Mathematics Commons^™

Spaces Of Sections Of Banach Algebra Bundles, Emmanuel Dror Farjoun, Claude Schochet

Mathematics Faculty Research Publications

Suppose that B is a G-Banach algebra over 𝔽 = ℝ or ℂ, X is a finite dimensional compact metric space, ζ : P → X is a standard principal G-bundle, and A_ζ = Γ(X,P x_G B) is the associated algebra of sections. We produce a spectral sequence which converges to π_∗(GL_oA_ζ) with

E_{_}²_p,q ≅ Ȟ^p(X ; π_q(GL_oB)).

A related spectral sequence converging to K_∗+1(A_ζ) (the real or complex topological …

The Seaborgium Chemical Table, Jeremiah Farrell

Scholarship and Professional Work - LAS

The diagram is an example of a connected, cubic graph with its ten nodes labelled with the letters of SEABORGIUM, chemical element 106. Connected means it is in one piece and cubic means that each node has exactly three edges on it.

Complete Multipartite Graphs And The Relaxed Coloring Game, Charles Dunn

Faculty Publications

Let k be a positive integer, d be a nonnegative integer, and G be a finite graph. Two players, Alice and Bob, play a game on G by coloring the uncolored vertices with colors from a set X of k colors. At all times, the subgraph induced by a color class must have maximum degree at most d. Alice wins the game if all vertices are eventually colored; otherwise, Bob wins. The least k such that Alice has a winning strategy is called the d-relaxed game chromatic number of G, denoted χ _g^d (G). …

Equivalence Theorems And The Local-Global Property, Aleams Barra

Theses and Dissertations--Mathematics

In this thesis we revisit some classical results about the MacWilliams equivalence theorems for codes over fields and rings. These theorems deal with the question whether, for a given weight function, weight-preserving isomorphisms between codes can be described explicitly. We will show that a condition, which was already known to be sufficient for the MacWilliams equivalence theorem, is also necessary. Furthermore we will study a local-global property that naturally generalizes the MacWilliams equivalence theorems. Making use of F-partitions, we will prove that for various subgroups of the group of invertible matrices the local-global extension principle is valid.

Resolutions And Tor Algebra Structures For Trivariate Monomial Ideals, Jared Lafayette Painter

Mathematics Dissertations - Archive

In this manuscript we explore properties of minimal free resolutions and their relationship to the Tor-algebra structure for trivariate monomial ideals. We begin with an in-depth analysis of minimal free resolutions of S = R / I, where R = k[x; y; z] is a polynomial ring over a field k, and I is a monomial ideal that is primary to the homogeneous maximal ideal m of R. We will de ne a special form of the minimal free resolution of S, and then determine when we get nonzero elements from I as entries in the matrices of the resolution. …

High Order Dns For Late Flow Transition, Ping Lu

Mathematics Dissertations - Archive

In this report, a new high order scheme for boundary points is introduced when calculating the derivative of smooth functions by Compact Scheme. The primitive function reconstruction method of ENO schemes is applied to obtain the conservative form of the Compact Scheme. Meanwhile, modified compact scheme is developed by using an effective shock detector to block upwinding compact scheme to cross the shock, a control function, and an adaptive scheme which uses some WENO flux near the shock. The new scheme makes the original upwinding compact scheme able to capture the shock sharper than WENO and, more important, keep high …

From Discrete To Continuous Models Of Cell Movement: An Application To Medical Implants, Alicia Prieto Langarica

Mathematics Dissertations - Archive

Mathematical modeling of cell movement is needed to aid in the deeper understanding of vital processes such as embryogenesis, angiogenesis, tumor metastasis, and immune reactions to foreign bodies. In this work, cell movement and growth in response to external stimulus and the interactions between cells and the stimulus are considered. In order to model the random nature of the movement, a discrete model is created to simulate cells moving in the presence of a growing and moving stimulus distribution. The model also includes the depletion of the stimulus under the presence of cells. The discrete model is then upscaled, based …

A Study On The Two Component Periodic Shallow Water Systems, Caixia Chen

Mathematics Dissertations - Archive

In this dissertation we study the generalized periodic two-component Camassa-Holm system and the generalized periodic two-component Dullin-Gottwald-Holm system, which can be derived from the Euler equation with nonzero constant vorticity in shallow water waves moving over a linear shear flow. The precise blow-up scenarios of strong solutions and several results of blow-up solutions with certain initial profiles are described in detail. The exact blow-up rates are also determined. Finally, the sufficient conditions for global solutions are established.

Applications Of Compressive Sensing To Surveillance Problems, Christopher Huff

Electronic Theses and Dissertations

In many surveillance scenarios, one concern that arises is how to construct an imager that is capable of capturing the scene with high fidelity. This could be problematic for two reasons: first, the optics and electronics in the camera may have difficulty in dealing with so much information; secondly, bandwidth constraints, may pose difficulty in transmitting information from the imager to the user efficiently for reconstruction or realization. In this thesis, we will discuss a mathematical framework that is capable of skirting the two aforementioned issues. This framework is rooted in a technique commonly referred to as compressive sensing. We …

Heat Equation, Wyatt Sherlock

A with Honors Projects

This document describes the process of deriving the heat equation from known thermodynamic laws followed by an analytic solution. Towards the end of the document, the heat equation is discussed in terms of practical engineering problems.

On Cise-Normal Subgroups Of Finite Groups, Yong Xu, Tao Zhao, Xianhua Li

Turkish Journal of Mathematics

A generalized normality CISE of subgroups of a finite group is introduced. Let F be a saturated formation containing the class of all supersolvable groups. We give a characterization of F by using CISE-normality of subgroups.

Convective Heat Transfer In Nanofluids, Steven Schraudner

Electronic Theses and Dissertations

In recent years, the study of fluid flow with nanoparticles in base fluids has attracted the attention of several researchers due to its various applications to science and engineering problems. Recent investigations on convective heat transfer in nanofluids indicate that the suspended nanoparticles markedly change the transport properties and thereby the heat transfer characteristics. Convection in saturated porous media with nanofluids is also an area of growing interest. In this thesis, we study the effects of radiation on the heat and mass transfer characteristics of nanofluid flows over solid surfaces. In Chapter 2, an investigation is made into the effects …

Squaring, Cubing, And Cube Rooting, Arthur T. Benjamin

All HMC Faculty Publications and Research

I still recall my thrill and disappointment when I read Mathematical Carnival, by Martin Gardner. I was thrilled because, as my high school teacher had recommended, mathematics was presented in a playful way that I had never seen before. I was disappointed because it contained a formula that I thought I had "invented" a few years earlier. I have always had a passion for mental calculation, and the following formula appears in Gardner's chapter on "Lightning Calculators." It was used by the mathematician A. C. Aitken to mentally square large numbers.

Adventures In Teaching: A Professor Goes To High School To Learn About Teaching Math, Darryl H. Yong

All HMC Faculty Publications and Research

During the 2009–2010 academic year I did something unusual for a university mathematician on sabbatical: I taught high school mathematics in a large urban school district. This might not be so strange except that my school does not have a teacher preparation program and only graduates a few students per year who intend to be teachers. Why did I do this? I, like many of you, am deeply concerned about mathematics education and I wanted to see what a typical high school in my city is like. Because I regularly work with high school mathematics teachers, I wanted to experience …

On The Hardness Of Counting And Sampling Center Strings, Christina Boucher, Mohamed Omar

All HMC Faculty Publications and Research

Given a set S of n strings, each of length ℓ, and a nonnegative value d, we define a center string as a string of length ` that has Hamming distance at most d from each string in S. The #CLOSEST STRING problem aims to determine the number of center strings for a given set of strings S and input parameters n, ℓ, and d. We show #CLOSEST STRING is impossible to solve exactly or even approximately in polynomial time, and that restricting #CLOSEST STRING so that any one of the parameters n, ℓ, or d is fixed leads to …

Increasing The Use Of Practical Activities Through Changed Practice, Frode Olav Haara, Kari Smith

The Mathematics Enthusiast

This study sets out to examine the influence of a value-based intervention on two elementary school teachers’ use of practical activities in mathematics teaching. The intervention was a “Values and Knowledge Education” (VaKE)-based in-service course that introduced the two teachers to a value-based approach to mathematics teaching. The introduction included examples that were supported by use of practical activities. Interviews prior to the intervention made the teachers aware of an inconsistency between the desired and actual practice of their own teaching. The intervention provided them with a possibility of narrowing the gap between vision and practice by changing practice. Qualitative …

Modeling Flow Rate To Estimate Hydraulic Conductivity In A Parabolic Ceramic Water Filter, Ileana Wald

Undergraduate Journal of Mathematical Modeling: One + Two

In this project we model volumetric flow rate through a parabolic ceramic water filter (CWF) to determine how quickly it can process water while still improving its quality. The volumetric flow rate is dependent upon the pore size of the filter, the surface area, and the height of water in the filter (hydraulic head). We derive differential equations governing this flow from the conservation of mass principle and Darcy's Law and find the flow rate with respect to time. We then use methods of calculus to find optimal specifications for the filter. This work is related to the research conducted …

The Elevation To Area Relationship Of Lake Behnke, Kaitlin Deutsch

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this project was to determine the area-to-depth relationship in Lake Behnke, which acts as the principal stormwater drainage basin for the University of South Florida campus in Tampa, Florida. Data previously collected in a stormwater management study by Jeffery Earhart illustrated a linear correlation between the lake's area and depth; however, that study was conducted in 1998, and this present work serves to double check that correlation. We analyzed a bathymetric map of Lake Behnke that displayed several contour lines indicating depth and approximated the area inside each closed curve with a contour integral. The resulting relationship …

Overfishing Of The Common Snook, Allison Ashcroft

Undergraduate Journal of Mathematical Modeling: One + Two

The chief aim of this project is to determine if the populations of the common snook, Centropomus Undecimalis, in the Atlantic and Gulf coast are being affected by overfishing. This is established by evaluating the intrinsic rate of change for these populations and their carrying capacities. It turns out that the carrying capacity for the population of the Atlantic coast is approximately one million snook and its intrinsic rate is 0.00621, while the carrying capacity of the Gulf coast's population is 2.9 million snook and its intrinsic rate is 0.00165. The decline of both populations is most likely due …

Complexity Of Mitochondrial Genome Sequences, Brandon Toun

Undergraduate Journal of Mathematical Modeling: One + Two

The purpose of this project is to compare the complexities of different species' mitochondrial genome sequences. Using an implementation of Deflate compression algorithm from Java standard library, we were able to compress mitochondrial genomes of nine different species. The complexity of each sequence is estimated as a ratio of the original sequence length to the length of the compressed sequence. In addition, we show how a notion of topological entropy from symbolic dynamics can be used as another complexity measure of nucleotide sequences.