Direct and inverse problems associated with inclined passing of SH-waves through 1d inhomogeneous medium

Wave process in a one-dimensional vertically-inhomogeneous medium induced by a sounding impulse moving from the depth is considered. Mathematical background of the algorithm for the reconstruction of the medium's mechanical parameters is given when the form of the initial wave and the surface seismogram are known. Theoretical results are illustrated...

alekseev.pdf8.33 MB

RK-method of advanced accuracy: new point of view

In the paper new concepts of construction and analysis of numerical schemes of solving ODE systems are used for RK-method of advance accuracy. The analysis of compatibility of equations, the expression for the truncation error are given. The new analitic technics is based on the combinatorial identities. The constructed theory...

kuznecov.pdf4.83 MB

Mixed spline approximation

The mixed spline approximation problem combines the peculiarities of the problems of spline interpolation and smoothing that were studied by many mathematicians. The monograph of Loran should be mentioned specially. It gives the conditions of existence and uniqueness of the interpolating and smoothing splines in the general form. In practice...

rozhenko.pdf6.69 MB