Algebraic Geometry Commons^™

Spacetime Geometry Of Acoustics And Electromagnetism, Lucas Burns, Tatsuya Daniel, Stephon Alexander, Justin Dressel

Mathematics, Physics, and Computer Science Faculty Articles and Research

Both acoustics and electromagnetism represent measurable fields in terms of dynamical potential fields. Electromagnetic force-fields form a spacetime bivector that is represented by a dynamical energy–momentum 4-vector potential field. Acoustic pressure and velocity fields form an energy–momentum density 4-vector field that is represented by a dynamical action scalar potential field. Surprisingly, standard field theory analyses of spin angular momentum based on these traditional potential representations contradict recent experiments, which motivates a careful reassessment of both theories. We analyze extensions of both theories that use the full geometric structure of spacetime to respect essential symmetries enforced by vacuum wave propagation. The …

Bbt Acoustic Alternative Top Bracing Cadd Data Set-Norev-2022jun28, Bill Hemphill

STEM Guitar Project’s BBT Acoustic Kit

This electronic document file set consists of an overview presentation (PDF-formatted) file and companion video (MP4) and CADD files (DWG & DXF) for laser cutting the ETSU-developed alternate top bracing designs and marking templates for the STEM Guitar Project’s BBT (OM-sized) standard acoustic guitar kit. The three (3) alternative BBT top bracing designs in this release are
(a) a one-piece base for the standard kit's (Martin-style) bracing,
(b) 277 Ladder-style bracing, and
(c) an X-braced fan-style bracing similar to traditional European or so-called 'classical' acoustic guitars.

The CADD data set for each of the three (3) top bracing designs includes …

Bbt Side Mold Assy, Bill Hemphill

STEM Guitar Project’s BBT Acoustic Kit

This electronic document file set covers the design and fabrication information of the ETSU Guitar Building Project’s BBT (OM-sized) Side Mold Assy for use with the STEM Guitar Project’s standard acoustic guitar kit. The extended 'as built' data set contains an overview file and companion video, the 'parent' CADD drawing, CADD data for laser etching and cutting a drill &/or layout template, CADD drawings in AutoCAD .DWG and .DXF R12 formats of the centerline tool paths for creating the mold assembly pieces on an AXYZ CNC router, and support documentation for CAM applications including router bit specifications, feeds, speed, multi-pass …

Effective Statistical Energy Function Based Protein Un/Structure Prediction, Avdesh Mishra

University of New Orleans Theses and Dissertations

Proteins are an important component of living organisms, composed of one or more polypeptide chains, each containing hundreds or even thousands of amino acids of 20 standard types. The structure of a protein from the sequence determines crucial functions of proteins such as initiating metabolic reactions, DNA replication, cell signaling, and transporting molecules. In the past, proteins were considered to always have a well-defined stable shape (structured proteins), however, it has recently been shown that there exist intrinsically disordered proteins (IDPs), which lack a fixed or ordered 3D structure, have dynamic characteristics and therefore, exist in multiple states. Based on …

Application And Evaluation Of Lighthouse Technology For Precision Motion Capture, Soumitra Sitole

Masters Theses

This thesis presents the development towards a system that can capture and quantify motion for applications in biomechanical and medical fields demanding precision motion tracking using the lighthouse technology. Commercially known as SteamVR tracking, the lighthouse technology is a motion tracking system developed for virtual reality applications that makes use of patterned infrared light sources to highlight trackers (objects embedded with photodiodes) to obtain their pose or spatial position and orientation. Current motion capture systems such as the camera-based motion capture are expensive and not readily available outside of research labs. This thesis provides a case for low-cost motion capture …

Higher Cluster Categories And Qft Dualities, Sebastián Franco, Gregg Musiker

Publications and Research

We introduce a unified mathematical framework that elegantly describes minimally supersymmetry gauge theories in even dimensions, ranging from six dimensions to zero dimensions, and their dualities. This approach combines and extends recent developments on graded quivers with potentials, higher Ginzburg algebras, and higher cluster categories (also known as m-cluster categories). Quiver mutations studied in the context of mathematics precisely correspond to the order-(m + 1) dualities of the gauge theories. Our work indicates that these equivalences of quiver gauge theories sit inside an infinite family of such generalized dualities.

Beurling-Lax Type Theorems In The Complex And Quaternionic Setting, Daniel Alpay, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

We give a generalization of the Beurling–Lax theorem both in the complex and quaternionic settings. We consider in the first case functions meromorphic in the right complex half-plane, and functions slice hypermeromorphic in the right quaternionic half-space in the second case. In both settings we also discuss a unified framework, which includes both the disk and the half-plane for the complex case and the open unit ball and the half-space in the quaternionic setting.

Iterative Solution Of Fractional Diffusion Equation Modelling Anomalous Diffusion, A. Elsaid, S. Shamseldeen, S. Madkour

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we study the fractional diffusion equation with spatial Riesz fractional derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution is obtained based on properties of Riesz fractional derivative operator and utilizing the optimal homotopy analysis method (OHAM). Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameter on the solution behavior.

Klein Bottle Queries, Austin Lowe

Georgia State Undergraduate Research Conference

No abstract provided.

Manipulating The Mass Distribution Of A Golf Putter, Paul J. Hessler Jr.

Senior Honors Projects

Putting may appear to be the easiest but is actually the most technically challenging part of the game of golf. The ideal putting stroke will remain parallel to its desired trajectory both in the reverse and forward direction when the putter head is within six inches of the ball. Deviation from this concept will cause a cut or sidespin on the ball that will affect the path the ball will travel.

Club design plays a large part in how well a player will be able to achieve a straight back and straight through club head path near impact; specifically the …

An Exploration Of A Discrete Rhombohedral Lattice Of Possible Engineering Or Physical Relevance (Revised Version) 2008, Jim Mcgovern

Conference Papers

A particular discrete rhombohedral lattice consisting of four symmetrically interlaced cuboctahedral point lattices is described that is interesting because of the high degree of symmetry it exhibits. The four constituent cuboctahedral lattices are denoted by four colours and the composite lattice is referred to as a 4-colour rhombohedral lattice. Each point of the 4-colour lattice can be referenced by an integer 4-tuple containing only the positive non-zero integers (the counting numbers). The relationship between the discrete rhombohedral lattice and a discrete Cartesian lattice is explained. Some interesting aspects of the lattice and of the counting-number 4-tuple coordinate system are pointed …

An Exploration Of A Discrete Rhombohedral Lattice Of Possible Engineering Or Physical Relevance, Jim Mcgovern

Conference Papers

A particular discrete rhombohedral lattice consisting of four symmetrically interlaced cuboctahedral or cubic point lattices is described that is interesting because of the high degree of symmetry it exhibits. The four constituent lattices are denoted by four colours and the composite lattice is referred to as a 4-colour rhombohedral lattice. Each point of the 4-colour lattice can be referenced by an integer 4-tuple containing only the positive non-zero integers (the counting numbers). The relationship between the discrete rhombohedral lattice and a discrete Cartesian lattice is explained. Some interesting aspects of the lattice and of the counting-number 4-tuple coordinate system are …

Aspects Of Conformal Field Theory From Calabi-Yau Arithmetic, Rolf Schimmrigk

Faculty and Research Publications

This paper describes a framework in which techniques from arithmetic algebraic geometry are used to formulate a direct and intrinsic link between the geometry of Calabi-Yau manifolds and aspects of the underlying conformal field theory. As an application the algebraic number field determined by the fusion rules of the conformal field theory is derived from the number theoretic structure of the cohomological Hasse-Weil L-function determined by Artin's congruent zeta function of the algebraic variety. In this context a natural number theoretic characterization arises for the quantum dimensions in this geometrically determined algebraic number field.

Like A Bridge Over Colored Water: A Mathematical Review Of The Rainbow Bridge: Rainbows In Art, Myth, And Science, John A. Adam

Mathematics & Statistics Faculty Publications

Commenting on a recent book, the author discusses various views of the rainbow: its role in culture, its scientific description, and its mathematical theory.

Gravity And Electromagnetism In Noncommutative Geometry, Giovanni Landi, Nguyen Ai Viet, Kameshwar C. Wali

Physics - All Scholarship

We present a unified description of gravity and electromagnetism in the framework of a Z 2 non-commutative differential calculus. It can be considered as a “discrete version” of Kaluza-Klein theory, where the fifth continuous dimension is replaced by two discrete points. We derive an action which coincides with the dimensionally reduced one of the ordinary Kaluza-Klein theory.