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Papers by Giorgi Rakviashvili

Journal of Mathematical Sciences, Sep 30, 2023

Tbilisi Mathematical Journal, Jun 1, 2018

Journal of Mathematical Sciences, Jul 22, 2009

Let R and Q be elements of a free, associative, finitely generated algebra A X over a field k. As... more Let R and Q be elements of a free, associative, finitely generated algebra A X over a field k. Assume that a leading homogeneous part Qv does not have two-sided divisors and RQ = QR and Rv = Q t v. In this paper, the solutions of the equation ΣixiRyi = z in A X are found and with their help, the identity theorem and Freiheitssatz for a finitely generated associative algebra k X; R = 0 with one defining relation are proved. As a consequence, similar theorems for Lie p-algebras with one defining relation are proved; these results are applied to the proof of the periodicity of cohomologies of Lie p-algebras with one defining relation.

Итоги науки и техники. Серия, Современные проблемы математики, фундаментальные направления, Apr 1, 2020

Для алгебраических KKK-функторов скрещенных произведений коммутативной алгебры и кокоммутативной ... more Для алгебраических KKK-функторов скрещенных произведений коммутативной алгебры и кокоммутативной алгебры Хопфа построено некоторое умножение; изучается вопрос о том, являются ли эти функторы функторами Фробениуса относительно построенного умножения.

Globalization and Business, 2020

Econophysics, or the theory of construction of models using physical assumptions in economics, al... more Econophysics, or the theory of construction of models using physical assumptions in economics, already has a long history. For this purpose, the gravitational law of attraction was probably first used in the modeling of trade models between two subjects. The laws of gravitational and electrostatic attraction were then used to study migration between countries. The article adopts two new models (containing dummy variables) of migration from Georgia to leading European countries and USA using multivariate linear regression. They are based on the Lewer and van der Berg generalized gravitational model of migration between countries of The Organisation for Economic Co-operation and Development (OECD). Their model contains dummy parameters of border, the proximity of the state languages and colonial links in past. In this article we introduce a new dummy parameter «religion» of the model of migration from Georgia; It is hypothesized that migration between neighbor countries may not be ana...

Journal of Mathematical Sciences, 2009

Globalization and Business, 2017

in this paper, the (Generalized) Gini, Hoover, Theil and Atkinson indexes are calculated for the ... more in this paper, the (Generalized) Gini, Hoover, Theil and Atkinson indexes are calculated for the Republic of Georgia, for his neighbor states Armenia, Azerbaijan, iran and Turkey, for some post soviet countries including the Russian Federation, for leading states of European Union, for USA, China and Japan. Previously only a small part of this indices were calculated, for example by United Nations, World Bank, CIA of USA, University of Texas and so on. An attempt was made to apply these calculations with the aim of building a mathematical model of the economic structure of Georgian society. it was known that Gini and Hoover indexes can be calculated by dif- ferent formulas, it is proved that these formulas actually give the same results. it is also considered the economical sense of above mentioned indexes in the terms of axioms which L. Bellu defined in some documents of Union Nations.

Advanced Studies: Euro-Tbilisi Mathematical Journal, 2022

The dimensions of zero and first regular cohomologies of a biparabolic subalgebra B of some simpl... more The dimensions of zero and first regular cohomologies of a biparabolic subalgebra B of some simple Lie algebra are calculated. Namely, it is proved that if S and T are subsets of simple roots such as B = H ⊕ L R S + ⊕ L R T − , where H is a splitting Cartan subalgebra and R S + and R T − are the positive (negative) roots generated by S (by T respectively) then the dimension d0 of the center of B is equal to the number of simple roots which is not contained in S ∪ T. If n = a0 + a1 + ... + ar = b0 + b1 + ... + bs where ai, bi ∈ N are ordered partititions of n and B is the corresponding biparabolic subalgebra of sl(n), then the dimension of outer derivations of B is equal to (r + s − d0)d0.

Itogi nauki i tekhniki. seriya "Algebra. geometriya. topologiya", 2020

It is proved that in certain cases a crossed group ring over a field of a positive characteristic... more It is proved that in certain cases a crossed group ring over a field of a positive characteristic has a purely inseparable splitting field. For such crossed group ring some properties of its radical are investigated. © 2011 Bull. Georg. Natl. Acad. Sci.

Let L be a finitely generated free Lie p-algebra and hai an ideal generated by a 2 L. It is prove... more Let L be a finitely generated free Lie p-algebra and hai an ideal generated by a 2 L. It is proved that L=hai is free if and only if hai is primitive (i.e. a belongs to some set of free generators of L). Earlier analogues theorems were proved for some objects, for example, for groups, Lie algebras, free algebras and so on.

Tbilisi Mathematical Journal