Mathematics Commons^™

Extensions Of The Theory Of Positive Operators And Their Relationship To Minimax Games., T. E.S. Raghavan Dr.

Doctoral Theses

The theory of positive matrices (matrioco with non- negative entries) nnd the the ory of positive operetors are used extensively in the study of vibrationa of mechanical eysteme l16], stochaatic proceuses (36] nd mathematical economics ((9] and L20].) It is well known from the claseical theoreme of Perron and Frobenius ((13), [14) and (25] that any non-eingul ar squere matrix with non-negative entries has a positive cigenvalue which ts maximal in modulus among al1 the eigenvalues of the matrix. Further for this positive eigenvalue, it has a non-null eigenvector with all components non-negative. If the matrix is also irroduc lble11) …

Solutions Of Some Balanced Doubly Balanced And Partially Balanced Statistical Designs., Chilakamarri Ramanujacharyulu Dr.

Doctoral Theses

The theory and methods of con struction of statistical designs have connections with Modern algebraic systems, theory of numbers, arithmetic theory of quadratic forms, information theory and construction of codes. The properties of finite linear spaces have been used for the construction of (i) complete set of mutually orthogonal latin squares (Bose and Nair, 1941) (ii) balanced incomplete block designs (Bose 1939) (iii) partially balanced incomplete block designs (Bose and Nair 1939) (iv) designs where some effects of treatments are confounded (Bose, 1947). Primrose (1951) studied quadric surfaces and used them in the construction of balanced incomplete block designs. Roychoudhuri …

External Graph Theoretic Problems With Applications To Communication Networks., Ramachandra Muthy Dr.

Doctoral Theses

Graphs havre now become recognized models for a wide variety of situations. Whenever we have a collection of è´¸bjects with a binary relation defined on them graphs serve as excellopt toola to study the combinatoria properties of the collection with respect to the binary relation. D. Konig was the firat person to recognize the usefulness of graph theoretic modols. He conceived of a unified study of grapha under an abstract set up. His book was a pioneering work in this field.The graph theoretic problems embodied in this thesis have been motivated, by situations arising in communicationhave been motivated, by situations …

Contributions To Stratified Sampling And Some Related Problems., V. K. Sethi Dr.

Doctoral Theses

In this thesis I have presented some of my results on problems connected with stratified sampling. Most of the results have already been published in various journals or have been submitted for publication. The thesis includes some extension of the published results and a much greater amount of evidence to support some conjectures than could be accomodated in papers submitted to journals.A major portion of the thesis in contained in Part I. This part deals with the problem of optimum stratification and the use of simple rules to approximate optimum stratification. In this thesis attention has been confined to Normal …

Convolution Properties Of Distributions On Topological Groups., S. R. S. Varadhan Dr.

Doctoral Theses

The collection of probability distributions on the real line which is a semigroup under the convolution operation and topological space under weak convergence has attracted, during the last quarter of a century, the attention of such great mathematicians as Khintchine, Kolmogorov, Bawly, Levy and others. Their results constitute a deep analysis of the factorization problems on the one hand and the asymptotic behavior of infinite convolutions on the other. However, a complete and systematic investigation of these problems is not available in considerable generality. The aim of the present thesis is to investigate the topological and algebraic properties and the …

Distribution Theory Of Some Classification Statistics., S. John Dr.

Doctoral Theses

This thesis eives the distri bution theory of four clae aifioation statistics. Sone parta of it were published a few years ago. The relevant publicationa are listed nt the end.What the author knows of related work by other authors is set out in the Introductions little material of this nature is given elsewhere in the theats. If a result is not explicitly credited to another author, it may be taken to nean that the author believes it to be hia worik.It will be noticed that three (U, R and 2) of the four statistics receive less a pace than the …

Some Problems Of Estimation In Sampling From Finite Populations., M. Murthy Dr.

Doctoral Theses

In this thesis the results of the research work done by the author in the field of sample surveys are presented. Scheme problems of estimation in sampling from finite populations were taken up for reset arch. A brief summary of this thesis is given below.In chapter 1, the author has developed a generalized theory of getting unbiased estimator for a certain class of parameters in sampling from finite population. The class of parameters considered are those which can be expressed as the sum of single-valued set functions defined over a class of sets of units belonging to a finite population. …

Some Contributions To The Theory Of Sampling., Pramod Kumar Pathak Dr.

Doctoral Theses

The work Presented here had originated from a pioneering paper by Basu1 and is essentially an extension of his ideas to different problem in sample surveys. The whole word mainly consists in deriving estimators uniformly better than those usually adopted in with replacement schemes.in with replacement sampling schemes, the 'order-statistic' (distinct sample unite arranged in an ascending order of their unit-indices) forms a sufficient statistic. Therefore, if any estimator (e.g., say of the population man) does not depend on the 'order-statistic', it can be uniformly improved by the use of the Rao-blalckwell theorem. The author has not hesitated to use …

A Compilation Of Published Research In Elementary Arithmetic Since 1931, Alfred C. Birdsell

Master's Theses or Doctor of Nursing Practice

Many articles are published each year pertaining to elementary arithmetic. Some of these may very properly be designated "mere opinion” while others may very properly be classified as "research". Because of the large number of such articles appearing in print pertaining to some aspect of arithmetic, no doubt a service may be rendered to teachers of the subject by evaluating and classifying them as research or otherwise. From this situation grew the problem of this thesis, the title of which may be stated as follows: A Compilation of Published Research in Elementary Arithmetic Since 1931. Such a guide should be …

Fourier Series And Some Applications, Lawrence D. Marcotte

Master's Theses or Doctor of Nursing Practice

The object of the author in writing this thesis was to make a compilation of material necessary to work certain problems in mathematical physics with one use of Fourier series. Although whole books have been written on different aspects of this thesis, all had some intervening material which was too advanced for the average student. Any students interested in mathematics or physics cannot fail to see the importance of Fourier series. To mention a few applications, the series is used in finding the solution to various problems in heat distribution, electrical transmission, and aircraft construction.

An Analytic Study Of Eight-Grade Pupil Performance As Revealed Through The Stanford Achievement Test In Arithmetic, Dominic J. Brungardt

Master's Theses or Doctor of Nursing Practice

The immediate purpose of the study were: (a) to determine how closely the grade equivalents of two-hundred and sixty pupils follow the normal curve ; (b) to plot the results of the one-step problems on a graph with an analytic explanation of the graph ; (c) to place the results of the two-step problems on a graph with an analytic explanation of the graph; to determine what types of error were most prevalent; to discover apparent causes of error ; (d) to make suggestions helpful to teachers for improving pupil achievement.

A Study Of Retention Of Percentage, Fred Dellett

Master's Theses or Doctor of Nursing Practice

The problem of this thesis was to determine by means of a test the retention of the fundamentals of percentage as shown by beginning eighth grade pupils, who were taught percentage the previous year in the seventh grade. The fundamentals of percentage are here considered as the changing of percents to decimal fractions or common fractions, the reverse procedures, and the three types of problems arising from the relation, base times rate equals part. These quantities, base, rate, and part, are represented in the example, 300 X 12% = 36, respectively. Because of the inherent relationship of decimal fractions and …

The Segregation Of Real Roots Of Lower Orders, Ross W. Bland

Master's Theses or Doctor of Nursing Practice

The purpose of this thesis is the presentation of the better algebraic methods of the segregation of real roots of equations of lower orders and a brief historical sketch of the advance made in the development of algebra. Mention is also made of a few of the men who have made notable contributions to this field of mathematics and the time, as nearly as it is possible to determine it, when new ideas were discovered.

Linearity In Factor Analysis, Opal Emmons

Master's Theses or Doctor of Nursing Practice

The uniqueness of mathematics in that it is a science complete in itself makes it possible to apply mathematical tools to sciences which, in themselves vary widely in content. There is, however, a particular difficulty which must be surmounted. A given mathematical procedure may be valid in the science of mathematics but invalid in another science, such as psychology. The reason for this is that sometimes there is a discrepancy between the implicit assumptions in the field of mathematics and those implicit in the field of application. The purpose of this investigation is twofold: (1) To point out that linearity …

Asymptotic Series, Bernard Martin

Master's Theses or Doctor of Nursing Practice

The purpose of this thesis is to follow the development of the asymptotic series from the beginning made by Euler, in his solution of problems, to the modern applications of asymptotic series, also to present a definition and an analysis of asymptotic series, explain some different theories of their use, and show the ways in which they find common usage. The use of asymptotic series is a comparative new development in the field of applied mathematics. The divergent series were not used as a method of calculation until Euler showed that they gave close approximations in the solution of problems. …

Methods Of Obtaining Asymptotes, Paul Sweetland

Master's Theses or Doctor of Nursing Practice

The purpose of this thesis is to present in logical order the more important methods of obtaining asymptotes. In several cases where two or more different methods for obtaining the same type of asymptotes were found the simpler method is given first and then the more difficult method. Most of the simpler methods are based on Analytic Geometry, while the more difficult are based on the Calculus.

A Dictionary Of Mathematical Terms For High School Students, Matilda O. Iverson

University of the Pacific Theses and Dissertations

In compiling and writing this dictionary the needs of the high school student and teacher interested in mathematics have been kept constantly in mind. The mathematics of the high school is perhaps the simplest of its kind and yet very few textbooks carefully define all technical terms as they are introduced. The thoughtful student may turn to an abridged or unabridged dictionary but will find in most cases that the definitions of the terms are vague, often misleading, and in some cases not given.

The words in the vocabulary have been arranged in alphabetical order so that the reference to …

Development Of Geometry And Its Assistance In Promoting Society, Nelson Jean

Electronic Theses and Dissertations

No abstract provided.

The Construction Of Conic Sections By Means Of Pascal's And Brianchon's Theorems, Benjamin Lee Welker Jr.

University of the Pacific Theses and Dissertations

The discovery of conic sections was made by Menaechmus (375-325 B.C.) an associate of Plato and a pupil of Eudoxus. This discovery, in the course of only a century, raised geometry to the loftiest height which it was destined to reach during antiquity.

History Of Applied Geometry, Evelyn Jackson

Electronic Theses and Dissertations

Mathematics: Just what does the word mean to us? After a moment of thought many different meanings may present themselves to our minds. At first we are inclined to say that the word mathematics covers a vast field. We are justified in so thinking because mathematics embraces a wide scope of study. Were we to say that it is a science we should place it in its proper genius, for it is truly a science of numbers and space. However, could not the science be the art of calculation or the art of computation?

History Of Applied Geometry, Evelyn Jackson

Electronic Theses and Dissertations

No abstract provided.

The Utility Of Mathematics, Jack R. Dunn

Electronic Theses and Dissertations

No abstract provided.

Inversion Applied To The Common Equations Of The Conic Sections, Edna Maria Cargill

Student and Lippitt Prize Essays

A solution of applying inversion to the mathematic equation of conic sections, beginning with a definition of inversion and statement of the problem.

Some Contributions Of Pure Math To Science, Herbert B.E. Case

Student and Lippitt Prize Essays

An examination of the connection between math and science through discoveries in the subjects of astronomy, mechanics, physics and chemistry.

The Voice Of The Phi Sigma -- 1881 -- Volume 03, No. 15, Phi Sigma

The Voice of the Phi Sigma

This item is part of the Phi Sigma collection at the College Archives & Special Collections department of Columbia College Chicago. Contact [email protected] for more information and to view the collection.