Selected research papers

  • A brief survey
  • A long survey
  • A survey in Italian
  • Foundations, logic, philosophy, and
    relations to traditional views
  • 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

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 infinitesime, La Matematica nella Società e nella Cultura: Rivista dell’Unione Matematica Italiana, Serie I, Vol.8, 111-147.

Gangle R., Caterina G., Tohmé F. (2020) A constructive sequence algebra for the calculus of indications, Soft Computing, 24, 17621-17629.

Tohmé F., Caterina G., Gangle R. (2020) Computing Truth Values in the Topos of Infinite Peirce’s α-Existential Graphs, Applied Mathematics and Computation, 385, article number 125343.

Caldarola F., Cortese D., d’Atri G., Maiolo M. (2020) Paradoxes of the Infinite and Ontological Dilemmas Between Ancient Philosophy and Modern Mathematical Solutions, Lecture Notes in Computer Science, LNCS 11973, 358-372.

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 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.

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 survey, Applied 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.

Iavernaro F., Mazzia F., Mukhametzhanov M.S., Sergeyev Y.D. (2021) Computation of higher order Lie derivatives on the Infinity Computer, Journal of Computational and Applied Mathematics,  383, article number 113135.

Sergeyev Y.D., Nasso M.C., Mukhametzhanov M.S., Kvasov, D.E (2021) Novel local tuning techniques for speeding up one-dimensional algorithms in expensive global optimization using Lipschitz derivatives, Journal of Computational and Applied Mathematics, 383, article number 113134.

De Leone R., Egidi N., Fatone L. (2020) The use of grossone in elastic net regularization and sparse support vector machines, Soft Computing, 24, 17669-17677.

Astorino A., Fuduli A. (2020) Spherical separation with infinitely far center, Soft Computing, 24, 17751-17759.

Falcone A., Garro A., Mukhametzhanov M.S., Sergeyev Y.D. (2020) Representation of grossone-based arithmetic in Simulink for scientific computing, Soft Computing, 24, 17525-17539.

De Leone R., Fasano G., Roma M., Sergeyev Y.D. (2020) Iterative grossone-based computation of negative curvature directions in large-scale optimization, Journal of Optimization Theory and Applications, 186(2), 554-589.

Lai L., Fiaschi L., Cococcioni M. (2020) Solving Mixed Pareto-Lexicographic Multi-Objective Optimization Problems: The Case of Priority Chains, Swarm and Evolutionary Computation, 55, 100687.

Cococcioni M., Cudazzo A., Pappalardo M., Sergeyev Ya.D. (2020) Solving the Lexicographic Multi-Objective Mixed-Integer Linear Programming Problem Using Branch-and-Bound and Grossone Methodology, Communications in Nonlinear Science and Numerical Simulation, 84, 105177.

De Leone R., Fasano G., Roma M., Sergeyev Ya D., (2019) How Grossone can be helpful to iteratively compute negative curvature directions, R. Battiti et 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 qualifications, Applied 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 computations, Applied 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 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.

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

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

Iavernaro F., Mazzia F., Mukhametzhanov M.S., Sergeyev Y.D. (2021) Computation of higher order Lie derivatives on the Infinity Computer, Journal of Computational and Applied Mathematics,  383, article number 113135.

Amodio P., Brugnano L., Iavernaro F., Mazzia F. (2020) On the use of the Infinity Computer architecture to set up a dynamic precision floating-point arithmetic, Soft Computing, 24, 17589-17600.

Falcone A., Garro A., Mukhametzhanov M.S., Sergeyev Y.D. (2020) Representation of grossone-based arithmetic in Simulink for scientific computing, Soft Computing, 24, 17525-17539.

Iavernaro F., Mazzia F., Mukhametzhanov M.S., Sergeyev Ya.D. (2020) Conjugate-symplecticity properties of Euler–Maclaurin methods and their implementation on the Infinity Computer, Applied Numerical Mathematics, 155, 58-72.

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., Maiolo M. (2020) On the topological convergence of multi-rule sequences of sets and fractal patterns, Soft Computing, 24, 17737-17749.

Antoniotti L.,  Caldarola F., and Maiolo M. (2020) Infinite Numerical Computing Applied to Hilbert’s, Peano’s, and Moore’s Curves, Mediterranean Journal of Mathematics, 17(3), article 99, 1-19.

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

Caldarola F. (2018) The Sierpinski curve viewed by numerical computations with infinities and infinitesimalsApplied 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.

Pepelyshev A., Zhigljavsky A. (2020) Discrete uniform and binomial distributions with infinite support, Soft Computing, 24, 17517-17524.

Calude C. S., Dumitrescu M.  (2020) Infinitesimal Probabilities Based on GrossoneSN Comput. Sci.1,  36.

Caldarola F., Maiolo  M., Solferino V. (2020) A new approach to the Z-transform through infinite computation, Communications in Nonlinear Science and Numerical Simulation, 82, 105019.

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

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

D’Alotto L. (2020) Infinite games on finite graphs using grossone, Soft Computing, 24, 17509-17515.

Rizza D. (2019) Numerical methods for infinite decision-making processes, International 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 infinities, The Mathematical Intelligencer, 37(2), 4-8.

Antoniotti L., Caldarola F., d’Atri G., Pellegrini M. (2020) New Approaches to Basic Calculus: An Experimentation via Numerical Computation, Lecture Notes in Computer Science, LNCS 11973, 329-342.

Ingarozza F., Adamo M.T., Martino M., Piscitelli A. (2020) A Grossone-Based Numerical Model for Computations with Infinity: A Case Study in an Italian High School, Lecture Notes in Computer Science, LNCS 11973, 451-462.

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.