The Application of Mathematics to the Sciences of Nature: Critical Moments and AspectsClaudio Pellegrini, Paola Cerrai, Paolo Freguglia Springer Science & Business Media, 6 déc. 2012 - 294 pages The historical and epistemological reflection on the applications of mathematical techniques to the Sciences of Nature - physics, biology, chemistry, and geology - today generates attention and interest because of the increasing use of mathematical models in all sciences and their high level of sophistication. The goal of the meeting and the papers collected in this proceedings volume is to give physicists, biologists, mathematicians, and historians of science the opportunity to share information on their work and reflect on the and mathematical models are used in the natural sciences today and in way mathematics the past. The program of the workshop combines the experience of those working on current scientific research in many different fields with the historical analysis of previous results. We hope that some novel interdisciplinary, philosophical, and epistemological considerations will follow from the two aspects of the workshop, the historical and the scientific· This proceedings includes papers presented at the meeting and some of the results of the discussions that took place during the workshop. We wish to express our gratitude to Sergio Monteiro for all his work, which has been essential for the successful publication of these proceedings. We also want to thank the editors of Kluwer AcademidPlenum Publishers for their patience and constant help, and in particular Beth Kuhne and Roberta Klarreich. Our thanks to the fallowing institutions: -Amministrazione Comunale di Arcidosso -Comunita Montana del Monte Amiata ·Center for the History of Physics, UCLA -Centre F. |
Table des matières
3 | |
An Optical Geometric Model of the Betatronic Motion | 25 |
Pattern Induced by Parameter Modulation in Spatiotemporal Chaos | 79 |
Chaos and Orbit Complexity | 87 |
On the RiemannMangoldt Constant | 101 |
LongTerm Stability in Circular Accelerators | 109 |
Mathematical Models in Beam Dynamics | 117 |
An Axiomatic Approach to Some Biological Themes | 139 |
The Supply | 179 |
Which Role for Mathematical | 191 |
The Mathematics Implied in the Laws of Nature and Realism or the Role | 207 |
Geometry the Calculus and the Use of Limits in Newtons Principia | 223 |
Objectivism vs Subjectivism | 233 |
ISSI Center for Research in Mathematics and Physics Locarno and Faculty of Natural Sciences | 245 |
Mathematization of the Science of Motion and the Birth of Analytical | 253 |
Porter Department of History University of California Los Angeles Los Angeles | 273 |
Domus Galilaeana Pisa | 155 |
Gabriele A Losa Laboratory of Cellular Pathology Institute for Interdisciplinary Scientific Studies | 161 |
The Arc an Unexpected and Still Not Explained Element of the Tracks | 171 |
Is Music Relevant for the History of Science? | 281 |
293 | |
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Expressions et termes fréquents
accelerator amplitude analysis analytical mechanics Application of Mathematics Axiom axiomatic basic beam Bell inequality betatronic betatronic motion Biology Buffon calculus century chaos chaotic Clairaut classical compact computable structure considered constant coordinates correlations defined definition density depends described differential ecology edited by Cerrai entropy equation evolution experiment fact field Figure finite force fractal fractal dimension function game theory geometrical Hamiltonian Hénon map interpretation invariant Lagrangian lattice limit linear living objects magnetic mathematical models measure membrane method method of fluxions metric space nature Newton non-linear normal operations optical orbit complexity oscillations parameters particle perturbation phase space phenomena physics Poincaré group point of view population possible Principia principle problem quantities Quantum Mechanics ratio recruitment recursive relations resonant simulations soliton solution speciation species speed theoretical theory Theory of Relativity trajectory variable vector Volterra zero