Mathematics Commons^™

Conventions, Definitions, Identities, And Other Useful Formulae, Robert A. Mcnees Iv

Physics: Faculty Publications and Other Works

As the name suggests, these notes contain a summary of important conventions, definitions, identities, and various formulas that I often refer to. They may prove useful for researchers working in General Relativity, Supergravity, String Theory, Cosmology, and related areas.

Godel, Escherian Staircase And Possibility Of Quantum Wormhole With Liquid Crystalline Phase Of Iced-Water - Part I: Theoretical Underpinning, Victor Christianto, T. Daniel Chandra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1,. 2, 2022), Our universe is but one page in a large book [4]. For example, things and Beings can travel between Universes, intentionally or unintentionally. In this short remark, we revisit and offer short remark to Neil’s ideas and trying to connect them with geometrization of musical chords as presented by D. Tymoczko and others, then to Escher staircase and then to Jacob’s ladder which seems to point to possibility to interpret Jacob’s vision as described in the ancient book of Genesis …

Godel, Escherian Staircase And Possibility Of Quantum Wormhole With Liquid Crystalline Phase Of Iced-Water - Part Ii: Experiment Description, Victor Christianto, T. Daniel Chandra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The present article was partly inspired by G. Pollack’s book, and also Dadoloff, Saxena & Jensen (2010). As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1, No. 2, 2022), for example, things and Beings can travel between Universes, intentionally or unintentionally [4]. In this short remark, we revisit and offer short remark to Neil Boyd’s ideas and trying to connect them with geometry of musical chords as presented by D. Tymoczko and others, then to Escherian staircase and then to Jacob’s ladder which seems to pointto possibility to interpret Jacob’s vision …

On The Motion Of The Nodes Of The Moon And The Variation Of Its Inclination To The Ecliptic (An English Translation Of De Motu Nodorum Lunae Eiusque Inclinationis Ad Eclipticam Variatione), Patrick T. Headley

Euleriana

In this paper Euler attempts to explain some features of the motion of the Moon using Newton’s inverse-square law of gravity. He describes the evidence in favor of Newton’s theory but also the lack of progress in the study of lunar motion due to the difficulty of the three-body problem, arising here since both the Sun and the Earth have large effects on the Moon. He proceeds to investigate the line of intersection between the planes of the Earth's orbit and the Moon's orbit, as well as the angle between the two planes.

Using Deep Neural Networks To Classify Astronomical Images, Andrew D. Macpherson

Honors Projects

As the quantity of astronomical data available continues to exceed the resources available for analysis, recent advances in artificial intelligence encourage the development of automated classification tools. This paper lays out a framework for constructing a deep neural network capable of classifying individual astronomical images by describing techniques to extract and label these objects from large images.

Du Undergraduate Showcase: Research, Scholarship, And Creative Works, Caitlyn Aldersea, Justin Bravo, Sam Allen, Anna Block, Connor Block, Emma Buechler, Maria De Los Angeles Bustillos, Arianna Carlson, William Christensen, Olivia Kachulis, Noah Craver, Kate Dillon, Muskan Fatima, Angel Fernandes, Emma Finch, Colleen Cassidy, Amy Fishman, Andrea Francis, Stacia Fritz, Simran Gill, Emma Gries, Rylie Hansen, Shannon Powers, Jacqueline Martinez, Zachary Harker, Ashley Hasty, Mykaela Tanino-Springsteen, Kathleen Hopps, Adelaide Kerenick, Colin Kleckner, Ci Koehring, Elijah Kruger, Braden Krumholz, Maddie Leake, Lyneé Alves, Seraphina Loukas, Yatzari Lozano Vazquez, Haley Maki, Emily Martinez, Sierra Mckinney, Mykaela Tanino-Springsteen, Audrey Mitchell, Kipling Newman, Audrey Ng, Megan Lucyshyn, Andrew Nguyen, Stevie Ostman, Casandra Pearson, Alexandra Penney, Julia Gielczynski, Tyler Ball, Anna Rini, Christina Rorres, Simon Ruland, Helayna Schafer, Emma Sellers, Sarah Schuller, Claire Shaver, Kevin Summers, Isabella Shaw, Madison Sinar, Claudia Pena, Apshara Siwakoti, Carter Sorensen, Madi Sousa, Anna Sparling, Alexandra Revier, Brandon Thierry, Dylan Tyree, Maggie Williams, Lauren Wols

DU Undergraduate Research Journal Archive

DU Undergraduate Showcase: Research, Scholarship, and Creative Works

Evaluation Of Black Holes In An Evolving Universe, John P. Naan

Theses and Dissertations

There are various solutions to the Einstein field equations that represent different physical assumptions, but how to represent multiple black holes within an expanding universe remains an area of open interest. The first step to resolving this question involves evaluating spacetime models that contain a single black hole in an expanding universe. Here, we are primarily interested in understanding the energy distribution of black hole models by solving Einstein's equations using the associated spacetime metric and comparing the propagation of waves within the model against other known spacetime models. Specifically, we will evaluate the combined Schwarschild-de Sitter solution under a …

Dynamical Aspects In (4+1)-Body Problems, Ryan Gauthier

Theses and Dissertations (Comprehensive)

The n-body problem models a system of n-point masses that attract each other via some binary interaction. The (n + 1)-body problem assumes that one of the masses is located at the origin of the coordinate system. For example, an (n+1)-body problem is an ideal model for Saturn, seen as the central mass, and one of its outer rings. A relative equilibrium (RE) is a special solution of the (n+1)-body problem where the non-central bodies rotate rigidly about the centre of mass. In rotating coordinates, these solutions become equilibria.

In this thesis we study dynamical aspects of planar (4 + …

Extended Duration Studies Of Energetic Particles In The Stratosphere, Ian Kuhl, Ashna Coondiah, Howard Brooks

Annual Student Research Poster Session

The Balloon Assisted Stratospheric Experiments (BASE) program aims to measure atmospheric muon concentration at the Pfotzer Maximum with Geiger Counters carried by weather balloons. The most intense radiation is found at the Pfotzer Maximum 18 - 22 km (11 - 13 mi) above ground level. During this summer, seven flights were conducted to attain maximum time in the Pfotzer Maximum using different strategies like underfilling and multiple balloon systems.

Introduction To Classical Field Theory, Charles G. Torre

All Complete Monographs

This is an introduction to classical field theory. Topics treated include: Klein-Gordon field, electromagnetic field, scalar electrodynamics, Dirac field, Yang-Mills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.

A New Non-Inheriting Homogeneous Solution Of The Einstein-Maxwell Equations With Cosmological Term, Charles G. Torre

Research Vignettes

No abstract provided.

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

A New Non-Inheriting Homogeneous Solution Of The Einstein-Maxwell Equations With Cosmological Term, Ian M. Anderson, Charles G. Torre

Publications

We find a new homogeneous solution to the Einstein-Maxwell equations with a cos- mological term. The spacetime manifold is R × S3. The spacetime metric admits a simply transitive isometry group G = R × SU(2) and is Petrov type I. The spacetime is geodesically complete and globally hyperbolic. The electromagnetic field is non- null and non-inheriting: it is only invariant with respect to the SU(2) subgroup and is time-dependent in a stationary reference frame.

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 …

Trapped Surfaces, Topology Of Black Holes, And The Positive Mass Theorem, Lan-Hsuan Huang, Dan A. Lee

Publications and Research

No abstract provided.

The Kepler Problem On Complex And Pseudo-Riemannian Manifolds, Michael R. Astwood

Theses and Dissertations (Comprehensive)

The motion of objects in the sky has captured the attention of scientists and mathematicians since classical times. The problem of determining their motion has been dubbed the Kepler problem, and has since been generalized into an abstract problem of dynamical systems. In particular, the question of whether a classical system produces closed and bounded orbits is of importance even to modern mathematical physics, since these systems can often be analysed by hand. The aforementioned question was originally studied by Bertrand in the context of celestial mechanics, and is therefore referred to as the Bertrand problem. We investigate the qualitative …

New Techniques In Celestial Mechanics, Ali Abdulrasool Abdulhussein

Graduate Theses, Dissertations, and Problem Reports

It is shown that for the classical system of the N body problem ( Newtonian Motion), if the motion of the N particles starts from a planar initial motion at t=t_{0}, then the motion of the N particles continues to be planar for every t\in[t_{0},t_{1}], assuming that no collisions occur between the N particles. Same argument is shown about the linear motion, namely, for the classical system of the N body problem, if the motion of the N particles starts from a linear initial motion at t=t_{0}, then the motion of the N particles continues to be linear for every …

On The Rectilinear Motion Of Three Bodies Mutually Attracting Each Other, Sylvio R. Bistafa

Euleriana

This is an annotated translation from Latin of E327 -- De motu rectilineo trium corporum se mutuo attrahentium (“On the rectilinear motion of three bodies mutually attracting each other”). In this publication, Euler considers three bodies lying on a straight line, which are attracted to each other by central forces inversely proportional to the square of their separation distance (inverse-square law). Here Euler finds that the parameter that controls the relative distances among the bodies is given by a quintic function.

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.

Towards Realism Interpretation Of Wave Mechanics Based On Maxwell Equations In Quaternion Space And Some Implications, Including Smarandache’S Hypothesis, Florentin Smarandache, Victor Christianto, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Towards Gross-Pitaevskiian Description Of Solar System & Galaxies, Florentin Smarandache, Victor Christianto, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we argue that Gross-Pitaevskii model can be a more complete description of both solar system and spiral galaxies, especially taking into account the nature of chirality and vortices in galaxies. We also hope to bring out some correspondence among existing models, e.g., the topological vortex approach, Burgers equation in the light of KAM theory, and the Cantorian Navier-Stokes approach. We hope further investigation can be done around this line of approach.

Response To Pitkanen’S Solar System Model: Towards Gross-Pitaevskiian Description Of Solar System And Galaxies And More Evidence Of Chiral Superfluid Vortices, Victor Christianto, Florentin Smarandache, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

In a new paper in recent issue of this journal (PSTJ), Prof. M. Pitkanen describes a solar system model inspired by spiral galaxies. While we appreciate his new approach, we find it lacks substantial discussion on the nature of vortices and chirality in galaxy. Therefore we submit a viewpoint that Gross-Pitaevskii model can be a more complete description of both solar system and also spiral galaxies, especially taking into account the nature of chirality and vortices in galaxies. In this article, we also hope to bring out some correspondence among existing models, so we discuss shortly: the topological vortice approach, …

On Possibility Of Binary Companion Of The Sun: A Serendipity Finding And Comparison With Uvs Model Of Solar System, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

While we completely understood that a binary dwarf companion of the Sun has not been accepted by majority of astronomers, allow us to present some new arguments, along with our own serendipitous encounter with such a binary companion of the Sun. We hope that the present note will be found useful for further investigations, in relation to Planet Nine and such a dwarf star companion of the Sun (sometimes dubbed as Nemesis). Nonetheless, this article is not an exhaustive review of such dwarf companion star theories.

Aspects Of Quantum Theory In General Relativity And Cosmology, Eamon Mccaughey

Doctoral

After a brief introduction to Cosmology some quantum aspects of General Relativity and cosmology are presented. The radial motion of a massive particles in the ergosphere of the Kerr Black Hole is considered. Screening of Hawking radiation and shielding of the Penrose process is examined in the context of the region of negative energy inside the ergosphere. Tunnelling of such particles between the boundaries of the classically forbidden region will be considered and the transmission coefficient determined. The evolution of Primordial black holes in standard and Loop Quantum Cosmology is reviewed. A stability analysis of Einstein’s universe in both classical …

There Is No Constant In Physics: A Neutrosophic Explanation, Victor Christianto, Robert Neil Boyd, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In Neutrosophic Logic, a basic assertion is that there are variations of about everything that we can measure; the variations surround three parameters called T,I,F (truth, indeterminacy, falsehood) which can take a range of values. Similarly, in this paper we consider NL applications in physics constants. Those constants actually all have a window of plus and minus values, relative to the average value of the constant. For example, speed of light, c, can vary in a window up to +/- 3000 m/s. Therefore it should be written: 300000 km/s +/- 3 km/s. We also discuss some implications of this new …

Three Possible Applications Of Neutrosophic Logic In Fundamental And Applied Sciences, Victor Christianto, Robert Neil Boyd, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In Neutrosophic Logic, a basic assertion is that there are variations of about everything that we can measure; the variations surround three parameters called T,I,F (truth, indeterminacy, falsehood) which can take a range of values. This paper shortly reviews the links among aether and matter creation from the perspective of Neutrosophic Logic. Once we accept the existence of aether as physical medium, then we can start to ask on what causes matter ejection, as observed in various findings related to quasars etc. One particular cosmology model known as VMH (variable mass hypothesis) has been suggested by notable astrophysicists like Halton …

A Review On Superluminal Physics And Superluminal Communication In Light Of The Neutrosophic Logic Perspective, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In a recent paper, we describe a model of quantum communication based on combining consciousness experiment and entanglement, which can serve as impetus to stop 5G-network-caused diseases. Therefore, in this paper we consider superluminal physics and superluminal communication as a bridge or intermediate way between subluminal physics and action-at-a-distance (AAAD) physics, especially from neutrosophic logic perspective. Although several ways have been proposed to bring such a superluminal communication into reality, such as Telluric wave or Telepathy analog of Horejev and Baburin, here we also review two possibilities: quaternion communication and also quantum communication based on quantum noise. Further research is …

New Foundation In The Sciences: Physics Without Sweeping Infinities Under The Rug, Florentin Smarandache, Victor Christianto, Robert Neil Boyd

Branch Mathematics and Statistics Faculty and Staff Publications

It is widely known among the Frontiers of physics, that “sweeping under the rug” practice has been quite the norm rather than exception. In other words, the leading paradigms have strong tendency to be hailed as the only game in town. For example, renormalization group theory was hailed as cure in order to solve infinity problem in QED theory. For instance, a quote from Richard Feynman goes as follows: “What the three Nobel Prize winners did, in the words of Feynman, was "to get rid of the infinities in the calculations. The infinities are still there, but now they can …

Graded Quivers, Generalized Dimer Models And Toric Geometry, Sebastián Franco, Azeem Hasan

Publications and Research

The open string sector of the topological B-model on CY (m+2)-folds is described by m-graded quivers with superpotentials. This correspondence extends to general m the well known connection between CY (m+2)-folds and gauge theories on the world-volume of D(5-2m)-branes for m = 0, ..., 3. We introduce m-dimers, which fully encode the m-graded quivers and their superpotentials, in the case in which the CY (m+2)-folds are toric. Generalizing the well known m = 1,2 cases, m-dimers significantly simplify the connection between geometry and m-graded quivers. A key …