Vol. 38 No. 1 (203) (2004)

The paper considers Legandre quasipolynomials, the great coefficients of which are equal to one, and total variation estimate of those polynomials is derived.

In $L^2(\mathbb R)$ space an m≥2 order self-adjoint differential operator is observed, the coefficients of which have precise behaviour in infinity. A Fourie expansion formula is derived by means of minimal system of general eigen functions of this operator.

In the present paper one more estimation on a rate of convergence of actual waiting time to its stationary value in the $GI|G|1|\infty$ model is obtained. It leads to a similar estimation for total empty time of a server when the traffic intensity of the model is more than one.

In the present paper we give a new construction of absolutely free binary algebra, the elements of which are called semiterms. These results are applied for Abelian algebras.

In the given article the behavior of transmission and reflection bands of flat electromagnetic wave falling inclined on ideal layered structure, subject to parameters of structure and wave angle of incidence was investigate. The condition at which the contact of transmission bands becomes possible is found. The given condition was the same view both in case of s- and p-waves. It was been shown, that independently of the kind of wave polarization in revealed points of band contacts the transmission coefficient of wave is equal to one.