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Articles 22021 - 22050 of 27446

Full-Text Articles in Physical Sciences and Mathematics

Asymptotic Solutions Of A Discrete Schrödinger Equation Arising From A Dirac Equation With Random Mass, Bernd Aulbach, Saber Elaydi, Klaus Ziegler Jan 2004

Asymptotic Solutions Of A Discrete Schrödinger Equation Arising From A Dirac Equation With Random Mass, Bernd Aulbach, Saber Elaydi, Klaus Ziegler

Mathematics Faculty Research

For a Dirac particle in one dimension with random mass, the time evolution for the average wavefunction is considered. Using the supersymmetric representation of the average Green’s function, we derive a fourth order linear difference equation for the low-energy asymptotics of the average wavefunction. This equation is of Poincar´e type, though highly critical and therefore not amenable to standard methods. In this paper we show that, nevertheless, asymptotic expansions of its solutions can be obtained.

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Faà Di Bruno’S Formula And Nonhyperbolic Fixed Points Of One-Dimensional Maps, Vadim Ponomarenko Jan 2004

Faà Di Bruno’S Formula And Nonhyperbolic Fixed Points Of One-Dimensional Maps, Vadim Ponomarenko

Mathematics Faculty Research

Fixed-point theory of one-dimensional maps of R does not completely address the issue of non-hyperbolic fixed points. This paper generalizes the existing tests to completely classify all such fixed points. To do this, a family of operators are exhibited that are analogous to generalizations of the Schwarzian derivative. In addition, a family of functions f are exhibited such that the MacLaurin series of f(f(x)) and x are identical.

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Radiotherapy Treatment Design And Linear Programming, Allen G. Holder Jan 2004

Radiotherapy Treatment Design And Linear Programming, Allen G. Holder

Mathematics Faculty Research

Intensity modulated radiotherapy treatment (IMRT) design is the process of choosing how beams of radiation will travel through a cancer patient to treat the disease, and although optimization techniques have been suggested since the 1960s, they are still not widely used. Instead, the vast majority of treatment plans are designed by clinicians through trial-and-error. Modern treatment facilities have the technology to treat patients with extremely complicated plans, and designing plans that take full advantage of the technology is tedious. The increased technology found in modern treatment facilities makes the use of optimization paramount in the design of successful treatment plans. …

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Simultaneous Data Perturbations And Analytic Center Convergence, Allen G. Holder Jan 2004

Simultaneous Data Perturbations And Analytic Center Convergence, Allen G. Holder

Mathematics Faculty Research

The central path is an infinitely smooth parameterization of the non-negative real line, and its convergence properties have been investigated since the middle 1980s. However, the central "path" followed by an infeasible-interior-point method relies on three parameters instead of one, and is hence a surface instead of a path. The additional parameters are included to allow for simultaneous perturbations in the cost and righ-hand side vectors. This paper provides a detailed analysis of the perturbed central path that is followed by infeasible-interior-point methods, and we characterize when such a path converges. We develop a set (Hausdorff) convergence property and show …

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Reduction Of Jump Systems, Vadim Ponomarenko Jan 2004

Reduction Of Jump Systems, Vadim Ponomarenko

Mathematics Faculty Research

A jump system is a set of integer lattice points satisfying an exchange axiom. We discuss an operation on lattice points, called reduction, that preserves the jump system two-step axiom. We use reduction to prove a weakened version of a matroid conjecture by Rota[3], as well as demonstrate new operations on matroids and delta-matroids.

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Effective Asymptotics For Some Nonlinear Recurrences And Almost Doubly-Exponential Sequences, Eugen J. Ionascu Jan 2004

Effective Asymptotics For Some Nonlinear Recurrences And Almost Doubly-Exponential Sequences, Eugen J. Ionascu

Faculty Bibliography

We develop a technique to compute asymptotic expansions for recurrent sequences of the form an+1 = f(an), where f(x) = x − axα + bxβ + o(x β) as x → 0, for some real numbers α, β, a, and b satisfying a > 0, 1 < α < β. We prove a result which summarizes the present stage of our investigation, generalizing the expansions in [Amer. Math Monthly, Problem E 3034[1984, 58], Solution [1986, 739]]. One can apply our technique, for instance, to obtain the formula: an = √ 3 √ n − 3 √ 3 10 ln n n √ n + 9 √ 3 50 ln n n2√ n + o ln n n5/2 , where an+1 = sin(an), a1 ∈ IR. Moreover, we consider the recurrences an+1 = a 2 n + gn, and we prove that under some technical assumptions, an is almost doubly-exponential, namely an = bk 2 n c, an = bk 2 n c + 1, an = bk 2 n − 1 2 c, or an = bk 2 n + 5 2 c for some real number k, generalizing a result of Aho and Sloane [Fibonacci Quart. 11 (1973), 429–437].

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Pokémon® Cards And The Shortest Common Superstring, Mark Stamp, Austin Stamp Jan 2004

Pokémon® Cards And The Shortest Common Superstring, Mark Stamp, Austin Stamp

Faculty Publications, Computer Science

Evidence is presented that certain sequences of Pokémon cards are determined by selecting consecutive elements from a longer sequence. We then consider the problem of recovering the shortest common superstring (SCS), i.e., the shortest string that contains each of the Pokémon card sequences as a consecutive substring. The SCS problem arises in many applications, most notably in DNA sequencing.

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Is Mathematics Education Taking A Step Backward?, Frances Kuwahara Chinn Jan 2004

Is Mathematics Education Taking A Step Backward?, Frances Kuwahara Chinn

Humanistic Mathematics Network Journal

This paper considers the recent history of mathematics teaching.

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Using Humanistic Content And Teaching Methods To Motivate Students And Counteract Negative Perceptions Of Mathematics, Roger Haglund Jan 2004

Using Humanistic Content And Teaching Methods To Motivate Students And Counteract Negative Perceptions Of Mathematics, Roger Haglund

Humanistic Mathematics Network Journal

This paper examines the following questions: How is math commonly taught, why is it taught this way, and what are the outcomes? Who are some of the voices calling for change and what are they saying? Can a humanistic approach produce positive results in students who have learned to dislike math and have not been successful in a traditional classroom?

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Taxicab Geometry As A Vehicle For The Journey Toward Enlightenment, Neil Greenspan Jan 2004

Taxicab Geometry As A Vehicle For The Journey Toward Enlightenment, Neil Greenspan

Humanistic Mathematics Network Journal

No abstract provided.

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Tesselland: A Mathematical Oddment, Martin Glover Jan 2004

Tesselland: A Mathematical Oddment, Martin Glover

Humanistic Mathematics Network Journal

No abstract provided.

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Bridging To Infinity, Mike Pinter Jan 2004

Bridging To Infinity, Mike Pinter

Humanistic Mathematics Network Journal

The author's own experiences as a mathematics student and teacher have influenced how he thinks about the infinite. Author Madeleine L'Engle has also shaped his thinking with her writing. The author offers some thoughts that connect some of L'Engle's writing with his experience.

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Man's Cards And God's Dice: A Conceptual Analysis Of Probability For The Advanced Student, Elie Feder Jan 2004

Man's Cards And God's Dice: A Conceptual Analysis Of Probability For The Advanced Student, Elie Feder

Humanistic Mathematics Network Journal

No abstract provided.

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Mathematics, The Liberal Arts, And Slavish Devotions, J. D. Phillips Jan 2004

Mathematics, The Liberal Arts, And Slavish Devotions, J. D. Phillips

Humanistic Mathematics Network Journal

No abstract provided.

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What Are Mathematical Problems?, Emam Hoosain Jan 2004

What Are Mathematical Problems?, Emam Hoosain

Humanistic Mathematics Network Journal

No abstract provided.

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A Linear Perspective To Art, Sarah Littler Jan 2004

A Linear Perspective To Art, Sarah Littler

Humanistic Mathematics Network Journal

No abstract provided.

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Humanistic Mathematics As Mathematics For All, Michael N. Fried Jan 2004

Humanistic Mathematics As Mathematics For All, Michael N. Fried

Humanistic Mathematics Network Journal

No abstract provided.

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A Brief Look At Mathematics And Theology, Philip J. Davis Jan 2004

A Brief Look At Mathematics And Theology, Philip J. Davis

Humanistic Mathematics Network Journal

No abstract provided.

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Humanistic Mathematics: Personal Evaluation And Excavations, Stephen I. Brown Jan 2004

Humanistic Mathematics: Personal Evaluation And Excavations, Stephen I. Brown

Humanistic Mathematics Network Journal

No abstract provided.

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Innumeracy And Its Perils, Numeracy And Its Promises, Ramakrishnan Menon Jan 2004

Innumeracy And Its Perils, Numeracy And Its Promises, Ramakrishnan Menon

Humanistic Mathematics Network Journal

No abstract provided.

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Book Review: Fermat's Enigma By Simon Singh, Matthew Becker Jan 2004

Book Review: Fermat's Enigma By Simon Singh, Matthew Becker

Humanistic Mathematics Network Journal

No abstract provided.

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Base And Subbase In A Number System, Walter S. Sizer Jan 2004

Base And Subbase In A Number System, Walter S. Sizer

Humanistic Mathematics Network Journal

No abstract provided.

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Are You A Quantitative Or Qualitative Runner?: 5.13 Miles And Rosemary-Lilac Shampoo, Shelly Sheats Harkness Jan 2004

Are You A Quantitative Or Qualitative Runner?: 5.13 Miles And Rosemary-Lilac Shampoo, Shelly Sheats Harkness

Humanistic Mathematics Network Journal

No abstract provided.

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Conversations Among Women In Mathematics (Program), University Of Dayton. Department Of Mathematics Jan 2004

Conversations Among Women In Mathematics (Program), University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

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Conversations Among Women In Mathematics (Workshop Information), University Of Dayton. Department Of Mathematics Jan 2004

Conversations Among Women In Mathematics (Workshop Information), University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

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2004 Alumni Presenters, University Of Dayton. Department Of Mathematics Jan 2004

2004 Alumni Presenters, University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

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2004 (Winter), University Of Dayton. Department Of Mathematics Jan 2004

2004 (Winter), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2004 Winter Colloquium

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Frobenius Classes In Alternating Groups, David P. Roberts Jan 2004

Frobenius Classes In Alternating Groups, David P. Roberts

Mathematics Publications

We present a method, based on an old idea of Serre, for completely computing Frobenius classes in alternating groups. We contrast this method with other approaches in examples involving the alternating groups A3 and A9. The method can be useful for proper subgroups of alternating groups as well, and we present examples involving the 168-element group PSL2(7) = GL3(2) and the Mathieu group M24.

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Nonic 3-Adic Fields, John W. Jones, David P. Roberts Jan 2004

Nonic 3-Adic Fields, John W. Jones, David P. Roberts

Mathematics Publications

We compute all nonic extensions of Q3 and find that there are 795 of them up to isomorphism. We describe how to compute the associated Galois group of such a field, and also the slopes measuring wild ramification. We present summarizing tables and a sample application to number fields.

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An Abc Construction Of Number Fields, David P. Roberts Jan 2004

An Abc Construction Of Number Fields, David P. Roberts

Mathematics Publications

We describe a general three step method for constructing number fields with Lie-type Galois groups and discriminants factoring into powers of specified primes. The first step involves extremal solutions of the matrix equation ABC = I. The second step involves extremal polynomial solutions of the equation A(x) + B(x) + C(x) = 0. The third step involves integer solutions of the generalized Fermat equation axp + byq + czr = 0. We concentrate here on details associated to the third step and give examples where the field discriminants have the form ±2a3b .

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