Applied Mathematics Commons^™

Critical Point Theory And The Number Of Solutions Of A Nonlinear Dirichlet Problem, Alfonso Castro, A. C. Lazer

All HMC Faculty Publications and Research

No abstract provided.

Double Stochastic Integrals, Tsung-Dow Huang

Mathematics & Statistics ETDs

In this paper we study the double stochastic integral or stochastic quadratic form

Q =integreal(integral(phi(x,y)Z(dx)Z(dy) ))

with respect to a Gaussian random spectral measure Z. Letting F be the corresponding spectral distribution function, the kernel function is required to satisfy a) the function phi(x,x) is integrable respect to F and b) phi(x,y) is square integrable with respect to FxF. A definition of Q is given in terms of a carefully constructed sequence of step functions converging to phi. Iterated integral formulae, a discussion of the stochastic contribution to Q due to the diagonal values of phi, and an improvement of …

Making Curriculum Decisions And The Nature Of Mathematics, Paul Zwier

ACMS Conference Proceedings 1979

This paper explores the pedagogical decisions made by those teaching mathematics by discussing the various values and priorities of a mathematics course.

Mathematics In The Christian Philosophy Of Life, C. Ralph Verno

ACMS Conference Proceedings 1979

It is universally agreed that mathematics is important, that it is indeed very significant in life. This would be admitted even by those who are ignorant of or who dislike mathematics. There would be much less agreement, however, about why mathematics is important or significant. Such disagreement exists even more among mathematicians and mathematics educators. Unhappily many of the Christians who think about such things (and there are not very many who think about them at all) basically share the utilitarian view of many non-Christian thinkers, although endeavoring to place it within a Christian context. They think it is wonderful …

Brief Position Paper For Panel Discussion On Relation Of Mathematics And Christianity, C. Ralph Verno

ACMS Conference Proceedings 1979

Some people view a conjoining of Christianity and Mathematics as improper. They miss the point of the relationship. The content of mathematics is not affected by Christianity. The relationship does not concern what, or how (the Christian doesn’t solve equations or differentiate differently), but it concerns why. It concerns such things as the interpretation and appreciation of the beauty, the symmetries, the coincidences, the remarkable properties, man’s creative role, etc. This paper explores the relationship between Christianity and mathematics as part of a panel discussion on the topic.

On Kuyk’S Complementarity In Mathematics, Gene B. Chase

ACMS Conference Proceedings 1979

This paper examines Willem Kuyk’s book, Complementarity in Mathematics, and the interplay between the subjects of mathematics.

Are Mathematical Objects Ontologically Real? Ideas And Suggestions, Frank R. Bernhart

ACMS Conference Proceedings 1979

This essay will consider a few ways that realism in the modern philosophy of mathematics might be understood and defined.

Intuitionism, Terence H. Perciante

ACMS Conference Proceedings 1979

Intuitionism derives philosophically from Kant's Conceptualism -- the object of the mathematical knowledge only have reality within the mind, they do not have reality apart from our thinking. This paper examines the nature of intuitionism and its strengths.

Two Philosophical Problems About Mathematics, Stephen Barker

ACMS Conference Proceedings 1979

Mathematics is a flourishing field of human endeavor, a field that is accorded great respect and high standing. For 2500 years or more, many of the best minds available have worked in this field; and the results produced have indirectly been of enormous value to other fields, such as physics, engineering, architecture, economics, and so on. But with is mathematics about? Physics studies moving bodies; engineering studies bridges; architecture studies buildings; economics studies commercial behavior: here there are phenomena we can point to that constitute the subject matter. But what does mathematics study? If you answer “Numbers”, or “Abstract types …

Axiomatic Structure And The Method Of Analysis: Shifting Styles In The History Of Mathematics, Calvin Jongsma

ACMS Conference Proceedings 1979

This article surveys the different views of mathematical methodology that occurred from ancient Greek times through the early modern period up until its codification around 1900. After summarizing the axiomatic approach advocated by Aristotle and implemented in mathematics by Euclid, the talk explores the character of analysis in ancient Greek times, its development into a symbolic algebra by Viete and Descartes, and its expansion into a calculus of fluxions and differentials by Newton and Leibniz. The article concludes by touching on the recovery and transformation of the deductive ideal for mathematics by Pasch, Peano, and Hilbert during the late nineteenth …

Non-Standard Calculus, Ron Friewald

ACMS Conference Proceedings 1979

This paper is intended to provide a very cursory introduction to how “nonstandard calculus” works, giving a sketch of how elementary calculus can be presented using hyperreal numbers.

Computer Usage In The College Curriculum, Dick A. Wood

ACMS Conference Proceedings 1979

No abstract provided.

Math & Society: An Introduction To Mathematical Thought, Verbal Snook

ACMS Conference Proceedings 1979

No abstract provided.

Mathematics And Christian Faith - Some Personal Perceptions, Richard Laatsch

ACMS Conference Proceedings 1979

No abstract provided.

Implications Of Recent Developments In Philosophy Of Science For An Axiological Approach To Foundations Of Mathematics, Harold Heie

ACMS Conference Proceedings 1979

No abstract provided.

Logic In The Mathematics Curriculum, Nigel Cutland

ACMS Conference Proceedings 1979

No abstract provided.

Introduction (1979), Robert Brabenec

ACMS Conference Proceedings 1979

No abstract provided.

Table Of Contents (1979), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1979

A Second Conference on the Foundations of Mathematics

Markovian Multiserver Queueing Systems With Servers In Series, Nancy Jean Boynton

Dissertations

No abstract provided.

Stochastic Approximation Procedures For Mixing Stochastic Processes, Katherine Campbell

Mathematics & Statistics ETDs

Stochastic approximation methods for estimating the parameters of a stationary autoregressive process of finite order are investigated. The emphasis is on robust methods, and the non-linear scoring functions associated with such methods require the development of new techniques for establishing convergence. A mixing condition falling between the traditional strong and uniform mixing conditions is investigated in detail, and used to establish almost sure and mean square convergence of the proposed algorithms when the underlying process satisfies this condition. A short Monte Carlo study verifies the desirable properties of the robust algorithm in the presence of heavy-tailed innovations.

A Semilinear Dirichlet Problem, Alfonso Castro

All HMC Faculty Publications and Research

Let Ω be a bounded region in R^n. In this note we discuss the existence of weak solutions (see [4, Section 2]) of the Dirichlet problem:

Δu(x) + g(x, u(x)) + f(x, u(x), ∇u(x)) = 0 ; x є Ω

u(x) = 0 ; x є ∂Ω

where Δ is the Laplacian operator, g : Ω x R → R and f : Ω x Rⁿ⁺¹ → R are functions satisfying the Caratheodory condition (see [2, Section 3]), and ∇ is the gradient operator.

Making Curriculum Decisions And The Nature Of Mathematics, Paul Zwier

ACMS Journal 2004

This paper clearly presents eight aspects of mathematics and contrasting perspectives in each that will affect the teaching of mathematics and the design of curricula. It also presents a collection of affirmations that could reasonably characterize a Christian perspective on teaching mathematics.

Evaluation And Improvement Of The Wu-Koh Model For The Prediction Of Multiple-Cell Cooling Tower Plumes, Michael Joseph Wastag

Masters Theses

This paper evaluates and improves the performance of the Wu-Koh mathematical model for the prediction of plume dispersion from multiple natural-draft (NDCT) and mechanical-draft (MDCT) cooling towers. The Wu-Koh multiple-tower model was chosen for study due to its advanced treatment of plume merging.

Our evaluation of the Wu-Koh model was carried out by comparing model predictions of field and laboratory data. Comparisons of model predictions of visible plume outlines were made to single- and multiple-tower visible plume data. The sites of the single-tower data were Lunen (300 MW_e), Chalk Point (630 MW_e) and Paradise (1100 MW …

Stochastic Dominance And Information Value, Young Koan Kwon, John C. Fellingham, D. Paul Newman

Research Collection School Of Accountancy

Incentives for producing and disseminating information have been analysed in many different contexts. Kihlstrom [6], for example, develops a Bayesian framework to analyze the properties of demand functions for information about product quality. From an entirely different perspective, Spence [8, 91 demonstrates the private value of “signalling” information. Similarly, Wilson [lo] considers the value to the firm of producing technological information and the effect of such production on equilibrium theory.

Sufficiency Of A Numerical Downstream Continuation, Charlie H. Cooke

Mathematics & Statistics Faculty Publications

(First paragraph) Customarily one does not impose n-th order boundary conditions on the solution of initial/boundary value problems whose characterizing partial differential equations are also n-th order. However, conjecture that such problems are not well-posed, or that a solution might not exist, is not always justified [l]. Perhaps a physically more natural example is provided by problems of computational fluid dynamics. Here boundary conditions which correctly should be applied at an infinite distance downstream from the region of interest are for computational convenience often applied at a finite location [2]. Results of numerical experimentation on viscous flows governed by …

An Illustrative Model Describing The Refraction Of Long Water Waves By A Circular Island, Gregory A. Kriegsmann

Department of Mathematics: Faculty Publications

The refraction of small shallow water waves by an idealized island is studied in this paper. The island's shoal is modeled by a quartic polynomial in the radial variable. This particular model allows the explicit construction of the rays (wave orthogonals) and the determination of several important features of the wave motion. The various shortcomings of the particular profile are discussed.

Groups Expressed As The Set-Theoretic Union Of Proper Subgroups, Lana Barrett

Masters Theses & Specialist Projects

In their paper “Groups as Unions of Proper Subgroups,” published in 1959, Haber and Rosenfeld posed the problem of characterizing groups which can be expressed as the set theoretic union of a finite collection of their proper subgroups. Haber and Rosenfeld established that a group G is the union of three proper subgroups (such a group G shall be called a U₃-group) if and only if the Klein 4-group is a homomorphic image of G. Further results concerning U₃-groups were obtained in the paper “Groups which are the Union of Three Subgroups” by Bruckhemier, Bryan and …

Estimation Of The Acceleration Function, Le Than Chap

Mathematics & Statistics ETDs

Let x1, x2,…, xm be a random sample of m failure times under normal conditions with the underlying distribution function F(x) and Y1, Y2,…, Yn be a random sample on n failure times under accelerated conditions with the underlying distribution function G(x):

G(x)=f(F(x))

Where f(x) is the acceleration function.

In this dissertation we propose several estimators for the acceleration function f(x) and investigate their properties.

A Random Walk In A Random Environment, Edwin Andrew Sanchez

Mathematics & Statistics ETDs

In this dissertation we consider a model of a random walk, (Z_n}, on R(1) where the distribution of (Z_n} is dependent on a stochastic process (Y_n} and is given by g_y(z) where Y_n-1 = y . Conditions on the environmental process (Y_n} are given for which transience or recurrence of the random walk (Z_n} can be detennined. The probability of n absorption and mean time problems are solved when (Y_n} is a finite Markov chain and (Z_n} is a classical random walk on …

Focal Sets Of Submanifolds, Thomas E. Cecil, Patrick J. Ryan

Mathematics and Computer Science Department Faculty Scholarship

This is a study of the manifold structure of the focal set of an immersed submanifold in a real space form M.