Algebra Commons^™

The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre

Downloads

This is the entire DifferentialGeometry package, a zip file (DifferentialGeometry.zip) containing (1) a Maple Library file, DifferentialGeometryUSU.mla, (2) a Maple help file DifferentialGeometry.help, (3) a Maple Library file, DGApplicatons.mla. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple.

Installation instructions

What's New In Differentialgeometry Release Dg2022, Ian M. Anderson, Charles G. Torre

Tutorials on... in 1 hour or less

This Maple worksheet demonstrates the salient new features and functionalities of the 2022 release of the DifferentialGeometry software package.

Hidden Symmetries Of The Kepler Problem, Julia Kathryn Sheffler

Senior Projects Spring 2022

The orbits of planets can be described by solving Kepler’s problem which considers the motion due to by gravity (or any inverse square force law). The solutions to Kepler’s problem, for energies less then 0, are ellipses, with a few conserved quantities: energy, angular momentum and the Laplace-Runge-Lenz (LRL) vector. Each conserved quantity corresponds to symmetries of the system via N ̈other’s theorem. Energy conservation relates to time translations and angular momentum to three dimensional rotations. The symmetry related to the LRL vector is more difficult to visualize since it lives in phase space rather than configuration space. To understand …

Topics In Gravitational Wave Physics, Aaron David Johnson

Graduate Theses and Dissertations

We begin with a brief introduction to gravitational waves. Next we look into the origin of the Chandrasekhar transformations between the different equations found by perturbing a Schwarzschild black hole. Some of the relationships turn out to be Darboux transformations. Then we turn to GW150914, the first detected black hole binary system, to see if the nonlinear memory might be detectable by current and future detectors. Finally, we develop an updated code for computing equatorial extreme mass ratio inspirals which will be open sourced as soon as it has been generalized for arbitrary inclinations.

Alpha Capture Reaction Rates For Nucleosynthesis Within An Ab Initio Framework, Alison Constance Dreyfuss

LSU Doctoral Dissertations

Clustering in nuclear systems has broad impacts on all phases of stellar burning, and plays a significant role in our understanding of nucleosynthesis, or how and where nuclei are produced in the universe. The role of alpha particles in particular is extremely important for nuclear astrophysics: ⁴He was one of the earliest elements produced in the Big Bang, it is one of the most abundant elements in the universe, and helium burning -- in particular, the triple-alpha process -- is one of the most important ``engines'' in stars. To better understand nucleosynthesis and stellar burning, then, it is important …

Spacetime Groups, Ian M. Anderson, Charles G. Torre

Publications

A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an algebraic classification of spacetime groups, that is, we determine a complete list of inequivalent spacetime Lie algebras, which are pairs (g,η), with g being a 4-dimensional Lie algebra and η being a Lorentzian inner product on g. A full analysis of the equivalence problem for spacetime Lie algebras is given which leads to a completely algorithmic solution to the …

Neutrosophic Triplet Structures - Vol. 1, Florentin Smarandache, Memet Sahin

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs, the properties of neutrosophic sets …

The Encyclopedia Of Neutrosophic Researchers - Vol. 3, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This is the third volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: …