Table Of ContentSpringer Proceedings in Mathematics & Statistics
George Jaiani
David Natroshvili Editors
Applications
of Mathematics
and Informatics in
Natural Sciences
and Engineering
AMINSE 2019, Tbilisi, Georgia,
September 23–26
Springer Proceedings in Mathematics &
Statistics
Volume 334
Springer Proceedings in Mathematics & Statistics
This book series features volumes composed of selected contributions from
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George Jaiani David Natroshvili
(cid:129)
Editors
Applications of Mathematics
and Informatics in Natural
Sciences and Engineering
AMINSE 2019, Tbilisi, Georgia,
–
September 23 26
123
Editors
George Jaiani DavidNatroshvili
I.VekuaInstituteofAppliedMathematics& Georgian Technical University
Faculty of Exactand NaturalSciences Tbilisi, Georgia
IvaneJavakhishvili TbilisiState University
Tbilisi, Georgia
ISSN 2194-1009 ISSN 2194-1017 (electronic)
SpringerProceedings in Mathematics& Statistics
ISBN978-3-030-56355-4 ISBN978-3-030-56356-1 (eBook)
https://doi.org/10.1007/978-3-030-56356-1
MathematicsSubjectClassification: 35-XX,74-XX,76-XX,17-XX,54-XX,03-XX
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Editorial Preface
The Fourth International Conference on Applications of Mathematics and
InformaticsinNaturalSciencesandEngineering(AMINSE2019)tookplaceinthe
Ilia Vekua Institute of Applied Mathematics of Ivane Javakhishvili Tbilisi State
University (Tbilisi, Georgia) on September 23–26, 2019.
The aim of AMINSE 2019 was to bring together scientists to discuss their
research in all the aspects of Mathematics, Informatics, and their Applications in
NaturalSciencesandEngineering.Accordingtothispremise,allthelecturerswere
invited personally for their active interest in their relative field. There were 80
participants from 10 countries. The main topics of the conference were: Partial
Differential Equations, Operator Theory, Numerical Analysis, Mechanics of
Deformable Solids, Fluid Mechanics and Computer Science. The program
included wo opening lectures, “Recent Developments on Numerical Solutions for
Hyperbolic Systems of Conservation Laws” presented by Rolf Jeltsch
(Switzerland) and “Progress in Mathematical and Numerical Modelling of
Piezoelectric Smart Structures” by Ayech Benjeddou (France). At the conference,
15 plenary lectures, 15 talks, were presented. The Satellite TICMI (Tbilisi
International Center of Mathematics and Informatis) Advanced Courses on
“Mathematical Models of Piezoelectric Solids and Related Problems” was held
parallel to the conference.
Thisvolumeincludes14peer-reviewedpapers presented attheconference.The
contributions are related to several important directions of Applied Mathematics,
Integral Equations, Variational Methods, Continuum Mechanics, Numerical
Analysis, Mathematical Modeling in Social Sciences, Financial Mathematics,
Theory of Probability and Statistics, Li algebra, and Mathematical Logic.
We are grateful to the organizations and individuals who helped orchestrate the
conference.TheconferencewasorganizedbyVIAM,FacultyofExactandNatural
Sciences of TSU, Georgian Mechanical Union, Georgian National Committee of
Theoretical and Applied Mechanics, and Tbilisi International Center of
Mathematics and Informatics. The conference was sponsored by the Shota
RustaveliNationalScienceFoundation.Thescientificorganizationwasentrustedto
the international committee consisting of George Jaiani (chair, Georgia), Gia
v
vi EditorialPreface
Avalishvili (Georgia), Nikoloz Avazashvili (Georgia), Ayech Benjeddou (France),
Lucian Beznea (Romania), Ramaz Botchorishvili (Georgia), Natalia Chinchaladze
(Georgia), Roland Duduchava (Georgia), Maribel Fernandez (UK), ALice
Fialowski (Hungary), Temur Jangveladze (Georgia), Rolf Jeltsch (Switzerland),
Alexsander Kharazishvili (Georgia), Omar Kikvidze (Georgia), Gela Kipiani
(Georgia), Vakhtang Kokilashvili (Georgia), Vakhtang Kvaratskhelia (Georgia),
Teimuraz Kutsia (Austria), Mircea Marin (Romania), Bernadette Miara (France),
Wolfgang H. Müller (Germany), Elizbar Nadaraya (Georgia), David Natroshvili
(Georgia), Jemal Rogava (Georgia), Tamaz Vashakmadze (Georgia). The local
arrangements of the conference were in the hands of the committee consisting of
Natalia Chinchaladze (Chair) Mariam Beriashvili (Scientific Secretary), Besik
Dundua, Bakur Gulua, Mikheil Rukhaia, and Manana Tevdoradze. We would like
to thank all of them for their hard and efficient work.
In the present book, the contributions of the participants have been ordered
alphabetically by the names of the presenting authors. The responsibility for the
contents of the papers lies solely with each author.
The editors wish to express their thanks to Natalia Chinchaladze for spending
time, patience, and for her valuable help in editing and layouting the book.
The editors are indebted to Springer-Verlag for their courteous and effective
production of these proceedings.
Tbilisi, Georgia George Jaiani
June 2020 David Natroshvili
Contents
On Variational Methods of Investigation of Mathematical Problems
for Thermoelastic Piezoelectric Solids . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Gia Avalishvili and Mariam Avalishvili
On NonparametricKernel-Type Estimate oftheBernoulli Regression
Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Petre K. Babilua and Elizbar A. Nadaraya
Scaling Property for Fragmentation Processes Related
to Avalanches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Lucian Beznea, Madalina Deaconu, and Oana Lupaşcu-Stamate
Conflict Resolution Models and Resource Minimization Problems. . . . . 47
Temur Chilachava and George Pochkhua
Modeling of Extreme Events and Regional Climate Variability
on the Territory of the Caucasus (Georgia) . . . . . . . . . . . . . . . . . . . . . . 61
Teimurazi Davitashvili, Inga Samkharadze, and Meri Sharikadze
Extending the qLog Calculus with Proximity Relations . . . . . . . . . . . . . 83
Besik Dundua, Temur Kutsia, Mircea Marin, and Cleo Pau
Specification and Analysis of ABAC Policies in a Rule-Based
Framework. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Besik Dundua, Temur Kutsia, Mircea Marin, and Mikheil Rukhaia
A Strategic Graph Rewriting Model of Rational Negligence
in Financial Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Nneka Ene, Maribel Fernández, and Bruno Pinaud
On Lie Algebras with an Invariant Inner Product. . . . . . . . . . . . . . . . . 135
Alice Fialowski
vii
viii Contents
Study of Three-Layer Semi-Discrete Schemes for Second
Order Evolution Equations by Chebyshev Polynomials . . . . . . . . . . . . . 153
Romeo Galdava, David Gulua, and Jemal Rogava
Notes on Sub-Gaussian Random Elements. . . . . . . . . . . . . . . . . . . . . . . 197
George Giorgobiani, Vakhtang Kvaratskhelia, and Vaja Tarieladze
Localized Boundary-Domain Integro-Differential Equations
Approach for Stationary Heat Transfer Equation . . . . . . . . . . . . . . . . . 205
Sveta Gorgisheli, Maia Mrevlishvili, and David Natroshvili
Boundary Value Problems of the Plane Theory of Elasticity
for Materials with Voids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
Bakur Gulua and Roman Janjgava
Objective and Subjective Consistent Criteria for Hypotheses
Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
Omar Purtukhia and Zurab Zerakidze
Review of Rational Electrodynamics: Deformation and Force Models
for Polarizable and Magnetizable Matter. . . . . . . . . . . . . . . . . . . . . . . . 245
Wilhelm Rickert and Wolfgang H. Müller
On Variational Methods of Investigation
of Mathematical Problems for
Thermoelastic Piezoelectric Solids
GiaAvalishviliandMariamAvalishvili
Abstract Inthispaperwepresenttheresultsofinvestigationoftheboundaryand
initial-boundary value problems corresponding to mathematical models of ther-
moelastic piezoelectric solids with regard to magnetic field. We consider three-
dimensionalstaticanddynamicmodelsofgeneralinhomogeneousanisotropicther-
moelasticpiezoelectricsolidswithmixedboundaryconditions,whenoncertainparts
oftheboundarydensityofsurfaceforce,andnormalcomponentsoftheelectricdis-
placement,magneticinduction,andheatfluxaregiven,andontheremainingparts
oftheboundarymechanicaldisplacement,temperature,electricandmagneticpoten-
tialsvanish.Weobtainvariationalformulationsoftheboundaryandinitial-boundary
valueproblemsinsuitablefunctionspacesandpresenttheexistence,uniquenessand
continuousdependenceresults.
·
Keywords Thermoelasticpiezoelectricsolids Boundaryandinitial-boundary
· ·
valueproblems Existenceanduniquenessofsolution Variationalmethods
·
Sobolevspaces Vector-valueddistributions
1 Introduction
The important integral parts of modern engineering constructions are smart struc-
tures, which involve actuators and sensors, and microprocessors that analyze the
responses from the sensors and use actuators to alter construction response. After
discoveryofpiezoelectriceffectbytheCuriebrothers[14],JacquesandPierre,the
B
G.Avalishvili( )
FacultyofExactandNaturalSciences,I.JavakhishviliTbilisiStateUniversity,3I.
TchavtchavadzeAve.,0179Tbilisi,Georgia
e-mail:[email protected]
M.Avalishvili
SchoolofScienceandTechnology,UniversityofGeorgia,
77aM.KostavaStr.,0175Tbilisi,Georgia
e-mail:[email protected]
©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicense 1
toSpringerNatureSwitzerlandAG2020
G.JaianiandD.Natroshvili(eds.),ApplicationsofMathematicsandInformatics
inNaturalSciencesandEngineering,SpringerProceedingsinMathematics
&Statistics334,https://doi.org/10.1007/978-3-030-56356-1_1
