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Full-Text Articles in Physical Sciences and Mathematics
The Fourth Movement Of György Ligeti's Piano Concerto: Investigating The Musical-Mathematical Connection, Cynthia L. Wong
The Fourth Movement Of György Ligeti's Piano Concerto: Investigating The Musical-Mathematical Connection, Cynthia L. Wong
Dissertations, Theses, and Capstone Projects
This interdisciplinary study explores musical-mathematical analogies in the fourth movement of Ligeti’s Piano Concerto. Its aim is to connect musical analysis with the piece’s mathematical inspiration. For this purpose, the dissertation is divided into two sections. Part I (Chapters 1-2) provides musical and mathematical context, including an explanation of ideas related to Ligeti’s mathematical inspiration. Part II (Chapters 3-5) delves into an analysis of the rhythm, form, melody / motive, and harmony. Appendix A is a reduced score of the entire movement, labeled according to my analysis.
Hamiltonian Bifurcations In Schrodinger Trimers, Casayndra H. Basarab
Hamiltonian Bifurcations In Schrodinger Trimers, Casayndra H. Basarab
Dissertations
The phase space of the three-mode discrete NLS in the nonlinear regime with periodic boundary conditions is investigated by reducing the degree of freedom from three down to two. The families of standing waves are enumerated and normal forms are used to describe several families of relative periodic orbits whose topologies change due to Hamiltonian Hopf bifurcations and transcritical bifurcations. The Hamiltonian Hopf bifurcation occurs when eigenvalues on the imaginary axis collide and split and has two types: elliptic and hyperbolic. These two types arise in the DNLS problem, and the families of periodic orbits are discussed as a conserved …
A Computational And Theoretical Exploration Of The St. Petersburg Paradox, Alexander Olivero
A Computational And Theoretical Exploration Of The St. Petersburg Paradox, Alexander Olivero
Undergraduate Honors Thesis Collection
This thesis displays a sample distribution, generated from both a simulation (for large n) by computer program and explicitly calculated (for smaller n), that is not governed by the Central Limit Theorem and, in fact seems to display chaotic behavior. To our knowledge, the explicit calculation of the sample distribution function is new. This project outlines the results that have found a relation to number theory in a probabilistic game that has perplexed mathematicians for hundreds of years.