George Giorgobiani

Academic Doctor of Science

Muskhelishvili Institute of Computational Mathematics

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Note on Chobanyan-Pecherski condition for the series in Banach spaces	G. Giorgobiani	article	GESJ: Computer Science and Telecommunications 2022, No.1(61), 13-18	-	ISSN 1512-1232		English	State Targeted Program
The law of large numbers for weakly correlated random elements in the spaces l_p,1≤p<∞.	V. Berikashvili, G. Giorgobiani, V. Kvaratskhelia	article	Lith. Math. J. 62, 308–314	WOS IF: 0.519, SJR - 0.295	ISSN: 0363-1672	10.1007/s10986-022-09564-x	English	State Targeted Program
Statistical analysis for efficient design of passenger transit system	G. Giorgobiani, T. Giorgobiani, K. Kandelaki, V. Kvaratskhelia, M. Tsatsanashvili	article	Bulletin of TICMI, vol. 24, No. 2, 2020, pp. 85-95.	SJR - 0.126	ISSN: 1512-0082		English	State Targeted Program
Notes on Sub-Gaussian Random Elements	Giorgobiani G., Kvaratskhelia V., Tarieladze V	article	In: Jaiani, G., Natroshvili, D. (eds) Applications of Mathematics and Informatics in Natural Sciences and Engineering. AMINSE 2019. Springer Proceedings in Mathematics & Statistics, vol. 334, p. 197-203. Springer, Cham., 2020	SJR - 0.203	ISSN 2194-1009	https://doi.org/10.1007/978-3-030-56356-1_11	English	State Targeted Program
Maximal inequalities and their applications to orthogonal and Hadamard matrices	G. Giorgobiani, V. Kvaratskhelia	article	Period. Math. Hung. (2020) 81:88-97	IF - 0.94, SJR - 0.462	ISSN: 0031-5303	10.1007/s10998-020-00314-5	English	State Targeted Program
Rearrangements of series	G. Giorgobiani	monograph	Journal of Mathematical Sciences, Vol. 239, No. 4, 2019, p. 438 -543.	SJR - 0.33	ISSN 1072-3374	DOI 10.1007/s10958-019-04315-9	English	Grant Project
Maximum Inequalities and their Applications to Hadamard Matrices	G. Giorgobiani, V. Kvaratskhelia, M. Menteshashvili	conference proceedings	Proceedings of 11th Int. Conf. Comp. Sc. Inf. Tech. (CSIT 2017). Yerevan, Armenia, September 25 – 29, 2017, p. 198 – 199	No	no		English	State Targeted Program
Rearrangement theorem for the weak topology	G. Chelidze, G. Giorgobiani, V. Tarieladze	article	Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, V.31, 2017, p. 19 – 22	No	ISSN 1512-0066		English	Grant Project
Sum Range of Quaternion Series	G. Chelidze, G. Giorgobiani, V. Tarieladze	article	J. Math. Sci., v. 216, 4, 2016, p. 519-521	SJR - 0.33	ISSN 1072-3374	DOI 10.1007/s10958-016-2908-9	English	Grant Project
Some Properties of Hadamard Matrices	G. Giorgobiani, V. Kvaratskhelia, M. Menteshashvili	conference proceedings	Comp. Sci. Inf. Tech. (CSIT), 2015, 64 – 65 (IEEE Conference Publications).	No	ISBN:978-1-4673-7562-7	10.1109/CSITechnol.2015.7358251	English	State Targeted Program
On rearrangement theorem in Banach spaces	S. Chobanyan, G. Giorgobiani, S. Levental, V. Kvaratskhelia, V. Tarieladze	article	Georgian Mathematical Journal, 2014, Volume 21, Issue 2, p. 157 – 163	WOS IF:0.537	ISSN: 1572-9176	https://doi.org/10.1515/gmj-2014-0016	English	State Targeted Program
One Approach to the Regime Optimization of Water-Power System	J. Giorgobiani, M. Nachkebia, G. Giorgobiani	article	GESJ: Computer Science and Telecommunications. 2013\|No.2(38). p. 120- 124.	No	ISSN: 1512-1232		English	State Targeted Program
Special universal series	G. Giorgobiani, V. Tarieladze	article	Several Problems of Applied Mathematics and Mechanics. Nova Science Publishers; Mathematics Research Developments, Editors: I. Gorgidze et al., 2013, p. 125-130	No	ISBN-10 ‏ : ‎ 1620816032		English	State Targeted Program
Signs and Permutations: Two Problems of the Function Theory	S. Chobanyan, G. Giorgobiani, V. Tarieladze	article	Proceedings of A. Razmadze Mathematical Institute. 160 (2012), 24-34.	No	ISSN 1512-0007		English	Grant Project
On Complex Universal Series	G. Giorgobiani, V. Tarieladze	article	Proceedings of A. Razmadze Mathematical Institute. 160 (2012), 53-63.	No	ISSN 1512-0007		English	Grant Project
Elections Management Information Communication System VoterBallot	Z. Tabagari, Z. Sanikidze, G. Giorgobiani	article	World Academy of Science, Engineering and Technology. 69, 2012, 1119-1121	No	ISSN 1512-0007		English	Grant Project
Markov decision process for the long-term control of hydro station with reservoir	J. Giorgobiani, M. Nachkebia, G. Giorgobiani	conference proceedings	Proc. Int. Conf. Dedic. 90-th Anniv. of GTU. Trans., Basic Paradigms in Science and Technology Development for the 21st Century, p. 444 - 447, Tbilisi, Georgia, September 19-21, 2012.	No	ISBN: 978-1-61324-870-6		English	State Targeted Program
Game-Theoretic Models of Dynamic Duopoly	J. Giorgobiani, M. Nachkebia, G. Giorgobiani	article	Georgian Engineering News. N 1, 2012	No	ISSN: 1512-1232		English	State Targeted Program
Game-Theoretic Models of Dynamic Duopoly	J. Giorgobiani, M. Nachkebia, G. Giorgobiani	article	GESJ: Computer Sciences and Telecommunications. No. 2(34), 2012. pp. 34-38	No	ISSN: 1512-1232		English	State Targeted Program
A note on the rearrangement theorem in a Banach space	S. Chobanyan, G. Giorgobiani, V. Kvaratskhelia, V. Tarieladze	article	Proc. Int. Sc. Conference ICTMC-2010 Devoted to the 80th Anniversary of I.V. Prangishvili. Nova Science Publishers; Computer Science, Technology and Applications. 2012. pp. 531-535	No	ISBN: 978-1-61324-870-6		English	State Targeted Program
A maximum inequality for rearrangements of summands and its applications to orthogonal series and scheduling theory processes	L. Chobanyan, S. Chobanyan G. Giorgobiani	article	Bulletin of the Georgian National Academy of Sciences, v.5. no.1, 2011. 16-20.	"SJR 2020: 0.192 CiteScore 2020: 0.8	ISSN: 0132-1447		English	Grant Project
Mathematical models of ecological pollution processes	M. Nachkebia, J. Giorgobiani, G. Giorgobiani	article	GESJ, Computer Sciences and Telecom, No 1(30), 2011, 78-86.	No	ISSN: 1512-1232		English	State Targeted Program
Greedy Algorithm Fails in Compact Vector Summation	G. Chelidze, S. Chobanyan, G. Giorgobiani, V. Kvaratskhelia.	article	Bulletin of the Georgian National Academy of Sciences, v. 4, no. 2, 2010. pp. 5-7.	SJR 2020: 0.192 CiteScore 2020: 0.8	ISSN: 0132-1447	არ აქვს	English	Grant Project
Mathematical model of one process of environmental pollution	G. Giorgobiani	article	Georgian Engineering News. N1, 2009, 90 – 92	არ აქვს	ISSN: 1512-0287		Russian	State Targeted Program
Convergent rearrangements of series of vector-valued functions	G. Giorgobiani	article	Georgian Mathematical Journal. v.7, (2000), N1. 43-51.	WOS IF:0.537	ISSN: 1572-9176	https://doi.org/10.1515/gmj.2000.43	English	State Targeted Program

XIII Annual International Meeting of the Georgian Mechanical Union	Batumi, Georgia	2022	24/08/2022 - 26/08/2022	Georgian Mechanical Union	About the series rearrangement problem	oral	The talk is about one sufficient condition for the affinity of the sum range of a series in a normed space. This condition is automatically fulfilled for the null-sequences in finite dimensional normed spaces. In this paper we describe some classes of null-sequences in an infinite dimensional normed space 1\leq p<\infty satisfying the mentioned condition	https://atsu.edu.ge/index.php/en/teqnikuri-news-eng/2776-xiii-conferencia-teqnikuri-eng
XIII Annual International Meeting of the Georgian Mechanical Union	Batumi, Georgia	2022	24/08/2022 - 26/08/2022	Georgian Mechanical Union	About the series rearrangement problem	oral	The talk is about one sufficient condition for the affinity of the sum range of a series in a normed space. This condition is automatically fulfilled for the null-sequences in finite dimensional normed spaces. In this paper we describe some classes of null-sequences in an infinite dimensional normed space 1\leq p<\infty satisfying the mentioned condition	https://atsu.edu.ge/index.php/en/teqnikuri-news-eng/2776-xiii-conferencia-teqnikuri-eng
XII Annual International Conference of the Georgian Mathematical Union	Batumi, Georgia	2022	29/08/2022 - 03/09/2022	Georgian Mathematical Union	On a condition for the affinity of the sum range of the series in a normed space	oral	The talk is about Chobanyan-Pecherski condition which is a sufficient condition for the affinity of the sum range of a series in a normed space. This condition is automatically fulfilled for the null-sequences in finite dimensional normed spaces. In this paper we describe some classes of null-sequences in an infinite dimensional normed space l_p, 1\leq p<\infty, satisfying the mentioned condition.	http://gmu.gtu.ge/Batumi2022/
XI Annual International Conference of the Georgian Mathematical Union	Batumi, Georgia	2021	23/08/2021 - 28/08/2021	Georgian Mathematical Union	The Law of Large Numbers for Weakly Correlated Random Elements in the Spaces lp	oral	The Law of Large Numbers for the weakly correlated random elements in lp spaces is presented	http://gmu.gtu.ge/Batumi2021/
13th International ISAAC Congress	Ghent, Belgium	2021	02/08/2021 - 06/08/2021	ISAAC; Ghent University, Department of Mathematics.	Rearrangement universality of the prime numbers' power series in a complex field	oral	The universality of signed primes power and the Dirichlet series in the complex field is discussed	https://cage.ugent.be/isaac2021/
Recent Trends in Statistical Theory and Applications- 2021 [WSTA 2021]	Trivandrum, India	2021	29/06/2021 - 02/07/2021	Kerala University	On the law of large numbers for dependent random elements	oral	The Law of Large Numbers for the dependent random elements in lp spaces is presented	https://sites.google.com/keralauniversity.ac.in/wsta-2021/home?authuser=0
XII Annual International Meeting of the Georgian Mechanical Union. Dedicated to 130 birthday anniversary of academician N. Muskhelishvili	Kutaisi, Georgia	2021	09/09/2021 - 11/09/2021	Georgian Mechanical Union	The Law of Large Numbers in lp spaces	oral	The Law of Large Numbers for the weakly correlated random elements in lp spaces is presented	https://atsu.edu.ge/index.php/en/teqnikuri-news-eng/2349-meqanikosta-yovelwliuri-saert-konferencia-eng
XXXV Enlarged Sessions of the Seminar of VIAM,	Tbilisi, Georgia	2021	21/04/2021 - 23/04/2021	I. Javakhishvili Tbilisi State University, VIAM	SLLN for weakly correlated random elements in the lp spaces	oral	An analogue of the famous Khinchine theorem for the dependent random variables is given for the case of random elements in Banach spaces lp	http://www.viam.science.tsu.ge/enlarged/2021/
Sixt Int. Conf. Statistics for Twenty-first Century - 2020 [ICSTC 2020]	Trivandrum, India	2020	16/12/2020 - 19/12/2020	Kerala University	On a numerical characteristic of the Hadamard matrices	oral	Some numerical properties of Hadamard matrices were discussed	https://sites.google.com/keralauniversity.ac.in/icstc-2020/home
XI Annual International Meeting of the Georgian Mechanical Union	Batumi, Georgia	2020	27/08/2020 - 29/08/2020	Georgian Mechanical Union	Statistical Analysis for the Municipal Transport of Tbilisi	oral	Rearrangement universality of signed Dirichlet series is considered	https://atsu.edu.ge/index.php/en/teqnikuri-news-eng/1988-mqanikosta-kavshiris-saertashoriso-konferencia-eng
X Int. Conf. of the Georgian Mathematical Union	Batumi, Georgia	2019	02/09/2019 - 06/09/2019		Subgaussian random elements and 2-summing operators	oral	Two theorems about the weakly Subgaussian and Subgaussian random elements in Hilbert and Banach spaces are presented	http://gmu.ge/Batumi2019/
12th International ISAAC congress.	Aveiro, Portugal	2019	29/07/2019 - 02/08/2019	ISAAC; University of Aveiro, Portugal	On the series with an affine sum range in a Banach space	poster	Talk is about the duality between the permutations and arrangements of signs for the series with terms in infinite dimensional Banach spaces. Some explicit constructions of the sequences in some concrete Banach spaces are constructed. Some classes of bounded, linear operators, which emerge in related problems are considered	http://isaac2019.web.ua.pt/Webpage/Welcome_files/abstracts-volume.pdf
CERN Cognitive Festival in Georgia	Tbilisi, Georgia	2018	22/10/2018 - 26/10/2018	Georgian Technical University	Some Properties of Hadamard Matrices	oral	Numerical characteristic of Hadamard matrices and its applications are considered	https://indico.cern.ch/event/766618/timetable/?view=standard_numbered
IX Int. Conf. of the Georgian Mathematical Union	Batumi, Georgia	2018	03/09/2018 - 08/09/2018	Georgian Mathematical Union	Maximum Inequalities and their Applications to Orthogonal and Hadamard Matrices	oral	Numerical characterizations for Hadamard and orthogonal matrices by use of maximal inequalities for the signed vector summands are considered	http://gmu.gtu.ge/Batumi2018/ENG/index.html
11th Int. Conf. Comp. Sc. Inf. Tech. (CSIT 2017).	Yerevan, Armenia	2017	25/09/2017 - 29/09/2017	Nat. Acad.Sci. Armenia; Inst. Inform. Aut. Problems	Maximum Inequalities and their Applications to Hadamard Matrices	oral	A new numerical characterization for Hadamard matrices is introduced. Its estimations for different norms are established by use of appropriate maximal inequalities for the signed vector summands.	https://csit.am/2017/
VIII Annual Int. Conf. of the Georgian Mathematical Union.	Batumi, Georgia	2017	08/09/2017 - 12/09/2017	Georgian Mathematical Union	Energy control issues	oral	Collaborative research with energy experts about some issues of energy control is presented. Based on the real, existing data the results of practical character is discussed	http://gmu.gtu.ge/Batumi2017/
XXXI Enlarged Sessions of the Seminar of VIAM, Dedicated to the 110th Birthday Anniversary of Academician Ilia Vekua	Tbilisi, Georgia	2017	19/04/2017 - 21/04/2017	I. Javakhishvili Tbilisi State University, VIAM	Rearrangement theorem for the weak topology	oral	Refined version of a rearrangement theorem for a weak topology is given	http://www.viam.science.tsu.ge/enlarged/2017/
4th Int. Conf. “Lie Groups, Differential Equations and Geometry”	Modica, Italy	2016	08/06/2016 - 15/06/2016	Marie Curie's International Research Staff Exchange Scheme Grants FP7-PEOPLE-2012-IRSES, 317721	Some Problems on the Rearrangements of Series	oral	Some Applications of Hadamard Matrices are discussed	https://indico.cern.ch/event/572800/
South Caucasus Grid&Cloud Computing Workshop (SCCTW 2016)	Tbilisi, Georgia	2016	03/10/2016 - 07/10/2016	Georgian Technical University	On Some Applications of Hadamard Matrices	oral	Some Applications of Hadamard Matrices are discussed	https://indico.cern.ch/event/572800/
Int. Sci. Conf. dedicated to the 85-th anniversary of academician I. V. Prangishvili- "Information and Computer Technologies, Modeling, Control	Tbilisi, Georgia	2015	03/11/2015 - 05/11/2015	Georgian Technical University	Some Properties of Hadamard Matrices. Proceedings pg. 71 – 72	oral	Some numeric properties of Hadamard matrices are investigated	http://ict-mc.gtu.ge/
10th International Conference on Computer Science and Information Technologies. CSIT 2015	Yerevan, Armenia	2015	28/09/2015 - 02/10/2015	Nat. Acad.Sci. Armenia; Inst. Inform. Aut. Problems	Some Properties of Hadamard Matrices	oral	One numerical characteristic of the Hadamard matrices is discussed	https://csit.am/2015/
South Caucasus Grid&Cloud Computing Workshop (SCCTW 2014)	Tbilisi, Georgia	2014	20/10/2014 - 24/10/2014	Georgian Technical University	Greedy Algorithm Fails in Compact Vector Summation	oral	It is shown that the greedy algorithm fails in a Compact Vector Summation problem	https://indico.cern.ch/event/335418/
V Annual Conference of the Georgian Mathematical Union.	Batumi, Georgia	2014	08/09/2014 - 12/09/2014	Georgian Mathematical Union	A version of Transference Lemma	oral	A version of Transference Lemma for the summands from the normed space is presented	http://www.gmu.ge/Batumi2014/
IV Annual Conference of the Georgian Mathematical Union.	Batumi, Georgia	2013	11/09/2013 - 15/09/2013	Georgian Mathematical Union	Signs and permutations in Ulyanov’s conjecture. Book of Abstracts, p. 113	oral	One theorem for the rearrangement version of Ulyanov's problem is discussed	http://gmu.gtu.ge/Batumi2013/
International Conference and Workshop Lie Groups, Differential Equations and Geometry	Batumi, Georgia	2013	10/06/2013 - 22/06/2013	Marie Curie's International Research Staff Exchange Scheme Grants FP7-PEOPLE-2012-IRSES, 317721	Complex and Quaternion Universal Series	oral	Universality theorems of Complex and Quaternion Series are discussed	http://rmi.tsu.ge/mma/
ICECECE 2012: International Conference on Electrical, Computer, Electronics, Communication Engineerin		2012	26/09/2012 - 27/09/2012	World Academy of Sciences	Elections Management Information Communication System VoterBallot	oral	Computerized elections management system is presented	http://www.waset.org/conferences/2012/rome/icecece
III International conference of the Georgian mathematical union.	Batumi, Georgia	2012	02/09/2012 - 09/09/2012	Georgian Mathematical Union	A version of the rearrangement theorem	oral	A version of the rearrangement theorem for the weak topology of a Banach space is presented	http://gmu.gtu.ge/Batumi2012/
International Scientific Conference dedicated to the 90-th anniversary of Georgian Technical University	Tbilisi, Georgia	2012	19/09/2012 - 21/09/2012	Georgian Technical University	Markov decision process for the long-term control of hydro station with reservoir	oral	A problem of the river flow control is considered from the point of view of the queuing theory and the theory of storage optimal control. mathematical model is posed in the frames of Markov decision process	http://gesj.internet-academy.org.ge/conf_gtu90/en/index_en.php
XXIV Enlarged Sessions of the Seminar of VIAM,	Tbilisi, Georgia	2010	21/04/2010 - 23/04/2010	I. Javakhishvili Tbilisi State University, VIAM	Some notes on convergent rearrangements of series of random variables	oral	Conditions for the existence of convergent rearrangements of series of random variables are presented	http://www.viam.science.tsu.ge/others/GS-2010.doc
International Conference «Information and Computational Technologies» (Dedicated to commemoration of Professors E. Dekanosidze and M. Tsuladze).	Tbilisi, Georgia	2010	02/05/2010 - 06/05/2010	N. Muskhelishvili Institute of Computational Mathematics & St. Andrew the First Called Georgian University of the Patriarchy of Georgia	Compact Vector Summation and its Applications to Problems of Scheduling Theory. Book of Abstracts, p. 150 -151	oral	An effective algorithmic method for finding an optimal permutation in CVS is presented, appropriate estimations are given	http://micm.edu.ge/wp-content/uploads/2020/06/Abstracts_CONF_MICM_2010.pdf
Fifth Congress of Mathematicians of Georgia	Batumi - Kutaisi, Georgia	2009	09/10/2009 - 11/10/2009	Georgian Mathematical Union	A maximum inequality for rearrangements of summands and its applications to orthogonal series and scheduling theory. Abstracts of contributed talks, p. 32.	oral	Two-sided maximum inequality for rearrangements is proved, which leads to the wellknown Garsia inequality	http://www.rmi.ge/~gmu/GMU_Conference/V_Kril_Tez.pdf

Web of Science: Citations=4, h-index=1
Scopus: Citations=17, h-index=2
Google Scholar: Citations =63, h-index=4

Doctoral Thesis Referee

Analysis and synthesis methods for the aggregated geometric model of ATLAS detector

Georgian Technical University

Assesment of the inovative project risks by use of the information models

Georgian Technical University

Efficient data processing and storage based on the built-in network infrastructure of the disk array distributed in the data warehouse

Georgian Technical University

Master Theses Supervisor

Statistical analysis for the early diagnostics of breast censer by use of antygens

Sokhumi State University

Doctoral Thesis Supervisor/Co-supervisor

Scientific editor of monographs in foreign languages

Scientific editor of a monograph in Georgian

Editor-in-Chief of a peer-reviewed or professional journal / proceedings

GESJ: Computer Sciences and Telecommunications

01/02/2021

Review of a scientific professional journal / proceedings

Journal of Mathematical Analysis and Applications

Elsevier

02/05/2021

AMS MathReview, Reviewer Number: 105708

USA

01/02/2021

Member of the editorial board of a peer-reviewed scientific or professional journal / proceedings

Participation in a project / grant funded by an international organization

FP7 - INCO. 2010-6.1: Eastern Europe and South Caucasus. Project N° 266155. “Re-creation and building of capacities in Georgian ICT Research Institutes” (GEO-RECAP)

საქართველო

2010-2012

Primary Coordinator

TEMPUS IV-6. “Modernization of Mathematics and Statistics curricula for Engineering and Natural Sciences studies in Georgian and Armenian Universities by introducing modern educational technologies (MATH-GEAR)”

European Commission საქართველო

2013-2016

Researcher

FP7. FP7-INCO-2013-9. Project N° 609531. “Knowledge Transfer Community to bridge the gap between research, innovation and business creation (NoGAP)”

European Commission საქართველო

2013-2016

Researcher

Participation in a project / grant funded from the state budget

Rearrangement of vectors, Theory and application in Probability, Statistics and Computer Networks; Grant # GEM1-3328-TB-03

Georgian Research and Development Foundation (GRDF)

2005-2006

Researcher

Sign-permutation duality in linear analysis. Applications to scheduling theory; Grant # GNSF/ST06/3-009

Georgian National Science Foundation, GNSF

2006-2008

Researcher

Maximum Inequalities for Rearrangements with Applications to Functional Analysis and Scheduling Theory; Grant # GNSF/ST08/3-384

Georgian National Science Foundation, GNSF

2009-2011

Researcher

Interrelation between signs and permutations in compact vector summation: theory and applications; RNSF, FR/539/5-100/13

Shota Rustaveli National Science Foundation

2014-2016

Researcher

Patent authorship

Membership of the Georgian National Academy of Science or Georgian Academy of Agricultural Sciences

Membership of an international professional organization

Membership of the Conference Organizing / Program Committee

National Award / Sectoral Award, Order, Medal, etc.

Honorary title

Monograph

Rearrangements of series. Journal of Mathematical Sciences, Vol. 239, No. 4, 2019, p. 438 -543.

Grant Project

The present work is devoted to the problems related to the rearrangements of series in metrizable topological vector spaces. The idea goes back to Dirichlet (most probably, he was the first who discovered the phenomenon that the sum of a scalar series may depend on the rearrangement of its terms), Riemann, P. Levy, E. Steinitz, Banach, Kolmogorov, and others.

Two main directions in this area, attracting the interest of many researchers, are considered. The first one concerns the problem of the structure of the sum range of conditionally convergent series. The other is the problem of the existence of an almost sure convergent rearrangement of a functional series,

including some classical problems on the convergence of Fourier series.

This book consists mainly of material included in the Ph.D. thesis and some recent works of the author and his colleagues.

https://link.springer.com/article/10.1007/s10958-019-04315-9

Handbook

Research articles in high impact factor and local Scientific Journals

Convergent rearrangements of series of vector-valued functions. Georgian Mathematical Journal. v.7, (2000), N1. 43-51.

State Target Program

A sufficient condition for the existence of an almost everywhere convergent rearrangement of series in Orlicz spaces of vector-valued functions is obtained. The results of this paper cover most of the related statements known previously for the series of scalar functions.

https://doi.org/10.1515/gmj.2000.43

Greedy Algorithm Fails in Compact Vector Summation. Bulletin of Georgian National Academy of Sciences, v. 4, no. 2, 2010, 5-7

Grant Project

We show that in any two-dimensional normed space there exists a collection of vectors such that the greedy algorithm fails to be optimal

http://science.org.ge/old/moambe/4-2/Chelidze.pdf

A maximum inequality for rearrangements of summands and its applications to orthogonal series and scheduling theory processes. Bulletin of the Georgian National Academy of Sciences, v.5. no.1, 2011. 16-20.

Grant Project

Two-sided estimation for the average of the partial sums of the vector with respect to permutations is proved. For the real numbers it implies the famous Garsia inequality. Constructive algorithm for finding an optimal permutation having applications in scheduling theory is given.

http://science.org.ge/old/moambe/5-1/16-20%20Chobaniani.pdf

On Complex Universal Series. Proceedings of A. Razmadze Mathematical Institute. 160 (2012), 53-63.

Grant Project

The necessary and sufficient conditions for the universality of the complex series are established

http://rmi.tsu.ge/proceedings/volumes/pdf/v160-4.pdf

Signs and Permutations: Two Problems of the Function Theory. Proceedings of A. Razmadze Mathematical Institute. 160 (2012), 24-34.

Grant Project

One variant of the transference lemma is proved. By its application we get a refined version of the Garsia inequality for orthogonal systems. Moreover, it is shown that the fulfillment of the “sigma-theta” condition for the Fourier series of a continuous periodic Banach space valued function implies the uniform convergence of a rearranged series to the function

http://www.rmi.ge/proceedings/volumes/pdf/v160-2.pdf

On rearrangement theorem in Banach spaces. Georgian Mathematical Journal, 2014, Volume 21, Issue 2, p. 157 – 163

State Target Program

It is shown that every infinite-dimensional real Banach space contains a sequence, were its subsequence satisfies some editional properties. This result implies, in particular, that the rearrangement theorem and the Dvoretzky–Hanani theorem fail drastically for infinite-dimensional Banach spaces.

https://doi.org/10.1515/gmj-2014-0016

Sum Range of Quaternion Series. J. Math. Sci., v. 216, 4, 2016, p. 519-521

State Target Program

In this paper we obtain a result which implies, in particular that the sum range of a special quaternion series is a closed proper subfield of the division ring of quaternions, isometrically isomorphic to the field of complex numbers

https://link.springer.com/article/10.1007/s10958-016-2908-9

Maximal inequalities and their applications to orthogonal and Hadamard matrices. Period. Math. Hung. (2020) 81:88-97

State Target Program

Maximal inequalities for the signed vector summands are established. Probabilistic estimations for the sets of appropriate signs are given. By use of the “transference technique” appropriate maximal inequalities are derived for the permutations.One application for orthogonal and Hadamard matrices is suggested.

DOI 10.1007/s10998-020-00314-5

Notes on Sub-Gaussian Random Elements. In: Applications of Mathematics and Informatics in Natural Sciences and Engineering. AMINSE 2019. Springer Proceedings in Mathematics & Statistics, vol. 334, p. 197-203

State Target Program

We give a short survey concerning sub-Gaussian random elements in a Banach space and prove a statement about the induced operator of a bounded random element in a Hilbert space

https://doi.org/10.1007/978-3-030-56356-1_11

Statistical analysis for efficient design of passenger transit system. Bulletin of TICMI, vol. 24, No. 2, 2020, pp. 85-95.

State Target Program

In this work we investigate performance of the bus transit system of city Tbilisi based on the statistical analysis of the passenger flow during the year 2019

http://www.viam.science.tsu.ge/others/ticmi/blt/vol24_2/giorgobiani.pdf

The law of large numbers for weakly correlated random elements in the spaces l_p,1≤p<∞. Lith Math J 62, 308–314

State Target Program

We prove an analogue of Khinchin’s theorem for weakly correlated random elements with values in the spaces l_p,1≤p<∞

DOI 10.1007/s10986-022-09564-x

Publication in Scientific Conference Proceedings Indexed in Web of Science and Scopus

A note on the rearrangement theorem in a Banach space. Proceedings of the International Scientific Conference ICTMC-2010 Devoted to the 80th Anniversary of I.V. Prangishvili. Nova Science Publishers, 2011

Grant Project

It is shown that the rearrangement theorem is not true for infinite-dimensional Banach spaces.

Some Properties of Hadamard Matrices. Comp. Sci. Inf. Tech. (CSIT), 2015, 64 – 65 (IEEE Conference Publications).

State Target Program

Hadamard transform is an important tool for the investigation of some problems of Quantum Computing, Coding Theory and Cryptology, Statistics, Image Analysis, Signal Processing, Fault-Tolerant Systems, Analysis of Stock Market Data, Combinatorial Designs and so on. Here we present one numerical property of Hadamard matrices

https://ieeexplore.ieee.org/document/7358251

George Giorgobiani

Academic Doctor of Science

Muskhelishvili Institute of Computational Mathematics

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About Me

Scientific Publications

Conferences

Citation Index

Research visit in a foreign research institution

Introduction of scientific achievements in practice / industrial experience

Participation in a scientific expedition

Educational activities

Doctoral Thesis Referee

Master Theses Supervisor

Doctoral Thesis Supervisor/Co-supervisor

Editing and referencing

Scientific editor of monographs in foreign languages

Scientific editor of a monograph in Georgian

Editor-in-Chief of a peer-reviewed or professional journal / proceedings

Review of a scientific professional journal / proceedings

Member of the editorial board of a peer-reviewed scientific or professional journal / proceedings

Projects / Grants

Participation in a project / grant funded by an international organization

Participation in a project / grant funded from the state budget

Intellectual property

Patent authorship

Activities

Membership of the Georgian National Academy of Science or Georgian Academy of Agricultural Sciences

Membership of an international professional organization

Membership of the Conference Organizing / Program Committee

National Award / Sectoral Award, Order, Medal, etc.

Honorary title

International Scientific Works

Monograph

Handbook

Research articles in high impact factor and local Scientific Journals

Publication in Scientific Conference Proceedings Indexed in Web of Science and Scopus