch-Kaufman procedure for the factorization of the matrix of the derived set of linear algebraic equations was built and implemented.
Show AbstractMathematical methods for pattern recognition and algorithms for the classification of diseases based on them are widely used to solve problems of medical diagnostics [1]. In [2], in order to classify functional disorders of the gastrointestinal tract, an algebraic model of the Kora algorithm was applied. In [3–5] it was shown that to solve many problems of medical diagnostics possibilistic methods for making a medical diagnosis are much more efficient. The present work considers a comparative analysis of probabilistic and possibilistic models of diagnostics, as well as Kora algorithms and the results of their application to solving problems of acute appendicitis diagnostics.
Show AbstractThe possibility of estimating the values of a function at given points of its domain is investigated. The estimation uses results of the measurements of a finite number of linear functionals; the results of the measurements are distorted by an error. It is shown that only the component of the functions from the linear finite-dimensional subspace can be estimated with a finite error. A method for estimating this component with accuracy control is proposed. The mathematical methods of measurement reduction proposed by Yu.P. Pyt’ev are used. An example of the estimation of an emission spectrum that is measured by a double-slit spectrometer is described.
Show AbstractA non-Hermitian fermion model containing a $\gamma_5$-matrix in the mass term $m \rightarrow m_1 + \gamma_5 m_2$ is considered. A new refined condition of the unbroken $\cal PT$ - symmetry of the theory is proposed that comprises an indication that the initial domain of unbroken $\cal PT$ - symmetry is divided into subdomains corresponding to the description of ordinary and exotic particles. A relationship is established between the theory under study and the quantum field theory with maximal mass $M$ developed on the basis of the geometric approach. The operator {ie223-1} is calculated explicitly, which is required for the construction of a new scalar product in the theory with a non-Hermitian Hamiltonian.
Show AbstractIn this paper we study the problem of admitting an exact solution of the effect of spin fluctuations on phase transition when modeling a multiferroic superconducting system in a strong magnetic field. New results are obtained for phase portraits of the system of equations for amplitudes of spin density and temperature waves. The possibility is justified for the transition of the system to a phase in which superconductivity and antiferromagnetic ordering coexist, particularly via slowly fluctuating spin-density waves.
Show AbstractThe possibility of production and separation of the $^{18}$F medical radioisotope at a race-track microtron with an accelerated electron energy of 55 MeV in the $^{23}$Na(γ, ɑ$_n$) photonuclear reaction is studied. Ion-exchange chromatography is used to separate $^{18}$F from irradiated NaOH targets.
Show AbstractThe rigidities of collective nuclear oscillations were calculated for 44 even-even atomic nuclei and compared to the charge radii. Correlations between the rigidity maxima and the minimal values of the r$_0$ parameter were revealed. These correlations were attributed to the high surface tension in nuclei with filled neutron shells and the associated increase in pressure on nuclear matter.
Show AbstractIn this paper we study the thermoelectric properties of $n$-and $p$-type PbTe theoretically in a wide temperature interval of 300 to 900 K. A three-band model of the PbTe electron-energy spectrum was used in these calculations for the first time. The full set of the relevant kinetic characteristics is calculated, including the electrical and thermal conductivities, as well as the Seebeck coefficient and the thermoelectric figure-of-merit. The calculated thermoelectric quantities are in good agreement with the available experimental data.
Show AbstractSystems of nonlinear parabolic partial differential equations were used for a computational study of circular self-oscillatory processes in the active medium of the atria. The FitzHugh-Nagumo nonlinear differential equation was used in this work. The following excitation pathways of circular reentry waves were considered: 1. Excitation combined with unilateral blockade of excitation; 2. The effect of a part of a simple autowave; 3. Excitation in the tail part of the autowave; and 4. Emergence of a temporarily refractory site in the fixed part of a channel. The pathways of circular autowave excitation listed above provide a comprehensive representation of the currently characterized excitation pathways for this type of wave. The results of computational experiments that illustrate the excitation pathways of circular reentry waves are reported in this work.
Show AbstractIn this paper a parameter was used, viz., the average difference between the heliocentric longitudes (ADL) of the planets Venus, Earth, and Jupiter. For the minimum ADL (the planets are in conjunction), as well as at the minimum deviation of the planets from a line passing through them and the Sun at the location of the planets on opposite sides from the Sun, an index was composed that uniquely describes the 11-year cycle of solar activity.
Show AbstractК 90-летию со дня рождения Германа Павловича Любимова
Show AbstractThe observations of the upper atmosphere after the severe Tohoku earthquake of March 11, 2011 are analyzed. The observations cover the Hawaii region and span the time interval from about 7 h after the main shock to about half an hour before the arrival of the tsunami wave generated this earthquake. We explore the factors that are responsible for the emergence of the ionospheric response, which comprises a series of waves propagating ahead of the tsunami. The contribution of the moving tsunami wave into the formation of such a pre-tsunami response is established by the numerical simulation of the equations of geophysical hydrodynamics with two-dimensional geometry.
Show AbstractThe characteristics of the motion of solid-body markers over a settled composite vortex surface were studied using a laboratory apparatus. The vortex was generated in a cylindrical container filled with water using a rotating disc on the container bottom. The paths of solid-body markers were visualized. The radial distribution of the angular velocity of marker revolution around the container center was obtained. A relationship between eigenrotation frequencies and rotation around the container center occurred for two types of polypropylene markers (a flat square plate and a voluminous small tube).
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