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2005

Mathematics

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Articles 1 - 30 of 449

Full-Text Articles in Physical Sciences and Mathematics

Almost Split Morphisms, Preprojective Algebras And Multiplication Maps Of Maximal Rank, Steven P. Diaz, Mark Kleiner Dec 2005

Almost Split Morphisms, Preprojective Algebras And Multiplication Maps Of Maximal Rank, Steven P. Diaz, Mark Kleiner

Mathematics - All Scholarship

With a grading previously introduced by the second-named author, the multiplication maps in the preprojective algebra satisfy a maximal rank property that is similar to the maximal rank property proven by Hochster and Laksov for the multiplication maps in the commutative polynomial ring. The result follows from a more general theorem about the maximal rank property of a minimal almost split morphism, which also yields a quadratic inequality for the dimensions of indecomposable modules involved.

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Finite-Dimensional Algebras With Smallest Resolutions Of Simple Modules, Shashidhar Jagadeeshan, Mark Kleiner Dec 2005

Finite-Dimensional Algebras With Smallest Resolutions Of Simple Modules, Shashidhar Jagadeeshan, Mark Kleiner

Mathematics - All Scholarship

Let lamda be an associative ring with identity and with the Jacobson radical r, let mod lamda be the category of finitely generated left lamda-modules, and let lamdaop be the opposite ring of lamda. All modules are left unital modules, and if X is a module then pd X is the projective dimension of X. If lamda is left artinian and M in mod labmda, we denote by P(M) a projective cover of M.

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Coordinate Systems And Bounded Isomorphisms, David R. Pitts, David R. Pitts Dec 2005

Coordinate Systems And Bounded Isomorphisms, David R. Pitts, David R. Pitts

Department of Mathematics: Faculty Publications

For a Banach D-bimoduleMover an abelian unital C*-algebraD, we define E1(M) as the collection of norm-one eigenvectors for the dual action of D on the Banach space dual M#. Equip E1(M) with the weak*-topology. We develop general properties of E1(M). It is properly viewed as a coordinate system for M when M C, where C is a unital C*-algebra containing D as a regular MASA with the extension property; moreover, E1(C) coincides with Kumjian’s twist in the context of C*-diagonals. We identify the C*-envelope of a subalgebra A of a C*-diagonal when D A C. For triangular subalgebras, each containing …

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Foundations Of Generalized Cwatsets, Jesse Beder Dec 2005

Foundations Of Generalized Cwatsets, Jesse Beder

Mathematical Sciences Technical Reports (MSTR)

We present a new, abstract definition for a generalized cwatset that produces notions of subcwatset and quotient cwatset that behave naturally. We use small cancellation theory to prove a result analogous to the statement that every group is isomorphic to some permutation group.

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Change Bell Ringing And Mathematics: A High School Student Excursion Into Graph Theory And Group Theory, Kristi Carlson Dec 2005

Change Bell Ringing And Mathematics: A High School Student Excursion Into Graph Theory And Group Theory, Kristi Carlson

Honors Theses

This unit was created as a way to introduce higher level mathematics concepts to advanced high school students. All five of the National Council of Teachers of Mathematics Process Standards are found in this unit. For most of the unit, students work within small groups

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Existence And Uniqueness Of V-Asymptotic Expansions And Colombeau’S Generalized Numbers, Todor D. Todorov Dec 2005

Existence And Uniqueness Of V-Asymptotic Expansions And Colombeau’S Generalized Numbers, Todor D. Todorov

Mathematics

We define a type of generalized asymptotic series called v-asymptotic. We show that every function with moderate growth at infinity has a v-asymptotic expansion. We also describe the set of v-asymptotic series, where a given function with moderate growth has a unique v-asymptotic expansion. As an application to random matrix theory we calculate the coefficients and establish the uniqueness of the v-asymptotic expansion of an integral with a large parameter. As another application (with significance in the non-linear theory of generalized functions) we show that every Colombeau’s generalized number has a v-asymptotic expansion. A similar …

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Smooth And Analytic Normal And Canonical Forms For Strict Feedforward Systems, Issa Amadou Tall, Witold Respondek Dec 2005

Smooth And Analytic Normal And Canonical Forms For Strict Feedforward Systems, Issa Amadou Tall, Witold Respondek

Miscellaneous (presentations, translations, interviews, etc)

Recently we proved that any smooth (resp. analytic) strict feedforward system can be brought into its normal form via a smooth (resp. analytic) feedback transformation. This will allow us to identify a subclass of strict feedforward systems, called systems in special strict feedforward form, shortly (SSFF), possessing a canonical form which is an analytic counterpart of the formal canonical form. For (SSFF)-systems, the step-by-step normalization procedure of Kang and Krener leads to smooth (resp. convergent analytic) normalizing feedback transformations. We illustrate the class of (SSFF)-systems by a model of an inverted pendulum on a cart.

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A Mathematical Journey Through The Land Of The Maya, Philip Scalisi, Paul Fairbanks Dec 2005

A Mathematical Journey Through The Land Of The Maya, Philip Scalisi, Paul Fairbanks

Bridgewater Review

No abstract provided.

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On The Existence Of Multiple Periodic Solutions For The Vector P-Laplacian Via Critical Point Theory, Haishen Lu, Donal O'Regan, Ravi P. Agarwal Dec 2005

On The Existence Of Multiple Periodic Solutions For The Vector P-Laplacian Via Critical Point Theory, Haishen Lu, Donal O'Regan, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

We study the vector p-Laplacian (∗){−(|u′|p−2u′)′=∇F(t,u)a.e.t∈[0,T],u(0)=u(T),u′(0)=u′(T),1

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The Relationship Between The Number Of Shots And The Quality Of Gamma Knife Radiosurgeries, D Cheek, Allen G. Holder, M Fuss, B Salter Dec 2005

The Relationship Between The Number Of Shots And The Quality Of Gamma Knife Radiosurgeries, D Cheek, Allen G. Holder, M Fuss, B Salter

Mathematics Faculty Research

Radiosurgery is a non-invasive alternative to brain surgery that uses a single focused application of high radiation to destroy intracerebral target tissues. A Gamma Knife delivers such treatments by using 201 cylindrically collimated cobalt-60 sources that are arranged in a hemispherical pattern and aimed to a common focal point. The accumulation of radiation at the focal point, called a \shot" due to the spherical nature of the dose distribution, is used to ablate (or destroy) target tissue in the brain. If the target is small and spherical, it is easily treated by choosing one of four available collimators (4, 8, …

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On Sequential And Fixed Designs For Estimation With Comparisons And Applications, Mekki Terbeche, Broderick O. Oluyede, Ahmed Barbour Dec 2005

On Sequential And Fixed Designs For Estimation With Comparisons And Applications, Mekki Terbeche, Broderick O. Oluyede, Ahmed Barbour

Department of Mathematical Sciences Faculty Publications

A fully sequential approach to the estimation of the difference of two population means for distributions belonging to the exponential family of distributions is adopted and compared with the best fixed design. Results on the lower bound for the Bayes risk due to estimation and expected cost are presented and shown to be of first order efficiency. Applications involving the Poisson and exponential distributions with gamma priors as well as the Bernoulli distribution with beta priors are given. Finally, some numerical results are presented.

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When A Mechanical Model Goes Nonlinear, Lisa D. Humphreys, P. J. Mckenna Dec 2005

When A Mechanical Model Goes Nonlinear, Lisa D. Humphreys, P. J. Mckenna

Faculty Publications

This paper had its origin in a curious discovery by the first author in research performed with an undergraduate student. The following odd fact was noticed: when a mechanical model of a suspension bridge (linear near equilibrium but allowed to slacken at large distance in one direction) is shaken with a low-frequency periodic force, several different periodic responses can result, many with high-frequency components.

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Five Years At The Magazine, Frank A. Farris Dec 2005

Five Years At The Magazine, Frank A. Farris

Mathematics and Computer Science

What do the editors of MAA journals do? What is so different about editing expository mathematics? After my five years as editor of Mathematics Magazine, I have strong opinions about these matters. The goal of most mathematics journals is to print the very latest results from the forefront of research. The goal of Mathematics Magazine is to remind us all why we loved mathematics in the first place, with stimulating articles and notes accessible to advanced undergraduates.

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Disc Separation Of The Schur Complement Of Diagonally Dominant Matrices And Determinantal Bounds, Jianzhou Liu, Fuzhen Zhang Dec 2005

Disc Separation Of The Schur Complement Of Diagonally Dominant Matrices And Determinantal Bounds, Jianzhou Liu, Fuzhen Zhang

Mathematics Faculty Articles

We consider the Gersgorin disc separation from the origin for (doubly) diagonally dominant matrices and their Schur complements, showing that the separation of the Schur complement of a (doubly) diagonally dominant matrix is greater than that of the original grand matrix. As application we discuss the localization of eigenvalues and present some upper and lower bounds for the determinant of diagonally dominant matrices.

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Looking Beyond The Curriculum In Jamaica, Jon T. Jacobsen, Michael E. Orrison Jr. Dec 2005

Looking Beyond The Curriculum In Jamaica, Jon T. Jacobsen, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

In August 2004, we had the opportunity to travel to Jamaica to lead a pilot workshop for Jamaican high school math teachers. The workshop focused on the importance of mathematical context in the teaching of mathematics. It was sponsored by the Gibraltar Institute, a Jamaica-based nongovernmental organization led by Trevor Campbell (Pomona College) and Reginald Nugent (Cal State Pomona), Jamaica’s College of Agriculture, Science and Education, and Harvey Mudd College.

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Pythagorean Primes And Palindromic Continued Fractions, Arthur T. Benjamin, Doron Zeilberger Dec 2005

Pythagorean Primes And Palindromic Continued Fractions, Arthur T. Benjamin, Doron Zeilberger

All HMC Faculty Publications and Research

In this note, we prove that every prime of the form 4m + 1 is the sum of the squares of two positive integers in a unique way. Our proof is based on elementary combinatorial properties of continued fractions. It uses an idea by Henry J. S. Smith ([3], [5], and [6]) most recently described in [4] (which provides a new proof of uniqueness and reprints Smith's paper in the original Latin). Smith's proof makes heavy use of nontrivial properties of determinants. Our purely combinatorial proof is self-contained and elementary.

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Recounting The Odds Of An Even Derangement, Arthur T. Benjamin, Curtis D. Bennet, Florence Newberger Dec 2005

Recounting The Odds Of An Even Derangement, Arthur T. Benjamin, Curtis D. Bennet, Florence Newberger

All HMC Faculty Publications and Research

No abstract provided in this article.

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Some New Orthogonal Arrays Oa (4r;R (1) 2(P);2), Warren F. Kuhfeld, Chung Yi Suen Dec 2005

Some New Orthogonal Arrays Oa (4r;R (1) 2(P);2), Warren F. Kuhfeld, Chung Yi Suen

Mathematics and Statistics Faculty Publications

We developed an algorithm to search for new orthogonal arrays, OA(4rOA(4r, r12pr12p, 2), for odd r . With it, we found new orthogonal arrays with 4r=364r=36 through 124 runs. Many other new arrays can be obtained from these new arrays.

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The Application Of Category Theory And Analysis Of Receiver Operating Characteristics To Information Fusion, Steven N. Thorsen Dec 2005

The Application Of Category Theory And Analysis Of Receiver Operating Characteristics To Information Fusion, Steven N. Thorsen

Theses and Dissertations

Multisensor data fusion is presented in a rigorous mathematical format, with definitions consistent with the desires of the data fusion community. A model of event-state fusion is developed and described. Definitions of fusion rules and fusors are introduced, along with the functor categories of which they are objects. Defining fusors and competing fusion rules involves the use of an objective function of the researcher's choice. One such objective function, a functional on families of classification systems, and in particular, receiver operating characteristics (ROCs), is introduced. Its use as an objective function is demonstrated in that the argument that minimizes it …

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Mathematical Functions: An Interactive Emodule, Sarah Jean Moody Dec 2005

Mathematical Functions: An Interactive Emodule, Sarah Jean Moody

Undergraduate Honors Capstone Projects

The National Library of Virtual Manipulatives (NLVM, http://nlvm.usu.edu/) is a widely used and highly praised teaching/learning resource for school mathematics. The NLVM is the result of a four-year USU project, funded primarily by the National Science Foundation, Award #9819107, to create a web-based, freely accessible, library of interactive virtual manipulatives to help students learn basic mathematics concepts. During a typical school day, the NLVM server receives more than 3 million hits.

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Multivalued Logic, Neutrosophy And Schrodinger Equation, Florentin Smarandache, Victor Christianto Dec 2005

Multivalued Logic, Neutrosophy And Schrodinger Equation, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of ‘identity’, which too often it has been accepted as given. Neutrosophy itself was developed in attempt to generalize Fuzzy-Logic introduced by L. Zadeh. While some aspects of theoretical foundations of logic are discussed, this book is not intended solely for pure mathematicians, but instead for physicists in the hope that some of ideas presented herein will be found useful. The book is motivated by …

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Recounting The Odds Of An Even Derangement, Arthur T. Benjamin, Curtis T. Bennett, Florence Newberger Dec 2005

Recounting The Odds Of An Even Derangement, Arthur T. Benjamin, Curtis T. Bennett, Florence Newberger

Mathematics Faculty Works

No abstract provided.

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The Stochastic Dance Of Early Hiv Infection, Stephen J. Merrill Dec 2005

The Stochastic Dance Of Early Hiv Infection, Stephen J. Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

The stochastic nature of early HIV infection is described in a series of models, each of which captures aspects of the dance of HIV during the early stages of infection. It is to this highly variable target that the immune response must respond. The adaptability of the various components of the immune response is an important aspect of the system's operation, as the nature of the pathogens that the response will be required to respond to and the order in which those responses must be made cannot be known beforehand. As HIV infection has direct influence over cells responsible for …

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Neutrosophic Methods In General Relativity, Florentin Smarandache, Dmitri Rabounski, Larissa Borissova Dec 2005

Neutrosophic Methods In General Relativity, Florentin Smarandache, Dmitri Rabounski, Larissa Borissova

Branch Mathematics and Statistics Faculty and Staff Publications

In this work the authors apply concepts of Neutrosophic Logic to the General Theory of Relativity to obtain a generalisation of Einstein’s fourdimensional pseudo-Riemannian differentiable manifold in terms of Smarandache Geometry (Smarandache manifolds), by which new classes of relativistic particles and non-quantum teleportation are developed. Fundamental features of Neutrosophic Logic are its denial of the Law of Excluded Middle, and open (or estimated) levels of truth, falsity and indeterminancy. Both Neutrosophic Logic and Smarandache Geometry were invented some years ago by one of the authors (F. Smarandache). The application of these purely mathematical theories to General Relativity reveals hitherto unknown …

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Parity Theorems For Combinatorial Statistics, Mark A. Shattuck Dec 2005

Parity Theorems For Combinatorial Statistics, Mark A. Shattuck

Doctoral Dissertations

A q-generalization Gn(q) of a combinatorial sequence Gn which reduces to that sequence when q = 1 is obtained by q-counting a statistic defined on a sequence of finite discrete structures enumerated by Gn. In what follows, we evaluate Gn(−1) for statistics on several classes of discrete structures, giving both algebraic and combinatorial proofs. For the latter, we define appropriate sign-reversing involutions on the associated structures. We shall call the actual algebraic result of such an evaluation at q = −1 a parity theorem (for the …

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Fibonacci Determinants — A Combinatorial Approach, Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn Nov 2005

Fibonacci Determinants — A Combinatorial Approach, Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn

All HMC Faculty Publications and Research

In this paper, we provide combinatorial interpretations for some determinantal identities involving Fibonacci numbers. We use the method due to Lindström-Gessel-Viennot in which we count nonintersecting n-routes in carefully chosen digraphs in order to gain insight into the nature of some well-known determinantal identities while allowing room to generalize and discover new ones.

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Classifcation Of Conics In The Tropical Projective Plane, Amanda Ellis Nov 2005

Classifcation Of Conics In The Tropical Projective Plane, Amanda Ellis

Theses and Dissertations

This paper defines tropical projective space, TP^n, and the tropical general linear group TPGL(n). After discussing some simple examples of tropical polynomials and their hypersurfaces, a strategy is given for finding all conics in the tropical projective plane. The classification of conics and an analysis of the coefficient space corresponding to such conics is given.

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Identity Configurations Of The Sandpile Group, William Chen '06 Nov 2005

Identity Configurations Of The Sandpile Group, William Chen '06

Distinguished Student Work

The abelian sandpile model on a connected graph yields a finite abelian group Q of recurrent configurations which is closely related to the combinatorial Laplacian. We consider the identity configuration of the sandpile group on graphs with large edge multiplicities, called “thick” graphs. We explicitly compute the identity configuration for all thick paths using a recursion formula. We then analyze the thick cycle and explicitly compute the identity configuration for the three-cycle, the four-cycle, and certain types of symmetric cycles. The latter is a special case of a more general symmetry theorem we prove that applies to an arbitrary graph.

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Mathematics And The Divine (Book Review), Calvin Jongsma Nov 2005

Mathematics And The Divine (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Teun Koetsier and Luc Bergmans, editors. Mathematics and the Divine. Boston: Elsevier, 2005. 701 pages. ISBN 0-444-50328-5

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A Reduced-Order Partial Differential Equation Model For Dynamics Of The Flow In Athermosyphon, Evangelos A. Coutsias, Elisabeth A. Burroughs, L. Romero Nov 2005

A Reduced-Order Partial Differential Equation Model For Dynamics Of The Flow In Athermosyphon, Evangelos A. Coutsias, Elisabeth A. Burroughs, L. Romero

Branch Mathematics and Statistics Faculty and Staff Publications

Flow in a closed loop thermosyphon heated from below exhibits a sequence of bifurcations with increasing Grashof number. Using the Navier-Stokes equations in the Boussinesq approximation we have derived a model where, in the case of a slender circular loop, the first Fourier modes exactly decouple from all other Fourier modes, leaving a system of three coupled nonlinear partial differential equations that completely describes the flow in the thermosyphon. We have characterized the flow through two bifurcations, identifying stable periodic solutions for flows of Prandtl number greater than 18.5, a much lower value than predicted previously. Because of the quadratic …

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