User:Levan Gavasheli

Full member (academician) of the International Academy of Ecology and Life Security Sciences associated with the United Nations Public Information Center, Doctor of Technical Sciences, Professor Levan Gavasheli

The main results of scientific, scientific-practical, pedagogical and social activities

1.First of all, it should be noted that Levan Gavasheli, based on the results of theoretical and experimental studies in mechanics and applied mathematics, published and known to the science known in the field, is considered to be a nonlinear mechanic with distributed parametersas one of the founders of the theory of initiation and development of studies of random oscillations of systems. Particularly noteworthy is LevanGavasheli's sequence of two previously known laws in mechanics and physics, namely Hooke's law and the sequence of changes in the equivalent stiffness of nonlinear mechanical systems in their static and dynamic systems detection of faults in the circuit, their experimental confirmation, new formulation, mathematical description and analysis for nonlinear mechanical systems. In additionLevan Gavasheli proved that the decadence modulus for nonlinear mechanical systems with hysteresis characteristics is not constant and it depends on the magnitude of the stress and consequently the magnitude of the deformation. These results, their mathematical description and analysis detection of faults in the circuit, their experimental confirmation, new formulation, mathematical description and analysis for nonlinear mechanical systems. In addition Levan Gavasheli proved that the decadence modulus for nonlinear mechanical systems with hysteresis characteristics is not constant and it depends on the magnitude of the stress and consequently the magnitude of the deformation. These results, their mathematical description and analysis It is recorded in LevanGavasheli's scientific works, most of which have been published in authoritative publications of leading countries in this field. Scientific departments, headed for years by Levan Gavasheli, at the Institute of Mining Mechanics of the Georgian Academy of Sciences and at the Mining Institute of the Academy of Sciences of the Russian Federation, in the two main areas of this field: the theory of vibration protection of nonlinear mechanical systems and methods and means of combating harmful vibrations; Technical diagnostics and non-destructive testing of mechanical systems - are recognized as leaders in the former Soviet Union, the Russian Federation and Georgia. In both spheres, a state was developed under the leadership and direct participation of Levan Gavasheli manual regulatory documents. The originality, usefulness and efficiency of the developed methods and tools are protected by 17 copyright certificates and patents. A solid number of certificates and patents were introduced in the major industrial facilities of the Soviet Union, the Russian Federation and Georgia, resulting in great economic, social and environmental effects, among them are papers from 2020-24 . 1.Leon Makharadze, Levan Gavasheli* Academy of Physical and Mathematical Sciences, Georgia.Journal of Applied Mathematics and Computation, 2020, 4(3), 57-63 https://www.hillpublisher.com/journals/JAMC/ ISSN Online: 2576-0653 ISSN Print: 2576-0645 DOI: 10.26855/jamc.2020.09.002 57 Journal of Applied Mathematics and Computation Deformation of Elastic Damping Bodies, Hysteresis Friction

2.Gavasheli L, Gavasheli A (2021) Random oscillations of nonlinear systems with distributed Parameter. Ann Math Phys 4(1): 084-091. DOI: https://dx.doi.org/10.17352/amp.000027.

3.Gavasheli L.Sh. and Gavasheli A.L. ANALYSIS OF LONGITUDINAL AND TRANSVERSE OSCILLATIONS OF NONLINEAR MECHANICAL SYSTEMS. GEORGIAN ENGINEERING NEWS, #1, 2022, 11 -19 4. Gavasheli L, Gavasheli A (2024) Study of vibration shock processes of non-linear mechanical systems with distributed parameters. Ann Math Phys 7(1): 072-075. DOI: https://dx.doi.org/10.17352/amp.000109 5. Levan Gavasheli, Anri Gavasheli (2024) Analytical Study of Random Oscillations of Vibration Protection Devices with an Elliptical Hysteresis Loop for Absorbing Harmful Energies by Non-Linear Mechanical Systems and their Elastic-Damping Elements. Journal of Physical Mathematics & its Applications. SRC/JPMA-132. 2.In addition, Levan Gavasheli developed a new diagnostic technology and a method for analyzing the condition of main pipelines, the bottoms of large volume tanks for storing oil and oil products at oil terminals. It is based on the forced response acoustic-emission method, including diagnostics of pipeline walls and tank bottoms, ultrasonic flaw detection and thickness measurement without decommissioning of objects, allows you to perform non-destructive testing and detect, classify, determine the nature, size and location of defects with high accuracy;calculations for strength and durability; evaluate the quality of factory and previously performed repairs, scratches, delaminations, pores, slag or other inclusions in metals; establish the stages of development of defects. The analysis technique is based on: automated information received from ultrasonic flaw detectors; release of reports on each surveyed object; diagnostic information in order to determine the patterns of distribution and development of defects; storage and systematization of information in the form of databases on the technical condition of the object being examined.The effectiveness and accuracy of the proposed diagnostic technology and analysis methodology has been established by the results of field studies at industrial facilities. In the first, it is actually proposed to combine the ultrasonic method with the magnetic memory method and the method of free vibrations, where the structural forms of the phase compositions of the metal are estimated in the informative frequency ranges: 17.82 - 50.2 Hz, characterizing the development of screw dislocations; 81.67 - 433.89 Hz, characterizing the development of edge dislocations; 1899.66 - 2674.25 Hz, characterizing the intensity and coherence of flows of free vacancies going to the deceleration of screw and edge dislocations due to shifts of maximum resonances - the density of the wave energy flux to their minimum frequency values, which reflects changes in the spectral atomic magnetic moments. The main advantage of the developed technology is the ability to perform non-destructive testing and to detect, classify, determine the nature, size and location of defects with high accuracy; perform strength and durability calculations; evaluate the quality of factory and previously performed repairs. 3. The developed theoretical and technical solutions (projects) are currently being implemented in large industrial facilities in the Russian Federation and Georgia. Levan Gavasheli is the author of more than 150 scientific papers and 3 monographs, most of which have been published in authoritative foreign publications, and has a high citation index. Most of the main results of theoretical studies and technical solutions are reflected in the above monographs. 4. Under the leadership and active participation of Levan Gavasheli, six scientific projects (grants) were implemented and implemented: with the funding of the Georgian National Academy of Sciences - 3; Funded by the Georgian National Science Foundation - 3. The results of the research were presented at more than 20 international, joint republican congresses, symposia and conferences. 5. In 1976 he graduated from Tbilisi State University, Faculty of Mechanics and Mathematics, majoring in Mathematics. In 1985 he defended the degree of Candidate of Technical Sciences at the Georgian Polytechnic Institute, the topic of his dissertation was "Analysis of the nature of oscillations of drilling pipes of conical drilling machines", for which he was awarded the degree of Candidate of Technical Sciences. In 1991 he defended his doctoral dissertation at the Moscow Mining Institute, the topic of the dissertation was "Theory and Methods of Effective Vibration Protection of Milling Machines and Operators", for which he was awarded a Doctor of Technical Sciences degree in "Mining Machinery". In 2003 he was awarded the academic title of Professor of Mining Machinery, Mining Transport Installations and Transport Department. 6. Under the scientific guidance of Levan Gavasheli, a large number of dissertations were prepared and defended for the scientific degrees of Candidate of Technical Sciences and Doctor of Technical Sciences, for Master's and Doctor's academic degrees.For a great contribution in the field of mining mechanics science and technology, the data are included in the bibliographic reference book of the famous Georgian science in the field of mathematics and engineering mechanics, which was published in Tbilisi in 2016. 7. Levan Gavasheli is the Founder of the Academy of Physical and Mathematical Sciences in Georgia, its full member and President, a full member of the International Academy of Ecology and Safety Sciences associated with the UN Public Information Center. By order of the Ministry of Fuel and Energy of the Russian Federation No. 5-13 in 1997 he was awarded the Badge of Labor Glory (III degree) for his merits listed in paragraphs.In 2014, he was awarded the Prize named after Academician A.A. Dzidziguriin the field of mining mechanics. It is especially noteworthy that Levan Gavasheli approved the “Fermat’s great theorem” known in mathematics and its recognition by renowned specialists in number theory. The first version of this approval was published by Levan Gavasheli in 1996. For some years mathematicians were skeptical and ambivalent about making certain conclusions about the recognition of this assertion. 2016 this yearLevan Gavasheli presented theses at the joint international conference of the Georgian Mathematicians Union and the Georgian Mechanics Union Vll and made a report on the validation of “Fermat's great theorem”. The participants of the conference positively evaluated the submitted approval and issued the relevant certificate. This was followed by an international response from renowned mathematicians and editorial boards of international mathematical journals,who acknowledged the sensational and universally understandable new proof of the farm presented by Levan Gavasheli, and offered to publish this proof in their journals. In 2018, Levan Gavasheli published a corrected and complete version of the theorem proof in the International Journal of Applied Mathematics and Computation. Gavasheli, L. (2018) “Fermat’S Great Theorem” . Journal of Applied Mathematics and Computation, 2(4), 136-142. Reviews and impressions of well-known specialists on the above approval Feedback and impressions about the fairness of this approval continue to this day. To introduce the original version of the approval to the mathematical community once again, Levan Gavasheli was invited to speak at the 1st European Conference on Engineering & Technology (ECETECH-2022) in July this year in France (Paris). Concerning the conclusions reached by mathematicians about the most difficult version of the “Fermat’s great theorem” proposed by the English mathematician Andrew Wiles, which is not a direct but a result of the most difficult mathematical calculations (120 pages of the printed version of the journal), it can be Mathematical Journal (Unsolved problems in Mathematics) ", 2011.

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