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Articles 1 - 5 of 5
Full-Text Articles in Other Applied Mathematics
Gravity-Driven Thin Liquid Films With Insoluble Surfactant: Smooth Traveling Waves, Rachel Levy, Michael Shearer, Thomas P. Witelski
Gravity-Driven Thin Liquid Films With Insoluble Surfactant: Smooth Traveling Waves, Rachel Levy, Michael Shearer, Thomas P. Witelski
All HMC Faculty Publications and Research
The flow of a thin layer of fluid down an inclined plane is modified by the presence of insoluble surfactant. For any finite surfactant mass, traveling waves are constructed for a system of lubrication equations describing the evolution of the free-surface fluid height and the surfactant concentration. The one-parameter family of solutions is investigated using perturbation theory with three small parameters: the coefficient of surface tension, the surfactant diffusivity, and the coefficient of the gravity-driven diffusive spreading of the fluid. When all three parameters are zero, the nonlinear PDE system is hyperbolic/degenerateparabolic, and admits traveling wave solutions in which the …
Mathematical Methods In Composing Melodies, Thomas Brown
Mathematical Methods In Composing Melodies, Thomas Brown
Undergraduate Theses and Capstone Projects
This thesis, “Mathematical Methods in Composing Melodies,” explores the different ways in which mathematics can be used to create music. Some research has been done in this field already. Richard F. Voss and John Clarke used fractals and different frequencies of noise to create music. The Greek composer Iannis Xenakis used Markovian Stochastic trees to create some of his compositions. Explored in this thesis are seven different methods to compose melodies. After compiling the different melodies, they were categorized by different musical periods based on the musical characteristics found in the melody. This thesis differs from other research that deals …
The Origin Of 2 Sexes Through Optimization Of Recombination Entropy Against Time And Energy, Bo Deng
The Origin Of 2 Sexes Through Optimization Of Recombination Entropy Against Time And Energy, Bo Deng
Department of Mathematics: Faculty Publications
Sexual reproduction in nature requires two sexes, which raises the question why the reproductive scheme did not evolve to have three or more sexes. Here we construct a constrained optimization model based on the communication theory to analyze trade-offs among reproductive schemes with arbitrary number of sexes. More sexes on one hand lead to higher reproductive diversity, but on the other hand incur greater cost in time and energy for reproductive success. Our model shows that the two-sexes reproduction scheme maximizes the recombination entropy-to-cost ratio, and hence is the optimal solution to the problem.
A Unifying Field In Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability And Statistics - 6th Ed., Florentin Smarandache
A Unifying Field In Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability And Statistics - 6th Ed., Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
It was a surprise for me when in 1995 I received a manuscript from the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philosophy - revealing paradoxes - and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) “neutrosophy” – study of neutralities as an extension of dialectics; b) and its derivative “neutrosophic”, such as “neutrosophic logic”, “neutrosophic set”, “neutrosophic probability”, and “neutrosophic statistics” and thus opening new ways of research in four fields: philosophy, logics, set theory, and probability/statistics. It was known to me his setting up in …
Collected Papers Vol. 1, Florentin Smarandache
Collected Papers Vol. 1, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.