
Besik Dundua, Temur Kutsia, Mario Florido, Mircea Marin, Constraint Logic Programming for Hedges: a Semantic Reconstruction, Proceedings of the 12th International Symposium on Functional and Logic Programming, FLOPS 2014. Volume 8475 of Lecture Notes in Computer Science, pages 285301, Springer, 2014
We describe the semantics of CLP(H): constraint logic programming over hedges. Hedges are finite sequences of unranked terms, built over variadic function symbols and three kinds of variables: for terms, for hedges, and for function symbols. Constraints involve equations between unranked terms and atoms for regular hedge language membership. We give algebraic semantics of CLP(H) programs, define a sound, terminating, and incomplete constraint solver, and describe some fragments of constraints for which the solver returns a complete set of solutions.
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Mariam Beriashvili, On some paradoxical subsets of the real line., Georgian Int. J. Sci. Technol. 6 (2014), no. 4, 265–275., Nova Sci. Publ, 2014
Some classical pathological subsets of the real line are considered and
their descriptive properties are investigated from the measuretheoretical viewpoint. In
addition, various combinations of such subsets are presented
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Temur Jangveladze, Zurab Kiguradze, Giorgi Lobjanidze, Variational Statement and Domain Decomposition Algorithms for BitsadzeSamarskii Nonlocal Boundary Value Problem for Poisson’s TwoDimensional Equation, International Journal of Partial Differential Equations, Volume 2014, Article ID 680760, 8 pages, Hindawi Publishing Corporation, 2014
The BitsadzeSamarskii nonlocal boundary value problem is considered. Variational formulation is done. The domain decomposition and Schwarztype iterative methods are used. The parallel algorithm as well as sequential ones is investigated.
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Lamara Bitsadze, Effective solution of the Dirichlet BVP of Thermoelasticity with microtemperatures for an elastic space with a spherical cavity, Seminar of I. Vekua Institute of Applied Mathematics REPORTS, Volume 40, 113, Tbilisi University Press, 2014
In the present paper the linear theory of thermoelasticity with microtemperatures is considered. The representation of regular solution for the equations of steady vibration of the 3D theory of thermoelasticity with microtemperatures is obtained. We use it for explicitly solving Dirichlet boundary value problem (BVP) for an elastic space with a spherical cavity. The obtained solutions are represented as absolutely and uniformly convergent series.
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Tomer Libal, Martin Riener, Mikheil Rukhaia, Advanced Proof Viewing in PROOFTOOL, In Christoph Benzmüller and Bruno Woltzenlogel Paleo: Proceedings Eleventh Workshop on User Interfaces for Theorem Provers (UITP 2014), EPTCS vol. 167, pp. 3547, Electronic Proceedings in Theoretical Computer Science, 2014
Sequent calculus is widely used for formalizing proofs. However, due to the proliferation of data, understanding the proofs of even simple mathematical arguments soon becomes impossible. Graphical user interfaces help in this matter, but since they normally utilize Gentzen's original notation, some of the problems persist. In this paper, we introduce a number of criteria for proof visualization which we have found out to be crucial for analyzing proofs. We then evaluate recent developments in tree visualization with regard to these criteria and propose the Sunburst Tree layout as a complement to the traditional tree structure. This layout constructs inferences as concentric circle arcs around the root inference, allowing the user to focus on the proof's structural content. Finally, we describe its integration into ProofTool and explain how it interacts with the Gentzen layout.
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Khimuri Rukhaia, Lali Tibua, Gela Chankvetadze, On an algorithmic process of establishing validity of some formulas of an unranked equational theory, Proceedings of Teoretical and Applied aspects of Programm Systems Development;TAAPSD 2014, kiev, 2014
Языки, в которых функциональные или предикатные
символы не имеют фиксированной арности (местности), в
последние годы стали предметом интенсивного изучения по
причине довольно широкой сферы их применимости [1]. Обычно
встречаются переменные двух типов: предметные переменные,
которые можно заменить одним термом, и последовательные
переменные (далее мы назовем их «предметными
последовательными переменными»), заменить которые можно
конечной последовательностью термов. В отличии от
вышеупомянутых языков, в изученном нами языке безранговой
эгалитарной теории встречаются два типа последовательностей
переменных: а) переменные предметной последовательности,
представить которые можно конечной последовательностью термов
и б) переменные пропозиционной последовательности, заменить
которые можно конечной последовательностью формул. Кроме
того, область операторов этой теории – , , , x , x , x не
зафиксирована – они безранговые операторы. Определение этих
операторов происходит в рамках рациональных правил введения
производных операторов Шалвы Пхакадзе [2]. На их основании в
216
безранговой эгалитарной теории были доказаны аналоги
результатов, полученных в эгалитарной теории Н. Бурбаки [3].
писок используемых источников
1. Kutsia T. Theorem Proving with Sequence Variables and Flexible
Arity Symbols / T. Kutsia // 9th International Conference, LPAR
2002 Tbilisi, Georgia, October 14–18, 2002 Proceedings. – 2002. –
P. 278291.
2. Пхакадзе Ш.С. Некоторые вопросы теории обозначений / Ш.С.
Пхакадзе. – Тбилиси: Издво Тбилисского университета, 1977. –
195 с.
3. Бурбаки Н. Теория Множеств / Н. Бурбаки. – Москва: Мир,
1965. – 456 с.
222
4. Rukhaia Kh. One Method of Constructing a Formal System / Kh.
Rukhaia, L. Tibua, G. Chankvetadze, B. Dundua // Applied
Mathematics, Informatics and Mechanics. – 2006. – V. 11, N. 2. – P.
8189.
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Onishchenko Oleg, Oleg Pokhotelov, Wendell Horton, Tamaz Kaladze, Rolls of the internal gravity waves in the Earth's atmosphere, Annales Geophysicae, v.32, No.2, pp 181186, Copernicus Publications for the European Geosciences Union, 2014
The effect of the wind shear on the roll structures of nonlinear internal gravity waves (IGWs) in the Earth's atmosphere with the finite vertical temperature gradients is investigated. A closed system of equations is derived for the nonlinear dynamics of the IGWs in the presence of temperature gradients and sheared wind. The solution in the form of rolls has been obtained. The new condition for the existence of such structures was found by taking into account the roll spatial scale, the horizontal speed and wind shear parameters. We have shown that the roll structures can exist in a dynamically unstable atmosphere.
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Tamaz Kaladze, Shahzad Mahmood, Ionacoustic cnoidal waves in plasmas with warm ions and kappa distributed electrons and positrons, Physics of Plasmas, v.21, No.3, 032306, American Institute of Physics, 2014
Electrostatic ionacoustic periodic (cnoidal) waves and solitons in unmagnetized electronpositronion (EPI) plasmas with warm ions and kappa distributed electrons and positrons are investigated. Using the reductive perturbation method, the Kortewegde Vries (KdV) equation is derived with appropriate boundary conditions for periodic waves. The corresponding analytical and various numerical solutions are presented with Sagdeev potential approach. Differences between the results caused by the kappa and Maxwell distributions are emphasized. It is revealed that only hump (compressive) structures of the cnoidal waves and solitons are formed. It is shown that amplitudes of the cnoidal waves and solitons are reduced in an EPI plasma case in comparison with the ordinary electronion plasmas. The effects caused by the temperature variations of the warm ions are also discussed. It is obtained that the amplitude of the cnoidal waves and solitons decreases for a kappa distributed (nonthermal) electrons and positrons plasma case in comparison with the Maxwellian distributed (thermal) electrons and positrons EPI plasmas. The existence of kappa distributed particles leads to decreasing of ionacoustic frequency up to thermal ions frequency.
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Futatani Shimpei, Wendell Horton, Laila Kahlon, Tamaz Kaladze, Shear flow driven RossbyKhantadze electromagnetic planetary vortices in the ionospheric Elayer, EPL (Europhysics Letters), v.106, No.2, 29001, IOP Publishing, 2014
A system of equations describing the nonlinear interaction of coupled RossbyKhantadze electromagnetic waves with a sheared zonal flow in the Earth's ionospheric Elayer is obtained. For the linear regime the corresponding region of phase velocities is analyzed and the appropriate stability condition of zonal flow is deduced. It is shown that the sheared zonal flow may excite solitary vortical structures in the form of a row of counterrotating vortices whose amplitudes decrease with the increase of the zonal flow parameter. This conclusion is consistent with the stabilizing idea of a sheared zonal flow. The possibility of an intense magneticfield generation is shown.
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Tamaz Kaladze, Nodar Tsintsadze, James W. Van Dam , Wendell Horton, Dynamics of the Electromagnetic Ion Cyclotron Nonlinear Solitary Structures in the Inner Magnetosphere, Journal of Physics: Conference Series, v.511, 012049, IOP Publishing, 2014
The nonlinear interaction of the electromagnetic ion cyclotron (EMIC) frequency waves
with plasma particles in the inner magnetosphere is studied. The emission is considered to be
circularly polarized electromagnetic waves propagating along the almost constant dipole geomagnetic
field in the equatorial region of the inner magnetosphere. Under the action of the ion cyclotron
ponderomotive force excitation of the magnetosonic waves through the amplitude modulation of the
EMIC waves is investigated. Two dimensional nonlinear Schrodinger equation for the EMIC waves is
derived. In the stationary case two solutions of the nonlinear Schrodinger equation with distinct
natures are found. The generation of both vortices and of a quasistatic magnetic field across the
geomagnetic field lines is discussed.
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Manana Kachakhidze, Nino Kachakhidze, Tamaz Kaladze, Explanation of LithosphereAtmosphereIonosphere Coupling System Anomalous Geophysical Phenomena on the Basis of the Model of Generation of Electromagnetic Emission Detected Before Earthquake, eprint arXiv:1407.5979, Cornell University Press , 2014
Recent satellite and groundbased observations proved that during an earthquake preparation period VLF/LF and ULF electromagnetic emissions are observed in the seismogenic area. The present work offers possible physical bases of earth electromagnetic emission generation detected in the process of earthquake preparation. According to the authors of the present paper electromagnetic emission in radiodiapason is more universal and reliable than other earthquake indicators and VLF/LF electromagnetic emission might be declared as the main precursor of earthquake. It is expected that in the period before earthquake namely earth electromagnetic emission offers us the possibility to resolve the problem of earthquake forecasting by definite precision and to govern coupling processes going on in lithosphereatmosphereionosphere (LAI) system.
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David Gordeziani, Iulia Meladze, Nonlocal Contact Problem for Two Dimensional Linier Elliptic Equations , Bulletin of the Georgian National Academy of Sciences vol.8, no 1, 2014, 4046, Georgian National Academy of Sciences, 2014
A nonlocal contact boundary problem for twodimensional linear elliptic equations is stated and investigated. The uniqueness of the solution is proved. The iteration process is constructed, which allows one not only to prove the existence of a regular solution of the problem, but also to develop an approximate algorithm of its solution. The solution of a nonlocal contact problem is reduced to the solution of classical boundary value problems, in particular to the solution of Dirichlet problems
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Maia Aptsiauri, Mikheil Gagoshidze , On One Nonlinear Averaged IntegroDifferential System with Source Terms, Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, Vol. 28, 58, Tbilisi University Press, 2014
One nonlinear averaged integrodifferential system with source terms is considered. The model arises on mathematical simulation of the process of penetration of a magnetic field into a substance. Semidiscrete difference scheme is studied.
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Archil Papukashvili, Yusuf Gulver , Zurab Vashakidze, To numerical realizations and stability of calculating process of some problems of theory of elasticity for crossshaped regions, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics. Volume 28, 2014. p. 9497. , Tbilisi University Press , 2014
New algorithms of the approached decision of Poisson equation (Dirichlet boundary problem) for a twodimensional crosswise body by means of Schwartz iterative method are considered. The unknown function expands into the FourierLegendre series. Differences of Legendre polynomial are used as basic functions. The fivedot linear system of the algebraic equations concerning unknown coefficients is received. The program code (on the basis of Matlab) for the approached decision of the considered problem is created; corresponding numerical experiments are made which revealed stability of the account process.
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Temur Jangveladze, Maia Kratsashvili, Asymptotic Behavior of Solution and SemiDiscrete Difference Scheme for One Nonlinear IntegroDifferential Equation with Source Term, Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, V.28, p.5053, Tbilisi University Press, 2014
One nonlinear partial integrodifferential equation with source term is considered. The model arises at describing penetration of a magnetic field into a substance and is based on the Maxwell system. Large time behavior of solution of the initialboundary value problem as well as semidiscrete finite scheme are studied. More wide class of nonlinearity is considered than one has been already investigated.
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Nuri Khomasuridze, Roman Janjgava, Natela Zirakashvili, Some nonclassical thermoelasticity problems for a rectangular parallelepiped, Meccanica, Volume 49, Issue 6, pp 13371342, Springer, 2014
In the Cartesian system of coordinates, thermoelastic equilibrium of an isotropic homogeneous rectangular parallelepiped is considered. On the lateral faces of a parallelepiped either symmetry or antisymmetry conditions are defined while the top and bottom faces are free of stress. The problem is that to define the temperature on the top and bottom faces of a parallelepiped so that the normal displacement or the tangential displacements would take a priori fixed values on some two planes parallel to the bases. The problems are solved analytically using the method of separation of variables. The problems are nonclassical, but they differ from other nonclassical problems known in literature and are of a practical importance.
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Nuri Khomasuridze, Roman Janjgava, Natela Zirakashvili, ANALYTICAL SOLUTION OF CLASSICAL AND NONCLASSICAL BOUNDARY VALUE CONTACT PROBLEMS OF THERM OELASTICITY FOR SPHERICAL BODIES CONSISTING OF COMPRESSIBLE AND INCOMPRESSIBLE ELASTIC LAYERS, APPLIED MATHEMATICS, INFORMATICS AND MECHANICS, AMIM, Vol. 19, No 1, 2014, 1739, Tbilisi University Press, 2014
Static thermoelastic equilibrium is considered for an Nlayer along the radial coordinate body bounded by coordinate surfaces of a spherical system of coordinates. Each layer is isotropic and homogeneous and some of the layers may be composed of an incompressible elastic material. On the spherical surfaces of the involved body
changes in the temperature or its normal derivative, stresses, displacements or their combinations are defined while on the remaining part of the boundary special type of homogeneous conditions are given. The stated problems are analytically solved using the method of separation of variables, the general solution being represented by means of harmonic functions. Problem solution is reduced to the solution of systems of algebraic equations with block diagonal matrices.
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Nuri Khomasuridze, Natela Zirakashvili, Roman Janjgava, Miranda Narmania, Analytical solution of classical and nonclassical boundary value contact problems of thermoelasticity for a rectangular parallelepiped consisting of compressible and incompressible elastic layers and, Archive of Applied Mechanics, Volume 84, Issue 12, pp 17011713, Springer, 2014
The paper deals with a static thermoelastic equilibrium of an Nlayer rectangular parallelepiped. The layers of the considered body are made of an isotropic homogeneous elastic material. A case when some of the layers consist of incompressible elastic materials, which are also assumed to be isotropic and homogeneous, is considered as well. Boundary conditions of symmetric or antisymmetric continuous extension of the solution are imposed on the lateral facets of the parallelepiped. Between the layers contact conditions of rigid, sliding or other type of contact can be defined. On the upper and lower facets of the parallelepiped, arbitrary boundary conditions are defined. Solution of the stated problems is made analytically using the method of separation of variables. The solution of the problems is reduced to the solution of systems of linear algebraic equations with block diagonal matrices. In the conclusion, a practical example establishing the elastic equilibrium of a threelayer rectangular parallelepiped is given.
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Teimurazi Davitashvili, Meri Sharikadze, On One Mathematical Model of Oil Penetration into Nonhomogeneous Soil, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics, 28, 2023, Tbilisi University Press, 2014
In the present article a mathematical model of the accidental spilled liquid’s penetration into the soil having nonhomogeneous structure in the vertical direction is discussed. The mathematical model is based on the integration of the nonlinear and nonstationary systems of the hydrodynamic equations. The numerical model is taking into consideration the spilled liquid’s evaporation process, the main characteristic parameters of soil and some physicalchemical processes characterizing nonstationary processes in the soil. Some results of numerical calculations are presented
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Nuri Khomasuridze, Roman Janjgava, Natela Zirakashvili, ANALYTICAL SOLUTION OF CLASSICAL AND NONCLASSICAL BOUNDARY VALUE CONTACT PROBLEMS OF THERMOELASTICITY FOR CYLINDRICAL BODIES CONSISTING OF COMPRESSIBLE AND INCOMPRESSIBLE ELASTIC LAYERS, APPLIED MATHEMATICS, INFORMATICS AND MECHANICS,Vol. 19, No 2, 2014, 1835, Tbilisi University Press, 2014
Static thermoelastic equilibrium is considered for an Nlayer along the radial coordinate body bounded by coordinate surfaces of a circular cylindrical system of coordinates. Each layer is isotropic and homogeneous and some of the layers may be composed of an incompressible elastic material. On the flat boundaries of the cylindrical body boundary conditions of either symmetrical or antisymmetrical continuous extension of the solution are imposed. Between the layers contact conditions of rigid, sliding or other type of contact may be defined. The stated problems are solved using the method of separation of variables,the general solution being represented by means of harmonic functions. The solution of the problems is reduced to the solution of systems of algebraic equations with block diagonal matrices. At the end of the paper an application example is given which illustrates the applied approach for an analytical solution of problems.
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Natela Zirakashvili, Strain control of the elastic infinite bodies with elliptic hole and cracks by means of boundary conditions variation, Report of Enlarged Session of the Seminar VIAM, V.28, pp. 118121, Tbilisi University Press, 2014
A twodimensional boundary value problem of elastic equilibrium of a planedeformed infinite body with an elliptic opening is studied. A part of the opening is fixed and from some points of the unfixed part of the cylindrical boundary there come curvilinear finite cracks. The problem is to find conditions for the fixed parts of the opening so that the damage caused by the crack, i.e. stresses on its surface, should be minimal. We should note that the crack ends inside the body are curved. The curve radii vary similar to boundary conditions.
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Temur Jangveladze, Zurab Kiguradze, Mikheil Gagoshidze , Large Time Behavior of Solution and SemiDiscrete Scheme for One Nonlinear IntegroDifferential Equation with Source Terms, Journal of Applied Mathematics and Mechanics, V.19, N2, p.1017, Elsevier, 2014

Manana Kachakhidze, Nino Kachakhidze, Tamaz Kaladze, LithosphereAtmosphereIonosphere Coupling System, St. Andrew The FirstCalled Georgian University of The Patriarchy of Georgia Iv. Javakhishvili Tbilisi State University, Institute of Applied Mathematics, Publishing House “UNIVERSAL”, 2014
The present work offers model of earth electromagnetic emission generation detected in the process of earthquake preparation on the basis of electrodynamics.Besides, scheme of the methodology of earthquake forecasting is created based on avalanchelike unstable model of fault formation and an analogous model of electromagnetic contour, synthesis of which, is rather harmonious. According to the authors of the work electromagnetic emission in radiodiapason is more universal and reliable that other anomalous variations geophysical phenomena in earthquake preparation period. Besides, VLF/LF electromagnetic emission might be declared as the main precursor of earthquake because it might turn out very useful with the view of prediction of large (M>5) inland earthquakes and to govern processes going on in lithosphereatmosphereionosphere coupling (LAIC) system.
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Jemal Rogava, Mikheil Tsiklauri, Convergence of a semidiscrete scheme for an abstract nonlinear second order evolution equation, Applied Numerical Mathematics Volume75, Pages 2236, , 2014

David Gulua, Jemal Rogava, Perturbation algorithm for implementing a finite difference approximation to an abstract evolutionary problem and explicit error estimation of its solution, Doklady Mathematics, Volume 89, Issue 3, pp 335–337, , 2014

Nana Dikhaminjia, Jemal Rogava, Mikheil Tsiklauri, Construction and Investigation of a Fourth Orderof Accuracy Decomposition Schemefor Nonhomogeneous Multidimensional Hyperbolic Equation, Numerical Functional Analysis and Optimization, Volume 35, Issue 3,p. 275293, , 2014

Natalia Chinchaladze, On a Cusped Doublelayered Prismatic Shell, Proceedings of I. Vekua Institute of Applied Mathematics, v. 64, 1323, Tbilisi University Press, 2014
The present paper is devoted to the system of degenerate partial differential equations that arise from the investigation of elastic two layered prismatic shells. The wellposedness of the boundary value problems (BVPs) under the reasonable boundary conditions at the cusped edge and given displacements at the noncusped edge is studied.
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Natalia Chinchaladze, Hierarchical Models for Biofilms Occupying Thin Prismatic Domains, Bulletin of TICMI, vol.18, No. 2, 102109, Tbilisi University Press, 2014
In this paper hierarchical models of biofilms occupying a thin prismatic domain are considered
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Natalia Chinchaladze, On Some Analytic Methods for Calculating of Cusped Prismatic Shells, PAMM, vol. 14, Issue 1, 185–186, Wiley, 2014
Some analytic methods for calculating of prismatic shells with two cusped edges are given.
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Mariam Beriashvili, Aleks Petre Kirtadze, ON RELATIVE MEASURABILITY OF REALVALUED FUNCTIONS WITH RESPECT TO SOME MEASURES IN THE SPACE R^N, Proc. A. Razmadze Math. Inst. 164(2014), 95–97, TSU / Proc. A. Razmadze Math. Inst., 2014
There exists nonzero, σfinite, diffused Borel measure χ on
RN, which is invariant with respect to an everywhere dense vector subspace
of RN and, in addition, is metrical transitive (i. e., ergodic) with respect
to the same subspace. We discuss relative measurability of realvalued functions with respect to some measures in the space R^N
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Elizbar Nadaraya, Petre Babilua, Grigol Sokhadze, On integral square deviation of two kernel estimators of Bernoulli regression functions, Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 28 (2014), 7477., Tbilisi State University Press, 2014
The limiting distribution of an integral square deviation between two kernel type estimators of Bernoulli regression functions is established in the case of two independent samples. The criterion of testing is constructed for both simple and composite hypotheses of equality of two Bernoulli regression functions. The question of consistency is studied. The asymptotics of behavior of the power of test is investigated for some close alternatives.
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Mariam Beriashvili, Aleks Petre Kirtadze, On the uniqueness property of nonseparable extensions of invariant Borel measures and relative measurability of realvalued functions, Georgian Mathematical Journal Volume 21 Issue 1, 4957, DE GRUYTER, 2014
It is shown that the class of all nonseparable extensions of a nonzero σfinite Borel measure in the topological vector space ℝℕ, which are invariant under some everywhere dense continual subgroup of ℝℕ and which possess the uniqueness property, has maximal cardinality 22c. Some related questions concerning the measurability properties of realvalued functions with respect to the class of nonseparable measures are also discussed.
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Elizbar Nadaraya, Petre Babilua, Grigol Sokhadze, Functionals of GasserMuller estimators, Turkish J. Math. 38 (2014), no. 6, 10901101., Tubitak, 2014
The asymptotic properties of a general functional of the Gasser–Muller estimator are investigated in the Sobolev space. The convergence rate, consistency, and central limit theorem are established.
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Elizbar Nadaraya, Petre Babilua, Grigol Sokhadze, On testing the hypothesis of equality of two Bernoulli regression functions, Bull. Georgian Natl. Acad. Sci. (N.S.) 8 (2014), no. 1, 1826., Georgian National Academy of sciences Press, 2014
The limiting distribution of an integral square deviation between two kernel type estimators of Bernoulli regression functions is established in the case of two independent samples. The criterion of testing is constructed for both simple and composite hypotheses of equality of two Bernoulli regression functions. The question of consistency is studied. The asymptotics of behavior of the power of test is investigated for some close alternatives.
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Elizbar Nadaraya, Petre Babilua, Grigol Sokhadze, About Testing the Hypothesis of Equality of Two Bernoulli Regression Curves, Journal of Mathematical Theory and Modeling. vol. 4, no. 9, 142150, 2014. , IISTE, 2014
The limiting distribution of an integral square deviation between two kernel type estimators of Bernoulli regression functions is established in the case of two independent samples. The criterion of testing is constructed for both simple and composite hypotheses of equality of two Bernoulli regression functions. The question of consistency is studied. The asymptotics of behavior of the power of test is investigated for some close alternatives.
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Tengiz Tetunashvili, Shakro Tetunashvili, On coefficients of series with respect to the Rademacher system, Trans. A.Razmadze Math. Inst., 165, 142146 , I. Javakhishvili Tbilisi State University, 2014
In the article theorems are given which are related to the reconstruction of coefficients of a $d$multiple Rademacher series (where $d$ is any natural number such that $d\geq 1$) by means of values of the sum of this series at appropriately chosen $2^{d}$ points. Well known theorems connected with Rademacher series as direct consequences of these theorems are considered.
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Ushangi Goginava, Artur Sahakian, On the convergence and summability of double WalshFourier series of functions of bounded generalized variation, Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 49 (6), 321–333, Allerton Press, 2014
The convergence of partial sums and Cesáro means of negative order of double WalshFourier series of functions of bounded generalized variation is investigated.
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Ushangi Goginava, Leri Gogoladze, Convergence in measure of logarithmic means of multiple Fourier series, Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 49 (2), 7077, Allerton Press, 2014
The maximal Orlicz space such that the mixed logarithmic means of rectangular partial sums of multiple Fourier series for the functions from this space converge in measure is found.
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Ushangi Goginava, Leri Gogoladze, Convergence in Measure of Strong logarithmic means of double Fourier series, Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 49 (3), 109116, Allerton Press, 2014
Nörlund strong logarithmic means of double Fourier series acting from space L log L (T2) into space L p (T2), 0 < p < 1, are studied. The maximal Orlicz space such that the Nörlund strong logarithmic means of double Fourier series for the functions from this space converge in twodimensional measure is found.
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Gia Avalishvili, Mariam Avalishvili, David Gordeziani, On the Investigation of Dynamical Hierarchical Models of Elastic MultiStructures Consisting of ThreeDimensional Body and Multilayer SubStructure, Bulletin of the Georgian National Academy of Sciences, 8, no. 3, 2031, Georgian National Academy of Sciences, 2014
In the present paper twodimensional model of prismatic shell is constructed. Existence and uniqueness of the solution of corresponding boundary value problem are proved, the rate of approximation of the solution of original problem by vectorfunction restored from the solution of twodimensional problem is estimated.
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Mikheil Rukhaia, Towards Theorem Proving Techniques in Formula Schemata, In Jangveladze, Temur and Kiguradze, Zurab (eds.): Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, vol. 28. pp. 102–105, Tbilisi University Press, 2014
The theorem proving techniques are divided into two parts, goaldirected and refutational. In this paper we present a goaldirected proofsearch algorithm, which is based on a sequent calculus. Usually sequent calculus inference rules can be applied freely, producing a redundant search space. The technique, called focusing, removes this nondeterminism and redundancy in proofsearch. Although we do not present a focused calculus, our algorithm is obtained according to the principles of focusing, achieving similar effect.
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Nino Khatiashvili, On the Hexagonal Quantum Billiard, Sem. I. Vekua Inst. Appl. Math., REPORTS, Vol,40;pp.1427.#GNSF/ST08/3395, TSU, 2014
In the paper a planar classical quantum billiard in the hexagonal type areas with the hard wall conditions is considered. The process is described by the Helmholtz Equation in the hexagon and hexagonal rug with the homogeneous boundary conditions. By means of the conformal mapping method the problem is reduced to the elliptic partial differential equation in the rectangle with the homogeneous boundary condition. It is assumed that one parameter of mapping is sufficiently small. In this case the equation is simplified and analyzed. The asymptotic solutions are obtained. The spectrum and the corresponding eigenfunctions are found near the boundary of the hexagon. The wave functions are found in terms of the Bessel’s functions. The results are applied for the estimation of the energy levels of electrons in graphene.
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Tengiz Tetunashvili, Shakro Tetunashvili, On divergent orthogonal series by the methods of summability with variable order, Trans. A.Razmadze Math. Inst., 165, 147153, I. Javakhishvili Tbilisi State University, 2014
In the article methods of summability with a variable order are presented and theorems related to orthogonal series divergent by these methods are formulated.
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Roman Koplatadze, Oscillation criteria for differential and discrete equations with several delays, Bulletin of TICMI, 18, 1017, Ivane Javakhishvili Tbilisi State University Press, 2014
Consider the first order differential and difference equations.
Sufficient oscillation conditions are presented for this equations

Roman Koplatadze, Alexander Domoshnitsky, On asymptotic behavior of solutions of generalized EmdenFowler differential equations with delay argument, Abstract and Applied Analysis, Art. ID 168425, 13 pp., Elsevier, 2014
Considered on asymptotic behavior of solutions of
generalized EmdenFowler differential equations with delay argument
In the case μ(t) ≡ const > 0, the oscillatory properties of given equation are extensively studied, where as for μ(t) ≢ const, to the best of authors’ know
ledge, problems of this kind were not investigated at all. We also establish new sufficient conditions for the equation to have Property B.
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Roman Koplatadze, Oscillation criteria for higher order nonlinear functional differential equations with advanced argument, J Math Sci 197, 45–65, Elsevier, 2014
We consider a differential equation
We say that the equation is almost linear if the condition lim inf
t μ(t) =1 is satisfied. At the same time, if lim sup t μ(t) ≠ 1 or lim inf t μ(t) ≠ 1, then
Eq. is called an essentially nonlinear differential equation. The oscillatory properties of almost linear
differential equations have been extensively studied. In the paper, new sufficient (necessary and
sufficient) conditions are established for a general class of essentially nonlinear functional
differential equations to have Property A.
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Temur Jangveladze, Some Properties and Numerical Solution of OneDimensional Nonlinear Electromagnetic Diffusion System. Advances in Applied and Pure Mathematics, Proceedings 7th International Conference on Finite Differences, Finite Elements, Finite Volumes, Boundary Elements, p.96100, Elsevier, 2014

Lamara Bitsadze, Fundamental solution in the theory of poroelasticity of steady vibrations for solids with double porosity, Proceedings of I. Vekua Institute of Applied Mathematics Volume 64, 312, Tbilisi University Press, 2014
In this paper the 2D full coupled theory of steady vibrations of poroelasticity for materials with double porosity is considered. There the fundamental and singular matrixes of solutions are constructed in terms of elementary functions. Using the fundamental matrix we will construct the simple and double layer potentials and study their properties near the boundary.
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Giorgi Geladze, Classification of foehns and their numerical modeling, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics, v. 28, pp. 3235, Tbilisi University Press, 2014
Genesis of Foehns is in detail investigated. They are classified on dryadiabatic, mostadiabatic and mostdryadiabatic Foehns. A problem about numerical modeling of Foehns in frame of a at, twodimensional mesoscale boundary layer is stated. The problem is at a stage of numerical realisation. The first encouraging results are received.
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Giorgi Geladze, Nino Begalishvili, Nodar Begalishvili, On the Mathematical Models of Transfer and Wet Washing Down of Aerozol in the Atmosphere, Transactions of the Institute of hydrometeorology at the Georgian Technical University; V. 120, pp. 89 – 92, GTU press, 2014
The process of wet washing down of aerosol particles in the atmosphere is examined. For the specially homogenous dispersive system containing aerosol particles and droplets (crystals), the analytic solution of coagulation kinetic equation is obtained under the conditions of constant generation of aerosol. The source in proportional to the initial distribution of particles. Using the solution the efficiency of wet washing down is assessed for different types of liquid precipitation (the relaxation time of aerosol particles). Microphysical lows of wet washing down in case of gravity coagulation are obtained as well.
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Kartlos Joseph Kachiashvili, Comparison of Some Methods of Testing Statistical Hypotheses. (Part I. Parallel Methods), International Journal of Statistics in Medical Research, 3(2): 174189, Published by: Lifescience Global, 2014
The article focuses on the discussion of basic approaches to hypotheses testing, which are Fisher, Jeffreys, Neyman, Berger approaches and a new one proposed by the author of this paper and called the constrained Bayesian method (CBM). Wald and Berger sequential tests and the test based on CBM are presented also. The positive and negative aspects of these approaches are considered on the basis of computed examples. Namely, it is shown that CBM has all positive characteristics of the abovelisted methods. It is a datadependent measure like Fisher’s test for making a decision, uses a posteriori probabilities like the Jeffreys test and computes error probabilities Type I and Type II like the NeymanPearson’s approach does. Combination of these properties assigns new properties to the decision regions of the offered method. In CBM the observation space contains regions for making the decision and regions for nomaking the decision. The regions for nomaking the decision are separated into the regions of impossibility of making a decision and the regions of impossibility of making a unique decision. These properties bring the statistical hypotheses testing rule in CBM much closer to the everyday decisionmaking rule when, at shortage of necessary information, the acceptance of one of made suppositions is not compulsory. Computed practical examples clearly demonstrate high quality and reliability of CBM. In critical situations, when other tests give opposite decisions, it gives the most logical decision. Moreover, for any information on the basis of which the decision is made, the set of error probabilities is defined for which the decision with given reliability is possible.
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Kartlos Joseph Kachiashvili, Comparison of Some Methods of Testing Statistical Hypotheses. Part II. Sequential Methods, International Journal of Statistics in Medical Research, 3: 189197, Published by: Lifescience Globa, 2014
The specific features of hypotheses testing regions of the Berger’s $T*$ test and CBM (see Part I of this paper), namely, the existence of the nodecision region in the $T*$ test and the existence of regions of
impossibility of making a unique or any decision in CBM give the opportunities to develop the sequential tests on their basis. Using the concrete example taken from [5], below these tests are compared among themselves and with the Wald sequential test [55]. For clarity, let us briefly describe these tests.
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Kartlos Joseph Kachiashvili, The Methods of Sequential Analysis of Bayesian Type for the Multiple Testing Problem, Sequential Analysis, 33(1): 2338, Taylor & Francis Group, 2014
New sequential methods of multiple testing problems based on special properties of hypoNew sequential methods of multiple testing problems based on special properties of hypotheses acceptance regions in the constrained Bayesian tasks of testing hypotheses are offered. Results of an investigation on the properties of one of these methods are given. They show the consistency, simplicity, and optimality of the results obtained in the sense of the chosen criterion. The essence of the criterion is to restrict from above the probability of the error of one type and to minimize the probability of the error of the second type. The facts of the validity of the suitable properties of the method are proved. Examples of testing of hypotheses for the sequentially obtained independent samples from the multivariate normal distribution with correlated components are cited. They show the high quality of the proffered methods. The results of the Wald sequential method are given for the examples with two hypotheses and compared with the results obtained by the proffered method theses acceptance regions in the constrained Bayesian tasks of testing hypotheses are offered. Results of an investigation on the properties of one of these methods are given. They show the consistency, simplicity, and optimality of the results obtained in the sense of the chosen criterion. The essence of the criterion is to restrict from above the probability of the error of one type and to minimize the probability of the error of the second type. The facts of the validity of the suitable properties of the method are proved. Examples of testing of hypotheses for the sequentially obtained independent samples from the multivariate normal distribution with correlated components are cited. They show the high quality of the proffered methods. The results of the Wald sequential method are given for the examples with two hypotheses and compared with the results obtained by the proffered method.
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George Jaiani, A BoundaryContact Problem for Two Rectangularly Linked Elastic Bars, BULL. TICMI, 18 (2), 82101, Tbilisi University Press, 2014
Static and dynamical boundarycontact problems for two rectangularly (with respect to their longitudinal axes) linked elastic bars with variable rectangular crosssections are considered within the framework of the (0, 0) approximation of hierarchical models. They may have a contact interface either really (in this case the bars may have different elastic constants) or mentally (in the case when two bars represent an entire (undivided) body).
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Kartlos Joseph Kachiashvili, Investigation of the method of sequential analysis of Bayesian type, Journal of Advances in Mathematics, 18(1): 13671380, KHALSA PUBLICATION, 2014

Kartlos Joseph Kachiashvili, Probability of errors in sequential methods of Bayesian type, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics, 28: 5861, Tbilisi Yniversity press, 2014
Formulae for computation of probability of errors in sequential method of Bayesian type are offered. In particular, some relations between the errors of the first and the second kinds in constrained Bayesian task and in sequential method of Bayesian type depending on the divergence between the tested hypotheses are given. Dependencies of the Lagrange multiplier and the risk function on the probability of incorrectly accepted hypotheses are also presented. Theses results are necessary for computation of errors of made decisions attesting multiple hypotheses using the offered new sequential methods of testing hypotheses. Computation results of some examples confirm the rightness of theoretical analysis.
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Gia Giorgadze, Nugzar Makhaldiani, On the algorithmic and non algorithmic solvable problems from quantum computing point of view, Proc. I. Vekua Inst. Appl. Math 64, 2430, Tbilisi University Press, 2014
Quantum computations can be implemented not only by the action
of quantum circuits, but by the adiabatic evolution of a system’s Hamiltonian. Quantum adiabatic statement allows to solve some classically non algorithmic problems. Our reasoning favor of this argument.
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Gogi Pantsulaia, Givi Giorgadze, A DESCRIPTION OF THE BEHAVIOR OF SOME PHASE MOTIONS IN TERMS OF ORDINARY AND STANDARD" LEBESGUE MEASURES" IN R [infinity], Georgian International Journal of Science, Technology and Medicine 6 (4), 285, Hauppauge, NY : Nova Science Publishers, 2014
This article presents main results of investigations of the authors which were obtained during the last five years by the partially support on the Shota Rustaveli National Science Foundation (Grant no. 31–24). These results are Liouvilletype theorems and describe the behavior of various phase motions in terms of ordinary and standard “Lebesgue measures” in R∞. In this context, the following three problems are discussed in this paper: Problem 1. An existence and uniqueness of partial analogs of the Lebesgue measure in various function spaces; Problem 2. A construction of various dynamical systems with domain in function spaces defined by various partial differential equations; Problem 3. To establish the validity of Liouvilletype theorems for various dynamical systems with domains in function spaces in terms of partial analogs of the Lebesgue measure.
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Gogi Pantsulaia, Nino Rusiashvili, On a certain version of the Erdös problem, Georgian International Journal of Science, Technology and Medicine 6 (3), 257, Hauppauge, NY : Nova Science Publishers, 2014
A certain version of the Erdos problem is studied. More precisely, it is proved that there does
not exist a finite constant c such that each plane set with the outer Lebesgue measure greater
than c contains the vertices of a triangle of area 1. It is shown that a sentence ”each plane set E
with Lebesgue outer measure +∞ contains the vertices of a triangle of area 1” is independent
from the theory (ZF)&(DC). The Erdos problem is studied for the shymeasure in an infinitedimensional separable Banach space and it is established that any number from the interval [0,1[
is Erdos constant for such a measure. It is constructed an example of a thick (in the sense of
shyness) subset of 2
l which does not contain vertices of a triangle of area 1.
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Gogi Pantsulaia, A Classification OF NONMEASURABLE REALVALUED FUNCTIONS DEFINED ON A METRIC SPACE, Georgian International Journal of Science, Technology and Medicine 6 (3), 249, Hauppauge, NY : Nova Science Publishers, 2014
Some classes of realvalued functions defined on a metric space V equipped with a nonzero sigmafinite diffused Borel measure µ were introduced and relationships between them (in the sense of inclusion) are studied. In particular, it is shown that when V is a Polish metric space then the properties of µmassiveness along trajectories of all continuous functions on V and of µmassiveness along trajectories of all measurable functions on V coincide. It is demonstrated also that relationships between these classes are rather different and surprising if (V, ρ) is not separable.
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Gogi Pantsulaia, Aleks Petre Kirtadze, ON WITSENHAUSENKALAI CONSTANTS FOR INFINITEDIMENSIONAL SURFACE DYNAMICAL MEASURES, Georgian International Journal of Science, Technology and Medicine 6 (2), 167, Hauppauge, NY : Nova Science Publishers, 2014

Gogi Pantsulaia, Tepper Gill, Givi Giorgadze, On a heat equation in an infinitedimensional separable Banach space with Schauder basis, Georgian International Journal of Science, Technology and Medicine 6 (2), 149, Hauppauge, NY : Nova Science Publishers, 2014
By using an infinitedimensional "Lebesgue measure" in an infinitedimensional separable Banach space B with Schauder basis a solution of a heat equation with initial value problem on B is constructed. Properties of uniformly distributed realvalued sequences in an interval of the real axis are used for a construction of a certain algorithm which gives an approximation of corresponding solutions.
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Gogi Pantsulaia, Aleks Petre Kirtadze, ON A CERTAIN MODIFICATION OF P. ERDÖS PROBLEM FOR TRANSLATIONINVARIANT QUASIFINITE DIFFUSED BOREL MEASURES IN POLISH GROUPS THAT ARE NOT LOCALLY COMPACT, Georgian International Journal of Science, Technology and Medicine 6 (2), 119, Hauppauge, NY : Nova Science Publishers, 2014
It is shown that for every translationinvariant quasifinite diffused Borel measure
µ in an uncountable nonlocally compact Polish group G that is dense in himself there
does not exist a positive constant c such that each Borel set E with the µmeasure
bigger than c contains three points such that an area defined by that points is equal
to one. This answers negatively to a certain modification of P. Erd¨os problem [P.
Erd¨os, Settheoretic, measuretheoretic, combinatorial, and number theoretic problems concerning point sets in Euclidean space, Real Anal. Exchange, 4(2), (1978/79),
113–138] stated by us for a translationinvariant quasifinite diffused Borel measure in
an uncountable nonlocally compact Polish group that is dense in himself.
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Gogi Pantsulaia, ON MAXIMAL PLANE SETS CONTAINING ONLY THE VERTICES OF A TRIANGLE WITH AREA LESS THAN ONE, Georgian International Journal of Science, Technology and Medicine 6 (2), 113, Hauppauge, NY : Nova Science Publishers, 2014
It is proved an existence of maximal ”small” plane sets in R^2 which contain only the vertices of a triangle of area less than one. It is shown also that the closing of each maximal ”small” plane set in R^2 contains the vertices of a triangle of area one.
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Gogi Pantsulaia, Givi Giorgadze, ON A REPRESENTATION OF THE SOLUTION OF A CERTAIN GENERALIZED HEAT EQUATION OF MANY VARIABLES IN A MULTIPLE TRIGONOMETRIC SERIES, Georgian International Journal of Science, Technology and Medicine 6 (2), 133, Hauppauge, NY : Nova Science Publishers, 2014
By using the technique of "Fourier differential operator" in R ∞ and Laplace transforms, a representation in a multiple trigonometric series of the solution of a certain generalized heat equation of many variables is obtained.
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Giorgi Geladze, Nodar Begalishvili, Nino Begalishvili, About classification and numerical modelling of Foehns, Transaction of the Instituti of Hydrometeorology, Georgian Technical University, V.120, pp.16 21, GTU press, 2014
Genesis of Foehns is in detail investigated. They are classified on dryadiabatic, mostadiabatic and mostdryadiabatic Foehns. It is stated a problem about numerical modelling of Foehns in frame of a flat, twodimensional mesoscale boundary layer. The problem is at a stage of numerical realisation. The first encouraging results are received.
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Gogi Pantsulaia, ON STRANGE NULL SETS IN SOME VECTOR SPACES, Georgian International Journal of Science, Technology and Medicine 6 (1), 41, Hauppauge, NY : Nova Science Publishers, 2014
For a group Γ of all rotations of the plane R^sup 2^ about it's origin, by using the technique developed in a paper [Kharazishvili A. B., Small sets in uncountable abelian groups. Acta Univ. Lodz. Folia Math. No. 7 (1995), 3139] it is proved an existence of a partition of the plane R^sup 2^ into absolutely Γnegligible subsets of R^sup 2^ for which an intersection of every element of the partition with each beam leaving the origin of R^sup 2^ includes exactly one line segment of length 1. By the method developed in the monograph [Pantsulaia G.R., Invariant and quasiinvariant measures in infinitedimensional topological vector spaces, Nova Science Publishers, Inc., New York, 2007. xii+234] it is shown that in Solovay's model an arbitrary nontrivial closed ball in an infinite dimensional nonseparable Banach space l^sup ∞^ is an infinitedimensionally Haar null set. This answers positively on the Problem 8 stated in [Shi H., MeasureTheoretic Notions of Prevalence, Ph.D.Dissertation (under Brian S. Thomson), Simon Fraser University, October 1997, ix+165] for Banach space l^sup ∞^.
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Temur Jangveladze, Some Properties of Solutions and Approximate Algorithms for One System of Nonlinear Partial Differential Equations, International Workshop on the Qualitative Theory of Differential Equations, QUALITDE – 2014, Dedicated to the 125th birthday anniversary of Professor A. Razmadze, p.5457, Tbilisi University Press, 2014
In mathematical modeling of many natural processes nonlinear nonstationary differential models are received very often. One such model is obtained at mathematical modeling of processes of electromagnetic field penetration in the substance. For thorough description of electromagnetic field propagation in the medium, it is desirable to take into consideration different physical effects, first of all heat conductivity of the medium has to be taken into consideration. In this talk difference schems for such systems are discussed.
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Inga Samkharadze, On mathematical modeling of some local meteorological processes for particular regions of Georgia , Tansactions of the Instituti of Hydrometeorology of Georgian Technical University. 2014, vol.120 , pp.1015., GTU press, 2014

Inga Samkharadze, Zurab Khvedelidze, Teimurazi Davitashvili, M. Tatishvili, N. Zotikishvil, On mathematical modeling of some local meteorological processes for particular regions of Georgia, Tansactions of the Instituti of Hydrometeorology of Georgian Technical University, vol.120, pp.1015, GTU press, 2014
In present report the peculiarities of the hydrodynamical flows in a narrow canals with small slope bottom ,at low velocities of the stream , have been studied. It has been shown that the velocity and power of the currents are inversely proportional to the square of the parameter characterized the special features of the canal’s bottom. In the Earth atmosphere there are often observed nonperiodical. Such kind atmosphere phenomenal events may be: powerful wind vortex, strong local microorographic winds, different arising air currents in the atmosphere lower boundary layer and constantly dominated some regional geophysical “phenomenal” eventsIn the present article on the bases of the hydrothermodynamic laws above mentioned phenomena is investigated. Namely it was proved that pressure in the wind vortex is arising proportionally with relief altitude and enlarged with augmentation of the angle between wind vortex axes and vertical direction. Obtained results are new and have as theoretical as well practical values
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Temur Jangveladze, Zurab Kiguradze, On Investigation and Approximate Solution of One Nonlinear Partial IntegroDifferential Equation with Source Term, Recent Advances in Applied Mathematics, Modelling and Simulation. Proceedings of the 8th International Conference on Applied Mathematics, Simulation, Modelling (ASM '14), p.5055, WSEAS Press, 2014
Initialboundary value problem with mixed boundary conditions is considered for one nonlinear integro differential equation with source term. Considered model is based on Maxwell’s system describing the process of the penetration of a magnetic field into a substance. Semidiscrete and finite difference schemes are studied. Attention is paid to the investigation more wide cases of nonlinearity than already were studied. Existence, uniqueness and longtime behavior of solutions are given too.
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Temur Jangveladze, Zurab Kiguradze, Semidiscrete Scheme for One Nonlinear IntegroDifferential System Describing Diffusion Process of Electromagnetic Field, Advances in Applied and Pure Mathematics, Advances in Applied and Pure Mathematics, 2014

Teimurazi Davitashvili, On Regional Climate Singularity: on Example of the Territory of Georgia, International Scienece Index, Vol. 8, No7, Part III, 507513, WASET press, 2014
In this paper, some results of numerical simulation of the air flow dynamics in the troposphere over the Caucasus Mountains taking place in conditions of nonstationarity of largescale undisturbed background flow are presented. Main features of the atmospheric currents changeability while air masses are transferred from the Black Sea to the land’s surface had been investigated. In addition, the effects of thermal and advectivedynamic factors of atmosphere on the changes of the West Georgian climate have been studied. It was shown that nonproportional warming of the Black Sea and Colkhi lowland provokes the intensive strengthening of circulation and effect of climate cooling in the western Georgia
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Gogi Pantsulaia, M Kintsurashvili, An effective construction of the strong objective infinite sample wellfounded estimate, Proc. A. Razmadze Math. Ins 166, 113119, A. Razmadze Mathematical Institute (Georgia), 2014

Lamara Bitsadze, On the representations of solutions in the plane theory of thermodynamics with microtemperatures, Bulletin of TICMI, 18 (2), 3651, Tbilisi University Press, 2014
In the present paper the mathematical model of the linear 2D dynamical theory of thermoelasticity with microtemperatures is considered. The representation of regular solution, the fundamental and singular solutions for a governing system of equations of this theory in the Laplace transform space are constructed. Finally, the singlelayer, doublelayer and volume
potentials are presented
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Ivane Tsagareli, Lamara Bitsadze, The boundary value problems in the full coupled theory of elasticity for plane with double porosity with a circular hole, Seminar of I. Vekua Institute of Applied Mathematics REPORTS, Volume 40, 6879, Tbilisi University Press, 2014
The purpose of this paper is to consider twodimensional version of the full coupled theory of elasticity for solids with double porosity and to solve explicitly the Dirichlet and Neumann BVPs of statics in the full coupled theory for an elastic plane with a circular hole. The explicit solutions of these BVPs are represented by means of absolutely and
uniformly convergent series. The questions on the uniqueness of a solutions of the problems are established.
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Gogi Pantsulaia, M Kintsurashvili, AN OBJECTIVE INFINITE SAMPLE WELLFOUNDED ESTIMATE OF A USEFUL SIGNAL IN THE LINEAR ONEDIMENSIONAL STOCHASTIC MODEL, Rep. Enlarged Sess. Semin. I. Vekua Appl. Math 28, 9093, VIAM, 2014
It is shown that limTfn := infn supm≥n Tfm and limTfn := supn
infm≥n Tfm are objective infinite sample wellfounded estimates of a useful signal θ in the linear onedimensional
stochastic model ξk = θ + ∆k (k ∈ N), where #(·) denotes a counting measure, ∆k is a sequence of independent identically distributed random variables on R with strictly increasing
continuous distribution function F, expectation of ∆1 does not exist and Tn : R
N → R (n ∈ N)
is defined by Tn((xk)k∈N) = −F
−1
(n
−1#({x1, · · · , xn} ∩ (−∞; 0])) for (xk)k∈N ∈ R
N.
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Tamaz Tadumadze, Nika Gorgodze, Variation formulas of a solution and initial data optimization problems for quasilinear neutral functional differential equations with discontinuous initial condition, Mem.Differential Equations Math.Phys. 63, 177, Tbilisi University Press, 2014
For the quasilinear neutral functional differential equation the continuous dependence of a solution of the Cauchy problem on the initial data and on the
nonlinear term in the righthand side of that equation is investigated, where the perturbation nonlinear term in the righthand side and initial data are small in the integral and standard sense, respectively. Variation formulas of a solution are derived, in which the effect of perturbations of the initial moment and the delay function, and also that of the discontinuous initial condition are detected. For initial data optimization problems the necessary conditions of optimality are obtained. The existence theorem for optimal initial data is proved.
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Tamaz Tadumadze, Nika Gorgodze, Variation formulas of solution for a class of controlled neutral functional differential equations considering delay function perturbation and the continuous initial condition, Sem. I. Vekua Inst. Appl. Math., Rep. 40(2014), 4549, Tbilisi University Press, 2014
Variation formulas of solution are obtained for linear with respect to prehistory of the phase velocity (quasilinear) controlled neutral functionaldifferential equation with variable delays. The effects of delay function perturbation and continuous initial condition are detected in the variation formulas
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Tamaz Tadumadze, Abdeljalili Nachaoui, On the existence of an optimal element in quasilinear neutral optimal problem, Sem. I. Vekua Inst. Appl. Math., Rep., 40, 5067, Tbilisi University Press, 2014
For an optimal control problem involving neutral differential equation, whose righthand side is linear with respect to prehistory of the phase velocity, existence theorems of optimal element are proved. Under element we imply the collection of delay parameters and initial functions, initial moment and vector, control and finally moment
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Tamaz Tadumadze, Conntinuous dependence of solutions of delay functional differential equations on the righthand side and initial data considering delay perturbations, Georgin International Journal of Science and Technology, V. 6, No. 4 , 353369, Nova Science Publishers, Inc., 2014
Theorems on the continuous dependence of solution on perturbations of the initial data and the righthand side of equation are proved. Under initial data we imply the collection of initial moment, variable delays, initial vector and initial function.
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Tamaz Tadumadze, Nika Gorgodze, Variation formulas of solution for a neutral functionaldifferential equation taking into account delay function perturbation and the discontinuous initial condition, Functional Differential Equations, V. 21, No. 34 , 147154, Ariel University Center of Samaria, 2014
Variation formulas of solution are obtained for linear with respect to prehistory of the phase velocity neutral functionaldifferential equations with variable delays and with the discontinuous initial condition. In the variation formulas are detected the
effects of perturbation of delay function entering in the phase coordinates and the discontinuous initial condition. The variation formula of solution plays the basic role in proving of the necessary conditions of optimality and under sensitivity analysis of mathematical models. Discontinuity of the initial condition means that the values of the initial function and the trajectory, in general, do not coincide at the initial moment.
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Tepper Gill, Aleks Petre Kirtadze, Gogi Pantsulaia, A Plichko, Existence and uniqueness of translation invariant measures in separable Banach spaces, Functiones et Approximatio Commentarii Mathematici 50 (2), 401419, Adam Mickiewicz University Press, Adam Mickiewicz University, 2014
It is shown that for the vector space R^ N (equipped with the product topology and the YamasakiKharazishvili measure) the group of linear measure preserving isomorphisms is quite rich. Using Kharazishvili's approach, we prove that every infinitedimensional Polish linear space admits a σfinite nontrivial Borel measure that is translation invariant with respect to a dense linear subspace. This extends a recent result of Gill, Pantsulaia and Zachary on the existence of such measures in Banach spaces with Schauder bases. It is shown that each σfinite Borel measure defined on an infinitedimensional Polish linear space, which assigns the value 1 to a fixed compact set and is translation invariant with respect to a linear subspace fails the uniqueness property. For Banach spaces with absolutely convergent Markushevich bases, a similar problem for the usual completion of the concrete σfinite Borel measure is solved positively. The uniqueness problem for nonσfinite semifinite translation invariant Borel measures on a Banach space X which assign the value 1 to the standard rectangle (i.e., the rectangle generated by an absolutely convergent Markushevich basis) is solved negatively. In addition, it is constructed an example of such a measure µ_0 on X, which possesses a strict uniqueness property in the class of all translation invariant measures which are defined on the domain of µ_0 and whose values on nondegenerate rectangles coincide with their volumes.
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Tamaz Tadumadze, Nika Gorgodze, Initial data optimization problem for the quasilinear neutral functional differential equation with variable delays and the discontinuous initial condition, Proceedings of I. Vekua Institute of Applied Mathematics, 64 , 6873, Tbilisi University Press, 2014
Necessary optimality conditions are obtained for initial data of linear with respect to prehistory of the phase velocity (quasilinear) neutral functional differential
equation. Here initial data implies the collection of initial moment and vector, delay function entering in the phase coordinates and initial function. In this paper, the essential novelty are optimality conditions of the initial moment and delay function. Discontinuity of the initial condition means that the values of the initial function and the trajectory, in general, do not coincide at the initial moment.
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Tamaz Tadumadze, Nika Gorgodze, Variation Formulas of Solution for a Functional Differential Equation with Delay Function Perturbation, Journal of Contemporary Mathematical Analysis , 49 (2), 53 63, Springer, 2014
Variation formulas of solution for a nonlinear functional differential equation with variable delay and continuous initial condition are proved. The effects of delay function perturbation and continuous initial condition are detected in the variation
formulas. The continuity of the initial condition means that the values of the initial function and the trajectory always coincide at the initial moment.
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Gogi Pantsulaia, Selected topics of invariant measures in Polish groups, Nova Publishers, Nova Publishers, 2014
This book explores a number of new applications of invariant quasifinite diffused Borel measures in Polish groups for a solution of various problems stated by famous mathematicians (for example, Carmichael, Erdos, Fremlin, Darji and so on). By using natural Borel embeddings of an infinitedimensional function space into the standard topological vector space of all realvalued sequences, (endowed with the Tychonoff topology) a new approach for the construction of different translationinvariant quasifinite diffused Borel measures with suitable properties and for their applications in a solution of various partial differential equations in an entire vector space is proposed.
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Tamaz Tadumadze, Variation formulas for solution of delay differential equations with mixed initial condition and delay perturbation, Nonlinear Oscillations, V. 17, No. 4, 503 532, Springer, 2014
Variation formulas for solution are proved for a nonlinear differential equation with constant delays. In this work, the essential novelty is an effect of delay perturbation in the variation formulas. The mixed initial condition means that at the initial
moment, some coordinates of the trajectory do not coincide with the corresponding coordinates of the initial function, whereas the others coincide. Variation formulas are used in the proof of necessary optimality conditions.
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Gogi Pantsulaia, M Kintsurashvili, Why is Null Hypothesis rejected for” almost every” infinite sample by some Hypothesis Testing of maximal reliability, Journal of Statistics: Advances in Theory and Applications 11 (1), 4570, Scientific Advances Publishers , 2014
The notion of a Haar null set introduced by Christensen in 1973 and reintroduced in 1992 in the context of dynamical systems by Hunt, Sauer and Yorke, has been used, in the last two decades, in studying exceptional sets in diverse areas, including analysis, dynamic systems, group theory, and descriptive set theory. In the present paper, the notion of “prevalence” is used in studying the properties of some infinite sample statistics and in explaining why the null hypothesis is sometimes rejected for “almost every” infinite sample by some hypothesis testing of maximal reliability. To confirm that the conjectures of Jum Nunnally [17] and Jacob Cohen [5] fail for infinite samples, examples of the so called objective and strong objective infinite sample wellfounded estimate of a useful signal in the linear onedimensional stochastic model are constructed.
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Nino Khatiashvili, Revaz Shanidze, Davit Janjgava, On effective solutions of the nonlinear Schrödinger equation, Journal of Physics;482(1),012020; #GNSF/ST08/3395, IOP Publishing, 2014
Cubic nonlinear Schrödinger type equation with specific initialboundary conditions in the infinite domain is considered. The equation is reduced to an equivalent system of partial differential equations and studied in the case of solitary waves. The system is modified by introducing new functions, one of which belongs to the class of functions of negligible fifth order and vanishing at infinity exponentially. For this class of functions the system is reduced to a nonlinear elliptic equation which can be solved analytically, thereby allowing us to present nontrivial approximated solutions of nonlinear Schrödinger equation. These solutions describe a new class of symmetric solitary waves. Graphics of modulus of the corresponding wave function are constructed by using Maple.
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Roman Janjgava, Construction of approximate solutions of some plane problems of thermoelasticity for transversal isotropic bodies, Reports of Enlarged Session of the Seminar of VIAM, 28, 5457, Tbilisi University Press , 2014
In this work the algorithm of the approximate solution of twodimensional boundary value problems of thermoelasticity is offered for transversal isotropic body. The offered algorithm is based on use of representation of the general solution of system of the equations of balance by means of harmonic functions.
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Maia Svanadze, Potential method in the linear theory of viscoelastic materials with voids, Journal of Elasticity, Volume 114, Issue 1, Pages 101126., Springer, 2014
In the present paper the linear theory of viscoelasticity for Kelvin–Voigt materials with voids is considered and some basic results of the classical theory of elasticity are generalized. Indeed, the basic properties of plane harmonic waves are established. The explicit expression of fundamental solution of the system of equations of steady vibrations is constructed by means of elementary functions. The Green’s formulas in the considered theory are obtained. The uniqueness theorems of the internal and external basic boundary value problems (BVPs) are proved. The representation of Galerkin type solution is obtained and the completeness of this solution is established. The formulas of integral representations of Somigliana type of regular vector and regular (classical) solution are obtained. The SommerfeldKupradze type radiation conditions are established.
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Maia Svanadze, On the solutions of equations of the linear thermoviscoelasticity theory for Kelvin–Voigt materials with voids, Journal of Thermal Stresses, Volume 37, Issue 3, Pages 253269, Taylor & Francis, 2014
In this article, the linear theory of thermoviscoelasticity for Kelvin–Voigt materials with voids is considered. The fundamental solution of the system of equations of steady vibrations is constructed by means of elementary functions and its basic properties are established. The representation of a Galerkintype solution is obtained. The formula of representation of the general solution for the system of homogeneous equations of steady vibrations in terms of six metaharmonic functions is established. The completeness of these representations of solutions is proved.
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Maia Svanadze, Potential method in the theory of thermoviscoelasticity for materials with voids, Journal of Thermal Stresses, Volume 37, Issue 8, Pages 905927, Taylor & Francis, 2014
In the present article, the linear theory of thermoviscoelasticity for Kelvin–Voigt materials with voids is considered. The SommerfeldKupradze type radiation conditions are established. The uniqueness theorems of the internal and external basic boundary value problems (BVPs) of steady vibrations are proved. The Green's formulas and integral representations of Somigliana type of regular vector and classical solution are obtained. The basic properties of thermoelastopotentials and singular integral operators are given. Finally, the existence theorems for classical solutions of the above mentioned BVPs are proved by using the potential method (boundary integral method) and the theory of singular integral equations.
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Alexander Kharazishvili, To the existence of projective absolutely nonmeasurable functions, Proceedings of A. Razmadze Mathematical Institute Vol. 166 (2014), 95–102, TSU, 2014
It is shown that under some appropriate settheoretical assumptions there exists an absolutely nonmeasurable function acting from [0, 1] into [0, 1], whose graph is a projective
subset of [0, 1]2
.
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Alexander Kharazishvili, On a theorem of Luzin and Sierpinski, Proc. A. Razmadze Math. Inst. 164(2014), 109–115, TSU, 2014
In this report three classical constructions of Lebesgue nonmeasurable
sets on the real line R are envisaged from the point of view of the thickness of those sets with respect to the standard Lebesgue measure λ on R.
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Bakur Gulua, Hierarchical Models of the Second Type for Spherical Shells, AMIM,19 (2), 39, Tbilisi University Press, 2014
In the present paper by means of the I. Vekua method the system of differential equations for shallow spherical shells is obtained, when on upper and lower face surface displacement are assumed to be known. Using the method of the small parameter approximate solutions of I. Vekua’s equations for approximations N = 0 is constructed. The small parameter ε = 2h/R, where 2h is the thickness of the shell, R is the radius of the sphere.
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Alexander Kharazishvili, On measurability properties of Bernstein sets, Proceedings of A. Razmadze Mathematical Institute Vol. 164 (2014), 63–70, TSU, 2014
We envisage Bernstein subsets of the real line R from the
point of view of their measurability with respect to certain classes of
measures on R. In particular, it is shown that there exists a Bernstein
set absolutely nonmeasurable with respect to the class of all nonzero
σfinite translation quasiinvariant measures on R, and that there
exist countably many Bernstein sets which collectively cover R and
are absolutely negligible with respect to the same class of measures.
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Tengiz Meunargia, წასასშლელი, წასასშლელი, Tbilisi University Press, 2014
In the present paper the solutions of Kirsch’s type problems are considered by means of different theories (E. Reissner, A. Lurie, I. Vekua). The obtained results are compared with each other.
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Alexander Kharazishvili, On partitions of the real line into continuum many thick subsets, Real Anal. Exchange, 201314 / 39, no. 2, 459468, Michigan State University Press, 2014
Three classical constructions of Lebesgue nonmeasurable sets on the real line R are envisaged from the point of view of the thickness of those sets. It is also shown, within ZF&DC theory, that the existence of a Lebesgue nonmeasurable subset of R implies the existence of a partition of R into continuum many thick sets.
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Alexander Kharazishvili, A characterization of uncountable sets in terms of their selfmappings and large invariant subsets, Georgian Math. J., 2014 / 21, no. 3, 297302, De Gruyter, 2014
One characterization of an uncountable set E is given in terms of mappings f of E into itself and “large” subsets of E which are invariant with respect to f.
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Alexander Kharazishvili, On some realvalued stepfunctions with strange measurability properties, Georgian Math. J., 2014 / 21, no. 1, 8387, De Gruyter, 2014
We analyze Sierpiński's example of a realvalued Lebesgue measurable function on ℝ which is not bounded from above by any realvalued Borel function. In this context, some realvalued stepfunctions with analogous properties are discussed.
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Alexander Kharazishvili, On countable almost invariant partitions of $G$spaces, Ukr. Math. J. 66, 572–579, Springer, 2014
For any σ finite Gquasiinvariant measure μ given in a Gspace, which is Gergodic and possesses the Steinhaus property, it is shown that every nontrivial countable μalmost Ginvariant partition of the Gspace has a μnonmeasurable member.
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Tengiz Meunargia, On the 2d nonlinear systems of equations for nonshallow shells, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics, Volume 28, 7073, Tbilisi University Press, 2014
I. Vekua has constructed several versions of the refined theory of thin and shallow shells. Using the reduction methods of I. Vekua, the 2D system of equations for geometrically and physically nonlinear theory of nonshallow shells is obtained.
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Bakur Gulua, About one boundary value problem for nonlinear nonshallow spherical shells, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics, Volume 28, 4245, Tbilisi University Press, 2014
In the present paper, using the method of I. Vekua, the three dimensional problems of the nonlinear theory of elasticity are reduced to the two dimensional problems of nonshallow spherical shells. Using the method of the small parameter, approximate solutions of these equations are constructed. One boundary value problems are solved for the approximation of order N=0.
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Bakur Gulua, Some basic boundary value problems for the hierarchical models, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics, Volume 28, 4649, Tbilisi University Press, 2014