In this report, we review an elegant technique, known as the Bogoliubov method, for deriving amplitude equations in pattern forming systems, through detailed solution to the classical problem of Rayleigh-Bénard convection, with both free and rigid upper and lower boundaries. The computation is facilitated by the use of a newly proposed diagrammatic technique. The resulting equation is a nonloca...

In this paper, position vector of a spacelike general helix with respect to standard frame in Minkowski space E 1 are studied in terms of Frenet equations. First, a vector differential equation of third order is constructed to determine position vector of an arbitrary spacelike general helix. In terms of solution, we determine the parametric representation of the general helices from the intrin...

The well-known Van der Pol equation with delayed feedback is considered. It assumed that the delay factor large enough. In study of dynamics, critical cases in problem stability zero equilibrium state are identified. shown they have infinite dimension. For such cases, special local analysis methods been developed. main result construction nonlinear evolutionary boundary value problems, which pl...