Sergeyev Ya.D. (2023) Lower and upper estimates of the quantity of algebraic numbers, Mediterranean Journal of Mathematics, 20(1), article 12.

Tohmé F., Caterina G., Gangle R. (2022) Observability in the Univalent Universe, Mediterranean Journal of Mathematics, 19, article 216.

Sergeyev Ya.D. (2022) Some paradoxes of infinity revisited, Mediterranean Journal of Mathematics, 19, article 143.

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 opposite, Foundations 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 seriously, Communications 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 bijections, p-Adic Numbers, UltrametricAnalysis and Applications, 3(3), 196-204.

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

Cococcioni M., Fiaschi L. (2025) Linear programming with infinite, finite, and infinitesimal values in the right-hand side, Applied Mathematics and Computation, 486, article number 129044.

Cococcioni M., Cudazzo A., Fiaschi L., Pappalardo M., Sergeyev Ya.D. (2024) A new cutting plane method for lexicographic multi-objective integer linear programming, Communications in Nonlinear Science and Numerical Simulation, 129, article number 107674.

Falcone A., Garro A., Mukhametzhanov M.S., Sergeyev Ya.D. (2023) Advantages of the usage of the Infinity Computer for reducing the Zeno behavior in hybrid system models, Soft Computing, 27(12), 8189-8208.

Lai L., Fiaschi L., Cococcioni M., Deb K. (2023) Pure and mixed lexicographic-paretian many-objective optimization: State of the art, Natural Computing, 22, 227–242.

Falcone A., Garro A., Mukhametzhanov M.S., Sergeyev Ya.D. (2022) Simulation of hybrid systems under Zeno behavior using numerical infinitesimals, Communications in Nonlinear Science and Numerical Simulation, 111, article number 106443.

Falcone A., Garro A., Mukhametzhanov M.S., Sergeyev Y.D. (2021) A Simulink-based software solution using the Infinity Computer methodology for higher order differentiation,  Applied Mathematics and Computation, 409, article 125606.

Fiaschi L., Cococcioni M. (2021) The Big-M method with the numerical infinite M, Optimization Letters, 15 (7), 2455-2468.

Lai L., Fiaschi L., Cococcioni M., Deb K. (2021) Solving mixed Pareto-Lexicographic multi-objective optimization problems: The case of priority levels, IEEE Transactions on Evolutionary Computation, 25 (5), 971–985.

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 scales, Communications 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 programming, Computational 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 optimization, Applied 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 algorithm, Applied Mathematics and Computation, 318, 298–311.

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.

Sergeyev Ya.D. (2011) Higher order numerical differentiation on the Infinity Computer, Optimization 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.

Falcone A., Garro A., Mukhametzhanov M.S., Sergeyev Ya.D. (2022) Simulation of hybrid systems under Zeno behavior using numerical infinitesimals, Communications in Nonlinear Science and Numerical Simulation, 111, article number 106443.

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 arithmetic, Mathematics 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 Computer, International Journal of Unconventional Computing, 12(1), 3–23.

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.

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 infinitesimals, Applied Mathematics and Computation, 318, 321–328.

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

Sergeyev 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.

Margenstern M. (2015) Fibonacci words, hyperbolic tilings and grossone, Communications 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 model, Communications 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 porosity, Applied 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 plane, Applied Mathematics and Computation, 218(16), 8005-8018.

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.

Sergeyev Ya.D. (2011) Using blinking fractals for mathematical modelling of processes of growth in biological systems, Informatica, 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 numbers, Chaos, 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 Grossone, SN 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 Paradox, Philosophia 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 system, International 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 grossone, Applied 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 function, p-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 domains, Nonlinear Analysis Series A: Theory, Methods & Applications, 71(12), e1688-e1707.

Cococcioni M., Fiaschi L., Lambertini L. (2021) Non-archimedean zero-sum games, Journal of Computational and Applied Mathematics, 393, 113483.

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 Computing, International 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.

Nasr L. (2023) Students’ resolutions of some paradoxes of infinity in the lens of the grossone methodology. Informatics and Education, 38(1), 83–91. DOI: 10.32517/0234-0453-2023-38-1-83-91

Mazzia F. (2022) A computational point of view on teaching derivatives, Informatics and education, 37(1), 79-86.

Nasr L. (2022) The effect of Arithmetic of Infinity Methodology on students’ beliefs of infinity, Mediterranean Journal for Research in Mathematics Education, 19, 5-19.

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.