The Application of Mathematics to the Sciences of Nature

Physics.- 1. Quantum Probability and the Interpretation of Quantum Mechanics: A Crucial Experiment.- 2. An Optical Geometric Model of the Betatronic Motion.- 3. Some Remarks on the Theory of Relativity and the Naïve Realism.- 4. Pattern Induced by Parameter Modulation in Spatiotemporal Chaos.- 5. Chaos and Orbit Complexity.- 6. On the Riemann-Mangoldt Constant.- 7. Long-Term Stability in Circular Accelerators.- 8. Mathematical Models in Beam Dynamics.- Biology.- 9. An Axiomatic Approach to Some Biological Themes.- 10. For an Axiomatic Theory of the Evolutionary Darwinian Ideas: A Proposal.- 11. Fractal Complexity of Membrane Structures in Normal and Neoplastic Cells During Growth and Apoptotic Cell Death.- 12. The Arc, an Unexpected and Still Not Explained Element of the Tracks of Creeping Ciliates.- 13. Natural Population and Community Structure and Dynamics: The “Supply-Side Ecology”, Theory and the Field Data.- History of science.- 14. The History of Theoretical Population Ecology: Which Role for Mathematical Modeling?.- 15. The Mathematics Implied in the Laws of Nature and Realism, or the Role of Functions Around 1750.- 16. Geometry, the Calculus and the Use of Limits in Newton’s Principia.- 17. The Two Faces of Mathematical Modeling: Objectivism vs. Subjectivism, Simplicity vs. Complexity.- 18. The Search for the Mathematization of the Social Disciplines.- 19. Mathematization of the Science of Motion and the Birth of Analytical Mechanics: A Historiographical Note.- 20. Models, Analogies, and Statistical Reason, 1760 – 1900.- 21. Is Music Relevant for the History of Science?.