Applied Mathematics Commons^™

The Consequences Of Believing In An Infinite God, John T. Noonan

ACMS Conference Proceedings 2005

No abstract provided.

Technology And Formation: How Does Computing Shape Us?, Cary C. Gray

ACMS Conference Proceedings 2005

No abstract provided.

Nicole Oresme - An Invitation, Fernando Q. Gouvea

ACMS Conference Proceedings 2005

No abstract provided.

Object Information Repository In Christian Theory Of Technology, Longy O. Anyanwu

ACMS Conference Proceedings 2005

No abstract provided.

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.

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.

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?

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.

Call For A Non-Euclidean, Post-Cantorian Theology, Saburo Matsumoto

ACMS Conference Proceedings 2005

In this paper I propose a new approach to theology, which I refer to as a "non-Euclidean, post-Cantorian" theology. I first review three accomplishments in modern mathematics with lasting philosophical implications: non-Euclidean geometry, set theory, and the Incompleteness Theorems of Gödel. Since all of these are ideas that came after much of traditional theology had already been formed, I challenge that theology be revisited in light of what we can learn from the mathematical struggles that produced these amazing and counter-intuitive truths. I give some concrete examples and propose that such an effort can make non-trivial contribution in theology and …

Vi.31: A Generalization Of The Pythagorean Theorem, Timothy Sipka

ACMS Conference Proceedings 2005

No abstract provided.

A Christian Perspective For A First Course In Calculus, Darrell E. Allgaier

ACMS Conference Proceedings 2005

No abstract provided.

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.

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.

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 …

Reflections Upon The Relationship Between Mathematical And Biblical Truth, Dale L. Mcintyre

ACMS Conference Proceedings 2005

No abstract provided.

Schedule (2005), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2005

Fifteenth Conference of the Association of Christians in the Mathematical Sciences

Table Of Contents (2005), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2005

Fifteenth Conference of the Association of Christians in the Mathematical Sciences

Fréchet Subdifferential Calculus And Optimality Conditions In Nondifferentiable Programming, Boris S. Mordukhovich, Nguyen Mau Nam, N. D. Yen

Mathematics Research Reports

We develop various (exact) calculus rules for Frechet lower and upper subgradients of extended-realvalued functions in general Banach spaces. Then we apply this calculus to derive new necessary optimality conditions for some remarkable classes of problems in constrained optimization including minimization problems for difference-type functions under geometric and operator constraints as well as subdifferential optimality conditions for the so-called weak sharp minima.

Introduction (2005), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2005

Fifteenth Conference of the Association of Christians in the Mathematical Sciences

Lower Bounds For Simplicial Covers And Triangulations Of Cubes, Adam Bliss '03, Francis E. Su

All HMC Faculty Publications and Research

We show that the size of a minimal simplicial cover of a polytope P is a lower bound for the size of a minimal triangulation of P, including ones with extra vertices. We then use this fact to study minimal triangulations of cubes, and we improve lower bounds for covers and triangulations in dimensions 4 through at least 12 (and possibly more dimensions as well). Important ingredients are an analysis of the number of exterior faces that a simplex in the cube can have of a specified dimension and volume, and a characterization of corner simplices in terms of their …

A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu

All HMC Faculty Publications and Research

In this paper, we propose and analyze a mathematical model, in the form of a system of ordinary differential equations, governing mutated strains of human immunodeficiency virus (HIV) and their interactions with the immune system and treatments. Our model incorporates two types of resistant mutations: strains that are not responsive to protease inhibitors, and strains that are not responsive to reverse transcriptase inhibitors. It also includes strains that do not have either of these two types of resistance (wild-type virus) and strains that have both types. We perform our analysis by changing the system of ordinary differential equations (ODEs) to …

Structure Preserving Algorithms For Computing The Symplectic Singular Value Decom Position, Archara Chaiyakarn

Dissertations

In this thesis we develop two types of structure preserving Jacobi algorithms for com puting the symplectic singular value decomposition of real symplectic matrices and complex symplectic matrices. Unlike general purpose algorithms, these algorithms produce symplectic structure in all factors of the singular value decomposition.

Our first algorithm uses the relation between the singular value decomposition and the polar decomposition to reduce the problem of finding the symplectic singular value decomposition to th a t of calculating the structured spectral decomposition of a doubly structured m atrix. A Jacobi-like m ethod is developed to compute this doubly structured spectral decomposition. …

Stratification And Domination In Graphs And Digraphs, Ralucca M. Gera

Dissertations

In this thesis we combine the idea of stratification with the one of domination in graphs and digraphs, respectively.

A graph is 2-stratified if its vertex set is partitioned into two classes, where the vertices in one class are colored red and those in the other class are colored blue. Let F be a 2-stratified graph rooted at some blue vertex v . An F -coloring of a graph G is a red-blue coloring of the vertices of G in which every blue vertexu belongs to a copy of F rooted at u . The F -domination number γ …

Global Optimality Conditions In Mathematical Programming And Optimal Control, Pariwat Pacheenburawana

Dissertations

We derive new first-order necessary and sufficient optimality conditions characterizing global minimizers in mathematical programming and optimal controlproblems. These conditions are based on level sets of an objective functional and they do not assume special structure of a problem (convexity, linearity, etc.). For a mathematical programming problem of minimization of a smooth functional on some compact convex set with equality nonlinear constraints, we derive first-order optimality conditions in the form of a generalized Lagrange multiplier rule. This rule should hold for any point from the level set of the objective functional corresponding to a global minimizer. We demonstrate that these …

Error Analysis Of Variable Degree Mixed Methods For Elliptic Problems Via Hybridization, Bernardo Cockburn, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

A new approach to error analysis of hybridized mixed methods is proposed and applied to study a new hybridized variable degree Raviart-Thomas method for second order elliptic problems. The approach gives error estimates for the Lagrange multipliers without using error estimates for the other variables. Error estimates for the primal and flux variables then follow from those for the Lagrange multipliers. In contrast, traditional error analyses obtain error estimates for the flux and primal variables first and then use it to get error estimates for the Lagrange multipliers. The new approach not only gives new error estimates for the new …

Balanced Scaling Vectors Using Linear Combinations Of Existing Scaling Vectors, Bruce Kessler

Mathematics Faculty Publications

The majority of the research done into creating balanced multiwavelets has involved establishing a series of conditions on the mask of the new scaling vector by solving a large nonlinear system. The result is a completely different new function vector solution to the dilation equation with the new matrix coefficients. The research presented here will show a way to use previously-constructed orthonormal scaling vectors to generate equivalent orthonormal scaling vectors that are balanced up to the approximation order of the previous scaling vector. The technique uses linear combinations of the integer translates of the previous-constructed scaling vector.

Erratum: “Uniqueness Theorems In Bioluminescence Tomography” [Med. Phys. 31, 2289–2299 (2004)], Ge Wang, Yi Li, Ming Jiang

Mathematics and Statistics Faculty Publications

In this Erratum, we present a correction to our proof of Theorem D.4 in Ref. 1.

Conformal Properties And Baecklund Transform For The Associated Camassa-Holm Equation, Rossen Ivanov

Articles

Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other examples, including the Camassa-Holm equation and the associated Camassa-Holm equation are investigated in this paper. It is shown that the B¨acklund transform is related to the conformal properties of these equations. Some particular solutions of the Associated Camassa-Holm Equation are discussed also.

Feedback Classification Of Multi-Input Nonlinear Control Systems, Issa Amadou Tall

Articles and Preprints

We study the feedback group action on multi-input nonlinear control systems with uncontrollable mode. We follow slightly an approach proposed in Kang and Krener [W. Kang and A. J. Krener, SIAM J. Control. Optim., 30 (1992), pp. 1319–1337] which consists of analyzing the system and the feedback group step by step. We construct a normal form which generalizes, on one hand, the results obtained in the single-input case and, on the other hand, those recently obtained by the same author in the controllable case. We illustrate our results by studying the Caltech Multi-Vehicle Wireless Testbed (MVWT) and the prototype …

A Symbolic Operator Approach To Several Summation Formulas For Power Series, Tian-Xiao He, Leetsch Hsu, Peter Shiue, D. Torney

Scholarship

This paper deals with the summation problem of power series of the form Sba (f; x) = ∑a ≤ k ≤ b f(k) xk, where 0≤ a < b ≤ ∞, and {f(k)} is a given sequence of numbers with k Є [a, b) or f(t) is a differentiable function defined on [a, b). We present a symbolic summation operator with its various expansions, and construct several summation formulas with estimable remainders for Sba (f; x), by the aid of some classical interpolation series due to Newton, Gauss and Everett, respectively.