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Articles 20101 - 20130 of 27476

Full-Text Articles in Physical Sciences and Mathematics

Elliptic Complexes And Generalized Poincaré Inequalities, Derek Gustafson Jan 2008

Elliptic Complexes And Generalized Poincaré Inequalities, Derek Gustafson

Mathematics - All Scholarship

We study first order differential operators with constant coefficients. The main question is under what conditions a generalized Poincar\'e inequality holds. We show that the constant rank condition is sufficient. The concept of the Moore-Penrose generalized inverse of a matrix comes into play.

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Load Sharing Models, Paul H. Kvam, Jye-Chyi Lu Jan 2008

Load Sharing Models, Paul H. Kvam, Jye-Chyi Lu

Department of Math & Statistics Faculty Publications

Consider a system of components whose lifetimes are governed by a probability distribution. Load sharing refers to a model of stochastic interdependency between components that operate within a system. If components are set up in a parallel system (see Parallel, Series, and Series–Parallel Systems) for example, the system survives as long as at least one component is operating. In a typical load-sharing system, once a component fails, the remaining components suffer an increase in failure rate due to the extra “load” they must encumber due to the failed component.

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Review: Lie Structure In Semiprime Superalgebras With Superinvolution, Gizem Karaali Jan 2008

Review: Lie Structure In Semiprime Superalgebras With Superinvolution, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

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How Is Mathematics Education Philosophy Reflected In The Math Wars?, David M. Davison, Johanna E. Mitchell Jan 2008

How Is Mathematics Education Philosophy Reflected In The Math Wars?, David M. Davison, Johanna E. Mitchell

The Mathematics Enthusiast

Throughout the duration of what has been termed the “math wars”, many overlygeneralized statements by both sides have detracted from the quest for a solution to the conflict between conceptual and procedural approaches to mathematics study. In terms of philosophies of mathematics education, the absolutist view posits that mathematical knowledge is certain and unchallengeable while the fallibilist view is that mathematical knowledge is never beyond revision and correction. We suggest that the major mathematics education reforms have been absolutist in focus and have not reflected the changing nature of the discipline. Thus we believe that true reform will reflect changing …

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Tme Volume 5, Number 1 Jan 2008

Tme Volume 5, Number 1

The Mathematics Enthusiast

No abstract provided.

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Optimal Selling Rules In A Regime-Switching Exponential Gaussian Diffusion Model, Paul W. Eloe, R. H. Liu, Masako Yatsuki Jan 2008

Optimal Selling Rules In A Regime-Switching Exponential Gaussian Diffusion Model, Paul W. Eloe, R. H. Liu, Masako Yatsuki

Mathematics Faculty Publications

This paper develops optimal selling rules in asset trading using a regime-switching exponential Gaussian diffusion model. The optimization problem is solved by a combined approach of boundary value problems and probabilistic analysis. A system of linear differential equations with variable coefficients and two-point boundary conditions, satisfied by the objective function of the problem, is derived. The existence and uniqueness of the solution are proved. A closed-form solution in terms of Weber functions is obtained for one-dimensional cases. For m-dimensional cases, a stochastic recursive algorithm for numerically searching the optimal value is developed. Numerical results are reported.

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Qualitative Properties Of Nonlinear Volterra Integral Equations, Muhammad Islam, Jeffrey T. Neugebauer Jan 2008

Qualitative Properties Of Nonlinear Volterra Integral Equations, Muhammad Islam, Jeffrey T. Neugebauer

Mathematics Faculty Publications

In this article, the contraction mapping principle and Liapunov's method are used to study qualitative properties of nonlinear Volterra equations of the form x(t)=a(t)−∫t0C(t,s)g(s,x(s))ds,t≥0. In particular, the existence of bounded solutions and solutions with various Lp properties are studied under suitable conditions on the functions involved with this equation.

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2008 Alumni Presenters, University Of Dayton. Department Of Mathematics Jan 2008

2008 Alumni Presenters, University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

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2008 (Winter), University Of Dayton. Department Of Mathematics Jan 2008

2008 (Winter), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2008 Winter Colloquium.

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Number Fields Ramified At One Prime, John W. Jones, David P. Roberts Jan 2008

Number Fields Ramified At One Prime, John W. Jones, David P. Roberts

Mathematics Publications

For G a finite group and p a prime, a G-p field is a Galois number field K with Gal(K/Q)≅G and disc(K)=±pa for some a. We study the existence of G-p fields for fixed G and varying p.

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Intersection Numbers Of Heegner Divisors On Shimura Curves, Kevin Keating, David P. Roberts Jan 2008

Intersection Numbers Of Heegner Divisors On Shimura Curves, Kevin Keating, David P. Roberts

Mathematics Publications

In foundational papers, Gross, Zagier, and Kohnen established two formulas for arithmetic intersection numbers of certain Heegner divisors on integral models of modular curves. In [GZ1], only one imaginary quadratic discriminant plays a role. In [GZ2] and [GKZ], two quadratic discriminants play a role. In this paper we generalize the two-discriminant formula from the modular curves X0(N) to certain Shimura curves defined over Q. Our intersection formula was stated in [Ro], but the proof was only outlined there. Independently, the general formula was given, in a weaker and less explicit form, in [Ke2]; there it was proved completely. …

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Origin Of Conductive Surface Layer In Annealed Zno, David C. Look, B. Claflin, Helen Smith Jan 2008

Origin Of Conductive Surface Layer In Annealed Zno, David C. Look, B. Claflin, Helen Smith

Mathematics and Statistics Faculty Publications

The highly conductive surface layers found in nearly all as-grown or annealed bulk ZnO wafers are studied by temperature-dependent Hall-effect and secondary-ion mass spectroscopy (SIMS) measurements. In this work, we have used annealing in N2 at 900 degrees C, and forming gas (5% H2 in N2) at 600 degrees C, to cause a large enough surface conduction that SIMS measurements can be reliably employed. The increased near-surface donor density, as determined from two-layer Hall-effect modeling, is consistent with an increased near-surface concentration of Al, Ga, and In atoms, resulting from diffusion. There is no evidence for …

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Becoming Critical Mathematics Pedagogues: A Journey, David W. Stinson, Carla R. Bidwell, Ginny C. Powell, Mary M. Thurman Jan 2008

Becoming Critical Mathematics Pedagogues: A Journey, David W. Stinson, Carla R. Bidwell, Ginny C. Powell, Mary M. Thurman

Middle-Secondary Education and Instructional Technology Faculty Publications

This session will report the findings of a study that explored the beginning transformations in the pedagogical philosophies and practices of three mathematics teachers (middle, high school, and 2-year college) who completed a graduate-level mathematics education course that focused on critical theory and teaching for social justice, and how these transformations are compatible (or not) with reform mathematics education as suggested by the National Council of Teachers of Mathematics (NCTM), and in turn, the new Georgia Performance Standards (GPS). The study employed Freirian participatory research methodology; in fact, the participants were not only coresearchers, but also co-authors of the study. …

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Scale-Distortion Inequalities For Mantissas Of Finite Data Sets, Arno Berger, Theodore P. Hill, Kent E. Morrison Jan 2008

Scale-Distortion Inequalities For Mantissas Of Finite Data Sets, Arno Berger, Theodore P. Hill, Kent E. Morrison

Research Scholars in Residence

In scientific computations using floating point arithmetic, rescaling a data set multiplicatively (e.g., corresponding to a conversion from dollars to euros) changes the distribution of the mantissas, or fraction parts, of the data. A scale-distortion factor for probability distributions is defined, based on the Kantorovich distance between distributions. Sharp lower bounds are found for the scale-distortion of n-point data sets, and the unique data set of size n with the least scale-distortion is identified for each positive integer n. A sequence of real numbers is shown to follow Benford’s Law (base b) if and only if the scale-distortion (base b) …

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Rogers-Ramanujan-Slater Type Identities, James Mclaughlin, Andrew V. Sills, Peter Zimmer Jan 2008

Rogers-Ramanujan-Slater Type Identities, James Mclaughlin, Andrew V. Sills, Peter Zimmer

Mathematics Faculty Publications

In this survey article, we present an expanded version of Lucy Slater’s famous list of identities of the Rogers-Ramanujan type, including identities of similar type, which were discovered after the publication of Slater’s papers, and older identities (such as those in Ramanujan’s lost notebook) which were not included in Slater’s papers. We attempt to supply the earliest known reference for each identity. Also included are identities of false theta functions, along with their relationship to Rogers Ramanujan type identities. We also describe several ways in which pairs/larger sets of identities may be related, as well as dependence relationships between identities.

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Some Identities Between Basic Hypergeometric Series Deriving From A New Bailey-Type Transformation, James Mclaughlin, Peter Zimmer Jan 2008

Some Identities Between Basic Hypergeometric Series Deriving From A New Bailey-Type Transformation, James Mclaughlin, Peter Zimmer

Mathematics Faculty Publications

We prove a new Bailey-type transformation relating WPBailey pairs. We then use this transformation to derive a number of new 3- and 4-term transformation formulae between basic hypergeometric series.

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Mirror Principle For Flag Manifolds, Vehbi Emrah Paksoy Jan 2008

Mirror Principle For Flag Manifolds, Vehbi Emrah Paksoy

Mathematics Faculty Articles

In this paper, using mirror principle developped by Lian, Liu and Yau [8, 9, 10, 11, 12, 13] we obtained the A and B series for the equivariant tangent bundles over homogenous spaces using Chern polynomial. This is necessary to obtain related cohomology valued series for given arbitrary vector bundle and multiplicative characteristic class. Moreover, this can be used as a valuable testing ground for the theories which associates quantum cohomologies and J functions of non-abelian quotient to abelian quotients via quantization

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Reaction To The Reactors, Ted Eisenberg Jan 2008

Reaction To The Reactors, Ted Eisenberg

The Mathematics Enthusiast

1. A comment. I discussed the contents of my paper with colleagues on many different occasions. By their reactions they seem to divide themselves into two camps. One camp takes the stance of: Are you crazy to mention such things in the classroom? We are charged to teach mathematics, and that’s it. Who cares if Einstein never learned to swim? The other camp however takes an opposite stance: Such items are really important for students to know because they help students to think about the lives and times of the men who created the material they are studying; our lessons …

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Consecutive Numbers, Steve Humble Jan 2008

Consecutive Numbers, Steve Humble

The Mathematics Enthusiast

The hidden secrets of our number system can often reveal the magical quality of mathematics. Through the process of discovery and discussion with fellow classmates, the hidden depths of maths takes on new appeal. Consecutive numbers is one such area that gives this excitement.

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Mathematically Gifted Elementary Students' Revisiting Of Euler's Polyhedron Theorem, Jaehoon Yim, Sanghun Song, Jiwon Kim Jan 2008

Mathematically Gifted Elementary Students' Revisiting Of Euler's Polyhedron Theorem, Jaehoon Yim, Sanghun Song, Jiwon Kim

The Mathematics Enthusiast

This paper explores how the constructions of mathematically gifted fifth and sixth grade students using Euler’s polyhedron theorem compare to those of mathematicians as discussed by Lakatos (1976). Eleven mathematically gifted elementary school students were asked to justify the theorem, find counterexamples, and resolve conflicts between the theorem and counterexamples. The students provided two types of justification of the theorem. The solid figures suggested as counterexamples were categorized as 1) solids with curved surfaces, 2) solids made of multiple polyhedra sharing points, lines, or faces, 3) polyhedra with holes, and 4) polyhedra containing polyhedra. In addition to using the monster-barring …

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Simulating Spatial Partial Differential Equations With Cellular Automata, Brian Paul Strader Jan 2008

Simulating Spatial Partial Differential Equations With Cellular Automata, Brian Paul Strader

Theses Digitization Project

The purpose of this project was to define the relationship and show how an important subset of spatial differential equations can be transformed into cellular automata. Contains source code.

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An Order Model For Infinite Classical States, Joe Mashburn Jan 2008

An Order Model For Infinite Classical States, Joe Mashburn

Mathematics Faculty Publications

In 2002 Coecke and Martin (Research Report PRG-RR-02-07, Oxford University Computing Laboratory,2002) created a model for the finite classical and quantum states in physics. This model is based on a type of ordered set which is standard in the study of information systems. It allows the information content of its elements to be compared and measured. Their work is extended to a model for the infinite classical states. These are the states which result when an observable is applied to a quantum system. When this extended order is restricted to a finite number of coordinates, the model of Coecke and …

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Some New Families Of Tasoevian- And Hurwitzian Continued Fractions, James Mclaughlin Jan 2008

Some New Families Of Tasoevian- And Hurwitzian Continued Fractions, James Mclaughlin

Mathematics Faculty Publications

We derive closed-form expressions for several new classes of Hurwitzian- and Tasoevian continued fractions, including [0; p − 1, 1, u(a + 2nb) − 1, p − 1, 1, v(a + (2n + 1)b) − 1 ]∞ n=0, [0; c + dmn] ∞n=1 and [0; eun, fvn] ∞n=1. One of the constructions used to produce some of these continued fractions can be iterated to produce both Hurwitzian- and Tasoevian continued fractions of arbitrary long quasi-period, with arbitrarily many free parameters and whose limits can be determined as ratios of certain infinite series. We also derive expressions for arbitrarily long finite …

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Envy-Free Cake Divisions Cannot Be Found By Finite Protocols, Walter Stromquist Jan 2008

Envy-Free Cake Divisions Cannot Be Found By Finite Protocols, Walter Stromquist

Mathematics & Statistics Faculty Works

We show that no finite protocol (even if unbounded) can guarantee an envy-free division of a cake among three or more players, if each player is to receive a single connected piece.

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Hermit Points On A Box, R. Hess, Charles M. Grinstead, M. Grinstead, Deborah J. Bergstrand Jan 2008

Hermit Points On A Box, R. Hess, Charles M. Grinstead, M. Grinstead, Deborah J. Bergstrand

Mathematics & Statistics Faculty Works

No abstract provided.

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Nonexistence Of Stable Exponentially Harmonic Maps From Or Into Compact Convex Hypersurfaces In R^{M+1}, Jiancheng Liu Jan 2008

Nonexistence Of Stable Exponentially Harmonic Maps From Or Into Compact Convex Hypersurfaces In R^{M+1}, Jiancheng Liu

Turkish Journal of Mathematics

In this paper, we study the nonexistence problems for stable exponentially harmonic map into or from compact convex hypersurface M^m \subset R^{m+1}, and show that every nonconstant exponentially harmonic map f, between M^m and any compact Riemannian manifold, is unstable if (4) holds.

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On The Distribution Of Random Dirichlet Series In The Whole Plane, Qiyu Jin, Daochun Sun Jan 2008

On The Distribution Of Random Dirichlet Series In The Whole Plane, Qiyu Jin, Daochun Sun

Turkish Journal of Mathematics

For some random Dirichlet series of order(R) infinite almost surely, every horizontal line is a strong Borel line of order(R) infinite and without exceptional Little functions.

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Killing And Geodesic Lightlike Hypersurfaces Of Indefinite Sasakian Manifolds, Fortune Massamba Jan 2008

Killing And Geodesic Lightlike Hypersurfaces Of Indefinite Sasakian Manifolds, Fortune Massamba

Turkish Journal of Mathematics

In this paper, we study a lightlike hypersurface of indefinite Sasakian manifold, tangent to the structure vector field \xi. Theorems on parallel and Killing distributions are obtained. Necessary and sufficient conditions have been given for lightlike hypersurface to be mixed totally geodesic, D-totally geodesic, D\perp-totally geodesic and D'-totally geodesic. We prove that, if the screen distribution of lightlike hypersurface M of indefinite Sasakian manifold is totally umbilical, the D\perp-geodesibility of M is equivalent to the D\perp-parallelism of the distribution T M^\perp of rank 1 (Theorem \ref{Theoscre}). Finally, we give the D\perp-version (Theorem 4.22) of the Theorem 2.2 ([11], page 88).

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Dual Quaternions In Spatial Kinematics In An Algebraic Sense, Bedi̇a Akyar Jan 2008

Dual Quaternions In Spatial Kinematics In An Algebraic Sense, Bedi̇a Akyar

Turkish Journal of Mathematics

This paper presents the finite spatial displacements and spatial screw motions by using dual quaternions and Hamilton operators. The representations are considered as 4 \times 4 matrices and the relative motion for three dual spheres is considered in terms of Hamilton operators for a dual quaternion. The relation between Hamilton operators and the transformation matrix has been given in a different way. By considering operations on screw motions, representation of spatial displacements is also given.

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Tessellations Of The Hyperbolic Plane, Roberto Carlos Soto Jan 2008

Tessellations Of The Hyperbolic Plane, Roberto Carlos Soto

Theses Digitization Project

In this thesis, the two models of hyperbolic geometry, properties of hyperbolic geometry, fundamental regions created by Fuchsian groups, and the tessellations that arise from such groups are discussed.

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