Physical Sciences and Mathematics Commons^™

Beta And Gamma Distributions, Calvin Rogers

Mathematics & Statistics ETDs

The purpose of this paper is to exhibit the main properties of Gamma and Beta distributions and show their relation to certain well known distributions.

In chapter II the Gamma and Beta distributions are defined in terms of Gamma and Beta functions. The moments of these distributions are calculated, and the moment generating function and cumulant generating function for the Gamma distribution are obtained. The curves are classified with respect to parameter values and the curves are graphically illustrated in Figures 1, 2, and 3. The exponential distribution, as a special case of interest, is shown to be a Gamma …

The Use Of Kamke's Transformation In Approximating The Zeros Of Orthogonal Polynomials, Robert L. Daniels

Mathematics & Statistics ETDs

The importance of the classical orthogonal polynomials has long been acknowledged. It has not been possible, however, to represent them in such a way that all of their important properties are immediately evident. In particular, the location of the zeros of these polynomials is of considerable interest.

This thesis is primarily concerned with a different technique in which Kamke's transformation is applied to the differential equations frequently used to define these polynomials. The resulting trigonometric differential equations cannot be explicitly solved either, but certain characteristics of these solutions facilitate the derivation of approximations to the zeroes of the solutions.

Diagnostic Abdominal Aspiration In Acute Abdominal Conditions, George Quan Lee

Loma Linda University Electronic Theses, Dissertations & Projects

[Abstract Not Included]

Stapes Ankylosis And Its Mobilization, Emery I. Pick

Loma Linda University Electronic Theses, Dissertations & Projects

[Abstract Not Included - Preface Included Here]

Otosclerosis is a frequent affliction resulting in progressive hearing loss. With the advance of ear surgery during the past 25 years various procedures have been proposed for the correction of this condition. Among their number surgical mobilization of the stapes has assumed considerable importance. In this paper, which is presented as a thesis to fulfill the requirements for the degree of Master of Science, the operation will be discussed on the basis of the literature and the author's own experiences with the procedure.

A Statistical Review Of 436 Submucous Resections With Post-Operative Results Of 338 Cases, D. Wilson Hales

Loma Linda University Electronic Theses, Dissertations & Projects

[Abstract Not Included]

The Variation Problems Of Weierstrass-Bliss And Radon, Douglas M. Gragg

Mathematics & Statistics ETDs

Problems of the Calculus of Variations are generalizations of the familiar minimum problems treated in the differential calculus. The relationships between the ordinary minimum problems of the calculus and the generalizations dealt with in the Calculus of Variations is possibly best seen by examining the general Hilbert-Moore minimum problem, and the special examples of such problems formulated in the table below.

Inverse Problems Of Hamel-Type., Robert G. Schrandt

Mathematics & Statistics ETDs

The formulation and discussion of the simplest (fixed) end point direct problem of the calculus of Variation is a necessary preliminary to attack on the inverse problems considered in Chapters II and III of this thesis. Since the plane problem is already comprehensively treated in the literature, only enough of its theory is developed here to render intelligible to the reader the inverse problems studied in the sequel.

The Darboux Inverse Problem In The Calculus Of Variations, Frank O. Lane

Mathematics & Statistics ETDs

The simplest non-parametric problem of the calculus of variation, the so-called direct problem of the plane, is the problem of finding that arc C_o of a family of admissible arcs y=y (x) joining two fixed pointed (x₁ , y₁ ), (x_1, y₂) in the x,y-plane such that along the C_o the integral takes on a minimum value.

An Investigation Of The Meaning Of Α3 As A Measure Of Skewness, John W. Coy

Mathematics & Statistics ETDs

The purpose of this study is the interpretation of α₃ by means of a relatively simple formula which will predict the amount of shift in the effective limits of the Type III curve for a given change in the skewness. The methods used are chiefly empirical.

An Investigation Of The Nature Of The Coefficients Of Entire Function, Marie Ann Philips

Mathematics & Statistics ETDs

The purpose of this study is to investigate the nature of the coefficients of certain power series. In particular, it is desired to know what characteristics the coefficients must possess in order that the series shall represent an entire function.

Studies Arising From A Problem In The Calculus Of Variations, John Gonzalez

Mathematics & Statistics ETDs

In mathematics, generalization is progress; so much so that oftentimes one loses sight of the fact that generalization is the result of arduous work in the consideration of the particular. In no other branch of mathematics is this better exemplified than in the Calculus of Variations. The beginning of a systematic development of the theory of the Calculus of Variations really started with the two Bernoulli brothers (1654-1748) in their discussion of the brachistochrone problem in 1696. The method devised by them were sufficiently powerful in the attack of a large number of problems. Euler (1707-85) further elaborated the geometrical …

Interpolation For The Median In A Frequency Distribution, Paul Cox

Mathematics & Statistics ETDs

It is the purpose of this study to discuss completely the median of a frequency distribution: first, by showing clearly what a median is; second, by showing the present and possible future applications for the median in the field of mathematical statistics; third, by taking all methods for interpolating for the median which have been advocated in the literature, or which may not have been advocated to date but appear plausible, and discuss these methods as to the way they are used, the plausibility of their use, and the accuracy obtained by their use.

Upon The Asymptotic Representation Of Certain Entire Functions In Distant Portions Of The Plane, Abraham Franck

Mathematics & Statistics ETDs

The purpose of this paper is to study two particular entire functions which satisfy the conditions set up in a theorem due to Newsom. It is to be hoped that this report may be preliminary to the invention of a method which will lend itself toward the solution of certain general problems.

New Formulae For The Determination Of The Yield Of A Bond, Marvin Roberts

Mathematics & Statistics ETDs

A written contract to pay a certain amount of money on a specified redemption date, and to pay equal periodical dividends, is called a bond from a mathematical standpoint. The principal mentioned in the contract is its face value, or par value. The amount redeemed, or the redemption value, is denoted by C, the dividends by D, and the principal by F. A bond is redeemed at a par if C and F are the same, and at a premium if C is greater than F. The divided rate, or bond rate, is the interest rate named in the bond. …

The Evolution Of The Concept Of Axiom, William Fred Jones

Mathematics & Statistics ETDs

The field of knowledge known as mathematics is composed of the totality of mathematical systems. A mathematical system consists of a body of propositions known as the axioms. The concern of this paper is with the axioms; in fact, with the change which has taken place during the centuries in the ideas of mathematicians about the axioms.

Upon The Asymptotic Representation Of Entire Functions Where The General Coefficient Is The Product Of Two Gamma Functions, James R. Ellis

Mathematics & Statistics ETDs

The essential purpose of this paper is to obtain further information in regard to the asymptotic representation of a power series.

Some Applications Of The Principles Of Isomorphism And Variation To The Teaching Of Geometry, Ralph Mock

Mathematics & Statistics ETDs

In summary, it should be stressed that the numerous examples of this paper are important only in so much as they illustrate the use of the devices and concepts emphasized in the study. It is our premise that plane geometry, as usually taught, does not possess the value which it might have. Certain changes in content as well as in presentation would materially improve the course. This study, then, presents suggestions for improving the ordinary course in two directions. First, by presenting logical propositions from the students' experiences which are partially isomorphic to the theorems of plane geometry, it is …

The Efficiency Of Approximation Formulae For Determining The Rate Of Interest In Amortization Schedules, Wade Ellis

Mathematics & Statistics ETDs

The problem of this study is to determine the relative efficiency of the more important formulae for approximating the rate of interest involved in an amortization plan when the amount of the debt, the amount of the periodic payment, and the number of periods are known. By efficiency this meant the degree of accuracy obtainable, and the time required for solution.

The Relation Of Statistics To The Design Of Educational And Psychological Investigations, Palmer O. Johnson

Journal of the Minnesota Academy of Science

No abstract provided.

The Asymptotic Development Of A Special Type Of Power Series, David A. Lawson

Mathematics & Statistics ETDs

It is the purpose of this study to consider certain aspects of the theorem due to Walter B. Ford, may be considered as a function g(w) of the complex variable w=x+iy and as such satisfies two conditions chosen by the author.

Marital And Population Composition Of Sheboygan County January 1, 1925 To December 31, 1936, Rhudolph John Ploetz

Bachelors’ Theses

This is a compilation of the marriage and the population figures of Sheboygan County, in the state of Wisconsin. The author has made a survey of both the rural and urban areas. Including the county figures, are the state and federal statistics for an analysis and comparison on the problems relative to the subject. The table of contents giving the title and page of tables, is intended to be of great value to the reader, in that just a particular table wanted is designated and well-outlined. Regarding a lengthy explanation for each or any one of the tables is really …

A Method Of Changing Certain Infinite Series To New But Equivalent Series, Moneta Gunilla Johnson

Mathematics & Statistics ETDs

The purpose of this investigation is to prove that the sum of a series of variable terms of a certain type is equal to a constant plus the sum of another series of variable terms. As a result of this proof it may be hoped that certain series, which so far have not been summed, may be shown equal to a constant plus another series for which the sum is known.

A Mathematical Compilation And Consideration Of News Sources Utilized By The Milwaukee Journal And The Wisconsin News, Eugene P. Hackett

Bachelors’ Theses

The purpose of this thesis is to determine the amounts of news drawn from the various news sources by the Milwaukee Journal, a home-owned newspaper, and the Wisconsin News, a chain newspaper, from day to day over a three months period, and from these compiled figures to cast monthly and daily averages and totals. The comparative ratios and amounts of local news will receive special attention.

Probability, The Historical Development Of The Theory And Its Application To Games Of Chance, Rose M. Brandt

Bachelors’ Theses

The theory of probability had its origin in isolated mathematical problems taken from games of chance. The beginnings of many of our modern theories and concepts can be traced back to Chinese origin. So too can the theory of probability. With the exception of the Chinese problem, dating from the beginning of the Christian era, no reference seems to have again been made to the theory prior to the latter part of the fifteenth century. In 1494 an Italian monk, Pacioli, was one of the first to introduce the "Problem of Points" into a treatise on mathematics. By the solution …

History And Proof Of The Binomial Theorem, Ethel B. Ray

Bachelors’ Theses

Everyone realizes what a wonderful place the world really is. Yet, we of this day little think of the many generations that have gone to make our universe as it is. We think we have done wonders. We pride ourselves on our modern way. There is a tendency in man to "pat himself on the back" and boast of how well he has done. Little do we realize that millions and millions of people have given their whole lives so that we might be as we are. Of course the soldier gives his life for his country; but what of …

Studies Concerning The Elimination Of Experimental Error In Comparative Crop Tests, T. A. Kiesselbach

Nebraska Agricultural Experiment Station: Historical Research Bulletins

It is apparent that many sources of error have unconsciously entered into comparative crop yield tests. The very important matter of overcoming variation in soil conditions as a source of experimental error has been quite extensively studied and reported by various investigators during the past decade. The means suggested for reducing such error have been (1) repetition of plats and (2) correction of yields according to check plats planted to a uniform variety or treatment at stated intervals. Both methods have proved of value and a combination of both may often be used advantageously. Some danger always exists of error …