The inequality in (a) is naturally the best possible. Theorem l(a) is connected with questions such as the Beck-Fiala theorem or the Koml6s conjecture (see [2J, [3J and [7]). Combinatorial motivations are presented exhaustively in [8J (see also [6]). In a slightly different form, Theorem l(a) was used in [IJ in the proof that nuclear Frechet spaces satisfy the Levy-Steinitz theorem on rearrange...

Today I start a series of lectures on the optimal control of systems with distributed parameters, that is to say, optimal control of systems described by partial differential equations. Optimal Control theory is the generalization of the classical calculus of variations where minimization of the functional is pursued in the class of non-smooth functions. In XX century optimal control theory mad...

A study on the behavior of off-site AC power failure recovery times at three nuclear plant sites is presented. It is shown, that power law is appropriate for the representation of failure frequency-duration correlation function of off-site power failure events, based on simple assumptions about component failure and repair rates. It is also found that the annual maxima of power failure duration...

In this study, we consider an optimal control problem for Euler-Bernoulli beam equation. The initial velocity of the system is given by function. We give sufficient conditions existence a unique solution hyperbolic and prove that considered exists unique. After obtaining Frechet derivative cost functional via adjoint problem, also iteration algorithm numerical using Gradient method. Finally, fu...