Using Blinking Fractals for Mathematical Modeling of Processes of Growth in Biological Systems

doi:10.15388/Informatica.2011.342

The Role of grossone in Nonlinear Programming and Exact Penalty Methods

Renato De Leone

https://doi.org/10.1007/978-3-030-93642-6_3

Book: Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 77

Examples of the Usage of Infinities and Infinitesimals in Numerical Computations

Yaroslav D. Sergeyev

https://doi.org/10.1007/978-3-319-12745-3_15

Book: Communications in Computer and Information Science (Advances in Artificial Life and Evolutionary Computation) Volume 445 (2014), p. 190

Grossone Infinity Computing

Yaroslav D. Sergeyev

https://doi.org/10.1007/978-1-4939-6883-1_685

Book: (2018), p. 663

Grossone Infinity Computing

Yaroslav D. Sergeyev

https://doi.org/10.1007/978-3-642-27737-5_685-1

Book: (2017), p. 1

Introduction

Yaroslav D. Sergeyev, Roman G. Strongin, Daniela Lera

https://doi.org/10.1007/978-1-4614-8042-6_1

Book: SpringerBriefs in Optimization (Introduction to Global Optimization Exploiting Space-Filling Curves) (2013), p. 1

Adopting the Infinity Computing in Simulink for Scientific Computing

Alberto Falcone, Alfredo Garro, Marat S. Mukhametzhanov, Yaroslav D. Sergeyev

https://doi.org/10.1007/978-3-030-93642-6_13

Book: Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 313

The Use of Infinities and Infinitesimals for Sparse Classification Problems

Renato De Leone, Nadaniela Egidi, Lorella Fatone

https://doi.org/10.1007/978-3-030-93642-6_6

Book: Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 151

The Grossone-Based Diagonal Bundle Method

Manlio Gaudioso, Giovanni Giallombardo, Marat S. Mukhametzhanov

https://doi.org/10.1007/978-3-030-93642-6_7

Book: Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 167

A New Computational Paradigm Using Grossone-Based Numerical Infinities and Infinitesimals

Yaroslav D. Sergeyev

https://doi.org/10.1007/978-3-030-93642-6_1

Book: Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 3

AIP Conference Proceedings

Yaroslav D. Sergeyev

https://doi.org/10.1063/1.5043649

Conference: AIP Conference Proceedings Volume 1978 (2018), p. 020004

New Approaches to Basic Calculus: An Experimentation via Numerical Computation

Luigi Antoniotti, Fabio Caldarola, Gianfranco d’Atri, Marco Pellegrini

https://doi.org/10.1007/978-3-030-39081-5_29

Book: Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 11973 (2020), p. 329

AIP Conference Proceedings

F. Mazzia, Ya. D. Sergeyev, F. Iavernaro, P. Amodio, M. S. Mukhametzhanov

https://doi.org/10.1063/1.4965397

Conference: AIP Conference Proceedings Volume 1776 (2016), p. 090033

The Grossone Methodology Perspective on Turing Machines

Yaroslav D. Sergeyev, Alfredo Garro

https://doi.org/10.1007/978-3-319-09039-9_7

Book: Emergence, Complexity and Computation (Automata, Universality, Computation) Volume 12 (2015), p. 139

Numerical Computations with Infinite and Infinitesimal Numbers: Theory and Applications

Yaroslav D. Sergeyev

https://doi.org/10.1007/978-1-4614-7582-8_1

Book: Springer Proceedings in Mathematics & Statistics (Dynamics of Information Systems: Algorithmic Approaches) Volume 51 (2013), p. 1

Computations with Grossone-Based Infinities

Yaroslav D. Sergeyev

https://doi.org/10.1007/978-3-319-21819-9_6

Book: Lecture Notes in Computer Science (Unconventional Computation and Natural Computation) Volume 9252 (2015), p. 89

Addressing Ill-Conditioning in Global Optimization Using a Software Implementation of the Infinity Computer

Marat S. Mukhametzhanov, Dmitri E. Kvasov

https://doi.org/10.1007/978-3-030-93642-6_14

Book: Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 347

Paradoxes of the Infinite and Ontological Dilemmas Between Ancient Philosophy and Modern Mathematical Solutions

Fabio Caldarola, Domenico Cortese, Gianfranco d’Atri, Mario Maiolo

https://doi.org/10.1007/978-3-030-39081-5_31

Book: Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 11973 (2020), p. 358

Percolation Transition and Related Phenomena in Terms of Grossone Infinity Computations

Dmitry I. Iudin, Yaroslav D. Sergeyev

https://doi.org/10.1007/978-3-319-33924-5_11

Book: Emergence, Complexity and Computation (Advances in Unconventional Computing) Volume 22 (2017), p. 239

A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic

P. Amodio, F. Iavernaro, F. Mazzia, M.S. Mukhametzhanov, Ya.D. Sergeyev

https://doi.org/10.1016/j.matcom.2016.03.007

Journal: Mathematics and Computers in Simulation Volume 141 (2017), p. 24

A mathematical investigation on the invariance problem of some hydraulic indices

Fabio Caldarola, Mario Maiolo

https://doi.org/10.1016/j.amc.2020.125726

Journal: Applied Mathematics and Computation Volume 409 (2021), p. 125726

A new approach to the Z-transform through infinite computation

Fabio Caldarola, Mario Maiolo, Viviana Solferino

https://doi.org/10.1016/j.cnsns.2019.105019

Journal: Communications in Nonlinear Science and Numerical Simulation Volume 82 (2020), p. 105019

Computation of supertrack functions for Chua’s oscillator and for Chua’s circuit with memristor

Fabio Caldarola, Pietro Pantano, Eleonora Bilotta

https://doi.org/10.1016/j.cnsns.2020.105568

Journal: Communications in Nonlinear Science and Numerical Simulation Volume 94 (2021), p. 105568

Fibonacci words, hyperbolic tilings and grossone

Maurice Margenstern

https://doi.org/10.1016/j.cnsns.2014.07.032

Journal: Communications in Nonlinear Science and Numerical Simulation Volume 21, Issue 1-3 (2015), p. 3

Independence of the Grossone-Based Infinity Methodology from Non-standard Analysis and Comments upon Logical Fallacies in Some Texts Asserting the Opposite

Yaroslav D. Sergeyev

https://doi.org/10.1007/s10699-018-9566-y

Journal: Foundations of Science Volume 24, Issue 1 (2019), p. 153

Infinigons of the hyperbolic plane and grossone

Maurice Margenstern

https://doi.org/10.1016/j.amc.2016.01.019

Journal: Applied Mathematics and Computation Volume 278 (2016), p. 45

Infinite Numerical Computing Applied to Hilbert’s, Peano’s, and Moore’s Curves

Luigi Antoniotti, Fabio Caldarola, Mario Maiolo

https://doi.org/10.1007/s00009-020-01531-5

Journal: Mediterranean Journal of Mathematics Volume 17, Issue 3 (2020)

Infinity computations in cellular automaton forest-fire model

D.I. Iudin, Ya.D. Sergeyev, M. Hayakawa

https://doi.org/10.1016/j.cnsns.2014.06.031

Journal: Communications in Nonlinear Science and Numerical Simulation Volume 20, Issue 3 (2015), p. 861

Lexicographic multi-objective linear programming using grossone methodology: Theory and algorithm

Marco Cococcioni, Massimo Pappalardo, Yaroslav D. Sergeyev

https://doi.org/10.1016/j.amc.2017.05.058

Journal: Applied Mathematics and Computation Volume 318 (2018), p. 298

Noise-induced kinetic transition in two-component environment

Dmitry I. Iudin, Fedor D. Iudin, Artem A. Syssoev, Vitaly Yu. Klimashov, Alexey A. Emelyanov

https://doi.org/10.1016/j.cam.2020.113268

Journal: Journal of Computational and Applied Mathematics Volume 388 (2021), p. 113268

Nonlinear programming and Grossone: Quadratic Programing and the role of Constraint Qualifications

Renato De Leone

https://doi.org/10.1016/j.amc.2017.03.029

Journal: Applied Mathematics and Computation Volume 318 (2018), p. 290

Numerical infinitesimals in a variable metric method for convex nonsmooth optimization

Manlio Gaudioso, Giovanni Giallombardo, Marat Mukhametzhanov

https://doi.org/10.1016/j.amc.2017.07.057

Journal: Applied Mathematics and Computation Volume 318 (2018), p. 312

On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales

Yaroslav D. Sergeyev, Dmitri E. Kvasov, Marat S. Mukhametzhanov

https://doi.org/10.1016/j.cnsns.2017.11.013

Journal: Communications in Nonlinear Science and Numerical Simulation Volume 59 (2018), p. 319

On the topological convergence of multi-rule sequences of sets and fractal patterns

Fabio Caldarola, Mario Maiolo

https://doi.org/10.1007/s00500-020-05358-w

Journal: Soft Computing Volume 24, Issue 23 (2020), p. 17737

Planar methods and grossone for the Conjugate Gradient breakdown in nonlinear programming

Renato De Leone, Giovanni Fasano, Yaroslav D. Sergeyev

https://doi.org/10.1007/s10589-017-9957-y

Journal: Computational Optimization and Applications Volume 71, Issue 1 (2018), p. 73

Representation of grossone-based arithmetic in simulink for scientific computing

Alberto Falcone, Alfredo Garro, Marat S. Mukhametzhanov, Yaroslav D. Sergeyev

https://doi.org/10.1007/s00500-020-05221-y

Journal: Soft Computing Volume 24, Issue 23 (2020), p. 17525

Reprint of Infinity computations in cellular automaton forest-fire model

D.I. Iudin, Ya.D. Sergeyev, M. Hayakawa

https://doi.org/10.1016/j.cnsns.2014.10.019

Journal: Communications in Nonlinear Science and Numerical Simulation Volume 21, Issue 1-3 (2015), p. 190

Single-tape and multi-tape Turing machines through the lens of the Grossone methodology

Yaroslav D. Sergeyev, Alfredo Garro

https://doi.org/10.1007/s11227-013-0894-y

Journal: The Journal of Supercomputing Volume 65, Issue 2 (2013), p. 645

Solving ordinary differential equations on the Infinity Computer by working with infinitesimals numerically

Yaroslav D. Sergeyev

https://doi.org/10.1016/j.amc.2013.04.019

Journal: Applied Mathematics and Computation Volume 219, Issue 22 (2013), p. 10668

Solving the Lexicographic Multi-Objective Mixed-Integer Linear Programming Problem using branch-and-bound and grossone methodology

Marco Cococcioni, Alessandro Cudazzo, Massimo Pappalardo, Yaroslav D. Sergeyev

https://doi.org/10.1016/j.cnsns.2020.105177

Journal: Communications in Nonlinear Science and Numerical Simulation Volume 84 (2020), p. 105177

The Olympic Medals Ranks, Lexicographic Ordering, and Numerical Infinities

Yaroslav D. Sergeyev

https://doi.org/10.1007/s00283-014-9511-z

Journal: The Mathematical Intelligencer Volume 37, Issue 2 (2015), p. 4

The Sierpinski curve viewed by numerical computations with infinities and infinitesimals

Fabio Caldarola

https://doi.org/10.1016/j.amc.2017.06.024

Journal: Applied Mathematics and Computation Volume 318 (2018), p. 321

The exact (up to infinitesimals) infinite perimeter of the Koch snowflake and its finite area

Yaroslav D. Sergeyev

https://doi.org/10.1016/j.cnsns.2015.07.004

Journal: Communications in Nonlinear Science and Numerical Simulation Volume 31, Issue 1-3 (2016), p. 21

The exact measures of the Sierpiński d-dimensional tetrahedron in connection with a Diophantine nonlinear system

Fabio Caldarola

https://doi.org/10.1016/j.cnsns.2018.02.026

Journal: Communications in Nonlinear Science and Numerical Simulation Volume 63 (2018), p. 228

Usage of infinitesimals in the Menger’s Sponge model of porosity

Maria C. Vita, Samuele De Bartolo, Carmine Fallico, Massimo Veltri

https://doi.org/10.1016/j.amc.2011.06.013

Journal: Applied Mathematics and Computation Volume 218, Issue 16 (2012), p. 8187

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