approximation

On a Approximate Solution of the Problem of Aspherical Convex Compact Set

Authors: Dudov S. I., Mesheryakova Е. А.

We examine a finite-dimensional problem of minimizing the ratio radius of the ball given a compact convex set (in an arbitrary norm) to the radius of the inscribed sphere through the choice of a common center of these balls. The article offers an approach to building the numerical method of its solution.

On a Limit Value of a Remainder of the Lagrange Constant Corresponding to the Lagrange Trigonometrical Polynomial

Authors: Shakirov I. A.

The behavior of Lebesgue constant of a trigonometrical Lagrange polynomial interpolating the periodic function in an odd number of clusters is studied. The limit value of the remainder in the known asymptotic formula for this constant is found. A special representation of a remainder allowed us to establish its strict decreasing. On this basis, for a Lebesgue constant, a non-improvable uniform bilateral logarithmic function estimate is received.

Calculation of Meteoroids Masses by Approximating the Trajectories

Authors: Lukashenko T. P.

At processing meteor observations the outdated and insufficiently reliable methods are commonly used. In particular, the finding outward-atmospheric meteoroid masses comes from the luminosity without providing any estimates of accuracy for calculations. However, in recent years a variety of new dynamics methods has been developed that quite good describe a motion of meteoroids in atmosphere, as well as changing their parameters. In this article, these methods were used by the author to obtain outwardatmospheric masses of meteoroids from the data of European Fireball Network.

On an Approach to Approximate Solving of the Problem for the Best Approximation for Compact Body by a Ball of Fixed Radius

Authors: Dudov S. I., Osipcev M. A.

In this paper, we consider the problem of the best approximation of a compact body by a fixed radius ball with respect to an arbitrary norm in the Hausdorff metric. This problem is reduced to a linear programming problem in the case, when compact body and ball of the norm are polytops.