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Articles 21511 - 21540 of 27475

Full-Text Articles in Physical Sciences and Mathematics

The Reflection Property In Normed Linear Planes With Applications To Generalized Conics, Edward J. O'Neill, Mostafa Ghandehari Jul 2005

The Reflection Property In Normed Linear Planes With Applications To Generalized Conics, Edward J. O'Neill, Mostafa Ghandehari

Mathematics Technical Papers

The ancient Greek mathematician Heron was the first to solve the problem of finding the shortest path from point A to point B on one side of the line L, subject to the condition that the path goes from A to L and then to B (figure 1). Figure 1. His solution involved going from A to point R on L and then to B such that the line segments AR and BR make equal angles with L. This is exactly the path a light ray from A to B if L were a mirror. Heron included this proposition in …

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Principal Component Regression For Construction Of Wing Weight Estimation Models, Humberto Rocha Jul 2005

Principal Component Regression For Construction Of Wing Weight Estimation Models, Humberto Rocha

Mathematics & Statistics Theses & Dissertations

The multivariate data fitting problem occurs frequently in many branches of science and engineering. It is very easy to fit a data set exactly by a mathematical model no matter how the data points are distributed. But building a response by using a limited number of poorly distributed data points is very unreliable, yet necessary in conceptual design process. This thesis documents the lessons learned from fitting the wing weight data of 41 subsonic transports by three types of interpolation methods---least polynomial interpolation, radial basis function interpolation, and Kriging interpolation. The objective of this thesis is to develop an automatic …

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Maximal Surfaces In Complexes, Allen J. Dickson Jun 2005

Maximal Surfaces In Complexes, Allen J. Dickson

Theses and Dissertations

Cubical complexes are defined in a manner analogous to that for simplicial complexes, the chief difference being that cubical complexes are unions of cubes rather than of simplices. A very natural cubical complex to consider is the complex C(k_1,...,k_n) where k_1,...,k_n are nonnegative integers. This complex has as its underlying space [0,k_1]x...x[0,k_n] subset of R^n with vertices at all points having integer coordinates and higher dimensional cubes formed by the vertices in the natural way. The genus of a cubical complex is defined to be the maximum genus of all surfaces that are subcomplexes of the cubical complex. A formula …

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An Exposition Of The Deterministic Polynomial-Time Primality Testing Algorithm Of Agrawal-Kayal-Saxena, Robert Lawrence Anderson Jun 2005

An Exposition Of The Deterministic Polynomial-Time Primality Testing Algorithm Of Agrawal-Kayal-Saxena, Robert Lawrence Anderson

Theses and Dissertations

I present a thorough examination of the unconditional deterministic polynomial-time algorithm for determining whether an input number is prime or composite proposed by Agrawal, Kayal and Saxena in their paper [1]. All proofs cited have been reworked with full details for the sake of completeness and readability.

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Proton Elastic Form Factor Ratios To Q2=3.5 Gev2 By Polarization Transfer, V. Punjabi, C. F. Perdrisat, K. A. Aniol, F. T. Baker, J. Berthot, P. Y. Bertin, W. Bertozzi, A. Besson, L. Bimbot, W. U. Boeglin, E. J. Brash, D. Brown, J. R. Calarco, L. S. Cardman, Z. Chai, C. C. Chang, J. P. Chen, E. Chudakov, S. Churchwell, E. Cisbani, D. S. Dale, R. De Leo, A. Deur, B. Diederich, J. J. Domingo, M. B. Epstein, L. A. Ewell, K. G. Fissum, A. Fleck, H. Fonvieille, S. Frullani, J. Gao, F. Garibaldi, A. Gasparian, G. Gerstner, S. Gilad, R. Gilman, A. Glamazdin, C. Glashausser, J. Gomez, V. Gorbenko, A. Green, J. O. Hansen, C. R. Howell, G. M. Huber, M. Iodice, C. W. De Jager, S. Jaminion, X. Jiang, M. K. Jones, W. Kahl, J. J. Kelly, M. Khayat, L. M. Kramer, G. Kumbartzki, M. Kuss, Enkeleida K. Lakuriqi, G. Laveissiere, J. J. Lerose, M. Liang, R. A. Lindgren, N. Liyanage, G. J. Lolos, R. Macri, R. Madey, S. Malov, D. J. Margaziotis, P. Markowitz, K. Mccormick, J. I. Mcintyre, R. L. J. Van Der Meer, R. Michaels, B. D. Milbrath, J. Y. Mougey, S. K. Nanda, E. A. J. M. Offermann, Z. Papandreou, L. Pentchev, G. G. Petratos, N. M. Piskunov, R. I. Pomatsalyuk, D. L. Prout, G. Quemener, R. D. Ransome, B. A. Raue, Y. Roblin, R. Roche, G. Rutledge, P. M. Rutt, A. Saha, T. Saito, A. J. Sarty, T. P. Smith, P. Sorokin, S. Strauch, R. Suleiman, K. Takahashi, J. A. Templon, L. Todor, P. E. Ulmer, G. M. Urciuoli, P. Vernin, B. Vlahovic, H. Voskanyan, K. Wijesooriya, B. B. Wojtsekhowski, R. J. Woo, F. Xiong, G. D. Zainea, Z. L. Zhou Jun 2005

Proton Elastic Form Factor Ratios To Q2=3.5 Gev2 By Polarization Transfer, V. Punjabi, C. F. Perdrisat, K. A. Aniol, F. T. Baker, J. Berthot, P. Y. Bertin, W. Bertozzi, A. Besson, L. Bimbot, W. U. Boeglin, E. J. Brash, D. Brown, J. R. Calarco, L. S. Cardman, Z. Chai, C. C. Chang, J. P. Chen, E. Chudakov, S. Churchwell, E. Cisbani, D. S. Dale, R. De Leo, A. Deur, B. Diederich, J. J. Domingo, M. B. Epstein, L. A. Ewell, K. G. Fissum, A. Fleck, H. Fonvieille, S. Frullani, J. Gao, F. Garibaldi, A. Gasparian, G. Gerstner, S. Gilad, R. Gilman, A. Glamazdin, C. Glashausser, J. Gomez, V. Gorbenko, A. Green, J. O. Hansen, C. R. Howell, G. M. Huber, M. Iodice, C. W. De Jager, S. Jaminion, X. Jiang, M. K. Jones, W. Kahl, J. J. Kelly, M. Khayat, L. M. Kramer, G. Kumbartzki, M. Kuss, Enkeleida K. Lakuriqi, G. Laveissiere, J. J. Lerose, M. Liang, R. A. Lindgren, N. Liyanage, G. J. Lolos, R. Macri, R. Madey, S. Malov, D. J. Margaziotis, P. Markowitz, K. Mccormick, J. I. Mcintyre, R. L. J. Van Der Meer, R. Michaels, B. D. Milbrath, J. Y. Mougey, S. K. Nanda, E. A. J. M. Offermann, Z. Papandreou, L. Pentchev, G. G. Petratos, N. M. Piskunov, R. I. Pomatsalyuk, D. L. Prout, G. Quemener, R. D. Ransome, B. A. Raue, Y. Roblin, R. Roche, G. Rutledge, P. M. Rutt, A. Saha, T. Saito, A. J. Sarty, T. P. Smith, P. Sorokin, S. Strauch, R. Suleiman, K. Takahashi, J. A. Templon, L. Todor, P. E. Ulmer, G. M. Urciuoli, P. Vernin, B. Vlahovic, H. Voskanyan, K. Wijesooriya, B. B. Wojtsekhowski, R. J. Woo, F. Xiong, G. D. Zainea, Z. L. Zhou

Enkeleida K. Lakuriqi

This paper was published online on 20 May 2005 without several of the authors’ corrections incorporated. Equation (13) has been replaced. The captions of Figs. 16–18 have also been replaced. Typographical errors on pages 4, 6, 14, 15, 18, 19, 22, and 24 have all been corrected. The paper has been corrected as of 8 June 2005. The text is correct in the printed version of the journal.

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On Multiscale Approaches To 3-Dimensional Modeling Of Morphogenesis, Rajiv Chaturvedi, Chengbang Huang, Bogdan Kazmierczak, T. Schneider, Jesus A. Izaguirre, Tilmann Glimm, H. George E. Hentschel, Stuart (Stuart A.) Newman, Mark Alber, James A. Glazier Jun 2005

On Multiscale Approaches To 3-Dimensional Modeling Of Morphogenesis, Rajiv Chaturvedi, Chengbang Huang, Bogdan Kazmierczak, T. Schneider, Jesus A. Izaguirre, Tilmann Glimm, H. George E. Hentschel, Stuart (Stuart A.) Newman, Mark Alber, James A. Glazier

Mathematics Faculty Publications

In this paper we present the foundation of a unified, object-oriented, three-dimensional (3D) biomodeling environment, which allows us to integrate multiple submodels at scales from subcellular to tissues and organs. Our current implementation combines a modified discrete model from statistical mechanics, the Cellular Potts Model (CPM), with a continuum reaction-diffusion (RD) model and a state automaton with well-defined conditions for cell differentiation transitions to model genetic regulation. This environment allows us to rapidly and compactly create computational models of a class of complex developmental phenomena. To illustrate model development, we simulate a simplified version of the formation of the skeletal …

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Matrix Representations Of Automorphism Groups Of Free Groups, Ivan B. Andrus Jun 2005

Matrix Representations Of Automorphism Groups Of Free Groups, Ivan B. Andrus

Theses and Dissertations

In this thesis, we study the representation theory of the automorphism group Aut (Fn) of a free group by studying the representation theory of three finite subgroups: two symmetric groups, Sn and Sn+1, and a Coxeter group of type Bn, also known as a hyperoctahedral group. The representation theory of these subgroups is well understood in the language of Young Diagrams, and we apply this knowledge to better understand the representation theory of Aut (Fn). We also calculate irreducible representations of Aut (Fn) in low dimensions and for small n.

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Statistical Properties Of Thompson's Group And Random Pseudo Manifolds, Benjamin M. Woodruff Jun 2005

Statistical Properties Of Thompson's Group And Random Pseudo Manifolds, Benjamin M. Woodruff

Theses and Dissertations

The first part of our work is a statistical and geometric study of properties of Thompson's Group F. We enumerate the number of elements of F which are represented by a reduced pair of n-caret trees, and give asymptotic estimates. We also discuss the effects on word length and number of carets of right multiplication by a standard generator x0 or x1. We enumerate the average number of carets along the left edge of an n-caret tree, and use an Euler transformation to make some conjectures relating to right multiplication by a generator. We describe a computer algorithm which produces …

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Computational Optical Biopsy, Yi Li, Ming Jiang, Ge Wang Jun 2005

Computational Optical Biopsy, Yi Li, Ming Jiang, Ge Wang

Mathematics and Statistics Faculty Publications

Optical molecular imaging is based on fluorescence or bioluminescence, and hindered by photon scattering in the tissue, especially in patient studies. Here we propose a computational optical biopsy (COB) approach to localize and quantify a light source deep inside a subject. In contrast to existing optical biopsy techniques, our scheme is to collect optical signals directly from a region of interest along one or multiple biopsy paths in a subject, and then compute features of an underlying light source distribution. In this paper, we formulate this inverse problem in the framework of diffusion approximation, demonstrate the solution uniqueness properties in …

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Classifying Homotopy Types Of One-Dimensional Peano Continua, Mark H. Meilstrup Jun 2005

Classifying Homotopy Types Of One-Dimensional Peano Continua, Mark H. Meilstrup

Theses and Dissertations

Determining the homotopy type of one-dimensional Peano continua has been an open question of some interest. We give a complete invariant of the homotopy type of such continua, which consists of a pair of subspaces together with a relative homology group. Along the way, we describe reduced forms for one-dimensional Peano continua.

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Three Pension Cost Methods Under Varying Assumptions, Linda S. Grizzle Jun 2005

Three Pension Cost Methods Under Varying Assumptions, Linda S. Grizzle

Theses and Dissertations

A pension plan administrator promises certain benefits in the future in exchange for labor today. In order to budget for this expense and create more security for the participant, the administrator uses a pension cost method. Each cost method assigns a portion of the future liability to the current year. This is called the normal cost. We calculate the normal cost under three cost methods using different annuity, interest and inflation assumptions. Then we make comparisons between cost methods as well as between assumption changes. The cost methods considered in this paper are the unit credit cost method, projected unit …

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Blaise Pascal - Mathematician, Mystic, Disciple, Tim Rogalsky Jun 2005

Blaise Pascal - Mathematician, Mystic, Disciple, Tim Rogalsky

ACMS Conference Proceedings 2005

This is the story of a multi-faceted Christian mathematician. Instrumental in the development of calculus, probability theory, and computing machines, Pascal (1623-1662) was a man equally enamoured with mind and spirit. His conversion experience was marked by both rational decision and mystical vision. He is perhaps best known for "Pascal's wager," which simplistic "fire insurance" version of Christianity, demanding little from the convert. However, a more careful reading of his work and his life reveals that Pascal knew much about discipleship and its cost.

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The Five Orders Of Ignorance: Knowledge, Ignorance, And The Nature Of Software, Phillip Armour Jun 2005

The Five Orders Of Ignorance: Knowledge, Ignorance, And The Nature Of Software, Phillip Armour

ACMS Conference Proceedings 2005

Software is not a product, it is a medium in which we store knowledge. As simple as this idea seems, the consequences of it are quite significant. If software is not a product, then software development is not a product of production activity, despite the common practice of managing it as such. Most organizations believe that job of software developers is to build a system that we then ship to a customer. It is not. The system we build and ship to the customer is actually the by-product of the real activity which is learning. Software development is the activity …

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Does The Success Of Mathematics Defeat Naturalism?, Russell W. Howell Jun 2005

Does The Success Of Mathematics Defeat Naturalism?, Russell W. Howell

ACMS Conference Proceedings 2005

This paper discusses the arguments for and against Intelligent Design from the perspectives of mathematics.

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Mathematics As Poesis: A Preliminary Project Report, Sam Stueckle, Jeremy Case, Ken Constantine, Troy Riggs Jun 2005

Mathematics As Poesis: A Preliminary Project Report, Sam Stueckle, Jeremy Case, Ken Constantine, Troy Riggs

ACMS Conference Proceedings 2005

This paper talks about the various viewpoints of mathematics, beginning with classical perspectives and ending with the idea of poesis, or the theology of math as the art of making.

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Jesus, Plato, Math And Theology: What Is Truth?, Paul Moffett Jun 2005

Jesus, Plato, Math And Theology: What Is Truth?, Paul Moffett

ACMS Conference Proceedings 2005

Mathematical ontology is relevant to Christians because so much of Christian theology has been historically shaped by Platonic mathematics and the ontology that goes with it. The various contributors to Mathematics in a Postmodern Age, edited by Howell and Bradley, seem to assume that Christians are necessarily realists in ontology, and they are not alone. But what is the cause of this Christian connection with mathematical realism in ontology? How much has our idea of God been shaped by Plato and his mathematics?

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The Artificial Gravity Pitch, Andrew Simoson Jun 2005

The Artificial Gravity Pitch, Andrew Simoson

ACMS Conference Proceedings 2005

Toss a ball into the air; we analyze and contrast the resultant trajectories when standing both on the Little Prince’s Asteroid B-612 of 1943 and in Arthur C. Clark’s rotating space ship Discovery of 2001.

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Integrating Catholic And Marianist Historical Perspectives In A Mathematics Coruse For Elementary Education Majors, Mary Wagner-Krankel Jun 2005

Integrating Catholic And Marianist Historical Perspectives In A Mathematics Coruse For Elementary Education Majors, Mary Wagner-Krankel

ACMS Conference Proceedings 2005

St. Mary's University in San Antonio recently reaffirmed their distinctive nature as a Catholic university promoting the Marianist tradition. This new affirmation is in response to the smaller number of Marianists serving in teaching and administrative positions on campus. Faculty have been encouraged to explore new ways to integrate Catholic and Marianist values and historical perspectives in their teaching and research. I will discuss some major Catholic mathematicians and some classroom activities that I developed for the course MT3304- Mathematics for the Elementary Teacher.

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The Divine Challenge: On Matter, Mind, Math And Meaning, By John Byl, Russell W. Howell Jun 2005

The Divine Challenge: On Matter, Mind, Math And Meaning, By John Byl, Russell W. Howell

ACMS Conference Proceedings 2005

A book review of The Divine Challenge: On Matter, Mind, Math and Meaning (2004, Banner of Truth Trust) by John Byl.

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Integration Of Faith, Learning, And Christian Vocation With First-Year Mathematics Majors, Doug Phillippy, Angela Hare Jun 2005

Integration Of Faith, Learning, And Christian Vocation With First-Year Mathematics Majors, Doug Phillippy, Angela Hare

ACMS Conference Proceedings 2005

The mission of Messiah College is "to educate men and women toward maturity of intellect, character, and Christian faith, in preparation for lives of service, leadership and reconciliation in church and society". Therefore, as faculty in the Mathematical Sciences Department at this college, how we build maturity in our students, not only a mature mathematical intellect, but also maturity of character and Christian faith, reflects our commitment to the mission of the College. Further, our departmental mission statement includes the objective "to challenge students to live out their faith in their vocation as they become servant leaders in society, church, …

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James Clerk Maxwell And Why Read Biographies, Sean Bird Jun 2005

James Clerk Maxwell And Why Read Biographies, Sean Bird

ACMS Conference Proceedings 2005

Why do we read about the lives of others? This paper discusses the value of reading biographies and examines the life of physicist-mathematician James Clerk Maxwell.

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Writing Math Lessons That Integrate Christian Beliefs: The Kuyers Institute Grant Project, Dave Klanderman, Gary Talsma Jun 2005

Writing Math Lessons That Integrate Christian Beliefs: The Kuyers Institute Grant Project, Dave Klanderman, Gary Talsma

ACMS Conference Proceedings 2005

In this paper, we describe multiple math lessons designed to incorporate a Christian perspective. A total of nine lessons, some with materials for multiple class sessions, will soon be published by the Kuyers Institute. These lessons are appropriate for use at the middle school and high school level.

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Explicit Null Space Of Discrete Laplacian, Hanna Vanderzee Jun 2005

Explicit Null Space Of Discrete Laplacian, Hanna Vanderzee

ACMS Conference Proceedings 2005

For a given partial differential equation, such as Poisson’s equation in two dimensions, stipulating the null-space component of the solution is sometimes a useful alternative to specifying boundary conditions in order to determine a unique solution. To implement this approach computationally, we need a sparse and well-conditioned representation of the null space of the relevant differential operator. We discuss how the null-space method works and present an explicit formula for generating a sparse null basis for a uniform, finite-difference discretization of Laplacian operator on the unit square. The formula makes use of a triangular array which has the large Schroeder …

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Artificial Intelligence: Can We Create Machines In Our Own Image?, Derek C. Shuurman Jun 2005

Artificial Intelligence: Can We Create Machines In Our Own Image?, Derek C. Shuurman

ACMS Conference Proceedings 2005

The field of Artificial Intelligence (AI) leads to many questions about what it means to be human. Some researchers claim that inevitably computers will reach a certain threshold of complexity that will enable them to “think” and artificial consciousness will emerge. This speculation, taken a step further, leads some to believe that computer technology will eventually set humans free from the frailty of their bodies and enable them to achieve immortality. Underlying these claims is a reductionistic philosophy about what it means to be human and how one approaches the mind-body problem. Ever since the fall people have wanted to …

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A Christian Constructivist? The Impact Of Worldview On Learning Theories And The Mathematics Education Research Community, Jeffrey Barrett, Dave Klanderman Jun 2005

A Christian Constructivist? The Impact Of Worldview On Learning Theories And The Mathematics Education Research Community, Jeffrey Barrett, Dave Klanderman

ACMS Conference Proceedings 2005

This paper analyzes the role of worldview and its impact on learning theories within the mathematics education research community. The authors propose a scholarly agenda for engaging this issue in future research projects.

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Monomial Nonnegativity And The Bruhat Order, Brian Drake, Sean Gerrish, Mark Skandera Jun 2005

Monomial Nonnegativity And The Bruhat Order, Brian Drake, Sean Gerrish, Mark Skandera

Dartmouth Scholarship

We show that five nonnegativity properties of polynomials coincide when restricted to polynomials of the form x1, pi(1) ... xn,pi(n) - x1, sigma(1) ... xn, sigma(n), where $\pi and sigma are permutations in Sn. In particular, we show that each of these properties may be used to characterize the Bruhat order on Sn.

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Explicit Computations Supporting A Generalization Of Serre's Conjecture, Brian Francis Hansen Jun 2005

Explicit Computations Supporting A Generalization Of Serre's Conjecture, Brian Francis Hansen

Theses and Dissertations

Serre's conjecture on the modularity of Galois representations makes a connection between two-dimensional Galois representations and modular forms. A conjecture by Ash, Doud, and Pollack generalizes Serre's to higher-dimensional Galois representations. In this paper we discuss an explicit computational example supporting the generalized claim. An ambiguity in a calculation within the example is resolved using a method of complex approximation.

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Asserting Cs != Can't Spcialize, Building Community In A Computer Science Program, Kim Kihlstrom Jun 2005

Asserting Cs != Can't Spcialize, Building Community In A Computer Science Program, Kim Kihlstrom

ACMS Conference Proceedings 2005

As humans, we are designed to live in community. "Just as each of us has one body with many members, and these members do not all have the same function, so in Christ we who are many form one body, and each member belongs to all the others" (Romans 12:4-5). We believe it is of critical importance to build community within a computer science program, first of all because it is part of God's calling for us. In addition, building communit allows us to equip students with the interpersonal skills that they need for a productive career, and to attract …

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Filtering The Bible And Filtering Spam, Gene B. Chase Jun 2005

Filtering The Bible And Filtering Spam, Gene B. Chase

ACMS Conference Proceedings 2005

I argue that John Craig (1996?–1731) is the first to do Bayesian statistics. Filtering email spam today using Bayes's analysis of 1763 is a new application of an old theorem. Craig 67 years before Bayes's theorem used subjective probabilities reasoning to argue that Jesus would return in the year 3150, because the Bible would eventually come into disrepute (become spam?) then.

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Bibliography Of Christianity And Mathematics, Gene B. Chase Jun 2005

Bibliography Of Christianity And Mathematics, Gene B. Chase

ACMS Conference Proceedings 2005

The invited address provides historiographic background for the second edition of Bibliography of Christianity and Mathematics. The second edition builds on the first edition written jointly with Calvin Jongsma, on the historiographic work of Ivor Grattan-Guiness, and on the computer skills of Gregory Ross.

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