This paper reviews the theoretical approaches and existing models of the solar wind interaction with the Local Interstellar Cloud (LIC). Models discussed take into account the multi-component nature of the solar wind and local interstellar medium. Basic results of the modeling and their possible applications to interpretation of space experiments are summarized. Open questions of global modelin...

In the present paper we give a fractional generalization of the Lauwerier formulation of the boundary value problem of the temperature field in oil strata. The Caputo fractional derivative operator and the Laplace transform are the important tools for solving the proposed problem. By using Efros’ theorem which is a modified form of convolution theorem for Laplace transform, the solution is obta...

We study stochastic convolutions providing by fundamental solutions of a class of integrodifferential equations which interpolate the heat and the wave equations. We give sufficient condition for the existence of function–valued convolutions in terms of the covariance kernel of a noise given by spatially homogeneous Wiener process.

The normal inverse Gaussian (NIG) distribution is a recent flexible closed form distribution that may be applied as a model of heavy-tailed processes. The NIG distribution is completely specified by four real valued parameters that have natural interpretations in terms of the shape of the resulting probability density function. By choosing the parameters appropriately, one can describe a wide r...

The random point field which describes the position distribution of the system of ideal boson gas in a state of Bose-Einstein condensation is obtained through the thermodynamic limit. The resulting point field is given by convolution of two independent point fields: the so called boson process whose generating functional is represented by inverse of the Fredholm determinant for an operator rela...

Let H be the general, reduced Heisenberg group. Our main result establishes the inverse-closedness of a class of integral operators acting on Lp(H), given by the off-diagonal decay of the kernel. As a consequence of this result, we show that if α1I+Sf , where Sf is the operator given by convolution with f , f ∈ Lv(H), is invertible in B(Lp(H)), then (α1I + Sf )−1 = α2I + Sg, and g ∈ Lv(H). We p...

For certain meromorphic function g and h, we study a class of functions f(z) = z−1 + ∑∞ n=1 fnz , (fn ≥ 0), defined in the punctured unit disk ∆∗, satisfying < ( (f ∗ g)(z) (f ∗ h)(z) ) > α (z ∈ ∆; 0 ≤ α < 1) . Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. Properties of an integral operator and its inverse defined on the new class is also...

Analytical expressions for the non-relativistic and relativistic Sunyaev-Zel'dovich effect (SZE) are derived by means of suitable convolution in-tegrals. The establishment of these expressions is based on the fact that the SZE disturbed spectrum, at high frequencies, possesses the form of a Laplace transform of the single line distortion profile (structure factor). Implications of this descript...