პუბლიკაციები

2025

• Giorgadze, G., Khimshiashvili, G., Triangular electrostatic ion traps revisited, Physics of particles and nuclei, 56 (2025), 1022-1024. 
• Khimshiashvili, G. On the abstract singular operators in the sense of B.Bojarski. Trans. A. Razmadze Math. Inst. 179 (2025), no. 2, 301-307.
•  Transactions of A. Razmadze Mathematical Institute (vol.179, issue 2, pp.277–289, 2025); 
• Journal of Thermal Stresses (ონლაინ 27.06.2025), DOI: https://doi.org/10.1080/01495739.2025.2517156;

2024

• Khimshiashvili, Giorgi. A note on three collinear point charges. Geometric methods in physics XL, 403--412, Trends Math., Birkhäuser/Springer, Cham, [2024], ©2024. MR4807471  
• Giorgadze, Grigori; Khimshiashvili, Giorgi. On topological aspects of numerical range. Analysis without borders, 95--108, Oper. Theory Adv. Appl., 297, Birkhäuser/Springer, Cham, [2024], ©2024. MR4786517  
• Elashvili, Alexander; Jibladze, Mamuka; Khimshiashvili, Giorgi. Remarks on invertible binomial singularities. Bull. Georgian Natl. Acad. Sci. (N.S.) 18 (2024), no. 1, 7--16. MR4767801
• M. Svanadze, Potential method in the coupled theory of thermoelastic triple-porosity nanomaterials, J. Thermal Stresses, vol. 47, Issue 10, pp. 1277-1296, 2024.
• M. Svanadze, Uniqueness theorems in the steady vibration problems of the Moore-Gibson-Thompson thermoporoelasticity. Georgian Mathematical J., 2024.

2023

• G.Giorgadze, G.Khimshiashvili, On the index of the gradient of a real invertible polynomial. Proc. Steklov Inst. Math. v.321(2023), 84-96.
• G.Giorgadze, G.Khimshiashvili, Three point charges on a flexible arc, J. Math. Sci. v.275(2023), 712-717
• G.Khimshiashvili, D.Siersma, Hooke and Coulomb energy of tripod spiders. arXiv: 2301.09314.
• M. Svanadze, External problems of steady vibrations in the theory of elastic materials with a triple porosity structure, PAMM-Proceedings in Applied Mathematics and Mechanics, vol. 22, Issue 1, e202200014 (6 pages), 2023. DOI: https://doi.org/10.1002/pamm.202200014.
• M. Svanadze, On the coupled linear theory of thermoelasticity for nanomaterials which triple porosity. Mechanics Research Communications, vol. 132, paper number 104161 (5 pages), 2023. DOI: https://doi.org/10.1016/j.mechrescom.2023.104161.
• M. Svanadze, Fundamental Solution in the coupled theory of thermoelastic nanoporous materials with triple porosity, PAMM-Proceedings in Applied Mathematics and Mechanics, 2023, e202300127. DOI: https://doi.org/10.1002/pamm.202300127 (in press).

2022

• G.Giorgadze, G.Khimshiashvili, Incenter of triangle as a stationary point, Georgian Math. J. vol. 29, No.4, 515-525.
• G.Giorgadze, G.Khimshiashvili, Riemann-Hilbert problems with coefficients in compact Lie groups, In: “Mechanics and Physics of Structured Media”, Chapter 15, 303-326, Academic Press, 2022.  
• G.Khimshiashvili, D.Siersma, Morse functions on spider linkages, Proc. I.Vekua Institute of Applied Mathematics, vol. 72, 2022. 8 pp. (accepted)
• G.Giorgadze, G.Khimshiashvili, On the index of gradient of real invertible polynomial, Proceedings of the Steklov Institute of Mathematics, vol. 321, 2023. 12 pp.
• M. Svanadze, Steady vibration problems in the coupled theory of elastic triple-porosity materials, Trans. A. Razmadze Math. Inst., vol. 176, Issue 1, pp. 83-98, 2022 (Scopus index 1.3).
• M. Svanadze, On the coupled theory of thermoelastic double-porosity materials, J. Thermal Stresses, vol. 45, Issue 7, pp. 576-596, 2022 (Impact factor 3.456)
• M. Svanadze, External problems of steady vibrations in the theory of elastic materials with a triple porosity structure, PAMM-Proceedings in Applied Mathematics and Mechanics, 2022 (in press). DOI:10.1002/pamm.202200014

2021

• G.Khimshiashvili, G.Panina, D.Siersma, Area-perimeter duality in polygon spaces, Mathematica Scandinavica 127(2021), no.2, 252-263.
• G.Giorgadze, G.Khimshiashvili, Triangles and electrostatic ion traps. J. Math. Phys. 62 (2021), no. 5, Paper No. 053501, 10 pp.
• G.Giorgadze, G.Khimshiashvili, On equilibrium points of three point charges, Bull. Georgian Natl. Acad. Sci. 15 (2021), no.3, 7-13. 
• M. Svanadze, Potential method in the coupled theory of elastic double-porosity materials, Acta Mechanica, vol. 232, issue 6, pp. 2307–2329, 2021.
•  S.Mukhigulashvili, Some two-point boundary value problems for systems of higher order functional differential equations, Mathematica Scandinavica 127(2021), no.2, 382-404. 
• S.Mukhigulashvili, V.Novotná, The periodic problem for the second order integro-differential equations with distributed deviation. Math. Bohem. 146 (2021), no. 2, 167--183. 
• T. Aliashvili, On the Stable Polynomial Mappings. Proceedings of I.Vekua Institute of Applied Mathematics. V.70. (2020).
• თ.  ალიაშვილი, ეილერის მახასიათებელი და ფერთა პრობლემა.  მათემატიკა - სამეცნიერო პოპულარული ჟურნალი, N7 (2021) ივ. ჯავახიშვილის სახ. თბილისის სახელწიფო უნივერსიტეტი
• M. Svanadze, Potential method in the coupled theory of elastic double-porosity materials, Acta Mechanica, vol. 232, issue 6, pp. 2307–2329, 2021. (Impact factor 2.698).

2020

• Svanadze, Potential Method in the coupled theory of elastic double-porosity materials, Acta Mechanica, 2020 
• Svanadze, Potential Method in the coupled linear theory of porous elastic solids, Mathematics and Mechanics of Solids, vol. 25(3), pp. 768-790, 2020 
• G.Khimshiashvili, Isoperimetric duality in polygon spaces, Bull. Georgian Natl. Acad. Sci. vol.14 (2020), no.1, 18-22. 
• G.Khimshiashvili, G.Panina, D.Siersma, Extremal areas of polygons with fixed perimeter. J. Math. Sci. (N.Y.)  vol.247 (2020), no. 5, 731-737.
• G.Giorgadze, G.Khimshiashvili, On three point charges on a flexible arc. Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., vol.177 (2020), 63–68. 
• G.Giorgadze, G.Khimshiashvili,  On area foliation in spaces of triangles, Bull. Georgian Natl. Acad. Sci. vol.15 (2020), no.2, 7-13.
• G.Khimshiashvili, Dual extremal problems in polygon spaces, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics  vol.34,  2020, 46-49.
• G.Khimshiashvili, Symmetric foliations in spaces of triangles, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics vol.34,  2020, 50-53.
• G.Khimshiashvili, G.Panina, D.Siersma, Area-perimeter duality in polygon spaces. Math. Scand.  2021. 10 pp. 
• G.Giorgadze, G.Khimshiashvili,   On stable equilibrium points of three point charges. Proc. I. Vekua Institute of Applied Mathematics

2019  

• G.Khimshiashvili, Remarks on quadratic mappings. J. Math. Sci. (N.Y.) 23, 2019, no.1, 135–146.
• G.Khimshiashvili, G.Giorgadze, Equilibria of three-point charges with quadratic constraints. J. Math. Sci. (N.Y.) 237, 2019, no. 1, 110–125.
• G.Khimshiashvili, G.Panina and D.Siersma, Extremal areas of polygons with a fixed perimeter. Zapiski V.Steklov Math. Inst. SPb. Branch 481, 2019, 136-145.
• G.Khimshiashvili, D.Siersma, Connecting cycles for concentric circles, Bull. Georgian Natl. Acad. Sci. 13, No.1, 2019, 13-21.
• G.Khimshiashvili, N.Machavariani , Milnor algebras of invertible polynomials, Bull. Georgian Natl. Acad. Sci. 13, No.2, 2019, 11-16.
• G.Khimshiashvili, Extremal problems in Kendall shape spaces, Bull. Georgian Natl. Acad. Sci. 13, No.4, 2019, 7-11.
• M. Svanadze, Fundamental solutions in the linear theory of thermoelasticity for solids with tripleporosity, Mathematics and Mechanics of Solids, vol. 24(4), pp. 919–938, 2019.
• M. Svanadze, On the linear theory of double porosity thermoelasticity under local thermal non equilibrium, J. Thermal Stresses, vol. 42(7), pp. 890-913, 2019.
• M. Svanadze, Potential method in the theory of thermoelasticity for materials with triple voids, Archivesof Mechanics, vol. 71, N 2, pp. 113-136, 2019.
• G.Rakviashvili, On algebraic K-functors of crossed restricted enveloping algebras of Lie p- algebras. Bull. Georgian Natl. Acad. Sci. 13, No. 4, 2019, 12-19.
• S.Mukhigulashvili, V.Novotna, Some two-point problems for second-order integro-differential equations with argument deviations, Topol. Methods Nonlinear Anal. (2019).
• S.Mukhigulashvili, M.Manjikashvili, Dirichlet BVP For The Second-Order Nonlinear Ordinary Differential Equations At Resonance. Mathematical Modelling and Analysis, 24, No.4, 2019, 585-597.

2018  

• G.Khimshiashvili, On equilibrium concyclic configurations, Doklady Mathematics 98, No.1, 377-381, 2018. (with G.Giorgadze)
• G.Khimshiashvili, Regular stars as critical points, Bull. Georgian Natl. Acad. Sci. vol.12, No.4, 13-18, 2018. (with G.Panina and D.Siersma)
• G.Khimshiashvili, Equilibria of point charges in a line segment, Proc. I.Vekua Inst. Appl. Math. 68, 23-32, 2018. (with G.Giorgadze)
• G.Khimshiashvili, Three-point charges on flexible contour, Proc. I.Vekua Inst. Appl. Math. 68, 33-38, 2018. (with G.Giorgadze and I.Murusidze)
• M. Svanadze, Potential method in the theory of elasticity for triple porosity materials, J. Elasticity, vol. 130, Issue 1, pp. 1-24, 2018.
• M. Svanadze, Steady vibrations problems in the theory of elasticity for materials with double voids, Acta Mechanica, vol. 229, pp. 1517–1536, 2018.
• M. Svanadze, Potential method in the linear theory of triple porosity thermoelasticity, J. Math. Anal. Appl., vol. 461, pp. 1585–1605, 2018.
• M. Svanadze, On the linear equilibrium theory of elasticity for materials with triple voids, Quart. J. Mech. Appl. Math., vol. 71, pp. 329-248, 2018.
• S.Mukhigulashvili, The mixed BVP for the second-order nonlinear ordinary differential equation at resonance. Miskolc Math. Notes 18, no. 2, 975-992, 2018.
• G.Rakviashvili. On algebraic K-functors of crossed group rings and its applications. Tbilisi Mathematical Journal 11(2) (2018), pp. 1-15.
• G.Rakviashvili, Inductive theorems and projective modules over crossed group rings, Bull. Georgian Natl. Acad. Sci. 12, No.1, 16-19, 2018.
• G. Rakviashvili, The Measuring of the Gini, Theil and Atkinson Indices for the Georgia Republic and Some other Countries. Globalization and Business, 2018, No. 5, 110-118.
• T.Aliashvili, On stable endomorphisms of the plane, Proc. I.Vekua Inst. Appl. Math. 68, 3-9, 2018.

2017  

• M. Svanadze, Boundary value problems of steady vibrations in the theory of thermoelasticity for materials with double porosity structure, Archives of Mechanics, vol. 69, No. 4-5, pp. 347-370, 2017.
• M. Svanadze, Potential method in the linear theory of triple porosity thermoelasticity, J. Math. Anal. Appl.,  2017 
• B. Straughan, M. Svanadze, On the linear theory of double porosity thermoelasticity under local thermal non-equilibrium, J. Elasticity, 2017 
• M. Svanadze, Fundamental solutions in the linear theory of thermoelasticity for solids with triple porosity, Mathematics and Mechanics of Solids,  2017
• M. Svanadze, On the linear equilibrium theory of elasticity for materials with triple voids, Quart. J. Mech. Appl. Math.  2017
• G.Khimshiashvili, G.Panina, D.Siersma, V.Zolotov, Point charges and polygonal linkages, J. Dyn. Control Syst., vol.23, No.41, 2017, 1-17.
• G.Khimshiashvili, Discrete invariants of quadratic endomorphisms, Bull. Georgian Natl. Acad. Sci. vol.11, No.3, 2017, 7-13.
• G.Khimshiashvili, Equilibria of point charges on elastic contour, Bull. Georgian Natl. Acad. Sci. vol.11, No.4, 2017, 9-15.
• G.Khimshiashvili, Extremal problems for bicentric quadrilaterals, Transactions of Ajara Regional Scientific Center of Georgian National Academy of Sciences, vol.2, 2017, 9-16.
• G.Khimshiashvili, Concyclic and aligned configurations of point charges, Proc. I.Vekua Inst. Appl. Math. 67, 2017, 35-46. (with G.Giorgadze)
• M. Svanadze, Potential method in the theory of elasticity for triple porosity materials, J. Elasticity, 2017
• M. Svanadze, Steady vibrations problems in the theory of elasticity for materials with double voids, Acta Mechanica, 2017
• M. Svanadze, External boundary value problems in the quasi-static theory of thermoelasticity for triple porosity materials, PAMM-Proceedings in Applied Mathematics and Mechanics, vol. 17, Issue 1, 2017
• M. Svanadze,Potential method in the linear theory of triple porosity thermoelasticity, J. Math. Anal. Appl.,  2017
• S.Mukhigulashvili, The mixed BVP for second order nonlinear ordinary differential equation at resonance. Math. Nachr. 290(2017), no. 2-3, 393–400.
• S.Mukhigulashvili, On one two-point BVP for the fourth order linear ordinary differential equation. Georgian Math. J. 24 (2017), no. 2, 265–275. (with M.Manjikashvili)
• T.Aliashvili, On the complex points of random polynomials, Bull. Georgian Natl. Acad. Sci. 11, No.1, 2017, 12 – 15.

2016  

• G.Khimshiashvili, G.Panina, D.Siersma, Equilibria of three constrained point charges, J. Geom.Phys. 106, No.1, 2016, 42–50.
• G.Khimshiashvili, Configurations of points as Coulomb equilibria, Bull. Georgian Natl. Acad. Sci. v.10, No.1, 2016, 20-27.
• G.Khimshiashvili, Remarks on homogeneous endomorphisms, Proc. I. Vekua Inst. Appl. Math. 66, 2016, 15-24.
• G.Khimshiashvili, N.Sazandrishvili, Extremal problems for sliding polygons, Proc. I. Vekua Inst.Appl. Math. 66, 2016, 25-32.
• M.Svanadze, Plane waves, uniqueness theorems and existence of eigenfrequencies in the theory of rigid bodies with a double porosity structure, In: B. Albers and M. Kuczma (eds), Continuous Media with Microstructure 2, pp. 287-306, Springer, 2016.
• M.Svanadze, Fundamental solutions in the theory of elasticity for triple porosity materials, Meccanica,vol. 51, pp. 1825-1837, 2016.
• M.Svanadze, On the linear theory of thermoelasticity for triple porosity materials, In: M. Ciarletta, V. Tibullo, F. Passarella (eds), Proceedings of the 11th International Congress on Thermal Stresses, 5-9 June, 2016, Salerno, Italy, pp. 259-262, 2016.
• M.Svanadze, External boundary value problems in the quasi-static theory of elasticity for triple porosity materials, PAMM-Proceedings in Applied Mathematics and Mechanics, vol. 16, Issue 1, pp. 495-496, 2016.
• G.Rakviashvili, On Regular Cohomologies of Biparabolic Subalgebras of sl(n), Bull. Georgian Natl.Acad. Sci. v.10, No.2, 2016, 20-24.
• T.Aliashvili, Topological invariants of random polynomials, Bull. Georgian Natl. Acad. Sci. v.10, No.4, 2016, 7-16.

2015  

• G.Khimshiashvili, Equilibria of point charges on convex curves, J. Geom. Phys. 98, 2015, 110-117. (with G.Panina and D.Siersma) 2014
• G.Khimshiashvili, Point charges and polygonal linkages, J. Dynam. Contr. Syst. 12 p., published online June 2015. (with G.Panina and D.Siersma) 2014 
• G.Khimshiashvili, On non-degeneracy of certain constrained extrema, Doklady Math. 465, No.3, 2015, 1-5. (with G.Giorgadze) 2014/2015
• G.Khimshiashvili, Cross-ratios of quadrilateral linkages, J. Sing. 13, 2015, 159-168. (with D.Siersma) Remarks on bicentric quadrilaterals, Proc. A.Razmadze Math. Inst. 168, 2015, 41-52.
• G.Khimshiashvili, Equilibria of point charges in convex domains, Bull. Georgian Natl. Acad. Sci. 9, No.2, 2015, 19-26. (with G.Giorgadze)
• G.Khimshiashvili, Equilibria of point charges on nested circles, Bull. Georgian Natl. Acad. Sci. 9, No.3, 2015, 43-49. (with G.Giorgadze)
• E.Scarpetta, M.Svanadze, Uniqueness theorems in the quasi-static theory of thermoelasticity for solids with double porosity, J. Elasticity, vol. 120, No 1, pp. 67-86, 2015 Impact factor – 1. 656.
• M.Svanadze, External boundary value problems of steady vibrations in the theory of rigid bodies with a double porosity structure, PAMM-Proceedings in Applied Mathematics and Mechanics, vol. 15, Issue 1, pp. 365-366, 2015

2014  

• G.Khimshiashvili, G.Panina, D.Siersma, Coulomb control of polygonal linkages,  J. Dyn. Control Syst., vol.20, No.4, 2014, 491-501.
• G.Khimshiashvili et. al., Proc. of 98th European Study Group with Industry,  The Mathematics of French Fries, 24-33, Delft Technical University, 2014. (ISBN: 978-94-6186-306-5)
• G.Khimshiashvili, Cross-ratios of poristic quadrilaterals,  Proc. I.Vekua Inst. Appl. Math., vol.64, 2014, 37-46.
• G.Rakviashvili, Primitive elements of free Lie p-algebras,  Bull. Georgian Natl. Acad. Sci., vol. 8, no. 2, 2014, 15–18.
• M.Svanadze, Uniqueness theorems in the theory of thermoelasticity for solids with double porosity,  Mecanicca, vol. 49, Issue 9, pp. 2099-2108, 2014.
• M.Svanadze, E. Scarpetta, V. Zampoli, Fundamental solutions in the theory of thermoelasticity for solids with double porosity,  J. Thermal Stresses, vol. 37, No 6, pp. 727-748, 2014
• M.Svanadze, M. Ciarletta, F. Passarella, Plane waves and uniqueness theorems in the coupled linear theory of elasticity for solids with double porosity,  J. Elasticity, vol. 114, Issue 1, pp. 55-68, 2014.
• M.Svanadze, On the theory of viscoelasticity for materials with double porosity, Discrete and Continuous Dynamical Systems – Series B (DCDS-B), vol. 19, No 9, pp. 2335-2352, 2014.
• M.Svanadze, A.Scalia, Potential method in the theory of thermoelasticity with microtemperatures for microstretch solids, Transaction of Nanjing University of Aeronautics and Astronautics, vol. 31, Issue 2, pp, 159-163, 2014.
• M.Svanadze, Basic theorems in thermoelastostatics of bodies with microtemperatures,  In: R.B. Hetnarski (ed), Encyclopedia of Thermal Stresses, 11 Volumes, 1st Edition, Springer, pp. 355-365, 2014.
• M.Svanadze, Fundamental solutions in thermoelasticity theory,  In: R.B. Hetnarski (ed), Encyclopedia of Thermal Stresses, 7 Volumes, 1st Edition, Springer, 11 Volumes, 1st Edition, Springer, pp. 1901-1910, 2014.
• M.Svanadze, Fundamental solutions in thermoelastostatics of micromorphic solids, In: R.B. Hetnarski (ed), Encyclopedia of Thermal Stresses, 11 Volumes, 1st Edition, Springer, pp. 1910-1916, 2014.
• M.Svanadze,Large existence of solutions in thermoelasticity theory of steady vibrations,  In: R.B. Hetnarski (ed), Encyclopedia of Thermal Stresses, 11 Volumes, 1st Edition, Springer, pp. 2677-2687, 2014.
• M.Svanadze, Potentials in thermoelasticity theory,  In: R.B. Hetnarski (ed), Encyclopedia of Thermal Stresses, 11 Volumes, 1st Edition, Springer, pp. 4013-4023, 2014.
• M.Svanadze, A. Scalia, Representations of solutions in thermoelasticity theory,  In: R.B. Hetnarski (ed), Encyclopedia of Thermal Stresses, 11 Volumes, 1st Edition, Springer, pp. 4194-4203, 2014.
• M. Ciarletta, F. Passarella, M. Svanadze, Plane waves and uniqueness theorems in the coupled linear theory of elasticity for solids with double porosity, Elasticity, vol. 114, Issue 1, pp. 55-68, 2014.

2013  

• G.Khimshiashvili, Complex geometry of polygonal linkages, J. Math. Sci. 189, No.1, 2013, 132-149.
• G.Khimshiashvili, On Poncelet porism for biquadratic curves, Bull. Georgian Natl. Acad. Sci. 7, No.1, 2013, 5-10.
• G.Khimshiashvili, Equilibria of constrained point charges, Bull. Georgian Natl. Acad. Sci. 7, No.2, 2013, 15-20.
• G.Khimshiashvili, G.Giorgadze, Cyclic configurations of spherical polygons, Doklady Akad. Nauk 450, No.3, 2013, 264-267.
• G.Khimshiashvili, D.Siersma, Critical configurations of planar multiple penduli, J. Math. Sci. 195, No.2, 2013, 198-212.
• G.Khimshiashvili, G.Khimshiashvili, G.Panina, D.Siersma and A.Zhukova, Critical configurations of planar robot arms, Centr. Eur. J. Math. 11, No.3, 2013, 519-529.
• M.Svanadze, A.Scalia, Mathematical problems in the coupled linear theory of bone poroelasticity, Comp. Math. Appl., vol. 66, No 9, pp. 1554-1566, 2013.
• M.Svanadze, S. De Cicco, Fundamental solutions in the full coupled linear theory of elasticity for solid with double porosity, Archives of Mechanics, vol. 65, No 5, pp. 367-390, 2013.
• M.Svanadze, Fundamental solution in the linear theory of consolidation for elastic solids with double porosity, J. Math. Sci., vol. 195, Issue 2, pp. 258-268, 2013.
• M.Svanadze, A.Scalia, Potential method in the theory of thermoelasticity with microtemperatures for microstretch solids, Proceedings of the 10th International Congress on Thermal Stresses, 31.05 – 4.06, 2013, Nanjing, China, CD of Papers, 4p.
• S.Mukhigulashvili, Nonlocal boundary value problem for strongly singular higher-order linear functional-differential equations. Electron. J. Qual. Theory Differ. Equ. 2013, No. 33, 38 pp.
• S.Mukhigulashvili, The Dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations. Czechoslovak Math. J. 63(138) (2013), no. 1, 235-263.