The Application of Mathematics to the Sciences of Nature

1. Front Matter

   Pages i-x

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2. Physics

   1. Front Matter

      Pages 1-1

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   2. Quantum Probability and the Interpretation of Quantum Mechanics: A Crucial Experiment

      • L. Accardi, M. Regoli

      Pages 3-23

   3. An Optical Geometric Model of the Betatronic Motion

      • A. Bazzani, P. Freguglia

      Pages 25-38

   4. Some Remarks on the Theory of Relativity and the Naïve Realism

      • Vieri Benci

      Pages 39-78

   5. Pattern Induced by Parameter Modulation in Spatiotemporal Chaos

      • Leone Fronzoni

      Pages 79-86

   6. Chaos and Orbit Complexity

      • Stefano Galatolo

      Pages 87-99

   7. On the Riemann-Mangoldt Constant

      • Danilo Merlini, Luca Rusconi

      Pages 101-108

   8. Long-Term Stability in Circular Accelerators

      • Walter Scandale

      Pages 109-116

   9. Mathematical Models in Beam Dynamics

      • Giorgio Turchetti

      Pages 117-136

3. Biology

   1. Front Matter

      Pages 137-137

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   2. An Axiomatic Approach to Some Biological Themes

      • Marco Forti, Paolo Freguglia, Lodovico Galleni

      Pages 139-154

   3. For an Axiomatic Theory of the Evolutionary Darwinian Ideas: A Proposal

      • Paolo Freguglia

      Pages 155-160

   4. Fractal Complexity of Membrane Structures in Normal and Neoplastic Cells During Growth and Apoptotic Cell Death

      • Gabriele A. Losa

      Pages 161-170

   5. The Arc, an Unexpected and Still Not Explained Element of the Tracks of Creeping Ciliates

      • Nicola Ricci, Rosalba Banchetti, Fabrizio Erra

      Pages 171-177

   6. Natural Population and Community Structure and Dynamics: the “Supply — Side Ecology”, Theory and the Field Data

      • Giovanni Santangelo

      Pages 179-187

4. History of Science

   1. Front Matter

      Pages 189-189

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   2. The History of Theoretical Population Ecology: Which Role for Mathematical Modeling?

      • Luciano Andreozzi

      Pages 191-205

   3. The Mathematics Implied in the Laws of Nature and Realism, or the Role of Functions Around 1750

      • Jean Dhombres

      Pages 207-222

   4. Geometry, the Calculus and the Use of Limits in Newton’s Principia

      • Niccolò Guicciardini

      Pages 223-232

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.

• Chaos
• History of Mathematics
• Natural Sciences
• biology
• mathematical modeling
• model
• modeling

• University of Pisa, Pisa, Italy

  Paola Cerrai

• University of L’Aquila, L’Aquila, Italy

  Paolo Freguglia

• Domus Galilaeana, Pisa, Italy

  Paolo Freguglia

• University of California, Los Angeles, Los Angeles, USA

  Claudio Pellegrini

Policies and ethics