Vol 27, No 1 (2016)

The article describes an algorithm that stabilizes the computation of a three-dimensional two-phase heterogeneous model of an aluminum electrolyzer based on a Navier–Stokes equation system. The computational stabilization method assumes zero total divergence of the mixture in the numerical region. This assumption smooths out the velocities of the different phases, which arise at the liquid–liquid mixing interface due to model idiosyncrasies. Results of computer experiments are reported.

We calculate the parameters for the optimal design of a cryogenic system used to cool a HiPER laser target. The optimality criteria are minimum sliding time and maximum rolling time of the target in the system. The solution is obtained by simulating the motion of a spherical target through a curvilinear channel and constructing the set of criterion values and its Pareto boundary.

The inner Neumann problem for the Poisson equation in a region filled with a piecewise-homogeneous conducting medium is reduced to a system of boundary integral equations. The conjugate system is constructed; the solvability conditions are derived for the boundary-value problem.

A computer algorithm using a volume integral equation in the spectral domain is developed for the analysis of the scattering properties of plane objects in the shape of elliptical cylinders on the surface of the wafer or near it. The capabilities of the proposed algorithm are demonstrated for the case of particles of different materials and different shapes.

The objective of this article is to apply the first integral method to construct the exact solutions for a higher-order dispersive cubic-quintic nonlinear Schrödinger equation describing the propagation of extremely short pulses. Using a simple transformation, this equation can be reduced to a nonlinear ordinary differential equation (ODE). Various solutions of the ODE are obtained by using the first integral method. Further results are obtained by using a direct method. A comparison between our results and the well-known results is given.

The article examines the construction of discrete functions such that a part of their value set specifies (generates) arbitrary linear functions. For prime k greater than 5, we prove the existence of such partial functions with no fewer than two variables and derive linear upper and lower bounds in the number of variables for the size of their definition domain.

Necessary and sufficient conditions of optimality are proved for some classes of constrained optimization problems with constraints in the form of operator and differential-operator equations. The optimization problems are considered subject to additional functional constraints. The Pontryagin maximum principle and the Lagrange multiplier rule are derived for the relevant problems from the optimality conditions proved in this article.