By using the asymptotic approach the solution of the Timoschenko-like equations governing the wave processes in the infinitely long elastic cylindrical shell lying on the non-homogeneous visco-elastic foundation has been constructed in the form of the wave packets traveling in the longitudinal direction. The solution represents the superposition of the bending and longitudinal waves.

The equation of characteristics for system of the equations of movement cubic anisotropic environment which thermal properties are described by the hyperbolic law of heat conductivity is obtained.

The new integral equations for brightness coefficients of pkineparellel dispersive medium of optical thickness Tq are obtained using invariance relations, involving usual Green’s functions or their generalization (for example, reduced Green’s functions) of radiation transfer equations. It is shown that the structure of these integral equations enables to obtain multiterm asimptotics ...

The paper presents the analysis of the mechanics the systems, which is modeling the motor-car with the basket jack - the telescopic lift. For the assumed mathenmtical model, its equations were introduced, solved by means of the Mathematica 5.2 software. The results are shown in the form of adequate graphs.

This work contains development of solution of the problem of optimization of the weight of beams from Hook's materials and also solution of this problem for nonlinear materials.