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On Strategies Of Sampling Finite Populations In One And Two Phases., Arun Kumar Adhikary Dr.

Doctoral Theses

This thesis is being submitted to the Indi an Statibtical Institute (ISI) in fulfilment of the primary requirements for the award of the degree of Doctor of Philosophy in Statistics.No part of this theais was submitted to any other Inatitute for any degree, diploma, certifioate etc.In this thesis we have mainly presented results of our investigation on optimal strategles for surveying finite populations in two phanes using selection procedures with varying probabilities. Incidentally we have added a few more resulta to the available literature on uni-phase sampling as are conaidered important in formulating appropriate doutbe sampling plans. Optimal and pragnatically …

Optimal Block Designs In One And Multi-Way Settings., Sunanda Bagchi Dr.

Doctoral Theses

The study of optimality of block designs formally began with wald (1943) proving a very important optimality property, designated as D-optimality of Iatin Square. Desi gns in a given physical set up. Next Ehrenfield (1955) proved the E-optimality property of Latin Square Designs. Since then, the work in: the area has primarily consisted in evolving a number of useful opti- mality oriteria for oomparing block design in a reasonable set up given and oharacterizing and/or constructing desi gns saiisfying the so called optimality criteria developed. But it was not until 1958, when the theory was given a proper and precise …

The Changing Concept Of Change: The Derivative From Fermat To Weierstrass, Judith V. Grabiner

Pitzer Faculty Publications and Research

Historically speaking, there were four steps in the development of today's concept of the derivative, which I list here in chronological order. The derivative was first used; it was then discovered; it was then explored and developed; and it was finally defined. That is, examples of what we now recognize as derivatives first were used on an ad hoc basis in solving particular problems; then the general concept lying behind them these uses was identified (as part of the invention of calculus); then many properties of the derivative were explained and developed in applications both to …

Erratum To "Ideals And Centralizing Mappings In Prime Rings", Joseph H. Mayne

Mathematics and Statistics: Faculty Publications and Other Works

No abstract provided.

Scs 80: Compact Ordered Spaces And Prime Wallman Compactifications: Summary Of Results, Oswald Wyler

Seminar on Continuity in Semilattices

Source: University archive of the Technische Universität Darmstadt.

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

Mathematics Technical Papers - Archive

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 - Archive

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.

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.

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.

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

Mathematics Technical Papers - Archive

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 - Archive

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 …

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

Research Scholars in Residence

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 …}

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 …

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

Mathematics Technical Papers - Archive

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 …

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. …

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.

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.

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.

An Outline Of A Complementarist Philosophy Of The Sciences, With A Special Reference To Mathematics, Willem Kuyk

ACMS Conference Proceedings 1983

No abstract provided.

A Neuropsychodynamical Theory Of Mathematics Learning, Willem Kuyk

ACMS Conference Proceedings 1983

No abstract provided.

One Possible Outline For A First Undergraduate Course In Philosophy Of Mathematics, Harold Heie

ACMS Conference Proceedings 1983

No abstract provided.

The Role Of Creativity In Mathematics, John M. Dubbey

ACMS Conference Proceedings 1983

No abstract provided.

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.

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

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

Mathematics Technical Papers - Archive

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.