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An algorithm of the simplex method not requiring an explicit updating of the LU decomposition in iterations is considered. Solutions obtained with fixed LU factors are corrected using small auxiliary matrices. The results of numerical experiments are presented.

The model of several interacting Cournot markets is considered. The markets are named interacting because the same number of producers act on each of them. Every producer chooses his own supply volumes on every market using the price situations, his own costs and production and delivery limitations. It is proved that in the case of the linear demand functions the problem of finding the Nash equilibria in the interacting Cournot markets model represents a potential game, i. e. it is equivalent to a mathematical programming problem. Nonlinear demand functions linearization procedures and preferences of initial problem reduction to the potential game are discussed.

Normality conditions are found for the operators associated with the semilinear analogs of the Stein matrix equation, namely, with the equations X A X B = C and X − AX*B = C.

In this paper, the kinematics of the tsunami wave ray and wave front above an uneven bottom is studied. The formula to determine the wave height along a ray tube is obtained. The exact analytical solution for the wave-ray trajectory above the bottom slope is derived. This solution gives the possibility to determine within the wave-ray approach the tsunami wave heights in an area with a sloping bottom relief. The distribution of the wave-height maxima in the area with the sloping bottom is compared to the one obtained by the numerical computation with a shallow-water model.

In this article, we discuss a new single sweep compact alternating group explicit method for the solution of time dependent viscous Burgers' equation both in Cartesian and polar coordinates. An error analysis for the new iterative method is discussed in detail. We have compared the results of the proposed iterative method with the results of a corresponding double sweep alternating group explicit (AGE) iterative method to demonstrate computationally the efficiency of the proposed method.

An economic damage optimization problem from local sources in a region has been formulated. An algorithm for solving the problem is proposed. Numerical experiments illustrating theoretical statements of the formulated problem and effectiveness of the algorithm proposed were carried out.

This paper presents a criterium, called the coefficients stability for inaccuracy in determining the coefficients of nonlinear regression models describing inexact data. A method for the coefficients stability estimation is also described. The proposed criterium is illustrated by a computational experiment with the data obtained by measurements of a refractive index dependence on the wavelength in 400−1000 nm band for a transparent polymer. The convergence of the proposed criterium to the known analytical solution for the case of linear regression is also studied.

In this paper, based on mathematical modeling, the convective heat transfer of an electroconductive liquid with regard to the internal sources of heat and the Joule dissipation in a spherical layer with heat from below is investigated. The structure of a flow, temperature field, magnetic field distribution and the Nusselt numbers are investigated.

In this paper, an implicit method of decomposition of 7-th degree Hermite splines to a series of «lazy» wavelets with displaced supports is investigated. A splitting algorithm for wavelet transforms of solving four five-diagonal s stems of linear equations with a strict diagonal dominance in parallel is justified. Results of numerical experiments on exactness for polynomials and on compression of spline-wavelet decomposition are presented.

Forest pyrology was used as a part of the forestry in the end of the nineteenth century. The founder of the forest pyrology in Russia was academician Ivan S. Melekhov. He defined it as a science of nature of forest fires, their effects, fire fighting methods, and positive function of fires in the forest. Formed as a branch of the forestry, forest pyrology became an independent science that developed as a theory and practice of forest protection. Separation of forest pyrology to an independent branch of the science was caused by the results of the much research that revealed great importance of the forest fires as a factor of the forest formation and as an ecological and evolutional factor that is of global importance. Fires greatly influence forest formation, their distribution, state, and productivity. In the paper, the short historical review of the main periods of Russian forest pyrology is given. Five periods were determined from the beginning of its origin to the further development. The total state of the science of forest fires in Russia is provided. It is noted that the organization of the laboratory of forest fires in 1959 in the V. N. Sukachev Institute of forest and wood SB AS USSR resulted in the academic recognition of the forest fires science; thus fire investigations in Siberia became systematic. The large contribution of the Russian scientists to the investigations of forest fires is emphasized. Many achievements of Russian forest fire scientists became world-famous.