Numerical Infinity and the Infinity Computer: Books, patents, research papers, presentations, visitors

Related awards and distinctions

·    Pythagoras International Prize for Mathematics (Premio Internazionale Pitagora per la Matematica), Croton, Italy, 2010

·    Honorary Fellowship, the highest distinction of the European Society of Computational Methods in Sciences, Engineering and Technology, 2015

·    Achievement Award from the World Congress in Computer Science, Computer Engineering, and Applied Computing, USA, 2015

for more information see

Curriculum Vitae of Prof. Yaroslav D. Sergeyev

The 2nd International Conference and Summer School “Numerical Computations: Theory and Algorithms”, June 19-25, 2016, Italy    Previous conferences: 2013   2010

Sergeyev Ya.D. (2015) Un semplice modo per trattare le grandezze infinite ed infinitesime, La Matematica nella Società e nella Cultura: Rivista dell’Unione Matematica Italiana, Serie I, Vol.8, 111-147.

Video lectures

Keynote Lecture opening the 4th International Conference on Computational Intelligence, Barcelona, Spain: The Infinity Computer and Numerical Computations with Infinities and Infinitesimals

Лекция на телеканале «Культура» "Системы записи чисел и их влияние на прогресс науки"

Лекция (с дискуссией) на IV Международной конференции "Математика, её приложения и математическое образование"

 

Yaroslav D. Sergeyev, Arithmetic of Infinity

 

Media citations

Computerworld, Computerra, IlSole24Ore,  Panorama, Quale Computer, Radio24, ITAR-TASS, TASS_TELECOM, RIA Novosti, Italia Oggi, Russian National TV Channel 1, Russian National TV Channel “Culture”, IpFrontline, Key4biz: Knowledge for Business, MIT Technology Review, New Scientist, Newton, Gazzettino Europeo, Voice of Russia, Tutto Misure, MF - Milano Finanza, Ведомости, Наука и Жизнь, Открытые системы, etc.

Paperback edition is available at European Amazon sites:   UK, DE, FR, IT, ES

Revised electronic edition is available at Amazon sites: COM, UK, DE, FR, IT, ES, CA, JP, BR,  IN, MX

12.02.2016 Amazon.it Kindle Store Best Sellers Rank:

# 1 in  eBook Kindle > eBook in lingua straniera > eBook in inglese > Scienze, tecnologia e medicina > Matematica

The book presents a new methodology that allows one to represent infinite and infinitesimal numbers by a finite number of symbols and to execute arithmetical operations with all of them in the same manner as we are used to do with finite quantities. The new approach is not related to the non-standard analysis and infinity is considered in the book in a coherent way different from those proposed by Georg Cantor, Abraham Robinson, and John Conway. However, the new approach does not contradict Cantor, it evolves his theory and supplies new more powerful tools to deal with different infinite and infinitesimal quantities.

From the methodological point of view, the principle of Ancient Greeks ‘The part is less than the whole’ is adopted and applied to all quantities (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The new positional system with the infinite radix introduced in the book allows one to consider infinite, finite, and infinitesimal numbers as particular cases of a unique framework. The new viewpoint gives detailed answers to many questions and paradoxes regarding infinite and infinitesimal quantities. Particularly, applications of the new approach to limit theory, measure theory, and set theory are given.

The book is mainly addressed to mathematicians, computer scientists, philosophers, physicists, and students. However, it is written in a popular way in order to allow any person having a high school education and interests in the foundations of these sciences to understand it easily.

13.06.2014 Amazon.com Best Sellers Rank:

#1 in Books > Science & Math > Mathematics > Infinity

#1 in Kindle Store > Kindle eBooks > Nonfiction > Science > Mathematics > Infinity

Reviews

published in International Journals

·   Article, MIT Technology Review, 2012

·   Computational Management Science, 2007, vol. 4(1), pages 85-86, written by Prof. D. Trigiante

·   Cybernetics & Systems Analysis, 2006, vol. 42(6), page 183, written by Prof. V.P. Shylo

·   Optimization Methods and Software, 2006, vol. 21(6), pages 995–996, written by Prof. O. Prokopyev

·   International Journal of Unconventional Computing, 2006, vol. 2(2), pages 193-194, written by the Editor-in-Chief Prof. A. Adamatzky

·   Journal of Global Optimization, 2006, vol. 34, pages 157–158, written by the Editor-in-Chief Prof. P.M. Pardalos

The Infinity Computer (European patent EP 1728149, Russian patent 2395111, US patent 7,860,914)

 

The main difference of the new approach with respect to non-standard analysis theories is its strong computational character opening a new exiting area in the theory and practice of computations – Infinity Computing. European patent 1728149 issued 03.06.2009 introducing “Computer system  for storing infinite, infinitesimal, and finite quantities and executing arithmetical operations with them” describes the Infinity Computer able to execute computations with infinite, finite, and infinitesimal numbers numerically (not symbolically) in a unique framework. Russian patent 2395111 has been granted 20.07.2010 and USA patent 7,860,914 has been awarded 28.12.2010.

There exist the first software prototype of the Infinity Computer and the Infinity Calculator able to execute arithmetical operations with numbers having finite parts and/or infinitesimal and infinite parts of different orders.

Here you can see a screenshot of the Infinity Calculator with an example of division and a brief comment.

The interested investors are invited to contact the author.

 

News

·   Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: http://si.deis.unical.it/%7Eyaro/media_file/image005.gifConference “Teaching the Arithmetic of Infinity”, 5 July 2016, University of East Anglia, Norwich, UK

·   Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: http://si.deis.unical.it/%7Eyaro/media_file/image005.gifLa nuova aritmetica dell'infinito: GRAVITÀ ZERO intervista il Prof. Davide Rizza

·   GRAVITÀ ZERO: Sotto la lente logica di Gabriele Lolli

·   Lolli G. (2015) Metamathematical investigations on the theory of Grossone, Applied Mathematics and Computation, 255, 3-14.

·   Sergeyev Ya.D. (2015) Un semplice modo per trattare le grandezze infinite ed infinitesime, La Matematica nella Società e nella Cultura: Rivista dell’Unione Matematica Italiana, Serie I, Vol.8, 111-147.

·   Special Issue of the journal Communications in Nonlinear Science and Numerical Simulation (Elsevier), vol. 21,  (2015) dedicated to the International Conference NUMTA-2013, Falerna, Italy, 2013

·   Interview to Russia Beyond The Headlines

·   Special Issue of the journal Applied Mathematics and Computation (Elsevier), vol. 255 (2015) dedicated to the International Conference NUMTA-2013

·   Article, MIT Technology Review

·   Articolo del Prof. G. Lolli per “Newton”

·   Articoli divulgativi del Dott. Walter Caputo

About the author                                                                                                          Top of this page

 

Yaroslav D. Sergeyev Ph.D., D.Sc., D.H.C. is Distinguished Professor at the University of Calabria, Rende, Italy and Head of Numerical Calculus Laboratory at the same university. He is also Professor (part-time) at the Lobachevsky State University, Nizhni Novgorod, Russia and Affiliated Researcher at the Institute of High Performance Computing and Networking, Rende, Italy. His research interests include numerical analysis, set theory, number theory, global optimization, parallel computing, and fractals. His list of publications contains more than 200 items including 5 books and more than 80 papers in prestigious international journals. He is a member of editorial boards of 5 international journals. He has been awarded several research prizes (Pythagoras International Prize in Mathematics, Italy, 2010; Outstanding Achievement Award from the 2015 World Congress in Computer Science, Computer Engineering, and Applied Computing, USA; Honorary Fellowship being the highest distinction of the European Society of Computational Methods in Sciences, Engineering and Technology, 2015; Lagrange Lecture, Turin University, Italy, 2010; MAIK Prize for the best scientific monograph published in Russian, Moscow, 2008, etc.).  Additional information about Prof. Sergeyev can be found here.

 

Selected research papers                                                                                                                                                                      Top of this page

 

A brief survey

Sergeyev Ya.D. (2010) Lagrange Lecture: Methodology of numerical computations with infinities and infinitesimals, Rendiconti del Seminario Matematico dell'Università e del Politecnico di Torino, 68(2), 95–113.

A long survey

Sergeyev Ya.D. (2013) Numerical computations with infinite and infinitesimal numbers: Theory and applications, in “Dynamics of Information Systems: Algorithmic Approaches” edited by Sorokin, A., Pardalos, P.M., Springer, New York, pp. 1-66.

In case you know Italian then this paper is a good choice to start

Sergeyev Ya.D. (2015) Un semplice modo per trattare le grandezze infinite ed infinitesime, La Matematica nella Società e nella Cultura: Rivista dell’Unione Matematica Italiana, Serie I, Vol.8, 111-147.

·  Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: http://si.deis.unical.it/%7Eyaro/media_file/image005.gifMargenstern M. (2016) Infinigons of the hyperbolic plane and grossone, Applied Mathematics and Computation, 278, 45–53.

·  Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: http://si.deis.unical.it/%7Eyaro/media_file/image005.gifSergeyev Ya.D., Mukhametzhanov M.S., Mazzia F., Iavernaro F., Amodio P. (2016) Numerical methods for solving initial value problems on the Infinity Computer, International Journal of Unconventional Computing, 12(1), 3–23.

·  Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: http://si.deis.unical.it/%7Eyaro/media_file/image005.gifSergeyev Ya.D. (2016) The exact (up to infinitesimals) infinite perimeter of the Koch snowflake and its finite area, Communications in Nonlinear Science and Numerical Simulation, 31(1–3):21–29.

·  Lolli G. (2015) Metamathematical investigations on the theory of Grossone, Applied Mathematics and Computation, 255, 3-14.

·  Sergeyev Ya.D. (2015) Computations with grossone-based infinities, C.S. Calude, M.J. Dinneen (Eds.), Proc. of the 14th International Conference “Unconventional Computation and Natural Computation”, Lecture Notes in Computer Science, vol. 9252, Springer,  89-106.

·  Sergeyev Ya.D. (2015) The Olympic medals ranks, lexicographic ordering and numerical infinities, The Mathematical Intelligencer, 37(2), 4-8.

·  Sergeyev Ya.D. (2015) Letter to the Editor, The Mathematical Intelligencer, 37(4), 2-3.

·  D’Alotto L. (2015) A classification of one-dimensional cellular automata using infinite computations, Applied Mathematics and Computation, 255, 15-24.

·  Margenstern M. (2015) Fibonacci words, hyperbolic tilings and grossone, Communications in Nonlinear Science and Numerical Simulation, 21(1–3), 3-11.

·  Sergeyev Ya.D., Garro A.  (2015) The Grossone methodology perspective on Turing machines, in "Automata, Universality, Computation", A. Adamatzky (ed.), Springer Series "Emergence, Complexity and Computation", Vol. 12, pp. 139-169.

·  Montagna F., Simi G., Sorbi A. (2015) Taking the Pirahã seriously, Communications in Nonlinear Science and Numerical Simulation, 21(1–3), 52-69.

·  Iudin D.I., Sergeyev Ya.D. Hayakawa M. (2015) Infinity computations in cellular automaton forest-fire model, Communications in Nonlinear Science and Numerical Simulation, 20(3), 861-870.

·  D’Alotto L. (2013) A classification of two-dimensional cellular automata using infinite computations, Indian Journal of Mathematics, 55, 143-158.

·  Sergeyev Ya.D., Garro A. (2013) Single-tape and multi-tape Turing machines through the lens of the Grossone methodology, Journal of Supercomputing, 65(2), 645-663.

·  Sergeyev Ya.D. (2013) Solving ordinary differential equations by working with infinitesimals numerically on the Infinity Computer, Applied Mathematics and Computation, 219(22), 10668–10681.

·  Sergeyev Ya.D. (2013) Numerical computations with infinite and infinitesimal numbers: Theory and applications, in "Dynamics of Information Systems:  Algorithmic Approaches", Eds. Alexey Sorokin and Panos M. Pardalos, Springer, New York, 2013, pp. 1-66.

·  Vita M.C., S. De Bartolo, C. Fallico, M. Veltri (2012) Usage of infinitesimals in the Menger’s Sponge model of porosity, Applied Mathematics and Computation, 218(16), 8187-8196.

·  D’Alotto L. (2012) Cellular Automata Using Infinite Computations, Applied Mathematics and Computation, 218(16), 8077-8082.

·  Lolli G. (2012) Infinitesimals and infinites in the history of Mathematics: A brief survey, Applied Mathematics and Computation, 218(16), 7979-7988.

·  Margenstern M. (2012) An application of Grossone to the study of a family of tilings of the hyperbolic plane, Applied Mathematics and Computation, 218(16), 8005-8018.

·  De Cosmis S., R. De Leone (2012) The use of Grossone in Mathematical Programming and Operations Research, Applied Mathematics and Computation, 218(16), 8029-8038.

·  Iudin D.I., Ya.D. Sergeyev, M. Hayakawa (2012) Interpretation of percolation in terms of infinity computations, Applied Mathematics and Computation, 218(16), 8099-8111.

·  Сергеев Я.Д., Cистемы записи чисел, их точность и выполнение на практике численных вычислений с конечными, бесконечно большими и бесконечно малыми величинами, Математика, её приложения и математическое образование: Материалы IV Международной конференции. – Ч.1. – Улан-Удэ: Изд-во ВСГТУ, 2011, с. 284-288.

·  Sergeyev Ya.D. (2011) Using blinking fractals for mathematical modelling of processes of growth in biological systems, Informatica, 2011, 22(4), 559–576.

·  Margenstern M. (2011) Using Grossone to count the number of elements of infinite sets and the connection with bijections, p-Adic Numbers, Ultrametric Analysis and Applications, 3(3), 196-204.

·  Sergeyev Ya.D. (2011) On accuracy of mathematical languages used to deal with the Riemann zeta function and the Dirichlet eta function, p-Adic Numbers, Ultrametric Analysis and Applications, 3(2), 129-148.

·  Sergeyev Ya.D. (2011) Higher order numerical differentiation on the Infinity Computer, Optimization Letters, 5(4), 575-585.

·  Sergeyev Ya.D., Garro A. (2010) Observability of Turing Machines: a refinement of the theory of computation, Informatica, 21(3), 425–454.

·  Sergeyev Ya.D. (2010) Counting systems and the First Hilbert problem, Nonlinear Analysis Series A: Theory, Methods & Applications, 72(3-4), 1701-1708.

·  Sergeyev Ya.D. (2009) Numerical point of view on Calculus for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains, Nonlinear Analysis Series A: Theory, Methods & Applications, 71(12), e1688-e1707.

·  Sergeyev Ya.D. (2009) Evaluating the exact infinitesimal values of area of Sierpinski's carpet and volume of Menger's sponge,  Chaos, Solitons & Fractals, 42,  3042–3046.

·  Sergeyev Ya.D. (2009) Numerical computations and mathematical modelling with infinite and infinitesimal numbers, Journal of Applied Mathematics and Computing, 29, 177-195.

·  Sergeyev Ya.D. (2008) A new applied approach for executing computations with infinite and infinitesimal quantities, Informatica, 19(4), 567-596.

·  Sergeyev Ya.D. (2007) Blinking fractals and their quantitative analysis using infinite and infinitesimal numbers, Chaos, Solitons & Fractals, vol. 33(1), 50-75.

·  Sergeyev Ya.D. (2008) Measuring fractals by infinite and infinitesimal numbers, Mathematical Methods, Physical Methods & Simulation Science and Technology, vol. 1(1), 217-237.

·  Sergeyev Ya.D. (2005) A few remarks on philosophical foundations of a new applied approach to Infinity, Scheria, vol. 26-27, pp. 63-72.

·  Sergeyev Ya.D. (2006) Misuriamo l’infinito: Un semplice modo per insegnare i concetti delle grandezze infinite, Periodico di Matematiche, vol. 6(2), 11-26, (In Italian).

Presentations                                                                                                                                                                                     Top of this page

 

The Infinity Computer technology and its applications together with the respective mathematical and methodological issues have been presented at the following congresses:

 

1.     tutorial, the 2nd International Conference and Summer School “Numerical Computations: Theory and Algorithms”, Pizzo Calabro, Italy, June 19–25, 2016

2.     plenary lecture, the 7th International Workshop “Data Analysis Methods for Software Systems”, Druskininkai, Lithuania, December 3 – 5, 2015

3.     plenary lecture, International Conference and School “High-Performance Computing, Optimization and Applications”, Nizhni Novgorod, Russia, November 16-20, 2015

4.     plenary lecture, the 13th International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2015, Rhodes, Greece, September 23-29, 2015

5.     plenary lecture, the 14th International Conference on Unconventional Computation & Natural Computation, Auckland, New Zealand, 31 August – 4 September, 2015

6.     keynote lecture, the 2015 World Congress in Computer Science, Computer Engineering, and Applied Computing, Las Vegas, USA, July 27-30, 2015

7.     plenary lecture, 1st International Summer School for Sciences, History and Philosophy of Sciences & Science Education, Lille, France, June 22-26, 2015

8.     invited semi-plenary lecture, New Trends in Numerical Analysis: Theory, Methods, Algorithms and Applications, Falerna (CZ), Italy June 18-21, 2015tutorial, International Conference “Theory and Practice of Systems Analysis”, Rybinsk, Russia, May 21-24, 2014;

9.     plenary lecture, the 9th Italian Workshop on Artificial Life and Evolutionary Computation, Vietri sul Mare, Salerno, Italy, May 14-15, 2014;

10.  plenary lecture opening the 11th International Conference “Theory and Applications of Models of Computation”, Chennai, India, April 11-13, 2014;

11.  tutorial, EURO Mini-conference on Optimization in the Natural Sciences, Aveiro, Portugal, February 5-9, 2014;

12.  plenary lecture, International Conference “Optimal decisions in statistics and data analysis”, Cardiff, UK, December 16-18, 2013;

13.  plenary lecture, International Science and Information Conference, London, UK, October 7-9, 2013;

14.  invited 90 minutes lecture, International Workshop “The Number Road”, Erice, Italy, September 27, 2013;

15.  tutorial, International Conference and Summer School “Numerical Computations: Theory and Algorithms”, Falerna (CZ), Italy, June 17–23, 2013;

16.  keynote lecture opening the 4th International Joint Conference on Computational Intelligence, Barcelona, Spain, October 3-7, 2012;

17.  tutorial, the 15th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerical Computations, Novosibirsk, Russia, September 24-28, 2012;

18.  plenary lecture, the 4th International Conference on the Dynamics of Information Systems, Gainesville, Florida, USA, February 20 - 22, 2012; 

19.  invited lecture, the 12th International Symposium “Frontiers of Fundamental Physics”, Udine, Italy, November 21-23, 2011;

20.  plenary lecture, the 7th International Asian Summer School “Optimization of Complex Systems”, Tashkent, Uzbekistan, October 17-27, 2011;

21.  tutorial, Summer School “Achievements and Applications of Contemporary Informatics, Mathematics and Physics”, Kiev, Ukraine, August 12-19, 2011;

22.  plenary lecture, the 4th International conference "Mathematics, its Applications and Mathematical Education" Russia, Ulan-Ude, Baikal, June 27 - July 1, 2011;

23.  invited lecture, the International Workshop “New Worlds of Computation”, Orléans, France, May 23-24, 2011;

24.  invited one-hour lecture, International Workshop of Natural Computing of the Ninth International Conference on Cellular Automata for Research and Industry, Ascoli Piceno, Italy, September, 21-24, 2010;

25.  plenary lecture, the Second International Conference on Mathematical Physics and Its Applications, Samara, Russia, August 29 - September 4, 2010;

26.  keynote lecture, the 3rd Yalta Optimization Conference, Yalta, Ukraine, August, 2-4, 2010;

27.  plenary lecture, International Conference on Optimization, Simulation and Control, Ulaanbaatar, Mongolia, July 25-28, 2010;

28.  keynote lecture, the 2010 World Congress in Computer Science, Computer Engineering, and Applied Computing, Las Vegas, USA, July 12-15, 2010;

29.  joint keynote lecture, the 2010 International Conference on Scientific Computing and Workshop on Cellular Automata, Theory and Applications, Las Vegas, USA, July 14, 2010;

30.  tutorial, International workshop “Infinite and Infinitesimal in Mathematics, Computing, and Natural Sciences”, Cetraro, Italy, May 17-21, 2010;

31.  plenary lecture, International conference "Optimization and Applications" (OPTIMA2009), Petrovac, Montenegro, September 21-25, 2009;

32.  tutorial, the international workshop “Optimization and Control with Applications”, Harbin, China, June 6-11, 2009

33.  invited one hour lecture, the First World Congress on Global Optimization in Engineering & Science, Hunan, China, June 1-5, 2009;

34.  invited one hour lecture, the International Workshop “New Worlds of Computation”, Orléans, France, January 12, 2009

35.  keynote lecture, Yalta Conference on Discrete and Global Optimization, Yalta, Ukraine, July, 31 – August, 2, 2008;

36.  keynote lecture, the general plenary session of the World Multi-Conference WMSCI 2008 held jointly with the conferences RMCI 2008, MEI 2008, EIC 2008, and BMIC 2008, Orlando, Florida, June, 29 - July, 2, 2008;

37.  invited one hour lecture, the World Congress of Nonlinear Analysts WCNA-2008, Orlando, Florida, July, 2-9, 2008;

38.  tutorial, the 48th international workshop on Nonsmooth Analysis, Optimization and Applications, Erice, Italy, under the auspices of the International School of Mathematics “G. Stampacchia”,  May, 9–17, 2008;

39.  plenary lecture, International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2007, September 16-20, 2007;

40.  invited lecture, the 8th Mediterranean Workshop and Topical Meeting "Novel Optical Materials and Applications", Cetraro, Italy, June 3-9, 2007;

41.  tutorial, the International Workshop on Learning and Intelligent Optimization, Andalo, Italy, February 12-18, 2007;

42.  invited one hour lecture, the 15th Euromicro Conference on Parallel, Distributed and Network-based Processing, Naples, February 7-9, 2007;

43.  plenary lecture opening the MATHESIS Congress, Trento, Italy, November 2-4, 2006;

44.  plenary lecture, the Third International Conference of Applied Mathematics, Plovdiv, Bulgaria, August 12-18, 2006;

45.  plenary lecture, International Conference “Applied Optimization and Metaheuristic Innovations”, Yalta, Ukraine, July 17-23, 2006;

46.  invited lecture, the second International Workshop on Variational Analysis and Partial Differential Equations, Erice, Italy, under the auspices of the International School of Mathematics “G. Stampacchia”, July 5-14, 2006;

47.  round table “Infinity Computer and Calculus”, the 8th Congress of SIMAI (La Societa' Italiana di Matematica Applicata e Industriale), Ragusa (Sicily), May 22-26, 2006;

48.  plenary lecture, the XXI Autumn Meeting of the Polish Information Processing Society, Katowice, Poland, December 5-9, 2005;

49.  plenary lecture, the International Workshop on Global Optimization, Almeria, Spain, September 18-22, 2005;

50.  tutorial, the International Conference on Complementarity, Duality, and Global Optimization in Science and Engineering, Blacksburg, Virginia, USA, August 15-17, 2005;

51.  plenary lecture, International Conference on Difference Equations, Special Functions and Applications, Munich, July 25-30, 2005;

52.  plenary lecture, International Conference “Numerical Analysis: the State of the Art”, Rende (CS), Italy, May, 19-21, 2005;

53.  invited semi-plenary lecture at the International conference on Selected Problems of Modern Mathematics, dedicated to the 200th anniversary of K.G. Jacobi and the 750th anniversary of the Koenigsberg foundation, Kaliningrad, April, 4-8, 2005;

54.  tutorial, the Workshop "Numerical Methods and Mathematical Software", Montecatini Terme (PT), January 31 - February 1, 2005;

55.  plenary lecture, the VI-th International Congress on Mathematical Modelling, Nizhni Novgorod, Russia, September, 21-26, 2004;

56.  opening invited lecture, the congress “Infinity in Mathematics, Physics, and Philosophy”, Pisa, Italy, 26.03.2004.

 

Results described in the book and in the patent have been also presented at the following universities, research institutes, and organizations:

 

Universities

Research Institutes, Academies, and Organizations

Aberdeen, Amsterdam, A&M Texas, Anna University of Chennai (India), Bari, Barcellona, Bergamo, Bergen (Norway), Bologna, Cagliari, Calabria, Cardiff (UK), Caserta, Catania, Dokuz Eylul (Izmir, Turkey), East China Normal University (Shanghai), Ferrara, Florence, Harbin Institute of Technology (China), Kaliningrad, N.I. Lobatchevsky State University of Nizhni Novgorod, Metz, Milan, Milan Polytechnic, Modena, Moscow M.V. Lomonosov State University, Moscow City Pedagogical University, Orléans, Padua, Palermo, Pereslavl-Zalessky, Pisa, Reggio Calabria, Rome “La Sapienza”, Salerno, Siena, St. Petersburg, Torino, Trento, Trieste, and UCLA

Institute d’Alamber CNRS, Cachan, France; Institute for High Performance Computing and Networking, Rende, and Institute of Applied Mathematics and Information Technology, Pavia, both of the Italian National Research Council; Institutes of the Russian Academy of Sciences:

·          Computing Centre of the Russian Academy of Sciences, Moscow;

·          Institute of Applied Physics, Nizhni Novgorod;

·          Institute of Control Sciences, Moscow;

·          Institute for Mathematical Modelling, Moscow;

·          Institute of Numerical Mathematics, Moscow;

·          Institute of Systems Analysis, Moscow;

·          The Program Systems Institute, Pereslavl-Zalessky; 

·          Steklov Mathematical Institute, Moscow;

·          Steklov Mathematical Institute, St. Petersburg;

Institute of Computer Science of the Academy of Sciences of the Czech Republic, Prague; Institute of Cybernetics and Institute of Mathematics, both of the National Ukrainian Academy of Sciences, Kiev; Russian Academy of Education, Moscow; Catania Astrophysical Observatory of the Italian National Institute of Astrophysics; Bologna Academy of Sciences; Italian Institute of Philosophical Studies, Naples; Moscow philosophical seminar “Philosophy of mathematics”; Simula, Oslo; Nizhni Novgorod Mathematical Society; etc.

 

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