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2013

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Articles 601 - 630 of 1053

Full-Text Articles in Mathematics

Primes Of The Form _A2_Qb2, Eugen J. Ionascu Jan 2013

Primes Of The Form _A2_Qb2, Eugen J. Ionascu

Faculty Bibliography

Representations of primes by simple quadratic forms, such as ±a 2±qb2 , is a subject that goes back to Fermat, Lagrange, Legendre, Euler, Gauss and many others. We are interested in a comprehensive list of such results, for q ≤ 20. Some of the results can be established with elementary methods and we exemplify that in some instances. We are introducing new relationships between various representations.

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Things To Do With A Broken Stick., Eugen J. Ionascu Jan 2013

Things To Do With A Broken Stick., Eugen J. Ionascu

Faculty Bibliography

In this article we consider variations of a classical geometric probability question in Euclidean Geometry. Our work is tightly related to the problem of constructing a triangles given three of its elements. In some cases we find exact similar probabilities or if the calculations turn out to be cumbersome we include numerical approximations for these probabilities

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Two Notes On Certain Relationships Among Triangular Numbers, Thomas Moore Jan 2013

Two Notes On Certain Relationships Among Triangular Numbers, Thomas Moore

Mathematics Faculty Publications

No abstract provided.

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Some Observations On Oblong Numbers, Thomas Moore Jan 2013

Some Observations On Oblong Numbers, Thomas Moore

Mathematics Faculty Publications

No abstract provided.

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An Investigation Relating Square And Triangular Numbers, Thomas Moore Jan 2013

An Investigation Relating Square And Triangular Numbers, Thomas Moore

Mathematics Faculty Publications

No abstract provided.

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Concatenation Of Consecutive Fibonacci And Lucas Numbers: A Lesson In Patterns Of Divisibility And Proof, Thomas Moore Jan 2013

Concatenation Of Consecutive Fibonacci And Lucas Numbers: A Lesson In Patterns Of Divisibility And Proof, Thomas Moore

Mathematics Faculty Publications

No abstract provided.

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Reforming The Placement Of Transfer Students In Introductory Level Mathematics Courses, Irina Seceleanu, Rebecca C. Metcalf Jan 2013

Reforming The Placement Of Transfer Students In Introductory Level Mathematics Courses, Irina Seceleanu, Rebecca C. Metcalf

Mathematics Faculty Publications

Transfer has become a significant pathway for obtaining a bachelor’s degree from four-year institutions. As a result, higher education institutions are faced with an increasing population of transfer students with varied academic backgrounds and readiness levels. Determining the placement of transfer students in the appropriate introductory-level mathematics course presents a distinctive challenge, and has not been the focus of many studies. In response, this article offers an analysis of the difficulties associated with the placement of transfer students and of the variety of practices regarding placement across select institutions. A narrative describing the placement system for transfer students adopted at …

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Multiclass Total Variation Clustering, X Bresson, T Laurent, David Uminsky, J Von Brecht Jan 2013

Multiclass Total Variation Clustering, X Bresson, T Laurent, David Uminsky, J Von Brecht

Mathematics

Ideas from the image processing literature have recently motivated a new set of clustering algorithms that rely on the concept of total variation. While these algorithms perform well for bi-partitioning tasks, their recursive extensions yield unimpressive results for multiclass clustering tasks. This paper presents a general framework for multiclass total variation clustering that does not rely on recursion. The results greatly outperform previous total variation algorithms and compare well with state-of-the-art NMF approaches.

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Modeling, Analysis, And Applications Of Complex Systems, Chuandong Li, Xiaodi Li, Shukai Duan, Yanzhi Zhang Jan 2013

Modeling, Analysis, And Applications Of Complex Systems, Chuandong Li, Xiaodi Li, Shukai Duan, Yanzhi Zhang

Mathematics and Statistics Faculty Research & Creative Works

Recent advances in theory and applications of complex dynamical systems have contributed much to the successful handling of certain problems in biology, physics, economics, engineering, and so forth that until recently were thought too difficult to be analyzed. These complex systems may be characterized by systems with uncertainty, impulse, time delay, stochastic perturbation, hybrid dynamics, distributed dynamics, and chaotic dynamics. The overall aim of this special issue is to bring together the latest or innovative knowledge and advances in mathematics for handling complex systems, which may depend largely on methods from mathematical analysis, artificial intelligence, statistics, and engineering, including nonlinear …

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A Bound On The Vertical Transport Of Heat In The 'Ultimate' State Of Slippery Convection At Large Prandtl Numbers, Xiaoming Wang, Jared P. Whitehead Jan 2013

A Bound On The Vertical Transport Of Heat In The 'Ultimate' State Of Slippery Convection At Large Prandtl Numbers, Xiaoming Wang, Jared P. Whitehead

Mathematics and Statistics Faculty Research & Creative Works

An upper bound on the rate of vertical heat transport is established in three dimensions for stress-free velocity boundary conditions on horizontally periodic plates. a variation of the background method is implemented that allows negative values of the quadratic form to yield 'small' (O.1=Pr/) corrections to the subsequent bound. for large (but finite) Prandtl numbers this bound is an improvement over the 'ultimate' Ra1=2 scaling and, in the limit of infinite Pr, agrees with the bound of Ra5=12 recently derived in that limit for stress-free boundaries. © 2013 Cambridge University Press.

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Well-Posedness Of The Hele-Shaw-Cahn-Hilliard System, Xiaoming Wang, Zhifei Zhang Jan 2013

Well-Posedness Of The Hele-Shaw-Cahn-Hilliard System, Xiaoming Wang, Zhifei Zhang

Mathematics and Statistics Faculty Research & Creative Works

We study the well-posedness of the Hele-Shaw-Cahn-Hilliard system modeling binary fluid flow in porous media with arbitrary viscosity contrast but matched density between the components. for initial data in Hs, s>d2+1, the existence and uniqueness of solution in C([0,T];Hs) ∪L2(0,T;Hs+2) that is global in time in the two-dimensional case (d=2) and local in time in the three-dimensional case (d=3) are established. Several blow-up criterions in the three-dimensional case are provided as well. One of the tools that we utilized is the Littlewood-Paley theory in order to establish certain key commutator estimates. © 2012 Elsevier Masson SAS.

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Remarks On Quadratic Bundles Related To Hermitian Symmetric Spaces, Tihomir Valchev Jan 2013

Remarks On Quadratic Bundles Related To Hermitian Symmetric Spaces, Tihomir Valchev

Conference papers

We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)\times U(n)). We discuss the spectral properties of scattering operator, develop the direct scattering problem associated with it and stress on the effect of reduction on these. By applying a modification of Zakharov-Shabat's dressing procedure we demonstrate how one can obtain reflectionless potentials. That way one is able to generate soliton solutions to the nonlinear evolution equations belonging to the integrable hierarchy associated with quadratic bundles under study.

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The Balm Copula, Boyan N. Dimitrov, Nikolai Kolev Jan 2013

The Balm Copula, Boyan N. Dimitrov, Nikolai Kolev

Mathematics Publications

The class of probability distributions possessing the almost-lack-of-memory property appeared about 20 years ago. It reasonably took place in research and modeling, due to its suitability to represent uncertainty in periodic random environment. Multivariate version of the almost-lack-of-memory property is less known, but it is not less interesting. In this paper we give the copula of the bivariate almost-lack-of-memory (BALM) distributions and discuss some of its properties and applications. An example shows how the Marshal-Olkin distribution can be turned into BALM and what is its copula.

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Ehrhart's Polynomial For Equilateral Triangles In Z3, Eugen J. Ionascu Jan 2013

Ehrhart's Polynomial For Equilateral Triangles In Z3, Eugen J. Ionascu

Faculty Bibliography

In this paper we calculate the Ehrhart’s polynomial associated with a 2-dimensional regular polytope (i.e. equilateral triangles) in Z3. The polynomial takes a relatively simple form in terms of the coordinates of the vertices of the triangle. We give some equivalent formula in terms of a parametrization of these objects which allows one to construct equilateral triangles with given properties. In particular, we show that given a prime number p which is equal to 1 or −5 (mod 8), there exists an equilateral triangle with integer coordinates whose Ehrhart polynomial is L(t) = (pt + 2)(t + 1)/2, t ∈ …

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On The Matrix Equation Xa + Ax_T = 0, Ii, Alice Zhuo-Yu Chan '14, Luis Alberto Garcia '14, Stephan Ramon Garcia, Amy L. Shoemaker '14 Jan 2013

On The Matrix Equation Xa + Ax_T = 0, Ii, Alice Zhuo-Yu Chan '14, Luis Alberto Garcia '14, Stephan Ramon Garcia, Amy L. Shoemaker '14

Pomona Faculty Publications and Research

The matrix equation $XA + AX^T = 0$ was recently introduced by De Ter\'an and Dopico to study the dimension of congruence orbits. They reduced the study of this equation to a number of special cases, several of which have not been explicitly solved. In this note we obtain an explicit, closed-form solution in the difficult Type 0-I interaction case.

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Concavity Of Solutions Of A 2n-Th Order Problem With Symmetry, Abdulmalik Altwaty, Paul W. Eloe Jan 2013

Concavity Of Solutions Of A 2n-Th Order Problem With Symmetry, Abdulmalik Altwaty, Paul W. Eloe

Mathematics Faculty Publications

In this article we apply an extension of a Leggett-Williams type fixed point theorem to a two-point boundary value problem for a 2n-th order ordinary differential equation. The fixed point theorem employs concave and convex functionals defined on a cone in a Banach space. Inequalities that extend the notion of concavity to 2n-th order differential inequalities are derived and employed to provide the necessary estimates. Symmetry is employed in the construction of the appropriate Banach space.

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The Effects Of Variable Viscosity On The Peristaltic Flow Of Non-Newtonian Fluid Through A Porous Medium In An Inclined Channel With Slip Boundary Conditions, Ambreen Afsar Khan, R. Ellahi, Muhammad Usman Jan 2013

The Effects Of Variable Viscosity On The Peristaltic Flow Of Non-Newtonian Fluid Through A Porous Medium In An Inclined Channel With Slip Boundary Conditions, Ambreen Afsar Khan, R. Ellahi, Muhammad Usman

Mathematics Faculty Publications

The present paper investigates the peristaltic motion of an incompressible non-Newtonian fluid with variable viscosity through a porous medium in an inclined symmetric channel under the effect of the slip condition. A long wavelength approximation is used in mathematical modeling. The system of the governing nonlinear partial differential equation has been solved by using the regular perturbation method and the analytical solutions for velocity and pressure rise have been obtained in the form of stream function. In the obtained solution expressions, the long wavelength and low Reynolds number assumptions are utilized. The salient features of pumping and trapping phenomena are …

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Prospective Teachers’ Interactive Visualization And Affect In Mathematical Problem-Solving, Inés Mª Gómez-Chacón Jan 2013

Prospective Teachers’ Interactive Visualization And Affect In Mathematical Problem-Solving, Inés Mª Gómez-Chacón

The Mathematics Enthusiast

Research on technology-assisted teaching and learning has identified several families of factors that contribute to the effective integration of such tools. Focusing on one such family, affective factors, this article reports on a qualitative study of 30 prospective secondary school mathematics teachers designed to acquire insight into the affect associated with the visualization of geometric loci using GeoGebra. Affect as a representational system was the approach adopted to gain insight into how the use of dynamic geometry applications impacted students’ affective pathways. The data suggests that affect is related to motivation through goals and self-concept. Basic instrumental knowledge and the …

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Editorial: (Why) Yet Another Issue On Problem Solving?, Bharath Sriraman Jan 2013

Editorial: (Why) Yet Another Issue On Problem Solving?, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

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Cognition And Affect In Mathematics Problem Solving With Prospective Teachers, Lorenzo J. Blanco, Eloisa Guerrero Barona, Ann Caballero Carrasco Jan 2013

Cognition And Affect In Mathematics Problem Solving With Prospective Teachers, Lorenzo J. Blanco, Eloisa Guerrero Barona, Ann Caballero Carrasco

The Mathematics Enthusiast

Recent studies relating the affective domain with the teaching and learning of mathematics, and more specifically with mathematics problem solving, have focused on teacher education. The authors of these studies have been ever more insistently pointing to the need to design educational programs that take an integrated cognitive and affective approach to mathematics education. Given this context, we have designed and implemented a program of intervention on mathematics problem solving for prospective primary teachers. We here describe some results of that program.

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The Beverton–Holt Q-Difference Equation, Martin Bohner, Rotchana Chieochan Jan 2013

The Beverton–Holt Q-Difference Equation, Martin Bohner, Rotchana Chieochan

Mathematics and Statistics Faculty Research & Creative Works

The Beverton–Holt model is a classical population model which has been considered in the literature for the discrete-time case. Its continuous-time analogue is the well-known logistic model. In this paper, we consider a quantum calculus analogue of the Beverton–Holt equation. We use a recently introduced concept of periodic functions in quantum calculus in order to study the existence of periodic solutions of the Beverton–Holt q-difference equation. Moreover, we present proofs of quantum calculus versions of two so-called Cushing–Henson conjectures. © 2013 The Author(s). Published by Taylor & Francis.

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Supercharacters, Exponential Sums, And The Uncertainty Principle, J.L. Brumbaugh '13, Madeleine Bulkow '14, Patrick S. Fleming, Luis Alberto Garcia '14, Stephan Ramon Garcia, Gizem Karaali, Matt Michal '15, Andrew P. Turner '14 Jan 2013

Supercharacters, Exponential Sums, And The Uncertainty Principle, J.L. Brumbaugh '13, Madeleine Bulkow '14, Patrick S. Fleming, Luis Alberto Garcia '14, Stephan Ramon Garcia, Gizem Karaali, Matt Michal '15, Andrew P. Turner '14

Pomona Faculty Publications and Research

The theory of supercharacters, which generalizes classical character theory, was recently introduced by P. Diaconis and I.M. Isaacs, building upon earlier work of C. Andre. We study supercharacter theories on $(Z/nZ)^d$ induced by the actions of certain matrix groups, demonstrating that a variety of exponential sums of interest in number theory (e.g., Gauss, Ramanujan, and Kloosterman sums) arise in this manner. We develop a generalization of the discrete Fourier transform, in which supercharacters play the role of the Fourier exponential basis. We provide a corresponding uncertainty principle and compute the associated constants in several cases.

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Fourteenth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics Jan 2013

Fourteenth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics

Kenneth C. Schraut Memorial Lectures

No abstract provided.

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Generalized Gauss Maps And Integrals For Three-Component Links: Toward Higher Helicities For Magnetic Fields And Fluid Flows, Dennis Deturck, Herman Gluck, Rafal Komendarczyk, Paul Melvin, Clayton Shonkwiler, David Shea Vela-Vick Jan 2013

Generalized Gauss Maps And Integrals For Three-Component Links: Toward Higher Helicities For Magnetic Fields And Fluid Flows, Dennis Deturck, Herman Gluck, Rafal Komendarczyk, Paul Melvin, Clayton Shonkwiler, David Shea Vela-Vick

Mathematics Faculty Research and Scholarship

To each three-component link in the 3-sphere we associate a generalized Gauss map from the 3-torus to the 2-sphere, and show that the pairwise linking numbers and Milnor triple linking number that classify the link up to link homotopy correspond to the Pontryagin invariants that classify its generalized Gauss map up to homotopy. We view this as a natural extension of the familiar situation for two-component links in 3-space, where the linking number is the degree of the classical Gauss map from the 2-torus to the 2-sphere. The generalized Gauss map, like its prototype, is geometrically natural in the sense …

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Extender Sets And Multidimensional Subshifts, Nic Ormes, Ronnie Pavlov Jan 2013

Extender Sets And Multidimensional Subshifts, Nic Ormes, Ronnie Pavlov

Mathematics Preprint Series

In this paper, we consider a Z d extension of the well-known fact that subshifts with only finitely many follower sets are sofic. As in [4], we adopt a natural Z d analogue of a follower set called an extender set. The extender set of a finite word w in a Z d subshift X is the set of all configurations of symbols on the rest of Z d which form a point of X when concatenated with w. As our main result, we show that for any d ≥ 1 and any Z d subshift X, if there exists …

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Symmetric Random Walks On Homeo+(R), B. Deroin, V. Klepstyn, A. Navas, Kamlesh Parwani Jan 2013

Symmetric Random Walks On Homeo+(R), B. Deroin, V. Klepstyn, A. Navas, Kamlesh Parwani

Faculty Research and Creative Activity

We study symmetric random walks on finitely generated groups of orientation-preserving homeomorphisms of the real line. We establish an oscillation property for the induced Markov chain on the line that implies a weak form of recurrence. Except for a few special cases, which can be treated separately, we prove a property of "global stability at a finite distance": roughly speaking, there exists a compact interval such that any two trajectories get closer and closer whenever one of them returns to the compact interval. The probabilistic techniques employed here lead to interesting results for the study of group actions on the …

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Functions Defined By Improper Integrals, William Trench Jan 2013

Functions Defined By Improper Integrals, William Trench

Mathematics Faculty Research

This is a supplement to the author's Introduction to Real Analysis. It has been judged to meet the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute's Textbook Initiative. It may be copied, modified, redistributed, translated, and built upon subject to the Creative Commons license Attribution-NonCommercial-ShareAlike 3.0 Unported License. A complete instructor's solution manual is available by email to [email protected] subject to verification of the requestor's faculty status.

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The Method Of Lagrange Multipliers, William Trench Jan 2013

The Method Of Lagrange Multipliers, William Trench

Mathematics Faculty Research

This is a supplement to the author's "Introduction to Real Analysis." It has been judged to meet the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute's Open Textbook Initiative. It may be copied, modified, redistributed, translated, and built upon subject to the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. A complete instructor's solution manual is available by email to [email protected], subject to verification of the requestor's faculty status.

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Bayesian Approach For Inconsistent Information, M. Stein, Michael Beer, Vladik Kreinovich Jan 2013

Bayesian Approach For Inconsistent Information, M. Stein, Michael Beer, Vladik Kreinovich

Departmental Technical Reports (CS)

In engineering situations, we usually have a large amount of prior knowledge that needs to be taken into account when processing data. Traditionally, the Bayesian approach is used to process data in the presence of prior knowledge. Sometimes, when we apply the traditional Bayesian techniques to engineering data, we get inconsistencies between the data and prior knowledge. These inconsistencies are usually caused by the fact that in the traditional approach, we assume that we know the {\it exact} sample values, that the prior distribution is {\it exactly} known, etc. In reality, the data is imprecise due to measurement errors, the …

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Topological Symmetry Groups Of Graphs In 3-Manifolds, Erica Flapan, Harry Tamvakis Jan 2013

Topological Symmetry Groups Of Graphs In 3-Manifolds, Erica Flapan, Harry Tamvakis

Pomona Faculty Publications and Research

We prove that for every closed, connected, orientable, irreducible 3-manifold there exists an alternating group A_n which is not the topological symmetry group of any graph embedded in the manifold. We also show that for every finite group G there is an embedding T of some graph in a hyperbolic rational homology 3-sphere such that the topological symmetry group of T is isomorphic to G.

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