List-Distinguishing Cartesian Products Of Cliques,
2017
University of Colorado, Denver
List-Distinguishing Cartesian Products Of Cliques, Michael Ferrara, Zoltan Füredi, Sogol Jahanbekam, Paul Wenger
Faculty Publications
The distinguishing number of a graph G, denoted D(G), is the minimum number of colors needed to produce a coloring of the vertices of G so that every nontrivial isomorphism interchanges vertices of different colors. A list assignment L on a graph G is a function that assigns each vertex of G a set of colors. An L-coloring of G is a coloring in which each vertex is colored with a color from L(v). The list distinguishing number of G, denoted Dℓ(G) is the minimum k such that every list assignment L that assigns a list of size at least …
A Numerical Solution Of Ermakov Equation Corresponding To Diffusion Interpretation Of Wave Mechanics,
2017
University of New Mexico
A Numerical Solution Of Ermakov Equation Corresponding To Diffusion Interpretation Of Wave Mechanics, Victor Christianto, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
It has been long known that a year after Schrödinger published his equation, Madelung also published a hydrodynamics version of Schrödinger equation. Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub‐diffusive law. In this paper we will review two different approaches, including Madelung hydrodynamics and also Bohm potential. Madelung formulation leads to diffusion interpretation, which after a generalization yields to Ermakov equation. Since Ermakov equation cannot be solved analytically, then we try to find out its solution with Mathematica package. …
Explicit Integration Of A Generic Hénon-Heiles System With Quartic Potential,
2017
Zayed University
Explicit Integration Of A Generic Hénon-Heiles System With Quartic Potential, Nicola Sottocornola
All Works
© 2017 the authors. There are seven time independent, integrable, Hénon-Heiles systems: three with cubic and four with quartic potential. The cubic and one of the quartic cases have been separated in the last decades. The other three cases 1:6:1, 1:6:8 and 1:12:16 have resisted several attempts in the last years. In this paper we focus our attention on the 1:12:16 case whose equations of motion have been separated only in the degenerate case ab = 0. We give here the separation coordinates for the generic case using a method introduced by Franco Magri in 2005 under the name of …
Mathematical Description And Mechanistic Reasoning: A Pathway Toward Stem Integration,
2017
Oakland University
Mathematical Description And Mechanistic Reasoning: A Pathway Toward Stem Integration, Paul J. Weinberg
Journal of Pre-College Engineering Education Research (J-PEER)
Because reasoning about mechanism is critical to disciplined inquiry in science, technology, engineering, and mathematics (STEM) domains, this study focuses on ways to support the development of this form of reasoning. This study attends to how mechanistic reasoning is constituted through mathematical description. This study draws upon Smith’s (2007) characterization of mathematical description of scientific phenomena as ‘‘bootstrapping,’’ where negotiating the relationship between target phenomena and represented relations is fundamental to learning. In addition, the development of mathematical representation presents a viable pathway towards STEM integration. In this study, participants responded to an assessment of mechanistic reasoning while cognitive interviews …
Rigorous Debates Over Debatable Rigor: Monster Functions In Introductory Analysis,
2017
Colorado State University-Pueblo
Rigorous Debates Over Debatable Rigor: Monster Functions In Introductory Analysis, Janet Heine Barnett
Analysis
No abstract provided.
Natural Color Symmetry,
2017
Santa Clara University
Natural Color Symmetry, Frank A. Farris
Mathematics and Computer Science
Existing techniques to create images with color-reversing (or other kinds of color symmetry) produce results that look less than natural. We produce images with approximate color symmetries by using the domain coloring algorithm with suitable complex Fourier series and photographs that have varying degrees of naturally occurring color symmetry. The technique yields patterns where the color symmetry looks less crystallographic than those previously produced, but perhaps more artistic. The technique produces an interesting combination of symmetrical and natural patterns.
Efficient Coarse-Grained Brownian Dynamics Simulations For Dna And Lipid Bilayer Membrane With Hydrodynamic Interactions,
2017
New Jersey Institute of Technology
Efficient Coarse-Grained Brownian Dynamics Simulations For Dna And Lipid Bilayer Membrane With Hydrodynamic Interactions, Szu-Pei Fu
Dissertations
The coarse-grained molecular dynamics (CGMD) or Brownian dynamics (BD) simulation is a particle-based approach that has been applied to a wide range of biological problems that involve interactions with surrounding fluid molecules or the so-called hydrodynamic interactions (HIs). From simple biological systems such as a single DNA macromolecule to large and complicated systems, for instances, vesicles and red blood cells (RBCs), the numerical results have shown outstanding agreements with experiments and continuum modeling by adopting Stokesian dynamics and explicit solvent model. Finally, when combined with fast algorithms such as the fast multipole method (FMM) which has nearly optimal complexity in …
Boundary Integral Equation Based Numerical Solutions Of Helmholtz Transmission Problems For Composite Scatters,
2017
New Jersey Institute of Technology
Boundary Integral Equation Based Numerical Solutions Of Helmholtz Transmission Problems For Composite Scatters, Haiyang Qi
Dissertations
In this dissertation, an in-depth comparison between boundary integral equation solvers and Domain Decomposition Methods (DDM) for frequency domain Helmholtz transmission problems in composite two-dimensional media is presented. Composite media are characterized by piece-wise constant material properties (i.e., index of refraction) and thus, they exhibit interfaces of material discontinuity and multiple junctions. Whenever possible to use, boundary integral methods for solution of Helmholtz boundary value problems are computationally advantageous. Indeed, in addition to the dimensional reduction and straightforward enforcement of the radiation conditions that these methods enjoy, they do not suffer from the pollution effect present in volumetric discretization. The …
Solving A System Of Linear Equations Using Ancient Chinese Methods,
2017
University of St Thomas
Solving A System Of Linear Equations Using Ancient Chinese Methods, Mary Flagg
Linear Algebra
No abstract provided.
How To Use Absolute-Error-Minimizing Software To Minimize Relative Error: Practitioner's Guide,
2017
The University of Texas at El Paso
How To Use Absolute-Error-Minimizing Software To Minimize Relative Error: Practitioner's Guide, Afshin Gholamy, Vladik Kreinovich
Departmental Technical Reports (CS)
In many engineering and scientific problems, there is a need to find the parameters of a dependence from the experimental data. There exist several software packages that find the values for these parameters -- values for which the mean square value of the absolute approximation error is the smallest. In practice, however, we are often interested in minimizing the mean square value of the relative approximation error. In this paper, we show how we can use the absolute-error-minimizing software to minimize the relative error.
The Definite Integrals Of Cauchy And Riemann,
2017
Ursinus College
The Definite Integrals Of Cauchy And Riemann, Dave Ruch
Analysis
Rigorous attempts to define the definite integral began in earnest in the early 1800's. One of the pioneers in this development was A. L. Cauchy (1789-1857). In this project, students will read from his 1823 study of the definite integral for continuous functions . Then students will read from Bernard Riemann's 1854 paper, in which he developed a more general concept of the definite integral that could be applied to functions with infinite discontinuities.
The Closure Operation As The Foundation Of Topology,
2017
Ursinus College
The Closure Operation As The Foundation Of Topology, Nicholas A. Scoville
Topology
No abstract provided.
A Compact Introduction To A Generalized Extreme Value Theorem,
2017
Ursinus College
A Compact Introduction To A Generalized Extreme Value Theorem, Nicholas A. Scoville
Topology
In a short paper published just one year prior to his thesis, Maurice Frechet gives a simple generalization one what we might today call the Extreme value theorem. This generalization is a simple matter of coming up with ``the right" definitions in order to make this work. In this mini PSP, we work through Frechet's entire 1.5 page paper to give an extreme value theorem in more general topological spaces, ones which, to use Frechet's newly coined term, are compact.
What Is The Optimal Bin Size Of A Histogram: An Informal Description,
2017
The University of Texas at El Paso
What Is The Optimal Bin Size Of A Histogram: An Informal Description, Afshin Gholamy, Vladik Kreinovich
Departmental Technical Reports (CS)
A natural way to estimate the probability density function of an unknown distribution from the sample of data points is to use histograms. The accuracy of the estimate depends on the size of the histogram's bins. There exist heuristic rules for selecting the bin size. In this paper, we show that these rules indeed provide the optimal value of the bin size.
An Introduction To Topology For The High School Student,
2017
John Carroll University
An Introduction To Topology For The High School Student, Nathaniel Ferron
Masters Essays
No abstract provided.
Primes, Divisibility, And Factoring,
2017
Central Washington University
Primes, Divisibility, And Factoring, Dominic Klyve
Number Theory
No abstract provided.
Babylonian Numeration,
2017
Central Washington University
Gaussian Integers And Dedekind's Creation Of An Ideal: A Number Theory Project,
2017
Colorado State University-Pueblo
Gaussian Integers And Dedekind's Creation Of An Ideal: A Number Theory Project, Janet Heine Barnett
Number Theory
No abstract provided.
Construction Of The Figurate Numbers,
2017
New Mexico State University
Construction Of The Figurate Numbers, Jerry Lodder
Number Theory
No abstract provided.
Pascal's Triangle And Mathematical Induction,
2017
New Mexico State University
Pascal's Triangle And Mathematical Induction, Jerry Lodder
Number Theory
No abstract provided.
