Mathematics Commons^™

Some Rather Mechanical Reflections On Symmetry: In Art, Science, Engineering, Mathematics, Etc., Jim Mcgovern

Articles

This Inaugural Lecture consists of some of my rather mechanical, being an engineer, reflections on symmetry in diverse areas such as art, science, engineering, mathematics, etc. I explain what symmetry is to me, giving examples with lots of images and mentioning or at least barely referencing art, science, architecture, engineering, heritage, cosmology, bicycles, flight, invention, ingenuity, history, wallpaper, mathematics, typography, structures, regular shapes, coordinate systems, spacetime, thermodynamics and suchlike.

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 …

How Students Use Mathematical Resources In An Electrostatics Context, Dawn C. Meredith, Karen A. Marrongelle

Mathematics and Statistics Faculty Publications and Presentations

We present evidence that although students’ mathematical skills in introductory calculus-based physics classes may not be readily applied in physics contexts, these students have strong mathematical resources on which to build effective instruction. Our evidence is based on clinical interviews of problem solving in electrostatics, which are analyzed using the framework of Sherin’s symbolic forms. We find that students use notions of “dependence” and “parts-of-a-whole” to successfully guide their work, even in novel situations. We also present evidence that students’ naive conceptions of the limit may prevent them from viewing integrals as sums.

Volume 01, Jessica Fields, Stephanie Neeley, Derek W. Hambright, Mary E. Lehman, Andrew R. Grzankowski, Zachary Johnson, Boone M. Prentice, Ashley M. Swandby, Victoria Morgan, Katie Williamson, Kristine G. Bender, Katelyn N. Romaine, D. Nicole Swann, Jessica Fox, Mike Mcateer, Alex Grabiec, Laura Nodtvedt, Nick Costa, Rachel Wolfe, Zack Dalton

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

Three Decades of Digging: Undergraduate Archeology at Longwood by Jessica Fields and Stephanie Neeley

Interactions of Allelopathy and Heat Stress in Plants by Derek W. Hambright and Mary E. Lehman

Inertial Electrostatic Confinement D-D Fusion Device: Construction and Simulation by Andrew R. Grzankowski

Shackled Nim by Zachary Johnson

Development of GC-MS and Chemometric Methods for the Analysis of Accelerants in Arson Cases by Boone M. Prentice

A Comparison of Image Analysis Methods in cDNA Microarrays by Ashley M. Swandby

Perceived Sexual Activity of Short and Long-Term Relationships by Victoria Morgan and Katie Williamson

Elderly …

The Adaptability Principle Of Mechanical Law And The Scale-Invariant Principle Of Mechanical Law In Fractal Space, Yang Xiaojun

Xiao-Jun Yang

The adaptability principle of mechanical law and the scale-invariant principle of mechanical law in fractal space are proved by using parameter-space and scale-space transforms in renormalization groups.From the space-transform angle,the transform of mechanical law from fractal space to European space is the scale-invariant transform while the transform of mechanical law from European space to fractal space is the adaptability transform.Their deductions are that law of conservation of energy and vectorial resultant of force and displacement in fractal space hold the line in form and Carpinteri's dimensional formula of fractal space is also proved. Namely,the spilling dimension of volume in fractal …

Fractional Definite Integral, Yang Xiaojun

Xiao-Jun Yang

Fractional definite integral is that a value of the integral calculus over given interva1．Under the circumstance of fractional dimension，fractional definite integral is important to compute some value in given interva1．It is complied with starting introducing definition，the properties，leads into fractional integral function of definition and the properties，and then induces to basic theorems for fractional integral calculus

Thermal Roots Of Correlation-Based Complexity, Philip Fraundorf

Physics Faculty Works

Bayesian maxent lets one integrate thermal physics and information theory points of view in the quantitative study of complex systems. Since net surprisal (a free energy analog for measuring “departures from expected”) allows one to place second law constraints on mutual information (a multimoment measure of correlations), it makes a quantitative case for the role of reversible thermalization in the natural history of invention, and suggests multiscale strategies to monitor standing crop as well. It prompts one to track evolved complexity starting from live astrophysically observed processes, rather than only from evidence of past events. Various gradients and boundaries that …

Nearly-Hamiltonian Structure For Water Waves With Constant Vorticity, Adrian Constantin, Rossen Ivanov, Emil Prodanov

Articles

We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for steady waves.

Thermal Roots Of Correlation-Based Complexity, Philip Fraundorf

Phil Fraundorf