# variation method

## The shell model of electron structure of negative hydrogen ion

In the frame of non-relativistic approximation, a compact approximate solution of the Schrödinger equation for the ion of $H^{-}$ has been obtained in the form of product for Legendre polynomials and variational functions of the Schull--Löwdin type. The accuracy of calculation of ion energy is of the same order that the results obtained using the multiparametric functions of Hylleraas and Pekeris.

## Аналіз прямих варіаційних методів розв’язку задач оптимального керування

Direct variation methods which are used for the decision of optimum controlproblems have been analyzed. The confidant a direct variation method which allows to simplify considerably the decision of optimum controlproblem is offered and to receive sufficient accuracy of the decision in practical use in real time of mechanical systemscontrol.

## Методика розрахунку шпонкових з’єднань залізобетонних елементів

Expounded pre-conditions and essence of method of calculation of strength of joints of the key of concrete and reinforceconcrete elements, which is based on the variation method of theory of plasticity of concrete. The algorithm of calculation of joints is presented at destruction «after the key» and «after guy-sutures». The expounded bases of calculation of connections of three-keys are with the different width of guy-sutures. Resulted limitations which simplify procedure of calculation.