
Tamaz Tadumadze, Phridon Dvalishvili, Abdeljalil Nachaoui, Mourad Nachaoui, On the Optimization Problem of One Market Relation Containing the delay Functional Differential Equation, The International Workshop on the Qualitative Theory of Differential Equations, Tbilisi, Georgia.

Temur Jangveladze, On Decomposition Method for BitsadzeSamarskii Nonlocal Boundary Value Problem for Nonlinear TwoDimensional Second Order Elliptic Equations, International Workshop on the Qualitative Theory of Differential Equations, QUALITDE–2023, Tbilisi, Georgia.

Tea Shavadze, Nika Gorgodze, Ia Ramishvili, On the Representation Formula of Solution for a Class of Perturbed Controlled Neutral Functional Differential equation, The International Workshop on the Qualitative Theory of Differential Equations, Tbilisi, Georgia.

Tea Shavadze, Tamaz Tadumadze, Representation formulas of the First Variation of Solution for One Class of Neutral FunctionalDifferential Equation with the Continuous and Discontinuous Initial Conditions, Global Conference on Education (GCEDU), Dubai, UAE.

Natela Zirakashvili, Examine of stressstrain state of a spongy bone of an implanted jaw, VII INTERNATIONAL SCIENTIFIC CONFERENCE  Mathematical Modeling , BOROVETS BULGARIA. (poster)
A spongy bone can be considered a multiporous area with its fissures and pores as the most evident components of a double porous system. The work studies the stressstrain state of a spongy jawbone near the implant under occlusal loading. A mathematical model of the problem is the contact problem of the theory of elasticity between the implant and the jawbone. The problem is solved by using the boundary element methods, which are based on the solutions of Flamant’s (BEMF) and Boussinesq’s (BEMB) problems. The cases of various lengths of implant diameter are considered. Stressed contours (isolines) in the jawbone are drafted and the results obtained by BEMF and BEMB for the different diameter implants are compared.
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Khatuna Elbakidze, Oleg Kharshiladze, Influence of the Solar activity on the Earth’s Climate Change via turbulence, Mediteranean Geosciences Union (MEDGU), Istanbul, Turkey.
The Earth's climate is determined by the complex interactions between the Sun, the oceans, the atmosphere, the cryosphere, the land surface, and the biosphere. The sun is the main driving force for Earth's weather and climate. The influence of solar activity on the global surface of the Earth is determined by temperature variations, which in turn causes instability and is expressed by turbulent effects. Standard approaches to identifying such relationships are often based on correlations between relevant time series. Here we present a new method of Granger causality that can infer/reveal the relationship between two fields. We compare solar activity–climate connections through magnetic turbulence revealed by correlation and Granger causality at different time scales.

Khatuna Elbakidze, Oleg Kharshiladze, Investigating the possibility of a solar activity minimum, Mediteranean Geosciences Union (MEDGU) , Annual Meeting, Istanbul, Turkey.

Teimurazi Davitashvili, Inga Samkharadze, Study of some characteristics of the thermodynamic state of the atmosphere for local convection processes, International Scientific Conference "Geophysical Processes in the Earth and its Envelopes", Tbilisi, Georgia.
The article presents the importance of studying the thermodynamic state of the atmosphere during the formation of convective clouds in the local area. Numerical values of the energy of instability for some regions of Eastern Georgia are given and the change of its numerical values during the day is determined.
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Khatuna Elbakidze, Oleg Kharshiladze, SOLAR ACTIVITY INFLUENCE ON THE CLIMATE VIA MAGNETIC TURBULENCE, International Scientific Conference "Geophysical Processes in the Earth and its Envelopes" Proceedings, Tbilisi, Georgia.
The Earth's climate is determined by the complex interactions between the Sun, the oceans, the atmosphere, the cryosphere, the land surface, and the biosphere. The sun is the main driving force for Earth's weather and climate. The influence of solar activity on the global surface of the Earth is determined by temperature variations, which in turn causes instability and is expressed by turbulent effects. Standard approaches to identifying such relationships are often based on correlations between relevant time series. Here we present a new method of Granger causality that can infer/reveal the relationship between two fields. We compare solar activity–climate connections through magnetic turbulence revealed by correlation and Granger causality at different time scales.

Elizbar Nadaraya, Petre Babilua, ბერნულის ორი რეგრესიის ფუნქციის ტოლობის ჰიპოთეზის შესახებ, შემთხვევითი პროცესებისა და მათემატიკური სტატისტიკის გამოყენებანი ფინანსურ ეკონომიკასა და სოციალურ მეცნიერებებში VIII, თბილისის მეცნიერებებისა და ინოვაციების 2023 წლის ფესტივალი, Tbilisi, Georgia.

Tamaz Vashakmadze, On the construction of exact and approximate solutions of a number of problems corresponding to the system of equations with some constant coefficients in mathematical physics, Workshop on Mathematical Problems of Mechanics of Continuous Environments and Related Issues of Analysis, Tbilisi, Georgia.
On the construction of exact and approximate solutions of a number of problems corresponding to the system of equations with some constant coefficients in mathematical physics. For certainty, a number of initialboundary problems of the spatial classical, moment, thermoelasticity theory of elasticity are considered, their reduction to the study of a relatively simple operational equation and the efficient construction of the corresponding exact and approximate solutions. Then, the extension of this class of problems to the CowinNunziato model of hollow porous elastic medium, the Kosera porous elastic medium with empty pores, the Kosera medium with two types of porosity, the thermoelastic medium with microtemperature consideration, and various relatively general systems that
It was discussed in my works (see Tamaz Vashakmadze75, pp. 174194, 2012, compiled by G. Kifiani, TSU publishing house).

Teimurazi Davitashvili, Nato Kutaladze, Inga Samkharadze, The Role of Dust Aerosols in Forming the Regional Climate of Georgia, 4th International Conference on Environmental Design, Athens, Greece.
The scope of this work is to study some aspects of the formation of the regional climate of the Caucasus (with a specific focus on Georgia) against the background of the impact of mineral aerosols using modelling (the RegCM interactively coupled with a dust module, WRFChem, and HYSPLIT models) and satellite data (MODIS, CALIPSO). The annual mean, as well as the error in summer and winter
temperatures, standard deviation and correlation coefficient compared to the CRU data were calculated for 8 subregions with different orographic and climate properties. The calculation results showed that dust aerosol is an active player in the climatic system of the Caucasus (Georgia). Numerical results showed that
the inclusion of dust radiative forcing in the RegCM numerical model brought the simulated summer temperature closer to the observed temperature values. The mean annual temperature increased throughout Georgia in simulations that took into account the direct impact of dust. Calculations using the WRFChem
and HYSPLIT models revealed that during the study period, aeolian dust was brought into the territory of the South Caucasus (Georgia) equally not only from Africa and the Middle East, but also from Central (Western) Asia deserts, which was not noted earlier
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Elizbar Nadaraya, Petre Babilua, Nonparametric Estimate of Poisson Regression Function, International UzbekUkrainian Conference: Modern problems of the theory of stochastic processes and their applications, Online.

Mikheil Rukhaia, Irakli Chitaia, Roland Omanadze, Project Presentation: Recursive Functions and Ontology Engineering, IEEE 19th International Conference on eScience, Limassol, Cyprus. (poster)
This poster is a presentation of the interdisciplinary project that aims at formulating unification and matching problems used in probabilistic ontology reasoning, and to search and compare algorithms for their solution. Additionally, when there is no algorithm for solving them, our project aims to study the algebraic structures of degrees induced by Turing and other algorithmic reducibilities.
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Teimurazi Davitashvili, Inga Samkharadze, Identification of Some Features of the Zonal Air Flow Over the Territory of Georgia to Study its Energy Characteristics, The 5th EuroMediterranean Conference for Environmental Integration (EMCEI2023), Rende (Cosenza), Italy.

Giorgi Geladze, Archil Papukashvili, Meri Sharikadze, Further Exploration of the Mesoscale Atmospheric Boundary Layer, The fourth international conference „modern problems in applied mathematics“ (MPAM2023) Dedicated to the 105th Anniversary of I. Javakhishvili Tbilisi State University & 55th Anniversary of I.Vekua In, Tbilisi, Georgia.
We continue the study of thermohydrodynamics and humidity processes based on the numerical model of the mesoscale atmospheric boundary layer (MBLA) developed by us.
A new classification of foehns (warm downward wind) is given.
An attempt is made to study foehns based on our numerical model.
A certain opinion is expressed about the movement of a fluid against
a gravitational field in different media.
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Giorgi Rukhaia, Teimurazi Davitashvili, Exploring the Possibilities of Using Renewable Energy in Georgia in the Context of Climate Change Issues, The Fourth International Conference "MODERN PROBLEMS IN APPLIED MATHEMATICS" Dedicated to the 105th Anniversary of I.Javakhishvili Tbilisi State University (TSU) & 55th Anniversary of I.Vekua Institut, Tbilisi, Georgia.
The territory of Georgia is rich in solar, wind, hydro, tidal, geothermal and biomass renewable energy sources (can be used for electricity generation, space heating and cooling and water, and for transport), but at present Georgia properly uses only hydro energy. In the context of current regional climate change challenges, Georgia needs cleaner energy from sources that naturally replenish rather than deplete. Wind, thermal and hydrogen energy are among the possible solutions as they are currently considered one of the most promising fuels of the future. In this article, based on a threedimensional hydrostatic mesoscale model, an air flow over the complex relief of the South Caucasus (Georgia) is studied. Numerical experiments have shown a strong influence of the orographic effects of the Caucasus (the Likhi Ridge) on the movement of air in the troposphere. Besides, the study of the wind regime and statistical characteristics of the Kolkhinsky region for the period 19602021 showed that the wind speeds were significant and important for the development of wind farms in Western Georgia.
This study discusses also one mathematical model that describes the flow of a mixture of natural gas and hydrogen substances in a pipeline. The distribution of pressure and gas flow through a branched gas pipeline has been studied. In addition, ways to reduce transportation costs are being studied, that is, the economic aspect of various methods of transporting hydrogen using hydrogen gas trailers, liquid hydrogen tanks and hydrogen pipelines of various technical levels is being studied
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Archil Papukashvili, About the Numerical Solutions of Two Nonlinear IntegroDifferential Equations, THE FOURTH INTERNATIONAL CONFERENCE „MODERN PROBLEMS IN APPLIED MATHEMATICS“ (MPAM2023) Dedicated to the 105th Anniversary of I. Javakhishvili Tbilisi State University & 55th Anniversary of I.Vekua In, Tbilisi Georgia.
In this work we consider the issues of the approximate solutions and the results of numerical
computations for the following two practical problems: 1. Nonlinear initialboundary value problem
for the J. Ball dynamic beam. 2. Nonlinear initialboundary value problem for the Kirchhoff
dynamic string.
The presented article is a direct continuation of the articles [1][5] that consider the construction
of algorithms and their corresponding numerical computations for the approximate solution
of nonlinear integrodifferential equations for the J. Ball dynamic beam (see [1][3]) and for the
Kirchhoff dynamic string (see [4][5]).
References
[1] A. Papukashvili, G. Papukashvili, M. Sharikadze. Numerical calculations of the J. Ball nonlinear
dynamic beam. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math., 32 (2018), 4750.
[2] A. Papukashvili, G. Papukashvili, M. Sharikadze. On a numerical realization for a Timoshenko
type nonlinear beam equation. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math., 33 (2019),
5154.
[3] A. Papukashvili, G. Geladze, Z. Vashakidze, M. Sharikadze. On the Algorithm of an Approximate
Solution and Numerical Computations for J. Ball Nonlinear IntegroDifferential Equation.
Rep. Enlarged Sess. Semin. I. Vekua Appl. Math., 36 (2022), 7578.
[4] G. Papukashvili, J. Peradze. A numerical solution of a string oscillation equation. Rep. Enlarged
Sess. Semin. I. Vekua Inst. Appl. Math., 23 (2009), 8083.
[5] J. Peradze. A numerical algorithm for the nonlinear Kirchhoff string equation. Numer. Math.,
102 (2005), 311342.
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David Natroshvili, Application of the potential method in the theory of elasticity, The Fourth International Conference "MODERN PROBLEMS IN APPLIED MATHEMATICS" Dedicated to the 105th Anniversary of I.Javakhishvili Tbilisi State University (TSU) & 55th Anniversary of I.Vekua Institut, Tbilisi, Georgia.
The presentation is devoted to the application of the potential and integral equations methods to the basic and mixed threedimensional boundary value and boundarytransmission problems of the theory of elasticity.
The main goals of the talk are an overview of the results obtained by
representatives of the Georgian Mathematical School in the second part
of the last century and new developments and extensions of the method
to refined mathematical models of solid mechanics taking into account
thermal and electromagnetic physical fields. We treat problems of statics, steady state elastic oscillations and general dynamics for isotropic and
anisotropic elastic solids.
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Natalia Chinchaladze, Zero Approximation of Hierarchical Models for Fluids in Pipes of Angular CrossSections, The Fourth International Conference "MODERN PROBLEMS IN APPLIED MATHEMATICS", Tbilisi, Georgia.
We investigate dynamical problem of zero approximation of hierarchical models for fluids. Applying the Laplace transform technique, we reduce the dynamical problem to the elliptic problem which depends on a complex parameter τ and prove the corresponding uniqueness and existence results. Further, we establish uniform estimates for solutions and their partial derivatives with respect to the parameter τ at infinity and via the inverse Laplace transform show that the original dynamical problem is uniquely solvable.
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Bakur Gulua, Roman Janjgava, On construction of general solutions of equations of the plane theory of elasticity in the coupled theory of doubleporosity materials, The Fourth International Conference „MODERN PROBLEMS IN APPLIED MATHEMATICS“, Tbilisi, Georgia.
In the present talk, the linear coupled model of elastic doubleporosity
materials are proposed in which the coupled phenomenon of the concepts of Darcy’s extended law and the volume fractions is considered. A two dimensional system of equations of plane deformation is written in the complex form and its general solution is represented by means of analytic functions of a complex variable and solutions of Helmholtz equations. The constructed general solution enables one to solve analytically a sufficiently wide class of plane boundary value problems of the elastic equilibrium of the coupled theory of elasticity for doubleporous bodies.
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Zurab Vashakidze, Jemal Rogava, On Convergence of a ThreeLayer SemiDiscrete Scheme for the Nonlinear Dynamic String Equation of KirchhoffType with TimeDependent Coefficients, The Fourth International Conference "MODERN PROBLEMS IN APPLIED MATHEMATICS" Dedicated to the 105th Anniversary of I. Javakhishvili Tbilisi State University (TSU) & 55th Anniversary of I. Vekua Instit, Tbilisi, Georgia.
In this talk, we shall investigate an initialboundary value problem associated with the Kirchhofftype nonlinear dynamic string equation featuring timevarying coefficients. Our objective is to devise a temporal discretization algorithm capable of approximating the solution to the initialboundary value problem. To accomplish this, we employ a symmetric threelayer semidiscrete scheme with respect to the temporal variable, where the nonlinear term is evaluated at the midpoint node. This approach facilitates the computation of numerical solutions at each temporal step by inverting linear operators, resulting in a system of secondorder linear ordinary differential equations. We have established the local convergence of the proposed scheme, which reveals quadratic convergence with respect to the step size of the time discretization within the local temporal interval. Finally, we have conducted several numerical experiments using the proposed algorithm for various test problems, and the obtained numerical results are in accordance with the theoretical findings.
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Omar Purtukhia, Tamaz Tadumadze, Mathematics at the Ivane Javakhishvili Tbilisi State University., The Fourth International Conference „Modern Problems in Applied Mathematics“ (MPAM2023), Tbilisi, Georgia.

Tea Shavadze, Tamaz Tadumadze, On the Representation Formula of Solution for a Class of Perturbed Controlled Neutral FunctionalDifferential Equation, The Fourth International Conference „Modern Problems in Applied Mathematics“ (MPAM2023), Tbilisi, Georgia.

Besiki Tabatadze, Mikheil Gagoshidze , Temur Jangveladze, Zurab Kiguradze, Two Methods of the Numerical Solution of One System of Nonlinear Partial Differential Equations, Fourth International Conference "MODERN PROBLEMS IN APPLIED MATHEMATICS" Dedicated to the 105th Anniversary of I.Javakhishvili Tbilisi State University (TSU) & 55th Anniversary of I.Vekua Institute of, Tbilisi, Georgia.
Two different approaches were used to construct approximate solutions of the initialboundary problem for the system of equations corresponding to a twodimensional nonlinear model [1]. Such type models are studied in many works (see, for example, [2][7] and references therein). The first approach used a decomposition method based on an averaged model [3]. An appropriate scheme and necessary algorithms for computer implementation were built. The program was compiled and calculations were made for various tests. The second approach used a variable direction difference scheme [4]. Necessary algorithms for computer implementation were also built for this method. The number of operations was determined for both methods. The time required for the realization of the algorithms and the accuracy of the numerical experiments were compared with each other. An analysis of the obtained results was carried out, and appropriate conclusions were drawn.
Acknowledgment
This research has been supported by the Shota Rustaveli
National Science Foundation of Georgia under the grant FR212101.
References
[1] G. I. Mitchison, A model for vein formation in higher plants. Proc. R. Soc. Lond. B. volume 207, pages 79109, 1980.
[2] J. Bell, C. Cosner, W. Bertiger, Solution for a fluxdependent diffusion model. SIAM J. Math. Anal. volume 13, pages 758769, 1982.
[3] T. A. Dzhangveladze, Averaged model of sum approximation for a system of nonlinear partial differential equations (Russian). Proc. I.Vekua Inst. Appl. Math. volume 19, pages 6073, 1987.
[4] T. A. Jangveladze, The difference scheme of the type of variable directions for one system of nonlinear partial differential equations. Proc. I.Vekua Inst. Appl. Math. volume 42, pages 4566, 1992.
[5] T. Jangveladze, M. Nikolishvili, B. Tabatadze, On one nonlinear twodimensional diffusion system. Proc. 15th WSEAS Int. Conf. Applied Math. (MATH 10), pages 105108, 2010.
[6] T. Jangveladze, Z. Kiguradze, B. Tabatadze, M. Gagoshidze, Comparison of two methods of numerical solution of Mitchison biological system of nonlinear partial differential equations. International Journal of Mathematics and Computers in Simulation, volume 11, pages 25–31. 2017.
[7] T. Jangveladze, Z. Kiguradze, M. Gagoshidze, Economical difference scheme for one multidimensional nonlinear system. Acta Mathematica Scientia. volume 39, no. 4, pages 971988, 2019.
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Tamaz Vashakmadze, Giorgi Buzhgulashvili, Approximate solution of boundary value problems for universal differential equations, Fourth international conference "Modern problems of applied mathematics", Tbilisi, Georgia.
For certainty, a number of initialboundary problems of the spatial classical, moment, thermoelasticity theory of elasticity are considered, their reduction to the study of a relatively simple operational equation and the efficient construction of the corresponding exact and approximate solutions. Then the extension of this class of problems to the CowinNunciato model of hollow porous elastic medium, Kosserat porous elastic medium with empty pores, Kosserat medium with two types of porosity, thermoelastic medium with microtemperature consideration and various relatively general systems discussed in my works will be consider (see ”Tamaz Vashakmadze75,pp.174194,” Reduction by G.Kipiani,2012,Tbilisi SU public.).

Roman Koplatadze, On Asymptotic Behavior of Solutions of Higher Order EmdenFowler Type Difference Equations with Deviating Argument, The Fourth International Conference "MODERN PROBLEMS IN APPLIED MATHEMATICS", Tbilisi, Georgia.
Consider the EmdenFowler type difference equation.
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Elizbar Nadaraya, Petre Babilua, On the Testing Hypothesis of Equality of Two Bernoulli Regression Functions, The Fourth International Conference “Modern Problems Applied Mathematics” MPAM 2023, Tbilisi, Georgia.

Roman Koplatadze, On asymptotic behavior of solutions of higher order EmdenFowler type difference equations, The Fourth International Conference „Modern Problems in Applied Mathematics“ (MPAM2023), Tbilisi, Georgia.

Maia Svanadze, Problems of Steady Vibrations in the Linear Coupled Theory of Thermoviscoelasticity of Porous Materials, The Fourth International Conference “MODERN PROBLEMS IN APPLIED MATHEMATICS”, Tbilisi, Georgia.
In this talk, a linear mathematical model of thermoviscoelasticity for
porous materials is proposed in which the coupled effect of Darcys law and the concept the volume fraction of pores is considered. The basic internal and external boundary value problems (BVPs) of steady vibrations of this model are investigated. Indeed, the fundamental solution of the system of steady vibration equations is constructed. The uniqueness theorems for the regular (classical) solutions of the BVPs of steady vibrations are proved. The singlelayer and doublelayer potentials are constructed and the basic properties of these potentials are given. Finally, the existence theorems for classical solutions of the BVPs of steady vibrations are proved by means of the potential method and the theory of singular integral equations.
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David Kaladze, Luba Tsamalashvili, On the exact solutions of the Gardner equations via tanhcoth method, The Fourth International Conference "MODERN PROBLEMS IN APPLIED MATHEMATICS", Tbilisi,Georgia.
Using the tanhcoth method the traveling wave special exact solutions of (1 + 1) and (2 + 1)D nonlinear Gardner partial differential equations are represented. The results are expressed through hyperbolic functions and have spatially isolated structural forms.
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George Jaiani, On fluids in angular pipes and wedgeshaped canals, The Fourth International Conference "MODERN PROBLEMS IN APPLIED MATHEMATICS", Tbilisi, Georgia.
On fluids in angular pipes and wedgeshaped canals
Abstract. In the zero approximation of hierarchical models for fluids the full accordance is shown of peculiarities of setting the Dirichlet and Keldysh type boundary conditions by motion of the fluids in pipes of angular crosssections with the results of experiments carried out by J. Nikuradze in L. Prandtl’s Laboratory at University of Göttingen.
JefferyHamel flow is the flow between two planes that meet at an angle was analyzed by Jeffery (1915) and Hamel (1916).
We consider the flow between two surfaces that meet at the edge a dihedral (angle), whose sides are the tangents of the surfaces at the edge of dihedral.
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Archil Papukashvili, Giorgi Papukashvili, Jemal Peradze, Meri Sharikadze, On the Approximation of the Solution for a Kirchhoff’stype Equation Describing the Dynamic Behavior of a String, XIII International Conference of the Georgian Mathematical Union, Batumi, Georgia.
The presented discourse serves as a direct extension of the research papers [1, 2], which delve into the investigation of an initialboundary value problem associated with Kirchhoff’s integrodifferential equation. This mathematical model effectively characterizes the dynamic behaviour of a string. To seek an approximate solution for this problem, a combined approach involving a Galerkin method, a stable symmetric finite difference scheme, and a Picardtype iterative method is employed. In article [1], the algorithm is tested using a simple test example, providing the error
solely for the difference method. However, this work considers a more complex test example that allows us to assess the errors for both the difference method and the Galerkin method. Numerical computations are performed to validate the proposed approach, and the resulting findings are presented in both tabular and graphical formats.
References
[1] G. Papukashvili and J. Peradze, A numerical solution of string oscillation equation. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 23 (2009), 80–83.
[2] J. Peradze, A numerical algorithm for the nonlinear Kirchhoff string equation. Numer. Math. 102 (2005), no. 2, 311–342.
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Nino Khatiashvili, On the Stokes Flows , XIII International Conference of the Georgian Mathematical Union, Batumi, September 4 – 9, 2023 , Batumi, GEORGIA.
We consider incompressible viscous fluid flow for the small Reynolds number in the infinite domains. The velocity components of the flow satisfy the Stokes linear system with the equation of continuity and suitable initialboundary conditions. The steady and unsteady cases are considered. The novel exact solutions for the axial fluid flow over the ellipsoid and the countable number of discs are obtained.
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Teimurazi Davitashvili, Inga Samkharadze, Giorgi Rukhaia, Exploring the Development of Hydrogen Energy in Georgia in the Face of Climate Change, XIII International Conference of the Georgian Mathematical Union, Batumi, September 4 – 9, 2023, Batumi, Georgia.
Despite the fact that hydrogen in nature is not replenished naturally and is not depleted (by analogy with renewable energy sources), there is a growing interest around the world in using hydrogen for electricity generation or in industry, transport and other areas as a highly efficient energy source. Currently, Georgia uses only hydro, wind and geothermal energy from renewable energy sources and has good opportunities for producing and transporting hydrogen. Indeed, Kazakhstan,
Turkmenistan and Azerbaijan are planning to produce “green” and “blue” hydrogen (having a modern production infrastructure for petrochemicals and huge resource potential) and develop the infrastructure and operational components of the “Middle Corridor” for its transportation using the TRACECA route through Georgia and Turkey to EU countries. While efforts are being made in the long term to build a dedicated hydrogen infrastructure (pipeline), blending hydrogen into
the existing gas pipeline network is a more promising strategy for transporting hydrogen in the short term. Thus, studying the behavior of mixed flow in a pipeline is relevant to the analysis of several potential problems that arise when mixing hydrogen in natural gas networks. This article focuses on exploring how much hydrogen can be integrated into a gas pipeline from an operational point of view. Namely, on the basis of one mathematical model describing the flow of a mixture
of natural gas and hydrogen substances in a pipeline, the distribution of pressure and gas flow through a branched gas pipeline was analytically obtained. Some aspects of the production and transportation of hydrogen as a highly efficient source of energy on the territory of Georgia under the conditions of climate change are discussed
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Mikheil Rukhaia, Temur Kutsia, Mircea Marin, Similaritybased Set Matching, XIII Annual International Conference of Georgian Mathematical Union, Batumi, Georgia.
In this talk, we propose extending set matching to similarity relations. In this way, we incorporate some background knowledge into solving techniques with similarity relations. Although our set terms are interpreted as (finite) classical sets, their elements (arguments of set terms) might be related to each other by a similarity relation, which induces also a notion of similarity between set terms. We design a matching algorithm and study its properties. It can be useful in applications where the exact set matching techniques need to be relaxed to deal with quantitative extensions of equality such as similarity relations.
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Lali Tibua, Sequent Calculus for Unranked Probabilistic Logic, XIII Annual International Conference of Georgian Mathematical Union, Batumi, Georgia.
In this talk we discuss sequent calculus for unranked probabilistic logic. We show that the calculus is sound and complete.
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David Natroshvili, An alternative potential method for mixed steady state elastic oscillation problems, XIII International Conference of the Georgian Mathematical Union, Batumi, Georgia .
We consider an alternative approach to investigate threedimensional exterior mixed boundary value problems (BVP) for the steady state oscillation equations of the elasticity theory for isotropic bodies. The unbounded domain occupied by an elastic body, Ω− ⊂ R^3, has a compact boundary surface S = ∂Ω−, which is divided into two disjoint parts, the Dirichlet part S_D and the Neumann part S_N , where the displacement vector (the Dirichlet type condition) and the stress
vector (the Neumann type condition) are prescribed respectively. Our new approach is based on the classical potential method and has several essential advantages compared with the existing approaches. We look for a solution to the mixed boundary value problem in the form of a linear combination of the single layer and double layer potentials with densities supported on the Dirichlet and Neumann parts of the boundary respectively. This approach reduces the mixed BVP under
consideration to a system of boundary integral equations, which contain neither extensions of the Dirichlet or Neumann data nor the Steklov–Poincaré type operator involving the inverse of a special boundary integral operator, which is not available explicitly for arbitrary boundary surface. Moreover, the righthand sides of the resulting boundary integral equations system are vectorfunctions coinciding with the given Dirichlet and Neumann data of the problem in que stion. We
show that the corresponding matrix integral operator is bounded and coercive in the appropriate L_2based Bessel potential spaces. Consequently, the operator is invertible, which implies unconditional unique solvability of the mixed BVP in the class of vectorfunctions belonging to the Sobolev space [W^1_2,loc(Ω−)]^3 and satisfying the Sommerfeld–Kupradze radiation conditions at infinity.We also show
that the obtained matrix boundary integral operator is invertible in the Lpbased Besov spaces and prove that under appropriate boundary data a solution to the mixed BVP possesses C^αHölder continuity property in the closed domain Ω−
with α =1/2 − ε, where ε > 0 is an arbitrarily small
number.
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Tamar Kasrashvili, On one example of the existence of a nonmeasurable set on the real line R, XIII International Conference of the Georgian Mathematical Union, Batumi, Georgia.
It is well known the existence of nonmeasurable sets on the real line R (Vital’s set, Bernstein’s set, etc., see, for example). This report will present relationship between countable equid composability of sets and existence a nonmeasurability set with respect to Lebesgue measure on real line R. Since any two (bounded or unbounded) point sets of R with nonempty interiors are countably equid composable, we get that there exists a Lebesgue nonmeasurable set on R.
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Zurab Vashakidze, Jemal Rogava, Convergence and numerical experiments of a threelayer semidiscretization approach for the nonlinear Kirchhofftype dynamic string equation with timevarying coefficients, XIII Annual International Conference of the Georgian Mathematical Union, Batumi, Georgia.
In this talk, we shall delve into an initialboundary value problem associated with the Kirchhofftype nonlinear dynamic string equation. This equation features coefficients that change over time and has been discussed in detail in the paper [1]. Our main goal is to develop a method for discretizing time that can effectively estimate the solution to the initialboundary value problem. To achieve this objective, we apply a symmetrical threelayer semidiscrete approach that focuses on the temporal variable. Within this method, the nonlinear term is assessed at the midpoint node. By using this technique, we can calculate numerical solutions at each step of time by inverting linear operators. As a result, we end up with a set of secondorder linear ordinary differential equations. We have proved that this proposed approach locally converges and demonstrates a quadratic convergence pattern in relation to the time step size through the local time interval. Lastly, we performed several numerical experiments using the proposed algorithm to tackle various test issues. The numerical outcomes we obtained align well with the theoretical conclusions.
[1] J. Rogava and Z. Vashakidze. On Convergence of a Threelayer Semidiscrete Scheme for the Nonlinear Dynamic String Equation of Kirchhofftype with Timedependent Coefficients. arXiv preprint arXiv:2303.10350, 2023. DOI: 10.48550/arXiv.2303.10350.
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Mikheil Gagoshidze , Temur Jangveladze, Zurab Kiguradze, Some Properties and Numerical Solution of InitialBoundary Value Problem for One System of Nonlinear Partial Differential Equations, XIII International Conference of the Georgian Mathematical Union,, Batumi, Georgia.
Investigated model is based on the wellknown system of Maxwell’s equations and represents some of its generalizations. Such type models are studied in many works (see, for example, [1–6] and references therein). The onedimensional case with a threecomponent magnetic field is considered. The asymptotic behavior of solution for initialboundary value problem as time variable tends to infinity is studied. The question of linear stability of the stationary solution of the system and the possibility of the Hopftype bifurcation is investigated. A finitedifference scheme is constructed. The convergence of this scheme is studied and an estimate of the error of the approximate solution is obtained. Corresponding numerical experiments are carried out.
Acknowledgments
This research has been supported by the Shota Rustaveli National Science Foundation of Georgia under the grant # FR212101.
References
[1] T. A. Dzhangveladze, Stability of the stationary solution of a system of nonlinear partial differential equations. (Russian) Current problems in mathematical physics, Vol. I (Russian) (Tbilisi, 1987), 214–221, 481–482, Tbilis. Gos. Univ., Tbilisi, 1987.
[2] T. Jangveladze and M. Gagoshidze, Hopf bifurcation and its computer simulation for onedimensional Maxwell’s model. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 30 (2016), 27–30.
[3] T. Jangveladze, Investigation and numerical solution of nonlinear partial differential and integrodifferential models based on system of Maxwell equations. Mem. Differ. Equ. Math. Phys. 76 (2019), 1–118.
[4] T. Jangveladze, Some properties of the initialboundary value problem for one system of nonlinear partial differential equations. Bull. TICMI 25 (2021), no. 2, 137–143.
[5] T. Jangveladze, Finite difference scheme for one system of nonlinear partial differential equations. Bull. Georgian Natl. Acad. Sci. (N.S.) 16 (2022), no. 2, 7–13.
[6] Z. V. Kiguradze, On the stationary solution for one diffusion model. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 16 (2001), no. 13, 17–20.
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Besiki Tabatadze, Mikheil Gagoshidze , Temur Jangveladze, Zurab Kiguradze, Numerical Solution of One TwoDimensional System of Nonlinear Partial Differential Equations, XIII International Conference of the Georgian Mathematical Union, Batumi, Georgia.
The twodimensional system of nonlinear partial differential equations is considered. This system arises in the process of vein formation of young leaves [7]. There are many works where this and many models describing similar processes are also presented and discussed (see, for example, [1, 2, 8, 9] and references therein). Investigation and numerical solution of such type systems are discussed in many papers (see, for example, [1, 3–6] and references therein). In our note, the averaged model of sum approximation is used [3] and the variable directions difference scheme is also considered [4]. Comparison of numerical experiments of the proposed methods is done.
Acknowledgments
This research has been supported by the Shota Rustaveli National Science Foundation of Georgia under the grant # FR212101.
References
[1] J. Bell, C. Cosner and W. Bertiger, Solutions for a fluxdependent diffusion model. SIAM J. Math. Anal. 13 (1982), no. 5, 758–769.
[2] H. Candela, A. Martí́nezLaborda and J. L. Micol, Venation Pattern Formation inArabidopsis thalianaVegetative Leaves. Developmental Biology 205 (1999), no. 1, 205–216.
[3] T. A. Dzhangveladze, An averaged model of summary approximation for a system of nonlinear partial differential equations. (Russian) Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 19 (1987), 60–73.
[4] T. A. Jangveladze, The difference scheme of the type of variable directions for one system of nonlinear partial differential equations. Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 47 (1992), 45–66.
[5] T. Jangveladze, Z. Kiguradze and M. Gagoshidze, Economical difference scheme for one multidimensional nonlinear system. Acta Math. Sci. Ser. B (Engl. Ed.) 39 (2019), no. 4, 971–988.
[6] T. Jangveladze, M. Nikolishvili and B. Tabatadze, On one nonlinear twodimensional diffusion system. Proc. 15th WSEAS Int. Conf. Applied Math. (MATH 10), (2010), 105–108.
[7] G. J. Mitchison, A model for vein formation in higher plants. Proc. R. Soc. Lond. B. 207 (1980), no. 1166, 79–109.
[8] P. Prusinkiewicz, S. Crawford, R. S. Smith, K. Ljung, T. Bennett, V. Ongaro and O. Leyser, Control of Bud Activation by an Auxin Transport Switch. Proc. Nat. Acad. Sci. 106(41) (2009), 17431–17436.
[9] C. J. Roussel and M. R. Roussel, Reaction–diffusion models of development with statedependent chemical diffusion coefficients, Progress Biophys. Molecular Biology 86 (2004), no. 1, 113–160.
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Teimuraz Chkhikvadze, Mikheil Gagoshidze , Temur Jangveladze, Zurab Kiguradze, On One Nonlinear Parabolic IntegroDifferential Model, XIII International Conference of the Georgian Mathematical Union, Batumi, Georgia.
One type of model of nonlinear parabolic integrodifferential equations is considered. The analogous models partially are derived, on one hand, from the description of real diffusion processes and on the other hand, in the generalization of wellknown equations and systems of equations, the study of which devoted many scientific papers (see, for example, [18] and references therein). Models of such types still yield to the investigation for special cases. In this direction, the latest and rather complete bibliography can be found in the following monographs [6, 7]. In our research uniqueness, stability and asymptotic behavior of the solutions of the initialboundary value problems are studied. The finitedifference scheme is constructed and its convergence property is established. The approximate algorithm based on this scheme is constructed. Numerical implementation with various experiments for different values of the input parameters is performed to validate the theoretical conclusions.
Acknowledgments
This research has been supported by the Shota Rustaveli National Science Foundation of Georgia under the grant FR212101.
References
[1] M. M. Aptsiauri, T. A. Jangveladze and Z. V. Kiguradze, Asymptotic behavior of the solution of a system of nonlinear integrodifferential equations. (Russian) Differ. Uravn. 48 (2012), no. 1, 70–78; translation in Differ. Equ. 48 (2012), no. 1, 72–80.
[2] T. Chkhikvadze, On one system of nonlinear partial differential equations. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 36 (2022), 19–22.
[3] T. Dzhangveladze, An Investigation of the First BoundaryValue Problem for Some Nonlinear Parabolic Integrodifferential Equations. (Russian) Tbilisi State University, Tbilisi, 1983.
[4] D. G. Gordeziani, T. A. Dzhangveladze and T. K. Korshiya, Existence and uniqueness of the solution of a class of nonlinear parabolic problems. (Russian) Differentsial’nye Uravneniya 19 (1983), no. 7, 1197–1207; translation in Differ. Equ. 19 (1984), no. 7, 887–895.
[5] F. Hecht, T. Jangveladze, Z. Kiguradze and O. Pironneau, Finite difference scheme for one system of nonlinear partial integrodifferential equations. Appl. Math. Comput. 328 (2018), 287–300.
[6] T. Jangveladze, Investigation and numerical solution of nonlinear partial differential and integrodifferential models based on system of Maxwell equations. Mem. Differ. Equ. Math. Phys. 76 (2019), 1–118.
[7] T. Jangveladze, Z. Kiguradze and B. Neta, Numerical Solutions of Three Classes of Nonlinear Parabolic IntegroDifferential Equations. Elsevier/Academic Press, Amsterdam, 2016.
[8] T. Jangveladze, Z. Kiguradze, B. Neta and S. Reich, Finite element approximations of a nonlinear diffusion model with memory. Numer. Algorithms 64 (2013), no. 1, 127–155.
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Tamaz Vashakmadze, The Development of Complex Analysis Method for Essentially Non Linear Systems of DE and About its Numerical Analogies Tamaz Vashakmadze Ilia Vekua Institute of Applied Mathematics of Ivane Javakhishv, XIII International Conference of the Union of Mathematicians of Georgia., Batumi, Georgia.
In this report, it is extended the classical theory (for the linear case developed by E. Goursat, H.
Weyl, J. L. Walsh, S. Bergman, G. V. Koloson, N. Muskhelishvili, L. Bers, I. Vekua and so on) of
finding general solutions and some boundary value problems of partial differential equations by
applying complex analysis. We developed the method of solving system of essentially non
linear DEs when with Laplace and biharmonic operators, DEs containing composition for
example of Laplace and Monge–Ampére operator. The method gives possibility to solve some
boundary value problems as well. Then this method will be applied to the solution of boundary
value problems corresponding to refined theories in enlarged sense for elastic plates and shells.
In this direction, in the terminology of real analysis are constructed full numerical analogies to
refined theories are proved the convergence of corresponding iteration processes
Batumi, September 4 –9, 2023.

Elizbar Nadaraya, Petre Babilua, About hypothesis testing of equality of two Bernoulli regression functions, XIII International Conference of the Georgian Mathematical Union, Tbilisi, Georgia.

Besik Dundua, CLP(MS): Programming Using Multiple Similarity Constraints ., XIII International Conference of the Georgian Mathematical Union, Batumi, Georgia.
We describe the semantics of CLP(MS): constraint logic programming over multiple similarity
relations. Similarity relations are reflexive, symmetric, and transitive fuzzy relations. They help
to make approximate inferences, replacing the notion of equality. Similaritybased unification has
been quite intensively investigated, as a core computational method for approximate reasoning
and declarative programming. In this talk we consider solving constraints over several similarity
relations [1], instead of a single one. Multiple similarities pose challenges to constraint solving,
since we can not rely on the transitivity property anymore. Existing methods for unification
with fuzzy proximity relations (reflexive, symmetric, nontransitive relations) do not provide a
solution that would adequately reflect particularities of dealing with multiple similarities. To
address this problem, we develop a constraint solving algorithm for multiple similarity relations,
prove its termination, soundness, and completeness properties. We integrate the solving algorithm
into constraint logic programming schema and study semantics of obtained CLP(MS)
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David Natroshvili, An alternative potential method for mixed boundary value problems., The Tbilisi Analysis & PDE Workshop (TAPDE Workshop 2023), Tbilisi, Georgia.
We consider a new alternative potential method to investigate a mixed boundary value problem (BVP) for the Lamé system of elasticity in the case of the threedimensional bounded domain Ω ⊂ R^3, when the boundary surface
S = ∂Ω is divided into two disjoint parts, S_D and S_N , where the Dirichlet and Neumann type boundary conditions are prescribed respectively for the displacement vector and the stress vector. Our approach is based on the potential
method. We look for a solution to the mixed boundary value problem in the form of a linear combination of the single layer and double layer potentials with densities supported respectively on the Dirichlet and Neumann parts of the
boundary. This approach reduces the mixed BVP under consideration to a system of pseudodifferential equations which contain neither extensions of the Dirichlet or Neumann data, nor the SteklovPoincaré type operator. Moreover,
the righthand sides of the resulting pseudodifferential system are vectors coinciding with the Dirichlet and Neumann data of the problem under consideration. The corresponding pseudodifferential matrix operator is bounded and
coercive in the appropriate L_2based Bessel potential spaces. Consequently, the operator is invertible, which implies the unconditional unique solvability of the mixed BVP in the Sobolev space [W^1_2(Ω)]^3 and representability of solutions
in the form of a linear combination of the single layer and double layer potentials with densities supported respectively on the Dirichlet and Neumann parts of the boundary. Using a special structure of the obtained pseudodifferential
matrix operator, it is also shown that the operator is invertible in the Lpbased Besov spaces with 4/3 < p < 4, which under appropriate boundary data implies C^αHölder continuity of the solution to the mixed BVP in the closed domain Ω with α =1/2 − ε, where ε > 0 is an arbitrarily small number.
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Zurab Vashakidze, Jemal Rogava, On a Convergence of a ThreeLayer SemiDiscrete Approach for Solving the Nonlinear Dynamic KirchhoﬀType String Equation with TimeVarying Coeﬃcients, The Tbilisi Analysis & PDE Workshop (TAPDE Workshop 2023), Tbilisi, Georgia.
In this talk, we explore an initialboundary value problem (IBVP) linked to the nonlinear dynamic string equation of Kirchhofftype. This equation includes time dependent coefficients and has been discussed in the work [1]. Our aim is to develop a method for discretizing time that can effectively estimate the solution to the IBVP. To achieve this goal, we employ a symmetrical threelayer semidiscrete technique concerning the time variable. In this approach, we evaluate the nonlinear term at the middle node points, simplifying the computation of numerical solutions at each time step by inverting linear operations. As a result, this leads to a system of secondorder linear ordinary differential equations. We have demonstrated the local convergence of the proposed strategy, which reveals a quadratic rate of convergence in relation to the time discretization step within the local time interval. Lastly, we have performed several numerical experiments using the suggested method for various test scenarios. The obtained numerical results align well with the theoretical findings.
[1] J. Rogava and Z. Vashakidze. On Convergence of a Threelayer Semidiscrete Scheme for the Nonlinear Dynamic String Equation of Kirchhofftype with Timedependent Coefficients. arXiv preprint arXiv:2303.10350, 2023. DOI: 10.48550/arXiv.2303.10350.
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Besiki Tabatadze, Temur Jangveladze, Mikheil Gagoshidze , Comparative Analysis of Approximate Solutions for a Numerical Solution of a TwoDimensional Nonlinear Model., The Tbilisi Analysis & PDE Workshop (TAPDE Workshop 2023), Tbilisi, Georgia.

Archil Papukashvili, Giorgi Geladze, Zurab Vashakidze, Meri Sharikadze, On the numerical computations to J. Ball’s beam equation in the case where the material's effective viscosity is dependent on its velocity, XIV Annual International Meeting of the Georgian Mechanical Union, Poti, Georgia.
The present article is a continuation of the previously published papers [1][3], which examine the initialboundary value problem for J. Ball's integrodifferential equation. The equation models the dynamic behaviour of a beam. To obtain an approximate solution, a combination of the Galerkin method, a stable symmetric difference scheme, and the Jacobi iteration method is utilized. In papers [1][2], the numerical algorithm is validated using numerical samples. The present paper, along with [3], focuses on the application of the numerical solution to a practical problem. In particular, the numerical results of the initialboundary value problem for a specific iron beam are presented, where the effective viscosity of the material depends on its velocity. The results are summarized in a tables and graphics.
References
1. Papukashvili, Archil; Papukashvili, Giorgi; Sharikadze, Meri. Numerical calculations of the J. Ball nonlinear dynamic beam. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 32 (2018), 4750.
2. Papukashvili, Archil; Papukashvili, Giorgi; Sharikadze, Meri. On a numerical realization for a Timoshenko type nonlinear beam equation. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 33 (2019), 5154.
3. Papukashvili, Archil; Geladze, Giorgi; Vashakidze, Zurab; Sharikadze, Meri. On the Algorithm of an Approximate Solution and Numerical Computations for J. Ball Nonlinear IntegroDifferential Equation. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 36 (2022), 7578.
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Giorgi Geladze, Archil Papukashvili, Manana Tevdoradze, On the thermohydrodynamic mathematical model of foehns, XIV Annual International Meeting of the Georgian Mechanical Union, Poti, Georgia.
The thermohydrodynamic foundations for the development of foehns are considered. A new classification of hair dryers is given.
The possibility of laboratory simulation of foehn heat release is considered.
Certain recommendations are given for the regulation of foehn processes in the real meteorological conditions.
We continue the study of foehn processes on the basis of our numerical model of the mesoscale 2dimensional boundary layer of the atmosphere
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Natalia Chinchaladze, George Jaiani, I. Vekua Institute of Applied Mathematics of TSU  55, XIV Annual International Meeting of the Georgian Mechanical Union, Poti, Georgia.
The talk concerns 55 years long history of Ilia Vekua Institute of Applied Mathematics of Ivane Javaxishvili Tbilisi State University. The Institute was founded by Georgian mathematician and mechanist Ilia Vekua on October 29, 1968.
The aim of the Institute was to carry out research on important problems of applied mathematics, to involve University professors, teachers and students in
research activities on topical problems of applied mathematics in order to integrate mathematics into the study processes and research, and to implement mathematical methodologies and calculating technology in the nonmathematical fields of the University. In 1978,the Institute was named after its founder and first
director Ilia Vekua. In December, 2006  May, 2009 the Institute was acting at the Faculty of the Exact and Natural Sciences. In June, 2009  September, 2016 the Institute was directly subordinated to the University Administration. Since the end of September, 2016 the Institute has a status of the Independent ScientificResearch Institute. At present, the Institute successfully continues and develops activities launched by his founder in the following four main scientific directions:
Mathematical problems of mechanics of continua and related problems of analysis;
Mathematical modelling and numerical mathematics;
Discrete mathematics and theory of algorithms;
Probability Theory and mathematical Statistics.
The institute sees its mission as threefold:
Carrying out fundamental and practical scientific research in applied mathematics, mathematical and technical mechanics, industrial mathematics and informatics, undertaking state and private sector contracts to provide expert services;
Offering the university a highlevel computer technology base for University professors and teachers, research employees and students undertaking their scientific research activities;
Supporting PhD and postgraduate students to attain scientific grants, as well as
through employment within the Institute and participation in scientific conferences.

Roman Janjgava, Boundary value problems for rectangular plates with voids having two circular holes, XIV Annual International Meeting of the Georgian Mechanical Union, Poti, Georgia.
In the paper, boundary value problems for rectangular plates with voids having two circular holes are approximately solved. Stress concentration factors are calculated for various tension
compression boundary value problems. The basic twodimensional equations for plates are obtained from the threedimensional CowinNunziato equations by the I. Vekua method.
To construct approximate solutions of boundary value problems, general representations of the solution and the method of fundamental solutions are used

Bakur Gulua, On one problem of the coupled theory of elasticity for a doubleporous body, XIV Annual International Meeting of the Georgian Mechanical Union, Poti, Georgia.
The present talk deals with linear model of elastic doubleporosity materials in which the coupled phenomenon of the concepts of Darcy’s law and the volume fractions is considered. For the plane deformation the corresponding system of differential equations is written in a complex form and its general solution is presented with the use of analytic functions of a complex variable
and a solutions of the Helmholtz equations. The boundary value problems are solved for a circle.

Tamaz Vashakmadze, To von Kármán Model and Elastic Thinwalled Structures, on the Construction of a Unified Theory, XIV Annual International Conference of the Union of Mechanics of Georgia., Foti, Georgia.
The issue of establishing von Kármán's nonlinear system of differential equations will be
discussed in relation to the works of August Föpll, Timoshenko, Lev Landau, Ciarlet, Antman,
PodioGuidugli. The incompleteness of the corresponding equations will be shown in the sense
that the first dependence of the von Kármán model, in which the main term is the biharmonic
operator with respect to bending, is an equation, while the dependence containing the
biharmonic operator of the Airy function is the SaintVenantBeltrami compatibility condition and
not an equation. This fact is in full accordance with this with the opinions expressed by Truesdel
regarding this model.
A threedimensional analogue of the spatial variable with a residual term will be presented. By
truncation of the error, a nonstationary anisotropic nonlinear parameterdependent system of
differential equations of the von Kármán ReissnerMindlin type will be obtained.

Tamaz Vashakmadze, On the reduction of threedimensional models of elastic thinwalled structures., XIV Annual International Conference of the Union of Mechanics of Georgia, Foti, Georgia.
Along with the perturbation method for linear operator equations, an alternative method
of its solution is also considered; the design is performed not only when the basic
system is a qualitative row, but also when we use any complete system defined on the
area (for example, for a onedimensional interval  a system of orthogonal polynomials).
The quantity for each finite part of which the solving algorithm can efficiently obtain an
approximate solution

Teimurazi Davitashvili, Giorgi Rukhaia, Meri Sharikadze, Studying some aspects of the renewable energy in Georgia in the face of climate change, XIV Annual International Meeting of the Georgian Mechanical Union, Poti, Georgia.
Renewable energy is energy derived from sources that naturally replenish and do not deplete. The most popular such energy sources are: solar, wind, hydro, tidal, geothermal and biomass energies. The territory of Georgia is rich in such renewable energy sources (which can be used for electricity generation, space heating and cooling and water, and for transport), but at present Georgia properly uses only hydro and geothermal energy.
In the face of the current challenges of climate change, the world needs cleaner (renewable) energy and hydrogen is one possible solution as hydrogen is currently considered one of the most promising fuels of the future. Turkmenistan and Azerbaijan plan to become a leader in the production of "green" and "blue" hydrogen (having a modern production infrastructure for petrochemistry and a huge resource potential) and its transportation along the TRACECA route through Georgia and Turkey to the EU countries. Thus, the study of the behavior of a mixture of natural gas and hydrogen substances when moving through pipelines has become an urgent task of our time and has attracted the attention of a number of scientists.
This article discusses one mathematical model that describes the flow of a mixture of natural gas and hydrogen substances in a pipeline. The distribution of pressure and gas flow through a branched gas pipeline has been studied and presented. In addition, ways to reduce transportation costs are being studied, that is, the economic aspect of various methods of transporting hydrogen using hydrogen gas trailers, liquid hydrogen tanks and hydrogen pipelines of various technical levels is being studied.
Acknowledgements. The research is funded by Shota Rustaveli National Scientific Foundation Grant No. FR2218445.

George Jaiani, On Fluids in Angular Pipes, XIV Annual International Meeting of the Georgian Mechanical Union, Poti, Georgia.
In the zero approximation of hierarchical models for fluids the full accordance of peculiarities of setting of the Dirichlet and Keldysh type boundary conditions by motion of the fluids in pipes of angular crosssections with the results of experiments carried out by J. Nikuradze in L. Prandtl's Laboratory at University of Göttingen.

Natalia Chinchaladze, A DYNAMICAL PROBLEM OF ZERO APPROXIMATION OF HIERARCHICAL MODELS FOR FLUIDS, XIV Annual International Meeting of the Georgian Mechanical Union, Poti, Georgia.
We investigate dynamical problem of zero approximation of hierarchical models for fluids [Jaiani, G. Mathematical Hierarchical models for fluids. Book of Abstracts of XIII Annual International Meeting of the Georgian Mechanical Union, (2022), p. 151].
Applying the Laplace transform technique, we reduce the dynamical problem to the elliptic problem which depends on a complex parameter τ and prove the corresponding uniqueness and existence results. Further, we establish uniform estimate for solutions and their partial derivatives with respect to the parameter $\tau$ at infinity and via the inverse Laplace transform
show that the original dynamical problem is uniquely solvable.

Giorgi Kapanadze, On one problem of the plane theory of viscous elasticity for a doublyconnected domain bounded by a circle and a convex polygon, XIV Annual International Meeting of the Georgian Mechanical Union, Poti, Georgia.
The problem of the plane theory of viscous elasticity based on the KelvinVoigt model for a doublyconnected plate bounded by a circle and a convex polygon is concidered. Constant normal stresses (pressure) are acting at the points of the circumference, and constant normal stresses (or constant normal displacements) are given on the sides of the hole, and the lateral stresses are zero.
Based on the theory of analytic functions, the problem of searching for complex potentials is reduced to the RiemannHilbert problem, and by solving the latter, the mentioned potentials are effectively constructed (in analytical form). Their estimates in the vicinity of the vertices of the
corners are given and different specific cases  triangle, rectangle and rectilinear cut  are discussed.

Elizbar Nadaraya, Petre Babilua, On the One Nonparametric Estimate of Poisson Regression Function, 5th International Conference On Problems of Cybernetics and Informatics PCI 2023, Baku, Azerbaijan.

David Natroshvili, Transmission problems for composite layered elastic structures containing interfacial cracks, 10th International Congress on Industrial and Applied Mathematics, Tokyo, Japan.

Mikheil Rukhaia, Anriette Michel Fouad Bishara, Lia Kurtanidze, Lali Tibua, Unranked Probabilistic Theory: Project Presentation, 19th International Conference Computability in Europe, Batumi, Georgia. (poster)
This poster is a presentation of the fundamental research project, that aims to develop an unranked probabilistic logic, study its properties and introduce reasoning method for it. It shows preliminary results obtained during the project preparation and objectives of the project, what is planned to be achieved.
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Mikheil Rukhaia, Temur Kutsia, Mircea Marin, ToleranceBased Techniques for Approximate Reasoning, 19th International Conference Computability in Europe, Batumi, Georgia. (poster)
This poster is a presentation of the fundamental research project, that addresses the problem of developing novel symbolic techniques for supporting automated or semiautomated reasoning activities in theories modulo proximity and similarity relations.
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Teimurazi Davitashvili, Sensitivity of Caucasus Glaciers to Regional Climate Changes, XXI INQUA Congress, Rome, Italy.
The glaciers of the Caucasus (Georgia) have undergone significant changes against the background of global warming. Most of them have disappeared, and some have suffered degradation. The glacier area has decreased during the retreat, but at the same time the total number of glaciers has increased. Generally the glaciers play a major role in formation the water balance of the region and their reduction or disappearance poses significant damage to the natural ecosystems and economy. This article presents an analysis of the change in the surface area of the glacier using multitemporal data sets for the Greater Caucasus, based on manual digitization of largescale (1:50,000) topographic maps of the 1960s. and satellite images of 1964 (Corona), 1986 (Landsat 5) and 2014 (Landsat 8, ASTER). The paper deals with major meteorological factors operating on glaciers and the melting of direct solar radiation on the basis of the melting energy model of the Enguri basin glacier. Modern climate change is characterized by fluctuations in the balance of radiative energy in the lower troposphere, which determines the process of fluctuations in glaciers (melting of the thickness). Since the interaction between glacier and climate is a complex nonlinear process, we use mathematical modeling to predict the future adaptation of Georgia's glaciers to current climate changes. With the help of a twodimensional mathematical model of the dynamics of changes in the thickness of the glaciers, the configuration of the upper surface of the Caucasus glaciers were studied. Some typical problems of mathematical and numerical modeling of glaciers are discussed. For the first time, with the help of mathematical modeling, the process of melting of the Caucasus glaciers (Kazbeg 5030m) was estimated. Some simulation results are presented and analyzed.
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Teimurazi Davitashvili, Study of eolian dust transport and its activity in the formation of the regional climate of the Caucasus (Georgia), XXI INQUA Congress, Rome, Italy.
Dust aerosols represent one of the main pollutants on the territory of Georgia and impact on regional climate. In this study, the WRF/Chemistry model with dust module was used to study dust particles transportations on the territory of Georgia from the Sahara and Sahel in Africa, Arabian and arRub’ alKhali deserts located in the Middle East, Kyzylkum, Karakum and Great Salty in the Central Asia. The results of calculations have shown the WRF model was able to well simulate dust aerosols transportation on the territory of Caucasus in conditions of a complex relief of the environment (verified with CALIPSO and MODIS satellite products and HYSPLIT model). In addition we have executed sets of 30 years simulations (1985–2014) with and without dust effects by RegCM 4.7 model with 16.7 km resolution over the Caucasus domain and with 50 km resolution encompassing most of the Sahara, the Middle East, the Great Caucasus with adjacent regions. Results of calculations have shown that mineral dust aerosol influences on temperature and precipitations (magnitudes) spatial and temporally inhomogeneous distribution on the territory of Georgia. According to results of comparisons of the simulated dust aerosol optical depth seasonal distributions against to the observed ones gave a good agreement. Also dust radiative forcing inclusion has improved simulated summer time temperature, and seasonal distribution of simulated precipitation, but gives over estimation in annual total precipitation. Results of calculations have shown that dust aerosol is an interactive player in the climate system of Georgia
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Gia Giorgadze, On the partial indices of the piecewise constant matrix functions induced from Fuchsian system, Workshop to celebrate to 150 years since to formation Wales first University, Aberystwyth, UK.
In the talk we discuss relation between the Fuchsiam systems of differential equations and Riemann–Hilbert boundary value problem with piecewise con stant transition functions on the Riemann sphere.In particular, we prove that, for any Fuchsian system there exists a rational matrix function whose
partial indices coincide with the splitting type of the canonical vector bundle induced from the Fuchsiansystem. From this we obtain solution of the Riemann–Hilbert boundary value problem for piecewise
constant matrix func tion in terms of holomorphic sections of vector bundle and we give algorithmfor calculating Lppartial indices for the piecewise constant matrix functions induced from monodromy representation of the Fuchsian system. The results given in the talk based on the work [1] and [2].
Acknowledgment: This work was supported by the EU through the H2020MSCARISE2020 project EffectFact, Grant agreement ID: 101008140.
References
[1] Giorgadze, G. (2022). On the factorization and partial indices of piecewise constant matrix functions.Transactions of A. Razmadze Mathematical Institute, 176(3), 367–372.
[2] Giorgadze, G., Gulagashvili, G. (2022). On the splitting type of holomorphic vector bundles induced fromregular systems of differential equation. Georgian Mathematical Journal, 29(1), 25–35.
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David Natroshvili, An alternative potential method for mixed boundary value problems, Partial Differential Equations in Applied Mathematics: a hybrid conference in honour of Ioannis Stratis, Athens, Greece.
We consider a new alternative potential method to investigate a mixed boundary value problem (BVP) for the Lam ́e system of elasticity in the case of threedimensional bounded domain Ω ⊂ R^3, when the boundary surface S = ∂Ω is divided into two disjoint parts, S_D and S_N , where the Dirichlet and
Neumann type boundary conditions are prescribed respectively for the displacement vector and the stress vector. Our approach is based on the potential method. We look for a solution to the mixed boundary
value problem in the form of linear combination of the single layer and double layer potentials with densities supported respectively on the Dirichlet and Neumann parts of the boundary. This approach reduces the mixed BVP under consideration to a system of pseudodifferential equations which contain neither extensions of the Dirichlet or Neumann data, nor the SteklovPoincar ́e type operator. Moreover,
the right hand sides of the resulting pseudodifferential system are vectors coinciding with the Dirichlet and Neumann data of the problem under consideration. The corresponding pseudodifferential matrix operator is bounded and coercive in the appropriate L_2based Bessel potential spaces. Consequently, the operator is invertible, which implies the unconditional unique solvability of the mixed BVP in the Sobolev space [W^1_ 2 (Ω)]^3 and representability of solutions in the form of linear combination of the single layer and double layer potentials with densities supported respectively on the Dirichlet and Neumann parts of the boundary. Using a special structure of the obtained pseudodifferential matrix operator, it is also shown
that the operator is invertible in the Lpbased Besov spaces with 4/ 3 < p < 4, which under appropriate boundary data implies C^αH ̈older continuity of the solution to the mixed BVP in the closed domain Ω with α =1/ 2 − ε, where ε > 0 is an arbitrarily small number.
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Mikheil Gagoshidze , Temur Jangveladze, Zurab Kiguradze, On two systems of nonlinear partial differential equations, Third International Conference MATHEMATICS IN ARMENIA Advances and Perspectives, Dedicated to the 80th anniversary of foundation of Armenian National Academy of Sciences, Yerevan, Armenia.

Besiki Tabatadze, Teimuraz Chkhikvadze, Temur Jangveladze, Zurab Kiguradze, On one nonlinear fourthorder integrodifferential parabolic equation, Third International Conference MATHEMATICS IN ARMENIA: Advances and Perspectives. Dedicated to the 80th anniversary of foundation of Armenian National Academy of Sciences, Yerevan, Armenia.

Tea Shavadze, Tamaz Tadumadze, On the Representation of a Solution for the Perturbed Quasi Linear Controlled Neutral Functional Differential Equation, 17th Annual International Conference on Mathematics: Teaching, Theory & Applications, Athens, Greece.

Nino Khatiashvili, On the Axisymmetric Stokes Flow, Symmetry 2023  The 4th International Conference on Symmetry, Barselona, Spain.
Axial symmetry occurs in various physical processes such as fluid flow in pipes, atmospheric vortices, astrophysical fluids. We study the axisymmetric homogeneous incompressible Newtonian fluid flow of large viscosity for the small Reynolds number over the axis of symmetry in the infinite area. Such flows are called Stokes flows or creeping flows. Creeping fluids (such as some oils, polymers) are widely used in industrial processes and microelectromechanical systems (MEMS).
Velocity components of the flow satisfy the Stokes system (STS) with the equation of continuity and suitable initialboundary conditions. The Stokes system is the Stokes approximation of the NavierStokes Equations (NSE) for the creeping flows and represents the linear system of parabolic equations. We consider STS in the cylindrical polar coordinates under the action of certain pressure. The existence of the bonded solutions of this system is proved.
By the separation of variables the novel exact solutions of the Stokes system for the specific pressure are obtained in the unsteady case. The profiles of the velocity and the vortex are constructed by means of “MAPLE”.
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Tamar Kasrashvili, On various aspects of definitions of equidecomposability of sets, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia.
The present report is devoted to some aspects of geometrical and settheoretical definetions of equidecomposability of point sets. Connections between the notions of finite equidecomposability and countable equidecomposability of point sets (figures) are shown.
In particular:
(a) if sets X and Y are finitely equidecomposable, then they are also countably equidecomposable, but the converse assertion does not hold;
(b) if in the space R^n some sets X and Y are such that \lamda_n(X)>0
and \lamda_n(Y)=0, then these sets are not countably equidecomposable under the group of all affine transformations of R^n ;
(c) in R^n there exist two sets X and Y such that card(X)=card(Y)=c and X is not countably equidecomposable with Y, under a sufficiently large group of transformations of R^n;
(d) in R^n two points sets are countably equidecomposable if both of them have interior points.
The latter implies that in the space R^n there exists a nonmeasurable set with respect to the Lebesgue measure.
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Tengiz Tetunashvili, On the stability question for one problem of combinatorial geometry, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia.
In the talk the following two related questions are considered and answered:
1) Let $d$ be an arbitrary fixed nonnegative real number and let $n$ be an arbitrary fixed natural number such that $n\geq 3$. Is there a nonnegative real number $r_{n,d}$ having the property: if $S$ is a subset of the Euclidean plane with $\text{card}(S)=n$ such that, for every straight line $L_{a,b}$ passing through two distinct points $a$ and $b$ of $S$, there exists a point $c$ of $S$ such that $a \neq c$ and $b \neq c$ and the distance between $L_{a,b}$ and $c$ does not exceed $d$, then there exists a straight line $L$ in the plane such that the distance from an arbitrary point of $S$ to $L$ is less than or equal to $r_{n,d}$?
2) Let $N_3$ be the set of all natural numbers greater than 2, $d$ be an arbitrary fixed positive real number, and let $n$ be an arbitrary fixed natural number such that $n\geq 3$. Is there a function of two variables $\f(m.y)$ acting from $N_3 \times (0,+\infty)$ into $(0,+\infty)$, satisfying $\lim\limits_{y\rightarrow 0+}f(m.y)=0$ for every $m\in N_3$, and if $S$ is a subset of the plane with $\text{card}(S)=n$ such that, for every straight line $L_{a,b}$ passing through two distinct points $a$ and $b$ of $S$ there exists a point $c$ of $S$ such that $a \neq c$ and $b \neq c$ and the distance from $c$ to $L_{a,b}$ does not exceed $d$, then there exists a straight line $L$ in the plane such that the distance from an arbitrary point of $S$ to $L$ is less than or equal to$f_{n,d}$?
Also, an interrelation between the presented questions and the SylvesterGallai wellknown theorem (see, e.g., [1], [2], [3]) is considered.
.
References
1. H. Hadwiger and H. Debrunner, Combinatorial Geometry in the Plane. Translated by Victor Klee. With a new chapter and other additional material supplied by the translator, Holt, Rinehart and Winston, New York, 1964.
2. A. Kharazishvili, Elements of Combinatorial Geometry, Part I, Tbilisi, 2016.
3. J. J. Sylvester, Question 11851, Educational Times, 59(1893), p. 98.
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Shakro Tetunashvili, Tengiz Tetunashvili, On universality of Rademacher series, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia.
The existence of almost everywhere convergent and divergent Rademacher series such that they are universal in the sense of convergence to any given continuous function on the everywhere dense set is established.
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Archil Papukashvili, Giorgi Geladze, Zurab Vashakidze, Meri Sharikadze, On the numerical solution to J. Ball’s beam equation in the case where the material's effective viscosity is dependent on its velocity, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia.
The current article is a continuation of the previously published papers [1][3], which
examine the initialboundary value problem for J. Ball's integrodifferential equation. The equation models the dynamic behaviour of a beam. To obtain an approximate solution, a combination of the Galerkin method, a stable symmetric difference scheme, and the Jacobi iteration method is utilized. In papers [1][2], the numerical algorithm is validated using numerical samples. The present paper, along with [3], focuses on the application of the numerical solution to a practical problem. In particular, the numerical results of the initialboundary value problem for a specific iron beam are presented, where the effective viscosity of the material depends on its velocity. The results are summarized in a table.
References:
1. Papukashvili, A., Papukashvili, G., Sharikadze, M. Numerical calculations of the J. Ball nonlinear dynamic beam. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 32 (2018), 4750.
2. Papukashvili, A., Papukashvili, G., Sharikadze, M. On a numerical realization for a Timoshenko type nonlinear beam equation. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 33 (2019), 5154.
3. Papukashvili, A., Geladze, G., Vashakidze, Z., Sharikadze, M. On the Algorithm of an Approximate Solution and Numerical Computations for J. Ball Nonlinear IntegroDifferential Equation. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 36 (2022), 7578.
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Jemal Peradze, Archil Papukashvili, Giorgi Papukashvili, Meri Sharikadze, On the solution of an initialboundary value problem of a string, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia.
A three–step method for a nonlinear integrodifferential hyperbolic equation which
describes the behavior of a dynamic string is presented. The method has been tested on an example.
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Kartlos Joseph Kachiashvili, Quasioptimal rule of testing directional hypotheses, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia.
The problem of testing directional hypotheses is examined using the consideration of the basic and alternative hypotheses in pairs, allowing implementing computation easily and faster with guaranteed reliability. The concept of mixed directional false discovery rate (mdFDR) is used for the decision rule optimality. The fact of guaranteeing the quality of a decision (in the developed approach) on the desired level theoretically is proved and practically is demonstrated by computation of practical examples. The developed method is applied for testing multiple hypotheses that guarantee the restriction of the total mdFDR on the desired level. It is also shown that the offered method can be used for solving the problems of intersectionunion, unionintersection hypotheses. The offered method is adapted for testing large numbers of the subsets of individual hypotheses at testing multiple
hypotheses that saves computational time and resources. Reliability and convenience of the developed method for big data are demonstrated.
References
1. Bahadur, R. R. (1952). A property of the tstatistics. Sankhya, 12, 7988.
2. Bansal, N. K., Hamedani, G. G. & Maadooliat, M. Testing Multiple Hypotheses with Skewed Alternatives, Biometrics, 72, 2 (2016), 494502.
3. Kachiashvili K. J. The Methods of Sequential Analysis of Bayesian Type for
the Multiple Testing Problem. Sequential Analysis, 33, 1 (2014), 2338.
4. Kachiashvili, K. J. (2018) Constrained Bayesian Methods of Hypotheses Testing: A New Philosophy of Hypotheses Testing in Parallel and Sequential Experiments.
Nova Science Publishers, Inc., New York, 361 p.
5. Kachiashvili K. J., Kachiashvili J. K. & Prangishvili I. A. (2020) CBM for Testing
Multiple Hypotheses with Directional Alternatives in Sequential Experiments.
Sequential Analysis: Design Methods and Applications.
(ID: 1727166 DOI:10.1080/07474946.2020.1727166).
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Teimurazi Davitashvili, Giorgi Rukhaia, Modeling the dynamics of a mixture of natural gas and hydrogen in pipeline, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia.
Hydrogen is currently considered one of the most promising fuels of the future. It is
expected to be used in a wide variety of applications such as the generation and storage of electricity, automotive fuels and reactive devices, various industries and even our domestic energy needs [1]. At present, the problems of efficient production, storage and transportation of gaseous hydrogen are the main focus of many researchers around the world. The study of the behavior of a mixture of natural gas and hydrogen substances during flow in pipelines has become an urgent task of our time and has attracted the attention of a number of scientists [14]. This work is devoted to one mathematical model describing the flow of a mixture of natural gas and hydrogen substances in a pipeline. A quasinonlinear
system of twodimensional partial differential equations is considered, which describes the unsteady flow of a mixture of natural gas and hydrogen substances in a pipe. The distribution of pressure and gas flow through a branched gas pipeline has been studied.
Some results of numerical calculations of a mixture of natural gas and hydrogen in a gas pipeline are presented.
Acknowledgements. The research was funded by Shota Rustaveli National Scientific Foundation Grant No. FR2218445.
1. Ball, M., Basile, A., Veziroglu, T.N. Compendium of Hydrogen Energy: Hydrogen Use, Safety and the Hydrogen Economy; Woodhead Publishing: Cambridge, UK, 2015.
2. Hosseini, S.F., Wahid, M.A. Hydrogen production from renewable and sustainable energy resources: Promising green energy carrier for clean development. Renew. Sustain. Energy Rev. 2016, 57, 850–866.
3. Davitashvili, T. On liquid phase hydrates formation in pipelines in the course of gas nonstationary flow. E3S Web of Conferences 230, 01006 (2021),
DOI: https://doi.org/10.1051/e3sconf/202123001006.
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Mikheil Rukhaia, Anriette Michel Fouad Bishara, Lia Kurtanidze, Lali Tibua, Unranked Probabilistic Theory: Project Presentation, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics, Tbilisi, Georgia.
Since the early days of Artificial Intelligence logical and probabilistic methods have been independently used in order to solve tasks that require some sorts of intelligence. Probability theory deals with the challenges posed by uncertainty, while logic is more often used for reasoning with perfect knowledge. Considerable efforts have been devoted to combining logical and probabilistic methods in a single framework, which influenced the development of several formalisms and programming tools.
All probabilistic logic formalisms studied so far permit only individual variables, that can be instantiated by a single term. On the other hand, theories and systems that use also sequence variables (these variables can be replaced by arbitrary finite, possibly empty, sequences of terms) and unranked symbols (function and/or predicate symbols without fixed arity) have emerged. The unranked term is a firstorder term, where the same function symbol can occur in different places with different number of arguments. Unranked function symbols and sequence variables bring a great deal of expressiveness in language. Therefore, it is actual to study extension of probabilistic logic with sequence variables and flexiblearity function and predicate symbols.
This talk is a presentation of the fundamental research project, that aims to develop an unranked probabilistic logic, study its properties and introduce reasoning method for it. We discuss preliminary results obtained during the project preparation and objectives of the project, what is planned to be achieved.
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Natela Zirakashvili, Theona Zirakashvili, STUDY OF THE PROPAGATION OF ACTION POTENTIALS IN HEART TISSUE USING CABLE EQUATION, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University. , Tbilisi, Georgia.
Cardiovascular diseases are still the leading factors of mortality worldwide. Particularly noteworthy, major reason of death is caused by the heart failure, for example, due to a heart attack and development of a fatal arrhythmia. The direct cause of fatal cardiac arrhythmias is still not completely investigated, however, in many cases the cause can be traced to a failure of the cardiac action potential to propagate correctly. Remarkably, the propagation of action potential is still not completely understood in spite of many years of investigation. Therefore, the study remains a critical topic of many modern scientific studies. The aim of the current work is to investigate the prevalence of action potentials in cardiac tissue using the cable equation. In the variation of the cable equation, developed by Lord Kelvin for modeling the propagation of electrical signals of underwater telegraphs, the passive onedimensional cable equation is obtained, which is a model of monodomain and bidomain, which describes the electrical behavior of the cell membrane of the heart tissue and the propagation of the action potential. A homogeneous representation of heart tissue includes a large number of identical cells, which can be imagined as two interconnected spaces  intracellular and extracellular. Cells are connected to each other by gap junctions. The paper discusses 1D model of continuously connected myocytes. Here, due to the assumption of continuity, the electrical behavior in the tissue is average for many cells, so we will study the behavior of the transmembrane potential for a single cell. For monodomain, in the absence of current at the beginning and end of the cable (cell), numerical modeling in Matlab is carried out. Figures of the corresponding contours (isolines), 2D and 3D graphs of the obtained numerical results are presented.
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Nino Khatiashvili, ON THE AXISYMMETRIC FLUID FLOW IN CASE OF SMALL REYNOLDS NUMBER , XXXVII Enlarged Sessions (April 1922, 2023) of the Seminar of I. Vekua Institute of Applied Mathematics of I. Javakhishvili Tbilisi State University, Tbilisi State UniversityIA.
We consider the axisymmetric incompressible unsteady fluid flow over the axis of symmetry for the small Reynolds number. The velocity components of the flow satisfy the nonlinear Navier  Stokes equations (NSE) with the suitable initialboundary conditions. For the small Reynolds number NSE can be reduced to the Stokes linear system (STS) . We have studied the Stokes system in the axisymmetric case when the pressure depends on time exponentially. By the separation of variables the exact solutions of STS are obtained.
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Bakur Gulua, Ucha Todria, Basic boundary value problems for the plane theory of elasticity of porous Cosserat media for circular ring with voids, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia.
მოხსენებაში განსახილავი სხეული არის დრეკადი კოსერას გარემო
სიცარიელეებით. ბრტყელი დეფორმაციის შემთხვევის შესაბამისი განტოლებების ორგანზომილებიანი სისტემა ჩაწერილია კომპლექსური ფორმით და მისი ზოგადი ამონახსნი წარმოდგენილია კომპლექსური ცვლადის ორი ანალიზური ფუნქციისა და ჰელმჰოლცის განტოლების ორი ამონახსნის გამოყენებით. ზოგადი წარმოდგენის საფუძველზე ამოხსნილია კონკრეტული სასაზღვრო ამოცანები წრიული რგოლისათვის.
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Giorgi Kapanadze, On one problem of the plane theory of viscoelasticity for circular plate with a polygonal hole, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia.
განხილულია ბლანტი დრეკადობის ბრტყელი თეორიის ამოცანა წრიული ფირფიტისათვის მრავალკუთხა ხვრელით კელვინფოიგტის მოდელის საფუძველზე. იგულისხმება, რომ ფირფიტის გარე საზღვარზე მოქმედებენ ნორმალური მკუმშავი ძალვები (წნევა), ხოლო ხვრელში ჩადგმულია შედარებით დიდი ზომის ხისტი შაიბა ისე, რომ საზღვრის წერტილთა ნორმალური გადაადგილებები ღებულობენ მუდმივ მნიშვნელობებს და ხახუნის ძალები ნულის ტოლია.
კონფორმულ ასახვათა და ანალიზურ ფუნქციათა სასაზღვრო ამოცანების თეორიის მეთოდების საფუძველზე საძიებელი კომპლექსური პოტენციალები აგებულია ეფექტურად (ანალიზური ფორმით). მოყვანილია აღნიშნული პოტენციალების შეფასება კუთხის წვეროების მახლობლად. განხილულია ზღვრული შემთხვევები (მართკუთხედი, სწორხაზოვანი ჭრილი).
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Roman Janjgava, Approximate solution of some boundary value problems of stress concentration for perforated plates with voids, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics, Tbilisi, Georgia.
We consider tensioncompression problems for rectangular porous aluminum plates with
one or two circular holes. The corresponding twodimensional system of equilibrium
equations is obtained from the linear threedimensional CowinNunziato model by the
method of successive differentiation. Boundary value problems are solved by an
approximate method, for which general representations of the solution of a system of
equilibrium equations and the method of fundamental solutions are used. Stress
concentration factors on the contours of the hole are calculated.

Tamaz Tadumadze, Abdeljalil Nachaoui, Mourad Nachaoui, SENSITIVITY COEFFICIENTS OF A CONTROLLED FUNCTIONALDIFFERENTIAL MODEL OF THE IMMUNE RESPONSE CONSIDERING OF THE MIXED INITIAL CONDITION AND VARIATION OF THE INITIAL MOMENT, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia.

Mikheil Gagoshidze , Numerical Solution Of One Nonlinear Partial Differential Multidimensional System, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (VIAM) of Ivane Javakhisvili Tbilisi State University (TSU), Dedicated to the 105th Anniversary of, Tbilisi, Georgia.
A multidimensional analogue of one nonlinear twodimensional system of partial differential equations describing some biological processes is studied [1]. The averaged model of sum approximation [2] and the variable direction difference scheme [3] for an initialboundary problem are considered. Various numerical experiments have been conducted and a comparative analysis of the obtained results is given. Acknowledgements. This work was supported by Shota Rustaveli National Science
Foundation of Georgia (SRNSFG) [grant number FR212101].
References
[1]. Mitchison, G.J. The polar transport of auxin and vein patterns in plants. Philos. Trans. R. Soc. Lond. B Biol. Sci., 295 (1981), 461471.
[2]. Dzhangveladze, T.A. Averaged model of sum approximation for a system of nonlinear partial dierential equations. Proc. I. Vekua Inst. Appl. Math., 19 (1987), 6073 (Russian).
[3]. Jangveladze, T., Kiguradze, Z., Gagoshidze, M., Nikolishvili, M. Stability and convergence of the variable directions dierence scheme for one nonlinear twodimensional model. International Journal of Biomathematics. 8, 5 (2015), 1550057 (21 pages), DOI: 10.1142/S1793524515500576.
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Temur Jangveladze, On the system of Maxwell's nonlinear partial differential equations, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (VIAM) of Ivane Javakhisvili Tbilisi State University (TSU), Tbilisi, Georgia.

Tamaz Vashakmadze, Giorgi Buzhgulashvili, On the approximate solution of the boundary value problem for the ordinary differential equation, XXXVII international extended sessions of the seminar of the Ilia Vekua Institute of Applied Mathematics of Ivane Javakhishvili Tbilisi State University., Tbilisi, Georgia.
Along with the perturbation method for linear operator equations, an alternative method
of its solution is also considered; the design is performed not only when the basic
system is a qualitative row, but also when we use any complete system defined on the
area (for example, for a onedimensional interval  a system of orthogonal polynomials).
The quantity for each finite part of which the solving algorithm can efficiently obtain an
approximate solution

Roman Koplatadze, ON THE OSCILATORY PROPERTIES OF THE SECOND ORDER EMDENFOWLER TYPE DIFFRENCE EQUATIONS WITH DEVIATING ARGUMENT, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia.
განვიხილოთ მეორე რიგის გადახრილ არგუმენტიანი ემდენფაულერის ტიპის
სხვაობიანი განტოლება. დადგენილია ამონახსნების რხევადობის ახალი ტიპის საკმარისი პირობები.
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Elizbar Nadaraya, Petre Babilua, On the NadarayaWatson type nonparametric estimator of the Poisson regression function, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics, Tbilisi, Georgia.

Tea Shavadze, Ia Ramishvili, On the wellposedness of the Cauchy problem for one class of controlled neutral functional differential equation considering perturbation of the initial data, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia.

Roman Koplatadze, ON THE OSCILATORY PROPERTIES OF THE SECOND ORDER EMDENFOWLER TYPE DIFFRENCE EQUATIONS WITH DEVIATING ARGUMENT, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics, Tbilisi, Georgia.

David Kaladze, Luba Tsamalashvili, On the exact solutions of the ZakharovKuznetsov dynamical equation in a ElectronPositronIon plasma, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics, Tbilisi,Georgia.
Using the expfunction method the traveling wave special exact solutions of the (2+1)D nonlinear ZakharovKuznetsov partial differential equation in an electronpositronion plasma are represented. The results are expressed in the forms of hyperbolic, trigonometric, exponential and rational functions and have spatially isolated structural forms. Traveling wave velocity is defined as the function of dynamic parameters.
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George Jaiani, ივანე ნიკურაძის ექსპერიმენტების შედეგებისა და კელდიშის სასაზღვრო ამოცანის მიმართების შესახებ , XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics, Tbilisi, Georgia.
In the zero approximation of hierarchical models for fluids [1] the full accordance of peculiarities of setting of the Dirichlet and Keldysh type boundary conditions by motion of the fluids in pipes of angular crosssections with the results of experiments carried out by J. Nikuradze (see [2] and also [3]) in L. Prandtl's Laboratory at University of Göttingen.
References
1. Jaiani, G. Mathematical Hierarchical models for fluids. Book of Abstracts of XIII Annual International Meeting of the Georgian Mechanical Union, (2022), p. 151.
2. Nikuradze, J. Untersuchungen über turbulente. Strömungen in nichtkreisförmigen Rohren. Ing. Arch. B. I. 1930. S306.
3. Kavtaradze, R. Johann (Iwane) Nikuradze. Mythos and Realitaet. Tbilisi, (2023), 154155 (in Georgian).
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Besik Dundua, HigherOrder Unification with Regular Types, XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics, Tbilisi, Georgia.
In this talk we extend simply typed lambda calculus with regular types and study properties
of the extended formalism. Moreover, we construct higherorder unification procedure for
regularly typed lambda terms, and prove soundness and completeness theorems.
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Tamaz Vashakmadze, The Problems of Numerical Realization for Some Class of the Operator Equations by Perturbation’s Theories Alternating Method, Seminar of Institute of Applied Mathematics named after TSU Ilia Vekua, Tbilisi, Georgia.
Along with the perturbation method for linear operator equations, an alternative method
of its solution is also considered; the design is performed not only when the basic
system is a qualitative row, but also when we use any complete system defined on the
area (for example, for a onedimensional interval  a system of orthogonal polynomials).
The quantity for each finite part of which the solving algorithm can efficiently obtain an
approximate solution.

Mariam Beriashvili, On some methods of extending measures, Winter School in Abstract Analysis 2023, Section Set Theory and Topology, Steken, Czech Republik.
The measure extension problem is one of the most important question in measure
theory. It is known that there exist various measures on the real line R which strictly
extend the classical Lebesgue measure λ on R and are invariant under the group of all
isometric transformations of R. An interesting direction in measure theory is concerned
with the investigation of properties of various (countablyadditive) extensions of initial
measures. In this connection, there are some wellknown methods of extending invariant
measures: Marczewski’s method; the method of Kodaira and Kakutani; the method of
Kakutani and Oxtoby; the method of surjective homomorphisms.
In the present talk we discuss, several methods of extending invariant and quasi
invariant measures. Moreover, we will demonstrate several classes of measures with a
different cardinality number.