Selected research papers

  • A brief survey
  • A long survey
  • A survey in Italian
  • Foundations and relations to traditional
    views on infinite and infinitesimal
  • Optimization and
    numerical differentiation
  • Turing machines and cellular automata
  • Solving ordinary differential equations
  • Fractals and tilings
  • Probability, summation,
    and factorisation
  • Game theory, ordering,
    and infinite decision processes
  • Teaching
  • Old introductory texts
Sergeyev Ya.D, (2010) Lagrange Lecture: Methodology of numerical computations with infinities and infinitesimalsRendiconti del Seminario Matematico dell'Università e del Politecnico di Torino, 68(2), 95–113.

Sergeyev Ya.D(2017) Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problemsEMS Surveys in Mathematical Sciences, 4(2), 219–320.

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

Sergeyev Ya.D. (2019) Independence of the grossone-based infinity methodology from non-standard analysis and comments upon logical fallacies in some texts asserting the oppositeFoundations of Science, 24(1), 153–170.

Lolli G. (2015) Metamathematical investigations on the theory of GrossoneApplied 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.

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

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

Margenstern M. (2011) Using Grossone to count the number of elements of infinite sets and the connection with bijectionsp-Adic Numbers, UltrametricAnalysis and Applications, 3(3), 196-204.

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

De Leone R., Fasano G., Roma M., Sergeyev YaD., (2019) How Grossone can be helpful to iteratively compute negative curvature directions, R. Battitiet al. (Eds.): Proc. of the 12th International Conference LION 12, Lecture Notes in Computer Science, vol. 11353, Springer, 80–183.

Sergeyev Ya.D., Kvasov D.E., Mukhametzhanov M.S. (2018) On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scalesCommunications in Nonlinear Science and Numerical Simulation, 59, 319-330.

De Leone R., Fasano G., Sergeyev Ya.D. (2018) Planar methods and grossone for the Conjugate Gradient breakdown in nonlinear programmingComputational Optimization and Applications, 71(1), 73-93.

Gaudioso M., Giallombardo G., Mukhametzhanov M.S. (2018) Numerical infinitesimals in a variable metric method for convex nonsmooth optimizationApplied Mathematics and Computation, 318, 312–320.

De Leone R. (2018) Nonlinear programming and grossone: Quadratic programming and the role of constraint qualificationsApplied Mathematics and Computation, 318, 290–297.

Cococcioni M., Pappalardo M., Sergeyev Ya.D. (2018) Lexicographic multiobjective linear programming using grossone methodology: Theory and algorithmApplied Mathematics and Computation, 318, 298–311.

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

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

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

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.

D’Alotto L. (2013) A classification of two-dimensional cellular automata using infinite computationsIndian 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 methodologyJournal of Supercomputing, 65(2), 645-663.

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

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

Amodio, P., Iavernaro, F., Mazzia, F., Mukhametzhanov, M.S., Sergeyev, Ya.D. (2017) A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmeticMathematics and Computers in Simulation, 141, 24–39.

Mazzia F., Sergeyev Ya. D., Iavernaro F., Amodio P., and Mukhametzhanov M. S. (2016) Numerical methods for solving ODEs on the infinity computer, AIP Conference Proceedings 1776, 090033.

Sergeyev Ya.D., Mukhametzhanov M.S., Mazzia F., Iavernaro F., Amodio P. (2016) Numerical methods for solving initial value problems on the Infinity ComputerInternational Journal of Unconventional Computing, 12(1), 3–23.

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

Caldarola, F. (2018) The exact measures of the Sierpiński d-dimensional tetrahedron in connection with a Diophantine nonlinear systemCommunications in Nonlinear Science and Numerical Simulation, 63, 228-238.

Caldarola F. (2018) The Sierpinski curve viewed by numerical computations with infinities and infinitesimals, Applied Mathematics and Computation, 318, 321–328.

Margenstern M. (2016) Infinigons of the hyperbolic plane and grossoneApplied Mathematics and Computation, 278, 45–53.

Sergeyev Ya.D. (2016) The exact (up to infinitesimals) infinite perimeter of the Koch snowflake and its finite areaCommunications in Nonlinear Science and Numerical Simulation, 31(1–3):21–29.

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

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

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

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

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

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

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. (2007) Blinking fractals and their quantitative analysis using infinite and infinitesimal numbersChaos, Solitons & Fractals, vol. 33(1), 50-75.

Rizza D. (2018) A Study of Mathematical Determination through Bertrand’s ParadoxPhilosophia Mathematica, 26(3), 375–395.

Sergeyev Ya.D. Numerical infinities applied for studying Riemann series theorem and Ramanujan summation, AIP Conference Proceedings 1978, 020004 (2018); doi: 10.1063/1.5043649

Sergeyev Ya.D. (2016) The difficulty of prime factorization is a consequence of the positional numeral systemInternational Journal of Unconventional Computing, Vol. 12 (5-6), 453–463.

A. Zhigljavsky (2012) Computing sums of conditionally convergent and divergent series using the concept of grossoneApplied Mathematics and Computation, 218, 8064–8076.

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

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

Rizza D. (2019) Numerical methods for infinite decision-making processesInternational Journal of Unconventional Computing, 14(2), 139-158.

Fiaschi L., Cococcioni M. (2018) Numerical asymptotic results in Game Theory using Sergeyev's Infinity ComputingInternational Journal of Unconventional Computing, 14(1), 1-25.

Rizza, D. (2018) How to make an infinite decision, Bulletin of Symbolic Logic, 24(2), p.227.

Rizza D. (2016) Supertasks and numeral systems,  AIP Conference Proceedings 1776, 090005.

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

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

Iannone P., Rizza D., Thoma A. (2018) Investigating secondary school students’ epistemologies through a class activity concerning infinity, in E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter (Eds.). Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, 131-138). Umeå, Sweden: PME.

Lepellere M.A., Piccinini L.C., Taverna M. (2018) From linguistic representation to fuzzy mathematics in grown up people, Proc. Int. Conf. “Society. Integration. Education”. Vol. III, May 25th -26th, 2018. 555-565.

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.

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. (2009) Numerical computations and mathematical modelling with infinite and infinitesimal numbersJournal of Applied Mathematics and Computing, 29, 177-195.

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

Sergeyev Ya.D. (2008) Measuring fractals by infinite and infinitesimal numbersMathematical 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 InfinityScheria, 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).