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2009

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Articles 421 - 450 of 693

Full-Text Articles in Mathematics

My Trig Book, Bruce Kessler Jan 2009

My Trig Book, Bruce Kessler

Mathematics Faculty Publications

This is the MATH 117 Trigonometry text developed by Dr. Bruce Kessler for the Gatton Academy of Math and Science at Western Kentucky University for the Math and Science sections of the course. The text has also been used in two online course offerings.

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Poisson Structures Of Equations Associated With Groups Of Diffeomorphisms, Rossen Ivanov Jan 2009

Poisson Structures Of Equations Associated With Groups Of Diffeomorphisms, Rossen Ivanov

Conference papers

A class of equations describing the geodesic flow for a right-invariant metric on the group of diffeomorphisms of Rn is reviewed from the viewpoint of their Lie-Poisson structures. A subclass of these equations is analogous to the Euler equations in hydrodynamics (for n = 3), preserving the volume element of the domain of fluid flow. An example in n = 1 dimension is the Camassa-Holm equation, which is a geodesic flow equation on the group of diffeomorphisms, preserving the H1 metric.

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Multiscale Registration Of Planning Ct And Daily Cone Beam Ct Images For Adaptive Radiation Therapy, Dana C. Paquin, Doron Levy, Lei Xing Jan 2009

Multiscale Registration Of Planning Ct And Daily Cone Beam Ct Images For Adaptive Radiation Therapy, Dana C. Paquin, Doron Levy, Lei Xing

Mathematics

Adaptive radiation therapy (ART) is the incorporation of daily images in the radiotherapy treatment process so that the treatment plan can be evaluated and modified to maximize the amount of radiation dose to the tumor while minimizing the amount of radiation delivered to healthy tissue. Registration of planning images with daily images is thus an important component of ART. In this article, the authors report their research on multiscale registration of planning computed tomography (CT) images with daily cone beam CT (CBCT) images. The multiscale algorithm is based on the hierarchical multiscale image decomposition of E. Tadmor, S. Nezzar, and …

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Review: Spectra Of Toeplitz Operators And Compositions Of Muckenhoupt Weights With Blaschke Products, Stephan Ramon Garcia Jan 2009

Review: Spectra Of Toeplitz Operators And Compositions Of Muckenhoupt Weights With Blaschke Products, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

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Review: A Class Of Solutions To The Quantum Colored Yang-Baxter Equation, Gizem Karaali Jan 2009

Review: A Class Of Solutions To The Quantum Colored Yang-Baxter Equation, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

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Review: Dynamical Yang-Baxter Maps With An Invariance Condition, Gizem Karaali Jan 2009

Review: Dynamical Yang-Baxter Maps With An Invariance Condition, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

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Characterization Of Partial Derivatives With Respect To Boundary Conditions For Solutions Of Nonlocal Boundary Value Problems For Nth Order Differential Equations, Jeffrey W. Lyons, Johnny Henderson Jan 2009

Characterization Of Partial Derivatives With Respect To Boundary Conditions For Solutions Of Nonlocal Boundary Value Problems For Nth Order Differential Equations, Jeffrey W. Lyons, Johnny Henderson

Mathematics Faculty Articles

Under certain conditions, solutions of the nonlocal boundary value problem, y(n) = f(x, y, y', ... , y(n- 1)), y(xi) = Yi for 1 £ i £ n- 1, and y(xn) - Σmk=1 Υiy (ni) = y n, are differentiated with respect to boundary conditions, where a < X1 < X2 < · · · < Xn-1 < n1 < · · · < nm < Xn < b, r1, ... , rm, Y1, ... , Yn ∈ R .

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The 2-Ranks Of Hyperelliptic Curves With Extra Automorphisms, Darren B. Glass Jan 2009

The 2-Ranks Of Hyperelliptic Curves With Extra Automorphisms, Darren B. Glass

Math Faculty Publications

This paper examines the relationship between the automorphism group of a hyperelliptic curve defined over an algebraically closed field of characteristic two and the 2-rank of the curve. In particular, we exploit the wild ramification to use the Deuring-Shafarevich formula in order to analyze the ramification of hyperelliptic curves that admit extra automorphisms and use this data to impose restrictions on the genera and 2-ranks of such curves. We also show how some of the techniques and results carry over to the case where our base field is of characteristic p > 2.

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Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, And Similarity, Joseph A. Cima, Stephan Ramon Garcia, William T. Ross, Warren R. Wogen Jan 2009

Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, And Similarity, Joseph A. Cima, Stephan Ramon Garcia, William T. Ross, Warren R. Wogen

Pomona Faculty Publications and Research

A truncated Toeplitz operator A φ : K Θ → K Θ is the compression of a Toeplitz operator T φ : H 2 → H 2 to a model space K Θ ≔ H 2 ⊖ Θ H 2 . For Θ inner, let T Θ denote the set of all bounded truncated Toeplitz operators on K Θ . Our main result is a necessary and sufficient condition on inner functions Θ 1 and Θ 2 which guarantees that T Θ 1 and T Θ 2 are spatially isomorphic (i.e., U T Θ 1 = T Θ 2 U …

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A Different Pencil Too Good To Be Ignored? A First Look At Wolfram|Alpha, Gizem Karaali, Bruce Yoshiwara Jan 2009

A Different Pencil Too Good To Be Ignored? A First Look At Wolfram|Alpha, Gizem Karaali, Bruce Yoshiwara

Pomona Faculty Publications and Research

So you came across several news pieces about Wolfram|Alpha and you’re wondering what all the fuss is about. Let’s start with the basics.

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Every Graph Has An Embedding In S³ Containing No Non-Hyperbolic Knot, Erica Flapan, Hugh Howards Jan 2009

Every Graph Has An Embedding In S³ Containing No Non-Hyperbolic Knot, Erica Flapan, Hugh Howards

Pomona Faculty Publications and Research

In contrast with knots, whose properties depend only on their extrinsic topology in S³ , there is a rich interplay between the intrinsic structure of a graph and the extrinsic topology of all embeddings of the graph in S³ . For example, it was shown by Conway and Gordon that every embedding of the complete graph K_7 in S³ contains a non-trivial knot. Later it was shown that for every m ∈ N there is a complete graph K_n such that every embedding of K_n in S³ contains a knot Q whose minimal crossing number is at least m. …

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Review: On Quantum Yang-Baxter Coherent Algebra Sheaves, Gizem Karaali Jan 2009

Review: On Quantum Yang-Baxter Coherent Algebra Sheaves, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

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Review: Set-Theoretic Solutions Of The Yang-Baxter Equation, Graphs And Computations, Gizem Karaali Jan 2009

Review: Set-Theoretic Solutions Of The Yang-Baxter Equation, Graphs And Computations, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

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Why Did Lagrange "Prove" The Parallel Postulate?, Judith V. Grabiner Jan 2009

Why Did Lagrange "Prove" The Parallel Postulate?, Judith V. Grabiner

Pitzer Faculty Publications and Research

In 1806, Joseph-Louis Lagrange read a memoir "proving" Euclid's parallel postulate to the Institut de France in Paris. The memoir still exists in manuscript, and we’ll look at what it says. We ask why he tried to prove the postulate, and why he attacked the problem in the way that he did. We also look at how the ideas in this manuscript are related to such things as Lagrange’s philosophy of mathematics, artists’ ideas about space, Newtonian mechanics, and Leibniz's Principle of Sufficient Reason. Finally, we reflect on how this episode changes our views about eighteenth-century attitudes toward geometry, space, …

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Search Bounds For Zeros Of Polynomials Over The Algebraic Closure Of Q, Lenny Fukshansky Jan 2009

Search Bounds For Zeros Of Polynomials Over The Algebraic Closure Of Q, Lenny Fukshansky

CMC Faculty Publications and Research

We discuss existence of explicit search bounds for zeros of polynomials with coefficients in a number field. Our main result is a theorem about the existence of polynomial zeros of small height over the field of algebraic numbers outside of unions of subspaces. All bounds on the height are explicit.

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Singular Points Of Real Quartic And Quintic Curves, David A. Weinberg, Nicholas J. Willis Jan 2009

Singular Points Of Real Quartic And Quintic Curves, David A. Weinberg, Nicholas J. Willis

Faculty Publications - Department of Mathematics

There are thirteen types of singular points for irreducible real quartic curves and seventeen types of singular points for reducible real quartic curves. This classification is originally due to D. A. Gudkov. There are nine types of singular points for irreducible complex quartic curves and ten types of singular points for reducible complex quartic curves. There are 42 types of real singular points for irreducible real quintic curves and 49 types of real singular points for irreducible real quintic curves. The classification of real singular points for irreducible real quintic curves is originally due to Golubina and Tai. There are …

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Magnetic Hole Formation From The Perspective Of Inverse Scattering Theory, Robert L. Hamilton, D A. Peterson, S M. Libby Jan 2009

Magnetic Hole Formation From The Perspective Of Inverse Scattering Theory, Robert L. Hamilton, D A. Peterson, S M. Libby

Faculty Publications - Department of Mathematics

The dynamics of oblique, weakly dispersive nonlinear Alfven waves in the presence of weak resistive damping are investigated numerically through an extension of the derivative nonlinear Schrodinger (DNLS) equation. It is observed numerically that the nonlinear dynamics are organized around the dynamics and allowed interactions of the underlying DNLS soliton families. There are three types of oblique Alfven solitons: the compressive two-parameter soliton and one-parameter bright soliton along with the rare factive one-parameter dark soliton. The damping of either of these compressive solitons is accompanied by the formation of one or more dark solitons. The implication of these processes is …

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A Direct Solution Of The Robin Inverse Problem, Weifu Fang, Suxing Zeng Jan 2009

A Direct Solution Of The Robin Inverse Problem, Weifu Fang, Suxing Zeng

Mathematics and Statistics Faculty Publications

We present a direct, linear boundary integral equation method for the inverse problem of recovering the Robin coefficient from a single partial boundary measurement of the solution to the Laplace equation.

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Rules And Insights: Connecting The Mathematical And Linguistic Abilities Of C.S. Lewis, Kim Regnier Jongerius Jan 2009

Rules And Insights: Connecting The Mathematical And Linguistic Abilities Of C.S. Lewis, Kim Regnier Jongerius

ACMS Journal 2008-2009

While most biographical works on C.S. Lewis give passing reference to Lewis' problems with elementary mathematics, few have made an attempt at diagnosing the difficulty or exploring its impact on his writing. A careful study of family correspondence, however, makes it clear that his learning difficulties were not with mathematics alone and suggests connections between attitudes toward and abilities in both mathematics and language. This paper will make these connections clear and will illustrate their ties to Lewis' effective mathematical references.

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The Erdős-Lovász Tihany Conjecture For Quasi-Line Graphs, J. Balogh, A. V. Kostochka, N. Prince, M. Stiebitz Jan 2009

The Erdős-Lovász Tihany Conjecture For Quasi-Line Graphs, J. Balogh, A. V. Kostochka, N. Prince, M. Stiebitz

Faculty Publications & Research

Erdős and Lovász conjectured in 1968 that for every graph G with χ(G) > ω(G) and any two integers s, t ≥ 2 with s + t = χ(G) + 1, there is a partition (S,T) of the vertex set V(G) such that χ(G[S]) ≥ s and χ(G[T]) ≥ t . Except for a few cases, this conjecture is still unsolved. In this note we prove the conjecture for quasi-line graphs and for graphs with independence number 2.

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Extremal Problems For Roman Domination, E. W. Chambers, W. Kinnersley, N. Prince, D. B. West Jan 2009

Extremal Problems For Roman Domination, E. W. Chambers, W. Kinnersley, N. Prince, D. B. West

Faculty Publications & Research

A Roman dominating function of a graph G is a labeling f: V(G) →{0,1,2} such that every vertex with a label 0 has a neighbor with label 2. The Roman domination number γR(G) of G is the minimum of ∑ʋϵV(G)f(v) over such functions. Let G be a connected n-vertex graph. We prove that γR(G) ≤ 4n/5, and we characterize the graphs achieving equality. We obtain sharp upper and lower bounds for γR(G) + …

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Discrete Mathematics With Proof Second Edition, Eric Gossett Jan 2009

Discrete Mathematics With Proof Second Edition, Eric Gossett

Faculty Books

Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications. The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions, and relations.

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The Uniqueness Of Minimal Acyclic Complexes, Meri Trema Hughes Jan 2009

The Uniqueness Of Minimal Acyclic Complexes, Meri Trema Hughes

Mathematics Dissertations - Archive

In this paper, we discuss conditions for uniqueness among minimal acyclic complexes of finitely generated free modules over a commutative local ring which share a common syzygy module. Although such uniqueness occurs over Gorenstein rings, the question has been asked whether two minimal acyclic complexes in general can be isomorphic to the left and non-isomorphic to the right. We answer the question in the negative for certain cases, including periodic complexes, sesqui-acyclic complexes, and certain rings with radical cube zero. In particular, we investigate the question for graded algebras with Hilbert series $H_R(t)=1+et+(e-1)t^2$, and such monomial algebras possessing a special …

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Local-To-Global Spectral Sequences For The Cohomology Of Diagrams, David Blanc, Mark W. Johnson, James M. Turner Jan 2009

Local-To-Global Spectral Sequences For The Cohomology Of Diagrams, David Blanc, Mark W. Johnson, James M. Turner

University Faculty Publications and Creative Works

We construct local-to-global spectral sequences for the cohomology of a diagram, which compute the cohomology of the full diagram in terms of smaller pieces. These are motivated by the obstruction theory of D. Blanc et al. [D. Blanc, M.W. Johnson, J.M. Turner, On realizing diagrams of Π-algebras, Algebraic Geom. Topol. 6 (2006) 763-807] for realizing a diagram of Π-algebras, but are valid in quite general algebraic settings. © 2008 Elsevier B.V. All rights reserved.

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Ham Sandwich With Mayo: A Stronger Conclusion To The Classical Ham Sandwich Theorem, John H. Elton, Theodore P. Hill Jan 2009

Ham Sandwich With Mayo: A Stronger Conclusion To The Classical Ham Sandwich Theorem, John H. Elton, Theodore P. Hill

Research Scholars in Residence

The conclusion of the classical ham sandwich theorem of Banach and Steinhaus may be strengthened: there always exists a common bisecting hyperplane that touches each of the sets, that is, intersects the closure of each set. Hence, if the knife is smeared with mayonnaise, a cut can always be made so that it will not only simultaneously bisect each of the ingredients, but it will also spread mayonnaise on each. A discrete analog of this theorem says that n finite nonempty sets in n-dimensional Euclidean space can always be simultaneously bisected by a single hyperplane that contains at least one …

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Some Curious Cut-Ups, Jeremiah Farrell, Ivan Moscovich Jan 2009

Some Curious Cut-Ups, Jeremiah Farrell, Ivan Moscovich

Scholarship and Professional Work - LAS

We have noticed a certain kind of n-gon dissection into triangles that has a wonderful property of interest to most puzzlists. Namely that any two triangles have at least one edge in common yet no two triangles need be congruent. In an informal poll of specialists at a recent convention, none of them saw immediately how this could be accomplished. But in fact it is very straightforward.

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The Hamiltonian Index Of Graphs, Yi Hong, Jian-Liang Lin, Zhi-Sui Tao, Zhi-Hong Chen Jan 2009

The Hamiltonian Index Of Graphs, Yi Hong, Jian-Liang Lin, Zhi-Sui Tao, Zhi-Hong Chen

Scholarship and Professional Work - LAS

The Hamiltonian index of a graph G is defined as h ( G ) = min { m : L m ( G ) is Hamiltonian } . In this paper, using the reduction method of Catlin [P.A. Catlin, A reduction method to find spanning Eulerian subgraphs, J. Graph Theory 12 (1988) 29–44], we constructed a graph H ̃ ( m ) ( G ) from G and prove that if h ( G ) ≥ 2 , then h ( G ) = min{ m : H ̃ ( m ) ( G ) has a spanning Eulerian subgraph …

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High-Order Numerical Schemes For High-Speed Flows, Maria Luisa Bambozzi Oliveira Jan 2009

High-Order Numerical Schemes For High-Speed Flows, Maria Luisa Bambozzi Oliveira

Mathematics Dissertations - Archive

A numerical scheme with high order of accuracy is necessary to resolve small length scales in flow transition and turbulence processes. However, numerical simulation for shock-boundary layer interaction, shock-acoustic interaction, porous media flow and multiple phase flow, among others, also require a numerical scheme that can successfully capture discontinuities. To accomplish this, it is essential that an effective shock/discontinuity detector is implemented to reduce damping of physically important high-frequency waves.In this work, two high-order shock capturing schemes - the Weighted Essentially Non-Oscillatory (WENO) scheme and the Weighted Compact Scheme (WCS) - are investigated. Based on this analysis, a shock/discontinuity detector …

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Mathematical Model Creation For Cancer Chemo-Immunotherapy, Lisette G. De Pillis, K Renee Fister, Weiqing Gu, Craig Collins, Michael Daub, David Gross '08, James Moore '07, Benjamin Preskill '09 Jan 2009

Mathematical Model Creation For Cancer Chemo-Immunotherapy, Lisette G. De Pillis, K Renee Fister, Weiqing Gu, Craig Collins, Michael Daub, David Gross '08, James Moore '07, Benjamin Preskill '09

All HMC Faculty Publications and Research

One of the most challenging tasks in constructing a mathematical model of cancer treatment is the calculation of biological parameters from empirical data. This task becomes increasingly difficult if a model involves several cell populations and treatment modalities. A sophisticated model constructed by de Pillis et al., Mixed immunotherapy and chemotherapy of tumours: Modelling, applications and biological interpretations, J. Theor. Biol. 238 (2006), pp. 841–862; involves tumour cells, specific and non-specific immune cells (natural killer (NK) cells, CD8 T cells and other lymphocytes) and employs chemotherapy and two types of immunotherapy (IL-2 supplementation and CD8 T-cell infusion) as treatment modalities. …

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Enhancing Statistics Instruction In Elementary Schools: Integrating Technology In Professional Development, Maria Meletiou-Mavrotheris, Efi Paparistodemou, Despina Stylianou Jan 2009

Enhancing Statistics Instruction In Elementary Schools: Integrating Technology In Professional Development, Maria Meletiou-Mavrotheris, Efi Paparistodemou, Despina Stylianou

The Mathematics Enthusiast

The research discussed in this article comes from an ongoing multifaceted program for the teaching and learning of early statistical reasoning in Cyprus. The initial stage of the program was concerned with the design of a line of instructional materials for the development of statistical reasoning. Central to this design was the functional integration with existing core curricular ideas of the recently developed dynamic statistics software Tinkerplots@, which provides young students with the opportunity to model and investigate real world problems of statistics. Next, professional development seminars for the teaching of statistics with the use of Tinkerplots® were designed and …

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