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Articles 1 - 30 of 435
Full-Text Articles in Physical Sciences and Mathematics
Almost Split Morphisms, Preprojective Algebras And Multiplication Maps Of Maximal Rank, Steven P. Diaz, Mark Kleiner
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.
Finite-Dimensional Algebras With Smallest Resolutions Of Simple Modules, Shashidhar Jagadeeshan, Mark Kleiner
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.
Coordinate Systems And Bounded Isomorphisms, David R. Pitts, David R. Pitts
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 …
Foundations Of Generalized Cwatsets, Jesse Beder
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.
Change Bell Ringing And Mathematics: A High School Student Excursion Into Graph Theory And Group Theory, Kristi Carlson
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
Existence And Uniqueness Of V-Asymptotic Expansions And Colombeau’S Generalized Numbers, Todor D. Todorov
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 …
Smooth And Analytic Normal And Canonical Forms For Strict Feedforward Systems, Issa Amadou Tall, Witold Respondek
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.
A Mathematical Journey Through The Land Of The Maya, Philip Scalisi, Paul Fairbanks
A Mathematical Journey Through The Land Of The Maya, Philip Scalisi, Paul Fairbanks
Bridgewater Review
No abstract provided.
On The Existence Of Multiple Periodic Solutions For The Vector P-Laplacian Via Critical Point Theory, Haishen Lu, Donal O'Regan, Ravi P. Agarwal
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
The Relationship Between The Number Of Shots And The Quality Of Gamma Knife Radiosurgeries, D Cheek, Allen G. Holder, M Fuss, B Salter
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, …
On Sequential And Fixed Designs For Estimation With Comparisons And Applications, Mekki Terbeche, Broderick O. Oluyede, Ahmed Barbour
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.
When A Mechanical Model Goes Nonlinear, Lisa D. Humphreys, P. J. Mckenna
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.
Five Years At The Magazine, Frank A. Farris
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.
Disc Separation Of The Schur Complement Of Diagonally Dominant Matrices And Determinantal Bounds, Jianzhou Liu, Fuzhen Zhang
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.
Looking Beyond The Curriculum In Jamaica, Jon T. Jacobsen, Michael E. Orrison Jr.
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.
Pythagorean Primes And Palindromic Continued Fractions, Arthur T. Benjamin, Doron Zeilberger
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.
Recounting The Odds Of An Even Derangement, Arthur T. Benjamin, Curtis D. Bennet, Florence Newberger
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.
Some New Orthogonal Arrays Oa (4r;R (1) 2(P);2), Warren F. Kuhfeld, Chung Yi Suen
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.
The Application Of Category Theory And Analysis Of Receiver Operating Characteristics To Information Fusion, Steven N. Thorsen
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 …
Mathematical Functions: An Interactive Emodule, Sarah Jean Moody
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.
Multivalued Logic, Neutrosophy And Schrodinger Equation, Florentin Smarandache, Victor Christianto
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 …
Recounting The Odds Of An Even Derangement, Arthur T. Benjamin, Curtis T. Bennett, Florence Newberger
Recounting The Odds Of An Even Derangement, Arthur T. Benjamin, Curtis T. Bennett, Florence Newberger
Mathematics Faculty Works
No abstract provided.
The Stochastic Dance Of Early Hiv Infection, Stephen J. Merrill
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 …
Parity Theorems For Combinatorial Statistics, Mark A. Shattuck
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 …
Neutrosophic Methods In General Relativity, Florentin Smarandache, Dmitri Rabounski, Larissa Borissova
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 …
Fibonacci Determinants — A Combinatorial Approach, Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn
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.
Classifcation Of Conics In The Tropical Projective Plane, Amanda Ellis
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.
Identity Configurations Of The Sandpile Group, William Chen '06
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.
Mathematics And The Divine (Book Review), Calvin Jongsma
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
A Reduced-Order Partial Differential Equation Model For Dynamics Of The Flow In Athermosyphon, Evangelos A. Coutsias, Elisabeth A. Burroughs, L. Romero
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 …