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# Перегляд Доповіді Національної академії наук України за назвою

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• (Доповіді НАН України, 2018)
An algebra L over a field F is said to be a Leibniz algebra (more precisely a left Leibniz algebra) if it satisfies the Leibniz identity: [[a, b], c] = [a, [b, c]] – [b, [a, c]] for all a, b, c ∈ L. Leibniz algebras are ...
• (Доповіді НАН України, 2017)
We give a short description of our recent results obtained by a new approach to the boundary-value problems, such as the Dirichlet, Hilbert, Neumann, Poincaré and Riemann problems, for the Beltrami equations and for ...
• (Доповіді НАН України, 2019)
Ion beam therapy is one of the most effective methods in treatment of cancer diseases. But up to nowadays, the mechanism of action of heavy ions on cancer cells has not been determined yet. Study of water fragmentation ...
• (Доповіді НАН України, 2018)
We study semilinear elliptic equations of the form div(A(z)∇u) = f(u) in Ω⊂ C, where A(z) stands for a symmetric 2×2 matrix function with measurable entries, det A =1, and such that 1/ K |ξ|² ≤ 〈A(z)ξ,ξ〉 ≤ K |ξ|², ξ ∈ R², ...
• (Доповіді НАН України, 2019)
We study the Hilbert boundaryvalue problem for the Beltrami equations in the Jordan domains satisfying the quasihyperbolic boundary condition by Gehring—Martio, generally speaking, without the standard (A)condition by ...
• (Доповіді НАН України, 2019)
A method for construction of exact solutions to the nonlinear heat equation ut = (F (u)ux)x + G (u)ux + H (u), which is based on the ansatz p(x) = ω₁(t) φ(u) + ω₂(t), is proposed. The function p(x) is a solution of the ...
• (Доповіді НАН України, 2020)
We consider the most general class of linear inhomogeneous boundary-value problems for systems of r-th order ordinary differential equations whose solutions and right-hand sides belong to appropriate Sobolev spaces. ...
• (Доповіді НАН України, 2020)
A subalgebra S of a Leibniz algebra L is called a contraideal, if an ideal, generated by S coincides with L. We study the Leibniz algebras, whose subalgebras are either an ideal or a contraideal. Let L be an algebra over ...
• (Доповіді НАН України, 2019)
We develop some methods for studying the modules over group rings, which are based on properties of induced modules and on the embedding of these modules in the modules over rings of quotients of group rings. Using these ...
• (Доповіді НАН України, 2017)
We obtain a description of solvable Leibniz algebras, whose subideals are ideals. A description of certain types of Leibniz T-algebras is also obtained. In particular, it is established that the structure of Leibniz ...
• (Доповіді НАН України, 2018)
We propose an algorithm of generation of the stable families of bijective polynomial maps f(n) of the n-dimensional affine space over a commutative ring K together with their inverse transformations. All maps are given ...
• (Доповіді НАН України, 2014)
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 ...
• (Доповіді НАН України, 2015)
A new key exchange protocol formulated in terms of multivariate cryptography and based on the elaboration of a common walk in the linguistic graph by correspondents is proposed. This algorithm is described in details in ...
• (Доповіді НАН України, 2017)
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 ...
• (Доповіді НАН України, 2018)
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, ...
• (Доповіді НАН України, 2019)
We study the Dirichlet problem for the semilinear partial differential equations div (A∇u) = f (u) in simply connected domains D of the complex plane C with continuous boundary data. We prove the existence of the weak ...
• (Доповіді НАН України, 2020)
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. ...
• (Доповіді НАН України, 2018)
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.
• (Доповіді НАН України, 2019)
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 ...
• (Доповіді НАН України, 2020)
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 ...

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