Mathematics Commons^™

A Note On Horner's Method, Tian-Xiao He, P. J.-S. Shiue

Scholarship

Here we present an application of Horner's method in evaluating the sequence of Stirling numbers of the second kind. Based on the method, we also give an e_cient way to calculate the diference sequence and divided diference sequence of a polynomial, which can be applied in the Newton interpolation. Finally, we survey all of the results in Proposition 1.4.

Singular Points Of Reducible Sextic Curves, David A. Weinberg, Nicholas J. Willis

Faculty Publications - Department of Mathematics

No abstract provided.

Two Integration Of Faith And Mathematics Projects For Freshmen Mathematics Majors, Nicholas J. Willis

Faculty Publications - Department of Mathematics

Two projects will be presented that integrate faith and Mathematics in a freshman Introduction to Proofs class at George Fox University. The first project asks students to look at the life of a Christian Mathematician. The focus of this project is to show students that many great mathematicians also had immense faith. The second project asks students to take a close look at their own life. How do they plan to live a life of Christian faith in their chosen profession? Both projects are designed to encourage students to look at their careers in Mathematics as a vocation.

A Class Of Nonsofic Multidimensional Shift Spaces, Ronnie Pavlov

Mathematics Preprint Series

In one dimension, sofic shifts are fairly well-understood and special examples of shift spaces which must satisfy very restrictive properties. However, in multiple dimensions there are very few known conditions which guarantee nonsoficity of a shift space. In this paper, we show that for any Z d sofic shift X which satisfies a uniform mixing condition called block gluing in all directions ~e2, . . . , ~ed, the set of legal rows of X in the ~e1-direction has a synchronizing word. This allows us to define a (new) large class of nonsofic Z d shift spaces

Euler's Early Work In Diophantine Analysis, Benjamin Livingston

Undergraduate Honors Theses

We examine the mathematical and historical context of Leonhard Euler's first paper on Diophantine Equations, "De Solutione Problematum Diophanteorum Per Numeros Integros," (E29). We reexamine and verify Euler's calculations, and we translate his work into modern notation. Euler struggled in working with Diophantine Equations at first, which makes his work difficult to follow. We found several perviously-unreported errors in the paper. We show how these errors can be fixed without changing the main idea of Euler's argument. We also compare E29 to another paper on Diophantine Equations which Euler wrote later in life. In this paper, Euler's mathematical ideas are …

Fibrewise Rational H-Spaces, Gregory Lupton, Samuel Bruce Smith

Mathematics and Statistics Faculty Publications

We prove fibrewise versions of classical theorems of Hopf and Leray-Samelson. Our results imply the fibrewise H-triviality after rationalization of a certain class of fibrewise H-spaces. They apply, in particular, to universal adjoint bundles. From this, we may retrieve a result of Crabb and Sutherland [Proc. London Math. Soc. (2000), 747-768], which is used there as a crucial step in establishing their main finiteness result.

Wireless Channel Equalization In Digital Communication Systems, Sammuel Jalali

CGU Theses & Dissertations

Our modern society has transformed to an information-demanding system, seeking voice, video, and data in quantities that could not be imagined even a decade ago. The mobility of communicators has added more challenges. One of the new challenges is to conceive highly reliable and fast communication system unaffected by the problems caused in the multipath fading wireless channels. Our quest is to remove one of the obstacles in the way of achieving ultimately fast and reliable wireless digital communication, namely Inter-Symbol Interference (ISI), the intensity of which makes the channel noise inconsequential.

The theoretical background for wireless channels modeling and …

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.

Approximate Groups Iii: The Unitary Case, Emmanuel Breuillard, Ben Green

Turkish Journal of Mathematics

By adapting the classical proof of Jordan's theorem on finite subgroups of linear groups, we show that every approximate subgroup of the unitary group U_n(C) is almost abelian.

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.

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 …

Excluded Minors For Apex Classes Of Graphs, Christine A. Derbins

Honors Capstones

No abstract provided.

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.