Volume 8, Issue 6

- Existence and uniqueness of the solution of the problem of finding a Riemannian metric in the case when some of the components of a corresponding curvature tensor is independent of one of the variables, are investigated.

- In this paper we develop the method of studying multi-dimensional inverse problems for kinetic equations. The method is based on spherical harmonics expansion. For finite expansion of given information, in particular, for finite Fourier transform, we formulate and prove the existence and uniqueness theorems in some classes of functions.

- The analog of the F. and M. Riesz theorem is proved for functions satisfying the operator equation of the Beltrami type. Such functions are called A -analytic. The interest to this class of functions is stimulated by the fact that they can be used for solving a wide class of boundary-value problems for second order elliptic systems of equations and integral geometry problems on the plane

- A section of the Earth’s crust is bounded (in the vertical direction) by two parallel plane interfaces; beneath the lower interface there is an extended body of gas which diffuses through the crust to the upper surface, where it disperses in the atmosphere. Adopting a mathematical model proposed in [6] for this diffusion process, we want to locate the position of the lower subsurface by surface measurements of the pressure and concentration gradients at some time T . We estimate a value for the depth L of the subsurface and show that the relative error is small as we please, provided the time T is large enough.

- In this paper, we discuss stability and Tikhonov regularization for the integral equation of the first kind with logarithmic kernel. Since the kernel is analytic in our case, the problem is severely ill-posed. We prove a convergence rate for the regularized solution and describe a method for its numerical calculation.

- For solving direct and inverse heat transfer problems in continuous casting of steel numerically, one needs to determine the heat transfer functions modelling secondary cooling as functions of the water flow rate. We present an approach based on regularization for identifying these heat transfer functions from temperature measurements on the strand surface; this approach works fine for simulated data with added noise and reasonably well for real data.