Аппарат линейных матричных неравенств применяется к решению классической задачи о линейно-квадратичном регуляторе. Показано, каким образом эта техника может приводить к оптимальному решению, получаемому через уравнение Риккати. Рассмотрены некоторые нежелательные эффекты, возникающие при использовании иных методов решения, известных из литературы; приведены численные примеры.

Mesh-free methods allow one to perform engineering calculations directly via a geometrical model constructed in the CAD system. They help to avoid the difficulties and errors in generation of a finite element mesh. In the present work, the most suitable techniques for analysis of complex solid-state constructions of polymeric composites are selected among mesh-free methods. A computation algorithm is also developed on the basis of these methods.

We consider systems of nonautonomous nonlinear differential equations with infinite delay. We introduce Carath´eodory type conditions for the right-hand side in an equation, which permit one, on the one hand, to cover a fairly broad class of systems and, on the other hand, include the right-hand side in a compact function space and construct the so-called limiting equations. In the investigation, we use the construction of admissible spaces with fading memory, which permits one to obtain constructive results for the class of equations under study.

The book proposes the model of the unitary quantum field theory (UQT) where the particle is represented as a wave packet of some unified field. The frequency dispersion equation is chosen so that the packet periodically appears and disappears without changing its form. The envelope of the process is identified with a conventional wave function. The equations of such a field are nonlinear and relativistic invariant. With proper adjustments, they are reduced to Dirac, Schroedinger and Hamilton-Jacobi equations. The numbers of the new experimental effects are predicted both for high and low energies. It is calculated with big precision mass spectrum of the elementary particles and the fine structure constant. Also theoretical mass of the Higgs bozon-131.7 GeV was calculated. UQT explains the existents of the low energy nuclear reactions, of other exceptional phenomena and the possibility to create new sources of energy, for example E-cat Andrea Rossi.