Physical Sciences and Mathematics Commons^™

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.

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

Faculty Work Comprehensive List

No abstract provided.

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.

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.

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 …

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 …

A New Approach To Computer Oriented, Quasi-Quantum Mechanical Dynamics, Donald Greenspan

Mathematics Technical Papers

A new approach to atomic and molecular dynamics is developed which combines both quantum and classical concepts. Applications are made to the hydrogen atom, the hydrogen ion, and the hydrogen molecule. An accurate computer technique for the approximation of bond lengths is developed and illustrative examples of electron motions are described and discussed. Uncertainty results naturally from a mathematical statement of total system energy, which is always quantized. Angular momentum can be zero and need not be quantized, thereby avoiding inconsistencies of Bohr-Sommerfeld type models.

Comparison Results For Reaction-Diffusion Equations In A Banach Space, V. Lakshmikantham

Mathematics Technical Papers

Let T be the temperature and n the concentration of a combustible substance. A simple model governing the combustion of the material is given by [see pdf for notations] (1.1) where the constant Q is the heat of reaction; the constants Kl , K2 are thermal, material diffusion coefficients; the term exp(-E/RT) is the Arrenhius rate factor; E is the activation energy; and R is the univeral gas constant. Equations (1.1) are considered on a bounded domain ^ with the boundary conditions [see pdf for notations] (1.2) together with initial conditions [see pdf for notations] (1.3) under the assumption T0(x) …

On The Determination Of Critical Values For Bartlett's Test, Jerome P. Keating, Danny D. Dyer

Mathematics Technical Papers

The exact critical values for Bartlett's test for homogeneity of variances based on equal sample sizes from several normal populations are tabulated. It is also shown how these values may be used to obtain highly accurate approximations to the critical values for unequal sample sizes.

Introduction (1979), Robert Brabenec

ACMS Conference Proceedings 1979

No abstract provided.

Scs 50: Scott Continuous Closure Operators And Modal Operators. More Self Functors To Which The Scott Construction Applies, Karl Heinrich Hofmann, Lester W. Jones

Seminar on Continuity in Semilattices

No abstract provided.

Scs 51: A New Lemma On Primes And A Topological Characterization Of The Category Dcl Of Continuous Heyting Algebras And Cl-Morphisms, Karl Heinrich Hofmann, Fred Watkins

Seminar on Continuity in Semilattices

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

The Qr Algorithm, Hsiao-Yin Edith Chu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this section, we will consider two methods for computing an eigenvector and in addition the associated eigenvalue of a matrix A.

On Mean Residence Times In Compartments, Jerome Eisenfeld

Mathematics Technical Papers

This paper is concerned with a set of parameters which measure the mean time a random particle resides in individual compartments in response to a given load distribution. These parameters are related to other time parameters and to each other.

On Numerical Treatment Of Free Surfaces For Incompressible Fluid-Flow Problems, Vincenzo Casulli

Mathematics Technical Papers

In this paper a detailed analysis of numerical schemes for treatment of free surfaces is presented. The kinematic free surface condition is solved by a new numerical scheme that, using the proper boundary conditions, conserves the total fluid volume. Some comparisons are given on a sample test problem.

Ua66/16/2 Ogden Instructional Computing Newsletter, Vol. 1, No. 1, Wku Mathematics & Computer Science

WKU Archives Records

Newsletter created to promote the Ogden College Computer Laboratory. This issue is a review of some projects, courses, hardware and software available from the computer lab.

Existence/Uniqueness And Validation Of Parameter Imbedding Equations For Nonlinear Fredholm Integral Equations, M. E. Lord

Mathematics Technical Papers

A parameter imbedding method for nonlinear Fredholm integral equations produces a Cauchy system involving the solution of the integral equation and an associated resolvent kernel. For such Cauchy systems sufficient conditions are given to guarantee local existence and uniqueness of solutions. A Picard type theorem utilizing a Lipschitz condition is obtained. This result then yields the validation of the Cauchy system.

On Identifiability Of Impulse-Response In Compartmental Systems, Jerome Eisenfeld

Mathematics Technical Papers

Structural identifiability in compartmental systems deals with the map from impulse-response parameters to model parameters. If the data is analyzed in terms of integral transforms sk (Fourier, moments, etc) then we may study also the map from the sk to impulse-response parameters. This paper is mainly concerned with the latter correspondence. In other words we discuss the possibility of removing (inadvertently or intentionally) decay terms in the process of forming integral transforms.

Study Of Indian Nuptiality., Chitta R. Malaker Dr.

Doctoral Theses

DEFINITION OF NUPTIALITYAccordi ng to the latest International Demographic Terminelogy (Grebeni k and ill, 1974), t he term 'nuptiality' is used to denote the whole subject of the formation and dissolutien of sexual uni ons, includi ng the study of marriage, consensual uni ons, separation, di vorce, widowhood etc. It is also used, in a narrower sense, as a synonym for marriage in such terms as nuptiality rates;and nuptiality probabilities, The study of nuptiality deals with the frequency of marriage, 1.e., unions between persons of opposite sexes which involve rights and obligations fixed by law and custom; with the characteriatics …

Theory Of Estimation In Algebraic And Analytic Exponential Families With Applications To Variance Components Models., Krishnan Unni Dr.

Doctoral Theses

There are many important statistical problems of the following kind. The family of probability measures O is parametrized by a vector parame ter n varying in a q-dimen- sional domain. P can be represented as an exponential family of probability distributions with k canonical para- me ters where k is greater than q. The canonical parameters do not vary in a domain in R, but are restricted by polyno- mial or analytic equations. They vary on a curved surface defined by the polynomial or analytic equations within the natural parame ter space of the exponential family. The present work is …

Price Rigidities, Rationing Schemes And Economic Efficiency., P. R. Nayak Dr.

Doctoral Theses

The prime concem of economist: traditionally has been the system of markets and their role in rasource allocat on. Walrasian equilibrium theory, which is believed to províde an ajequate framework for resource allocation through markets, has been extensively analysed in the recent past. At the sane time, it has been realined, mainly throunh Keynesian influence, that the market machanism is prone to failures, DOwnward Inflezibility of wages is an obvious example of this. It is further possi that a central authority concerned with improving general welfare may tamper vith the market mechanism or do away with it altoer.Thered ar three …

Choice Of Strategies In Survey Sampling., Geetha Ramachandran Dr.

Doctoral Theses

The main problam of sampling from finite populations consi sts of devi sing an appropriate proceduro for sel ecting a sample from a given population and developing an appropriate procedure for estimating the population parameter of interest in order to maximize the precision of the estimator subject to certain restrictions on the cost for the survey or alternatively minimi ze the cost for achieving a given l evel of precision. During the thirties and forties several contributions were made to develop the theoretical background of sample survey techni ques in order to solve this problem, The most significant works of …

Methodology For Testing Homogeneity Of Variances, Danny D. Dyer, Jerome P. Keating

Mathematics Technical Papers

Suppose random samples are drawn from each of n populations with unknown means and variances. Developing procedures to test the claim that the population variances are equal (homogeneity of variances) has frequently been a goal for statisticians. One widely used technique is due to Bartlett (1937) and is based on a slight modification of the generalized Neyman-Pearson likelihood ratio test. It is well known, however, that Bartlett's test is highly sensitive to the assumption that the underlying populations are normal (Box, 1953). If nonnormality is present, the use of Bartlett's test can often lead to the rejection of the claim …

Newtruck: A Comprehensive Long-Term Project In Computer Science, Daniel C. St. Clair

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

On The Existence Of Good Markov Strategies, Theodore P. Hill

Research Scholars in Residence

In contrast to the known fact that there are gambling problems based on a finite state space for which no stationary family of strategies is at all good, in every such problem there always exist ε-optimal Markov families (in which the strategy depends only on the current state and time) and also ε-optimal tracking families (in which the strategy depends only on the current state and the number of times that state has been previously visited). More generally, this result holds for all finite state gambling problems with a payoff which is shift and permutation invariant.

The Great Pretender, Richard C. Heyser

Unpublished Writings

This document contains drafts of Richard C. Heyser's article, which he intended to publish in AUIDO magazine. Heyser chronicles the history and perceptions of Group Delay, which he calls "The Great Pretender."

A Study Of Vertical And Horizontal Visibility Relationships Under Water, Jean J. Mccarthy

Journal of the Minnesota Academy of Science

A threefold study was undertaken to:

1) determine the nature of the mathematical relationship between vertical and horizontal visibility underwater

2) examine the feasibility of using the Secchi disc method to measure horizontal visibility in the photic zone;

3) obtain descriptive data on vertical and horizontal visibility in selected lakes of southern Minnesota.

The Secchi disc technique for measuring· visibility was modified to accommodate horizontal readings, and data were col1lected from 12 lakes at 5, 15 and 25 feet depths under controlled conditions. Reliability correlations were significant (p ( .01) and ranged from .764 to .994. Correlations and regression equations …