A method of construction of new examples of families of expander graphs of unbounded degree is presented. The property of being an expander seems significant in many of these mathematical, computational, and physical ...

We propose new multivariate cryptosystems over an n-dimensional free module over the arithmetical ring Zm based on the idea of hidden discrete logarithm for Z*m. These cryptosystems are based on the hidden Eulerian ...

Multivariate cryptosystems are divided into public rules, for which tools of encryption are open for users and systems of the El Gamal type, for which the encryption function is not given in public, and, for its generation, ...

We investigate the most general class of Fredholm one-dimensional boundary-value problems in the Sobolev—Slobodetskiy spaces. Boundary conditions of these problems may contain a derivative of the whole or fractional order. ...

Let L be an algebra over a field F. Then L is called a left Leibniz algebra if its multiplication operations [⋅, ⋅] additionally satisfy the so-called left Leibniz identity: [[a,b],c] = [a,[b,c]] – [b,[a,c]] for all ...

We find out an explicit formula for the distribution of a rotationally invariant α-stable process at that moment of time, when it hits a given hyperplane for the first time. The case of 1 < α ≤ 2 is considered.

We study the Hilbert boundary-value problem for analytic functions in the Jordan domains satisfying the quasi-hyperbolic boundary condition by Gehring—Martio. Assuming that the coefficients of the problem are functions ...

This paper devoted to the nonperiodic locally generalized radical groups, whose subgroups of infinite special rank are transitively normal. We proved that if such a group G includes an ascendant locally nilpotent subgroup ...

We study the Dirichlet problem for quasilinear partial differential equations of the form Δu(z) = h(z)f(u(z)) in the unit disk D ⊂ C with continuous boundary data. Here, the function h : D→R belongs to the class L^p(D), ...