Physical Sciences and Mathematics Commons^™

Determining A Fair Border, Theodore P. Hill

Research Scholars in Residence

In a general class of measure-partitioning or fair-division problems, the extremal case occurs when the measures are proportional. Applications are given to classical and recent fair-division problems, and to statistical decision theory.

Pressure Method For The Numerical Solution Of Transient, Compressible Fluid Flown, Donald Greenspan, Vincenzo Casulli

Mathematics Technical Papers

In this paper the pressure method for incompressible fluid flow simulation is extended and applied to the numerical simulation of compressible fluid flow. The governing equations, obtained from the physical principles of conservation of momentum, mass and energy, are first studied from a characteristic point of view. Then they are discretized with a semi-implicit finite difference technique in such a fashion that the Courant stability condition on the time step is not required. The resulting algorithm is fast, accurate and applies to problems with arbitrarily large speed of sound. As an example, the computer simulation of the von Kármán vortex …

Volterra Integral Equations In Abstract Cones And Monotone Iterative Technique, G. R. Shendge

Mathematics Technical Papers

The objective of this paper is to develop monotone technique for obtaining extremal solutions of Volterra integral equations in abstract Banach spaces via coupled lower and upper quasi-solutions. To generate the iterates, different schemes are given which would be of special interest from computational point of view.

Derivation And Test Of Predictions Of A Discrete Latent State Model For Signed Number Addition Test Performance, Kentaro Yamamoto

Dissertations and Theses

This study is an investigation of the performance of a discrete latent state model devised by Paulson (1982) to account for signed-number arithmetic test data gathered by Birenbaum and Tatsuoka (1980). One hundred twenty nine students took a test which consists of sixteen item types with four parallel arithmetic items of each type. The present study utilizes the five addition item types of four items each; hence, there are four parallel subtests. Responses to the addition items can be analyzed in terms of two components: the sign component (is the sign correct?), and the absolute value component (is the size …

Scs 79: The Lower Topology For Continuous Lattices Is A Monadic Functor, Oswald Wyler

Seminar on Continuity in Semilattices

No abstract provided.

On The Generators Of The First Homology With Compact Supports Of The Weierstrass Family In Characteristic Zero, Goro Kato

Mathematics

No abstract provided.

Stop Rule Inequalities For Uniformly Bounded Sequences Of Random Variables, Theodore P. Hill, Robert P. Kertz

Research Scholars in Residence

If X₀, X₁, ... is an arbitrarily-dependent sequence of random variables taking values in [0,1] and if V( X₀, X₁, ...) is the supremum, over stop rules t, of EX_f, then the set of ordered pairs {(x , y): x = V( X₀, X₁, ..., X_n and y = E(max_{jXj for some X0, ... , Xn} is precisely the set Cn = {(x, y): x < y < x(1 + n …}

A Stronger Form Of The Borel-Cantelli Lemma, Theodore P. Hill

Research Scholars in Residence

No abstract provided.

Monotone Method For Boundary Value Problems Describing Periodic Transport Processes, G. R. Shendge

Mathematics Technical Papers

One of the powerful methods of proving the existence of extremal solutions of initial and boundary value problems is the monotone iterative technique [1-4,6,7]. This has recently been applied [5] to a rather special type of boundary value problem [see pdf for notation] because, particular cases of (*) represent equations arising in the transport process of different types of particles moving in opposite directions, which are subjected to certain fluxes [8]. However (*) does not include situations in which the initial and final fluxes in a certain direction coincide. To cover this situation one needs to study a typical periodic …

Conserving Numerical Methods For X = F(X), Donald Greenspan

Mathematics Technical Papers

Physics is characterized by conservation laws and by symmetry [1]. Unfortunately, the application of numerical methodology in approximating solutions of initial value problems usually does not preserve either of these invariants. In this sense, the use of a computer destroys the physics of a dynamical model. We will show here how to conserve total energy when solving the nonlinear initial value problem [see pdf for notation] on a computer. Moreover, the energy conserved will be exactly that of (1.1), not a new "energy" which is defined by the numerical method (see, e.g., Langdon [5]). Two distinctly different methods will be …

Contributions To The Study Of Bayes Estimates: The Maximum Likelihood Estimate And Rao's Test., S. N. Joshi Dr.

Doctoral Theses

This the sis consists of two parts. In part I we have investigated problems concerning Bayes estimates, especially ex pansion of the integrated risk of the Bayes estinate (also referred to as the Bayes risk or the integrated Bayes risk), approximation of the Bayes estimate and expansion of the posterior distribution. In part II we have introduc ed a new opimun property for estimates and have concluded that the maximum likelihood estimate (m.1.e.) enjoys this property ; in this part we have also investigated what is known as Raos conjecture which saya that the test based on the score function …

An Interview With Albert W. Tucker, Stephen B. Maurer, A. W. Tucker

Mathematics & Statistics Faculty Works

The mathematical career of Albert W. Tucker, Professor Emeritus at Princeton University, spans more than 50 years. Best known today for his work in mathematical programming and the theory of games (e.g., the Kuhn-Tucker theorem, Tucker tableaux, and the Prisoner's Dilemma), he was also in his earlier years prominent in topology. Outstanding teacher, administrator and leader, he has been President of the MAA, Chairman of the Princeton Mathematics Department, and course instructor, thesis advisor or general mentor to scores of active mathematicians. He is also known for his views on mathematics education and the proper interplay between teaching and research. …

Existence Of Coupled Quasi-Solutions Of Systems Of Nonlinear Elliptic Boundart Value Problems, V. Lakshmikantham, G. S. Ladde, A. S. Vatsala

Mathematics Technical Papers

Systems of nonlinear elliptic boundary value problems arise in many applications such as multiple chemical reactions that take place in an isothermal or nonisothermal catalyst pellet and simple models of tubular chemical reactors [7,8,9]. Moreover, such problems also occur in a natural way as auxiliary problems in stability analysis of steady states of dynamic systems governed by reaction-diffusion systems. Constructive methods of proving existence results of such boundary value problems, which can also provide numerical procedures for the computation of solutions, are of greater value than theoretical existence results. The method of upper and lower solutions coupled with monotone iterative …

Mathematics: The Loss Of Certainty, Calvin Jongsma

ACMS Conference Proceedings 1983

Morris Kline was a contentious mathematician and author, documenting (as he saw it) both the deficiencies of mid-twentieth-century reformist trends in mathematics education and formalist views of the foundations (and practice) of mathematics. This brief introduction to a discussion of Kline's 1980 book and its mixed reception by the mathematics community provides a context for assessing his ideas as part of his overall views on the nature of mathematics.

Arrogance And Humility In The Philosophy Of Mathematics, James Murdock

ACMS Conference Proceedings 1983

This paper explores the philosophical, sociological, and theological questions related to the field of mathematics and whether or not it is ethical to pursue when its discoveries are used for evil.

The Activitiy And Application Of Mathematics, R. S. D. Thomas

ACMS Conference Proceedings 1983

There are four so-called philosophies of mathematics that I regard as totally discredited, formalism, intuitionism, logicism, and Platonism. It is a common feature of the ism philosophies of mathematics that they do not take the application of mathematics very seriously. This paper examines a view of mathematics that takes applications seriously.

Using Mathematical Concepts To Illustrate Scriptural And Spiritual Ideas, Robert Brabenec

ACMS Conference Proceedings 1983

Christian mathematics faculty and students respond in differing ways to this idea of applying mathematics to Scripture, and vice-versa. Mathematics is man-made, while Scripture is inspired by God, so they should be disjoint entities. However, it is well known that the Scripture used analogies of familiar human objects and ideas in order to explain spiritual ideas. This paper discusses various mathematical concepts and how they illustrate Scriptural and spiritual ideas.

A Comparative Study Of Christian Mathematical Realism And Its Humanistic Alternatives, Paul Zwier

ACMS Conference Proceedings 1983

This paper explores what sort of stance a Christian should have on important mathematical questions such as realism.

Introduction (1983), Robert Brabenec

ACMS Conference Proceedings 1983

No abstract provided.

Table Of Contents (1983), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1983

A Fourth Conference on Mathematics from a Christian Perspective

Edited by Robert L. Brabenec, Wheaton College

The Advantage Of Using Non-Measurable Stop Rules, Theodore P. Hill, Victor C. Prestien

Research Scholars in Residence

Comparisons are made between the expected returns using measurable and non-measurable stop rules in discrete-time stopping problems. In the independent case, a natural sufficient condition ("preservation of independence") is found for the expected return of every bounded non-measurable stopping function to be equal to that of a measurable one, and for that of every unbounded non-measurable stopping function to be arbitrarily close to that of a measurable one. For non-negative and for uniformly-bounded independent random variables, universal sharp bounds are found for the advantage of using non-measurable stopping functions over using measurable ones. Partial results for the dependent case are …

A Study Of Robustness Of Preliminary Tests In Conditionally Specified Regression Models, Chien-Pai Han

Mathematics Technical Papers

The selection of variables in regression analysis is usually done by using preliminary tests. When it is doubtful whether the regression coefficients of a set of variables are equal to zero or not, one may use a significance test. When the test rejects the null hypothesis, the set of variables is retained in the model otherwise the set is deleted from the model. The preliminary test is usually an F test based on normal theory. This paper examines the robustness of the preliminary test in model selection by a Monte Carlo study.

Microcomputer Algorithms For Prime Number Testing, Susan Dale Barton

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper gives a survey of different methods of prime number testing. Emphasis has been given to algorithms based upon Fermat's Theorem: if p is an odd prime number, then p divides a^p-a. All of the computer programs described in this paper have been written for use on microcomputers and so the feasibility of using microcomputers is also discussed. Finally, numbers of various forms have been considered for primality with special attention given to Mersenne and Fermat numbers. It is hoped that some of the information contained in this paper may provide worthwhile enrichment ideas for mathematics educators.

Cluster Analysis For Acid Rain Data In Norway, Ali Ghafourian

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper gives a description of three well known clustering methods, and discusses the advantages and disadvantages of each. Then, the results of these three clustering methods are compared through examining them on a specific set of data.

Greedy And Optimal Paths In A Weighted Graph Without Circuits And Applications To A Class Of Optimization Problems On Finite Posets, Irinel C. Dragan

Mathematics Technical Papers

In several recent papers B. Korte and L. Lovasz considered a mathematical structure called a simple language on which a greedy algorithm can operate (see [31,J41, OD. The concept of greedoid has been defined by relaxing an axiom and strengthening an other axiom from the definition of the matroid. Under some constraints imposed to the objective function of a combinatorial optimization problem on a greedoid, the greedy algorithm provides an efficient method for solving the problem. An algorithmic characterization of the greedoids, similar to that of the matroids, was further searched. The effort has been justified-by several examples of combinatorial …

An Information Theoretic Approach To Incorporating Prior Information In Binomial Sampling, Paul Chiou, Danny D. Dyer

Mathematics Technical Papers

The incorporation of prior information about [see pdf for notation], where [see pdf for notation] is the success probability in a binomial sampling model, is an essential feature of Bayesian statistics. Methodology based on information theoretic concepts is introduced which (a) quantifies the amount of information provided by the sample data relative to that provided by the prior distribution and (b) allows for a ranking of prior distributions with respect to conservativeness, where conservatism refers to restraint of extraneous information about [see pdf for notation] which is embedded in any prior distribution. In effect,, the most conservative prior distribution from …

Newsletter, Moorhead State University, Mathematics Department, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Who Gave You The Epsilon? The Origins Of Cauchy's Rigorous Calculus, Judith V. Grabiner

Pitzer Faculty Publications and Research

This paper recounts the history of how calculus came to get a rigorous basis in terms of the algebra of inequalities. The result is a brief history of the 150 years from Newton and Leibniz to Cauchy that produced the foundations of analysis.

Some Unusual Locus Problems, Stephen B. Maurer , '67

Mathematics & Statistics Faculty Works

No abstract provided.

Study Of The Robustness Of Inference Procedures In Linear Models With Specification Errors., Thomas Mathew Dr.

Doctoral Theses

We consid er the poneral lingar nodel Y = X v e, here Y io an nx1 rundor voctor taking valacs in 2, x is an nXu ratrix (the deni gn ratrix), ip an 1X1 vectur uf unknown partro tere varying in R and 1s an nx1 voctor of errors with E(e) = 0 and E(ee') - o2v,o2 boing a positive scalar (known or unknown) and is an nXn non-negative definite Ta trix. It in assurmod that n < n. Such a nodel (also known as the Gauss-Markov nodel) is usually denoted by (Y, Xβ,α2v). he defini tions ot un catinable lincar paranctric function, sinple least squires estimator (SLSE), best linear unbia sed estinator (BLUE), linsar ninir:un bias cstinator (IIMBE) and best Iinear nininum bias estinator (BIIMBE) under the nodel (Y, Xβ,α2v arc we 11. known and we retor to Rao and Mitra (1971, Chaptere 7 and B) for the details.Early contributions towärde estinating linear functionals of β are due to Logenire (i806), Gauss (1609) and Varkov (1912), where attention was concentrated on the case where R(X)= n and V = I, the identity natrix. Aitken (1934) considercd the problen of bost lincar unbianed catiration under the setup vhere R(x) = n and V is any positive definite natrix. Bose (1944) conside the casc where R(X) < n and V = 1, while Rao (1945) genera d this to any positive defini te V. Seal (1967) ives a good histo- rical account of the linear model upto 1935 and Plackott (194 9) givus a shorl histurical nute un the raothori uf Jount aquarce. WEE the covariance atixv is nunaingnlar ilh v is nunainglar . la V known und tiho nXn 15 Lrix X is of tnll ruk, i.c. o? runit n and when fur thor the culca ut the ratri are li orthonor- Lial igenvectcre ut v, tun it is at yasil wririahle fact that ie icontical1 ita its S13. his ract was first pointed aut by Andernon (1948) and nutice of it was lakon soon af ter by Durbir und watecn (1950). Fro thin tire cnards, the problen of deriving necessary and sufficient conditions under which the SISE't are e also corresponiing ELUE a hae received con- siderable attontion, mainly due to the norputationl advantage of the S1.SR over the ILUE. The present work is devoted to the study of the robuatness of cstiration and testiag: prucordarcs in linar codels with in- correct desim und dispersion aaa brices. Betore giving a surary of the probleris considUred we shull prosent a brief rovicw of th 1iterature in this area.A atatonant on vorious noceary anl nfricient ountitionn for the equalily of tha iaa aid correapotsiin BIJRse de by Zyakind (1962) On: of the cunlatiuna ota tod huru 1a that thore exista a nahuut of r udiponveetoro of V that forma banio uf the vector spucu spied by tho colunna of the design ratrix X. A proot thut the cáguvuotur ounition is both neoessary and auf- firient for the correapuiliny HTE arsl SLSE to huve the ae cuvarianeu natri: du oresoutua vdth X n all at ai 7 aonningular hy Ma, maa ant aGuáro (1962).