Applied Mathematics Commons^™

Cooking Up The Optimal Baking Algorithm, Tony Burand, Michael Tetzlaff, Jacob Smith

Colloquy Undergraduate Research Journal

Many conventional rectangular baking pans have a problem in that they bake the corners of the batter faster than the rest of the pan. Circular baking pans eliminate this problem, but take up more space in the oven. We propose a solution that given weights for baking consistency and space efficiency based on the importance of each will provide the optimal baking pan shape. We have come up with an algorithm for sorting the pans of area A effectively and formed a model that describes the heat flow into the pan as well as the baking mix itself. The model …

Research And Development Of The Positron Damping Rings For The Proposed International Linear Collider And At Cern In Geneva, Switzerland For The Large Hadron Collider Atlas Experiment's Integrated Simulation Framwork, Ryan Badman

Renée Crown University Honors Thesis Projects - All

The topic of part I of my capstone is electron clouds, studied in the Cornell synchrotron accelerator. Electron clouds are an important phenomenon to study in circular particle accelerators such as the Large Hadron Collider (LHC), the Cornell synchrotron, and the damping ring for the proposed International Linear Collider (ILC). Low energy background electrons are normally present in high energy accelerators and are often not detrimental to beam performance, but certain operation conditions cause them to interact strongly with the beam, as was first observed in the 1980s in positron storage rings. The generation and amplification of the electron cloud …

Scalars And Generating Bases For The Module Of Splines With Boundary Conditions C(R;0)(I, Gordon Michael Jones

Renée Crown University Honors Thesis Projects - All

See Full Document for Abstract

Influence Of Microstructure On Thermoelastic Wave Propagation, Arkadi Berezovski, Mihhail Berezovski

Publications

Numerical simulations of the thermoelastic response of a microstructured material on a thermal loading are performed in the one-dimensional setting to examine the influence of temperature gradient effects at the microstructure level predicted by the thermoelastic description of microstructured solids (Berezovski et al. in J. Therm. Stress. 34:413–430, 2011). The system of equations consisting of a hyperbolic equation of motion, a parabolic macroscopic heat conduction equation, and a hyperbolic evolution equation for the microtemperature is solved by a finite-volume numerical scheme. Effects of microtemperature gradients exhibit themselves on the macrolevel due to the coupling of equations of the macromotion …

The Effect Of Symmetry On The Riemann Map, Jeanine Louise Myers

Graduate Theses and Dissertations

The Riemann mapping theorem guarantees the existence of a conformal mapping or Riemann map in the complex plane from the open unit disk onto an open simply-connected domain, which is not all of the complex plane. Although its existence is guaranteed, the Riemann map is rarely known except for special domains like half-planes, strips, etc. Therefore, any information we can determine about the Riemann map for any class of domains is interesting and useful.

This research investigates how symmetry affects the Riemann map. In particular, we define domains with symmetries called Rectangular Domains or RDs. The Riemann map of an …

Gene Regulatory Network Reconstruction Using Dynamic Bayesian Networks, Haoni Li

Dissertations

High-content technologies such as DNA microarrays can provide a system-scale overview of how genes interact with each other in a network context. Various mathematical methods and computational approaches have been proposed to reconstruct GRNs, including Boolean networks, information theory, differential equations and Bayesian networks. GRN reconstruction faces huge intrinsic challenges on both experimental and theoretical fronts, because the inputs and outputs of the molecular processes are unclear and the underlying principles are unknown or too complex.

In this work, we focused on improving the accuracy and speed of GRN reconstruction with Dynamic Bayesian based method. A commonly used structure-learning algorithm …

Universal Cycles For Some Combinatorial Objects, Andre A. Campbell

Electronic Theses and Dissertations

A de Bruijn cycle commonly referred to as a universal cycle (u-cycle), is a complete and compact listing of a collection of combinatorial objects. In this paper, we show the power of de Bruijn's original theorem, namely that the cycles bearing his name exist for n-letter words on a k-letter alphabet for all values of k,n, to prove that we can create de Bruijn cycles for multi-sets using natural encodings and M-Lipschitz n-letter words and the assignment of elements of [n]={1,2,...,n} to the sets in any labeled subposet of the Boolean lattice; de Bruijn's theorem corresponds to the case …

A Gaming Application Of The Negative Hypergeometric Distribution, Steven Norman Jones

UNLV Theses, Dissertations, Professional Papers, and Capstones

The Negative Hypergeometric distribution represents waiting times when drawing from a finite sample without replacement. It is analogous to the negative binomial, which models the distribution of waiting times when drawing with replacement. Even though the Negative Hypergeometric has applications it is typically omitted from textbooks on probability and statistics and is not generally known. The main purpose of this thesis is to derive expressions for the mean and variance of a new application of the Negative Hypergeometric to gaming and gambling. Other applications are described as well.

Supersonic Turbine Cascade Studies Using Computational Fluid Dynamics And Water Table Experiments, Shelby E. Nelson

Honors College Theses

Design engineers use a variety of tools to perform calculations and to aid in the design process. For example, engineers designing gas turbines, specifically the aerodynamicists, use a combination of hand calculations, experimental data, and complex numerical codes to simulate air flow around each blade. Aerodynamicists designing gas turbines must predict the locations of the shocks to locate inefficiencies in the flow. In this thesis, three methods of calculating the shock angles are compared: analytical, experimental, and computational. Three different airfoil shapes are tested: a rectangular flat plate, a supersonic diamond, and a turbine airfoil. Cascade tests of the airfoil …

Hardy Space Properties Of The Cauchy Kernel Function For A Strictly Convex Planar Domain, Belen Espinosa Lucio

Graduate Theses and Dissertations

This work is based on a paper by Edgar Lee Stout, where it is shown that for every strictly pseudoconvex domain $D$ of class $C^2$ in $\mathbb{C}^N$, the Henkin-Ram\'irez Kernel Function belongs to the Smirnov class, $E^q(D)$, for every $q\in(0,N)$.

The main objective of this dissertation is to show an analogous result for the Cauchy Kernel Function and for any strictly convex bounded domain in the complex plane. Namely, we show that for any strictly convex bounded $D\subset\mathbb{C}$ of class $C^2$ if we fix $\zeta$ in the boundary of $D$ and consider the Cauchy Kernel Function

\mathcal{K}(\zeta,z)=\frac{1}{2\pi i}\frac{1}{\zeta-z}

as a …

Refining Environmental Satellite Data Using A Statistical Approach, Md Zahidur Rahman, Leonid Roytman, Abdelhamid Kadik

Publications and Research

The proposed approach in this article applies an efficient and novel statistical technique to accurately describe radiometric data measured by Advanced Very High Resolution Radiometers (AVHRR) onboard the National Oceanic and Atmospheric Administration’s (NOAA) Polar Orbiting Environmental Satellites (POES). The corrected data set will then be applied to improve the strength of NOAA Global Vegetation Index (GVI) data set for the 1982- 2003 period produced from AVHRR. The GVI is used extensively for studying and monitoring land surface, atmosphere and recently for analyzing climate and environmental changes. The POES AVHRR data, though useful, cannot be directly used in climate change …

On High-Performance Parallel Decimal Fixed-Point Multiplier Designs, Ming Zhu

College of Engineering: Graduate Celebration Programs

Decimal computations are required in finance, and etc.

• Precise representation for decimals (E.g. 0.2, 0.7… )
• Performance Requirements (Software simulations are very slow)

Four Named To Endowed Professorships, Kim Hill

News and Events (Discontinued Series)

No abstract provided.

Universal Scaling And Intrinsic Classification Of Electro-Mechanical Actuators, Sambit Palit, Ankit Jain, Muhammad A. Alam

Birck and NCN Publications

Actuation characteristics of electromechanical (EM) actuators have traditionally been studied for a few specific regular electrode geometries and support (anchor) configurations. The ability to predict actuation characteristics of electrodes of arbitrary geometries and complex support configurations relevant for broad range of applications in switching, displays, and varactors, however, remains an open problem. In this article, we provide four universal scaling relationships for EM actuation characteristics that depend only on the mechanical support configuration and the corresponding electrode geometries, but are independent of the specific geometrical dimensions and material properties of these actuators. These scaling relationships offer an intrinsic classification for …

Turrent Configurations And Particle Paths, Zihao Lawrence Jian

Undergraduate Research Conference

The research originated from the question of how many rows of soldiers or turrets could be placed and allow for all turrets to have a projectile path. We find the relationship between the safe radius for each turret/soldier and the number of rows for which each soldier will have a clear projectile path. As shown, we place turrets in a grid configuration in the Cartesian plane.

Research And Development Of The Positron Damping Rings For The Proposed International Linear Collider, And At Cern In Geneva, Switzerland For The Large Hadron Collider Atlas Experiment's Integrated Simulation Framework, Ryan Badman

Renée Crown University Honors Thesis Projects - All

Abstract not available. Please download the full Capstone for abstract.

Mathematical Modelling And Control Of Echinococcus In Qinghai Province, China, Liumei Wu, Baojun Song, Wen Du, Jie Lou

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

In this paper, two mathematical models, the baseline model and the intervention model, are proposed to study the transmission dynamics of echinococcus. A global forward bifurcation completely characterizes the dynamical behavior of the baseline model. That is, when the basic reproductive number is less than one, the disease-free equilibrium is asymptotically globally stable; when the number is greater than one, the endemic equilibrium is asymptotically globally stable. For the intervention model, however, the basic reproduction number alone is not enough to describe the dynamics, particularly for the case where the basic reproductive number is less then one. The emergence of …

Novel Algorithms And Instrumentation For Vibrational Spectroscopic Methods Of Analysis, Mohamed F. Abdelkader

Chemistry & Biochemistry Theses & Dissertations

Raman spectroscopy is a form of vibrational spectroscopy that has been increasingly applied to qualitative analysis of chemicals, explosives, pharmaceuticals, and fuels due to its non-invasive and non-destructive nature; its ease of sampling; and its high molecular specificity. These characteristics of Raman spectroscopy also facilitate its use for both in-line and at-line analysis. The principle limitation of Raman spectroscopy is optical interference arising from both analyte and non-analyte fluorescence. In this dissertation, a solution to this problem is presented in the form of a novel spectrometer design which operates in a sequentially shifted excitation mode to eliminate fluorescence backgrounds, fixed …

Superconvergence Of Finite Element Approximations For Partial Differential Equations, Rabeea Hadi Jari

Theses and Dissertations

The finite element methods (FEMs) are popular numerical methods for solving partial differential equations. They are widely used by mathematicians, scientists and engineers to solve real world problems. The superconvergence in the finite element method (FEM) is a phenomenon where the order of convergence of the numerical solution is higher than the order of convergence of the maximum of the finite element error. Improving the convergence rate by applying certain post-processing techniques to the standard finite element solutions is one of the most important and useful areas of superconvergence. Two model problems will be considered in this dissertation. They are …

Distributional Monte Carlo Methods For The Boltzmann Equation, Christopher R. Schrock

Theses and Dissertations

Stochastic particle methods (SPMs) for the Boltzmann equation, such as the Direct Simulation Monte Carlo (DSMC) technique, have gained popularity for the prediction of flows in which the assumptions behind the continuum equations of fluid mechanics break down; however, there are still a number of issues that make SPMs computationally challenging for practical use. In traditional SPMs, simulated particles may possess only a single velocity vector, even though they may represent an extremely large collection of actual particles. This limits the method to converge only in law to the Boltzmann solution. This document details the development of new SPMs that …

Propeller, Joel Kahn

The Transdisciplinary STEAM+ Journal

This image is based on several different algorithms interconnected within a single program in the language BASIC-256. The fundamental structure involves a tightly wound spiral working outwards from the center of the image. As the spiral is drawn, different values of red, green and blue are modified through separate but related processes, producing the changing appearance. Algebra, trigonometry, geometry, and analytic geometry are all utilized in overlapping ways within the program. As with many works of algorithmic art, small changes in the program can produce dramatic alterations of the visual output, which makes lots of variations possible.

Simulation Insights Using R, Boyan Kostadinov

Publications and Research

This article attempts to introduce the reader to computational thinking and solving problems involving randomness. The main technique being employed is the Monte Carlo method, using the freely available software R for Statistical Computing. The author illustrates the computer simulation approach by focusing on several problems of increasing difficulty. The simulation techniques and the specific problems discussed in this article would be of interest to STEM students and instructors, teaching courses in Monte Carlo simulations, stochastic modeling, probability and statistics. The R code for all problems is discussed in full detail so that the reader can get a taste of …

Duncan, Benjamin, 1772-1809 (Sc 678), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid only for Manuscripts Small Collection 678. Cipher book kept by Benjamin Duncan, of Culpeper County, Virginia and Fayette County, Kentucky. Includes samples of legal forms and letters.

How To Find Killing Vectors, Charles G. Torre

How to... in 10 minutes or less

We show how to compute the Lie algebra of Killing vector fields of a metric in Maple using the commands KillingVectors and LieAlgebraData. A Maple worksheet and a PDF version can be found below.

On The Quadratic Bundles Related To Hermitian Symmetric Spaces, Tihomir Valchev

Articles

We develop the direct scattering problem for quadratic bundles associated to Hermitian symmetric spaces. We adapt the dressing method for quadratic bundles which allows us to find special solutions to multicomponent derivative Schrodinger equation for instance. The latter is an infinite dimensional Hamiltonian system possessing infinite number of integrals of motion. We demonstrate how one can derive them by block diagonalization of the corresponding Lax pair.

Isomorphisms Of Lattices Of Bures-Closed Bimodules Over Cartan Masas, Adam H. Fuller, David R. Pitts

Department of Mathematics: Faculty Publications

For i = 1; 2, let (Mi;Di) be pairs consisting of a Cartan MASA Di in a von Neumann algebra Mi, let atom(Di) be the set of atoms of Di, and let Si be the lattice of Bures-closed Di bimodules in Mi. We show that when Mi have separable preduals, there is a lattice isomorphism between S1 and S2 if and only if the sets

f(Q1;Q2) 2 atom(Di) atom(Di) : Q1MiQ2 6= (0)g

have the same cardinality. In particular, when Di is nonatomic, Si is isomorphic to the lattice of projections in L1([0; 1];m) where m is Lebesgue measure, regardless …

Parametric Catalan Numbers And Catalan Triangles, Tian-Xiao He

Scholarship

Here presented a generalization of Catalan numbers and Catalan triangles associated with two parameters based on the sequence characterization of Bell-type Riordan arrays. Among the generalized Catalan numbers, a class of large generalized Catalan numbers and a class of small generalized Catalan numbers are defined, which can be considered as an extension of large Schroder numbers and small Schroder numbers, respectively. Using the characterization sequences of Bell-type Riordan arrays, some properties and expressions including the Taylor expansions of generalized Catalan numbers are given. A few combinatorial interpretations of the generalized Catalan numbers are also provided. Finally, a generalized Motzkin numbers …

A Spectral Order For Infinite Dimensional Quantum Spaces, Joe Mashburn

Mathematics Faculty Publications

In this paper we extend the spectral order of Coecke and Martin to infinite-dimensional quantum states. Many properties present in the finite-dimensional case are preserved, but some of the most important are lost. The order is constructed and its properties analysed. Most of the useful measurements of information content are lost. Shannon entropy is defined on only a part of the model, and that part is not a closed subset of the model. The finite parts of the lattices used by Birkhoff and von Neumann as models for classical and quantum logic appear as subsets of the models for infinite …

Some Minor-Closed Classes Of Signed Graphs, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics Faculty Publications

We define four minor-closed classes of signed graphs in terms of embeddability in the annulus, projective plane, torus, and Klein bottle. We give the full list of 20 excluded minors for the smallest class and make a conjecture about the largest class.

Sloane’S Gap: Do Mathematical And Social Factors Explain The Distribution Of Numbers In The Oeis?, Nicolas J.-P. Gauvrit, Jean-Paul Delahaye, Hector Zenil

Journal of Humanistic Mathematics

The Online Encyclopedia of Integer Sequences (OEIS) is a catalog of integer sequences. We are particularly interested in the number of occurrences of N(n) of an integer n in the database. This number N(n) marks the importance of n and it varies noticeably from one number to another, and from one number to the next in a series. “Importance” can be mathematically objective (2^10 is an example of an “important” number in this sense) or as the result of a shared mathematical culture (10^9 is more important than 9^10 because we use a decimal notation). The concept of algorithmic complexity …