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An Acceleration Technique For A Conjugate Direction Algorithm For Nonlinear Regression, Larry Wilmer Cornwell

Doctoral Dissertations

"A linear acceleration technique, LAT, is developed which is applied to three conjugate direction algorithms: (1) Fletcher-Reeves algorithm, (2) Davidon-Fletcher-Powell algorithm and (3) Grey's Orthonormal Optimization Procedure (GOOP). Eight problems are solved by the three algorithms mentioned above and the Levenberg-Marquardt algorithm. The addition of the LAT algorithm improves the rate of convergence for the GOOP algorithm in all problems attempted and for some problems using the Fletcher-Reeves algorithm and the Davidon-Fletcher-Powell algorithm. Using the number of operations to perform function and derivative evaluations, the algorithms mentioned above are compared. Although the GOOP algorithm is relatively unknown outside of the …

D-Structures And Their Semantics, Rohit J. Parikh

Publications and Research

"Many logicians are familiar with the game theoretic approach to semantics, due to Jaakko Hintikka. This paper by me contains class notes of a logic course at Boston University in fall 1972. It has similar game theoretic ideas, developed quite independently, but influenced by the work of A. Ehrenfeucht. It applies to a larger class of logics, including classical logic, intuitionistic logic and the *-semantics of Ehrenfeucht. The treatment is via D-structures which are finite approximations of infinite structures. For various reasons I did not publish this paper then, but some abstracts, both by myself as well as joint abstracts …

Generalized Inverse Matrices And Applications In Statistics, James Manville King Iv

All Master's Theses

In the theory of linear statistical models, one frequently encounters consistent systems of linear equations Ax= y. If A is nonsingular then a unique solution is given by x - 1 A y. If A is singular or rectangular however, then there are an infinite number of solutions; and the theory of generalized matrix inverses can be used to generate and characterize the solution set.

This thesis examines properties of generalized matrix inverses, and their use in solving linear equations, and in particular the role they play in treating the concept of estimability.

Transient Solutions For Field Propagated By An Electric Source In A Perfectly Conducting Cone, Jon A. Sholberg

All Master's Theses

This paper makes use of the results of the doctoral thesis written by Professor K. Gamon entitled "The propagation of waves and pulses in the presence of conical structures." The use of such results is made by considering the expression for the field of a cone due to a ring source excitation and then obtaining the solution of a new field propagated by a given pulse.

Also, the electric and magnetic components for these new fields are derived along with the expression for the radiated energy.

Mathematical Modeling Of River Water Temperatures, Leland Lovell Long

Doctoral Dissertations

"The applicability of power spectral density techniques, Fourier series analysis, and linear regression to the mathematical modeling of river water temperature is demonstrated. Consideration is also given to the problem of estimating thermal inputs to rivers from man-made sources such as electrical power plants. First, power spectral density techniques are used in the time-series analysis of water temperature records which were taken from the Missouri River. Two spectral ranges are then studied from the standpoint of their applicability to (1) mathematical model building and (2) detection and identification of cyclic thermal inputs. Next, a Fourier regression fit to the time-series …

Statistical Studies Of Various Time-To-Fail Distributions, James Addison Eastman

Doctoral Dissertations

"Three models are considered that have U-shaped hazard functions, and a fourth model is considered that has a linear hazard function. Several methods for estimating the parameters are given for each of these models. Also, various tests of hypotheses are considered in the case of the model with the linear hazard function. One of the models with a U-shaped hazard function has a location and a scale parameter, and it is proved in general that any other parameters in a distribution of this type are distributed independently of the location and scale parameters.

A new method used to estimate the …

Structure Of Zero Divisors, And Other Algebraic Structures, In Higher Dimensional Real Cayley-Dickson Algebras, Harmon Caril Brown

Doctoral Dissertations

"Real Cayley-Dickson algebras are a class of 2ⁿ-dimensional real algebras containing the real numbers, complex numbers, quaternions, and the octonions (Cayley numbers) as special cases. Each real Cayley-Dickson algebra of dimension greater than eight (a higher dimensional real Cayley-Dickson algebra) is a real normed algebra containing a multiplicative identity and an inverse for each nonzero element. In addition, each element a in the algebra has defined for it a conjugate element ā analogous to the conjugate in the complex numbers. These algebras are not alternative, but are flexible and satisfy the noncommutative Jordan identity. Each element in these algebras can …

A Comparison Of The Effectiveness Of Worksheets And Manipulative Games Used In Seventh-Grade Mathematics As Methods Of Drill On The Four Basic Operations With Whole Numbers And Fractions, Richard Lee Capps

Dissertations and Theses @ UNI

This study was conducted in the fall of 1971 at Nell McGowen Junior High School, Knoxville, Iowa. The subjects of the study were 146 seventh-grade mathematics students. The students were ability grouped by the principal. No attempt was made to keep a constant sex ratio. The problem of this study was the comparison of two methods of drill on the four basic operations with whole numbers and fractions. The methods were games and worksheets. An analysis of covariance design was used to analyze the data. Achievement and attitude pre-test scores were covariates. Achievement and attitude post-test scores were dependent variables. …

A New Test For Normality, Richard Leroy Roller

All Master's Theses

This paper presents a new test for normality which is based on a complete characterization of the normal distribution. Motivation for the test is given in terms of a proof of this characterization. The test is derived and evaluated by computer-simulated sampling from alternative distributions. The empirical powers of the test generated from such samplings are tabled and compared to nine commonly used tests. Evaluation of the proposed test is discussed and further avenues of investigation are suggested.

Imbedding Graphs In Pseudosurfaces, Wayne S. Petroelje

Masters Theses

No abstract provided.

The Constructive Theory Of Distributions, Elsie M. Gustafson

Masters Theses

No abstract provided.

A Comparative Investigation Of The Effects Of Frequent Testing Upon Achievement In Secondary Advanced Algebra, John Thomas Fullerton

All Master's Theses

Relatively speaking, few studies have concerned themselves with the problem of frequent testing, and as Keys pointed out, empirical evidence, uncomplicated by differences in the amount of testing material employed, on the effects of frequent testing is, at best, scarce (14:427). Also many studies used tests and test results for direct instruction, thus introducing additional variables. Furthermore, the choice of subjects and disciplines has been limited, the better part being taken from college psychology and sociology classes or high school science classes. This investigation was not an attempt to modify previous experiments, nor was it an attempt to identify which …

Orthogonality In Normed Spaces, Martin R. Mccarthy

All Master's Theses

This paper presents three definitions of orthogonality in normed spaces. Each definition is shown equivalent to the inner product being zero when restricted to an inner product space. The definitions arise from such properties in two space as the diagonals of a rectangle being equal and the Pythagorean Theorem. The third definition shows that the idea of an inner product can be generalized under certain conditions.

Lower Bounds In The Stekloff Problem, Shrikant Narayan Rao

Masters Theses

No abstract provided.

Some Applications Of Decompositions Of The Identity To Ordered Vector Spaces., John Annulis

Mathematics & Statistics ETDs

We study decompositions of the identity (for definition see Vulikh [13]) in Dedekind a-complete vector lattices. In Chapter 1, we define and develop a notion of continuous elements with respect to a decomposition of the identity. We shall also develop a spectral theory for these elements. In Chapter 2, two Stieltjes-type type integrals are defined with respect to decompositions of the identity. The relationship of these integrals to the continuous elements is then explored. In Chapter 3, we prove two results in ordered vector spaces. The first result is that every infinite dimensional Dedekind complete vector lattice has a base …

A Maximum Principle For An Optimal Control Problem With Integral Constraints., Vernon Bakke

Mathematics & Statistics ETDs

In this problem necessary conditions are obtained for an optimal control problem ·whose state variables are given in terms of integral equations. The conditions are obtained separately for Volterra equations and Fredholm equations. The main result for each case is the maximum principle and multiplier rule. For the Volterra equations, transversality conditions are obtained.

Relationships Between Reversible And Connected Automata, Robert Michael Johnson

All Master's Theses

The present investigation explores some of the relationships among special classes of automata defined by Bavel and Muller (1:231-240), Trauth (6:170-175), and Cutlip (2).

A Two-Stage Postnikov System Where E₂ ≠ E∞ In The Eilenberg-Moore Spectral Sequence, Claude Schochet

Mathematics Faculty Research Publications

Let ΩB → PB → B be the path fibration over the simply-connected space B, let ΩB → E → X be the induced fibration via the map ƒ : X → B, and let X and B be generalized Eilenberg-Mac Lane spaces. G. Hirsch has conjectured that H*E is additively isomorphic to Τοτ_H*B(Z₂,H*X), where cohomology is with Z₂ coefficients. Since the Elienberg-Moore spectral sequence which converges to H*E has E₂ = Τοτ_H*B(Z₂,H …

A New Confidence Interval For The Mean Of A Normal Distribution, David Lee Wallace

All Master's Theses

A typical problem in statistical inference is the following: An experimenter is confronted with a density function f(x; ϴ) which describes the underlying population of measurements. The form of f may or may not be known, and ϴ is a parameter (possibly vector-valued) which describes the population. The statistician's job is to estimate or to test hypotheses about the unknown parameter ϴ. In this paper, we shall consider interval estimation of the mean of the normal density function.

Convergence Rates For The Central Limit Theorem For Random Sums, Christopher E. Olson

Mathematics & Statistics ETDs

Let (X_i} be a sequence of independent, identically-distributed random variables with EX²_i < ꝏ and E(X_i - EX_i)² = 1.

Fourier Transforms Of Unbounded Measures, Loren Argabright, Jesus De La Lamadrid

Department of Mathematics: Faculty Publications

Let G be a locally compact abelian group. For a (generally unbounded) measure μ on G we shall say that μ is transformable if there is a measure μˆ on the character group Γ of G such that, for every ƒЄK(G), the space of continuous functions with compact support on G,ƒЄL₂(μ) and (1) ∫_Gƒ^**ƒ(x) dμ(x) = ∫_r|∫(γ^-1)|²dμ(γ). The resulting "Fourier transformation” μ→μˆ contains the classical theory and leads to generalizations of a variety of classical results, including the Plancherel theorem and the Poisson summation …

A Monte Carlo Evaluation Of A Nonparametric Technique For Estimating The Hazard Function, Sheng Jia Lin

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This research is primarily concerned with the estimation of the Hazard functions, the Hazard function is the failure rate at time t, and is defined as -R '(t)/R(t), so it plays an important role in Reliability.

In order to compare and evaluate the estimation methods, it is convenient to select one distribution in this research. Since the Weibull distribution is a useful distribution in Reliability, the Weibull distribution is used in this paper.

Torus Knots, David S. Bradley

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

We have compiled here many interesting results concerning a particular collection of knots called torus knots. Torus knots are merely simple closed curves imbedded in an unknotted torus T² in E³. We show that the fundamental groups of T², π(T²), is the direct product of the additive group of integers with itself. The ordered pair (p, q) in Z x Z determines an equivalence class of loops on the torus, and we show in Section II that the class [(p, q)] contains a loop whose image is a simple closed curve if and …

Integral Representation Theorems, Leiko Hatta

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Since F. Riesz showed in 1909 that the dual of C[0,1] is BV[0,1] (the functions of bounded variation on [0, 1] with || g ||_BV = V(g)) via the Stieltjes integral, obtaining representations for linear operators in various settings has been a problem of interest. This paper shows the historical manner of representations, the road map type theorems and representations obtained via the v-integral.

The Poincaré Conjecture, Joseph D. Peck

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The central theme for this paper is provided by the following three statements:

(1) Every compact connected 1-manifold is S1.

(2) Every compact connected simply connected 2-manifold is S2.

(3) Every compact connected simply connected 3-manifold is S3.

We provide proofs of statements (1) and (2). The veracity of the third statement, the Poincaré Conjecture, has not been determined. It is known that should a counter-example exist it can be found by removing from S3 a finite collect ion of solid tori and sewing them back differently. We show that it is not possible to find a counterexample by removing …

A Theory Of Multiplicity For Multiplicative Filtrations, Wayne Wilson Bishop

Dissertations

No abstract provided.

The *S-Product Of Arithmetic Functions, Kathryn Diane Kopec

Masters Theses

No abstract provided.

On Some Special Classes Of Partially Ordered Linear Algebras., Taen-Yu Dai

Mathematics & Statistics ETDs

R. DeMarr (unpublished) has begun a study of Banach algebras as subalgebras of partially ordered linear algebras which are Dedekind a -complete. In [3] he has shown that the real Banach algebra of norm-bounded linear operators (mapping a real Banach space into itself) can be made into a partially ordered linear algebra which is Dedekind a -complete. This leads us to study a more gen­eralized function algebra by using the order structure. In this paper from analytical point of view we will study some special classes of partially ordered linear algebras which are Dedekind a -complete. In chapter 1 we …

Statistical Study Of Tongue Pigmentation In Man., Dabeeru Chandrasekhara Rao Dr.

Doctoral Theses

Tongue pigmentation in man:The 'partioular' type of dark apots and patohes on the surface of the tongue, as investigated in the prosent thesis, wae first not ioed in human populations by Davis [5], who called it 'tongue piementation'. It is to be emphasized that not all colour piements come under this 'particular' type. There are some pathological conditione giving rise to transient discolouration of the tongue. This aspeot will be disouesed a little later. Such tongue pigmentation does not seem to have been reported for any population, human or otherwise.Tongue pigmentation be usually found on the upper surface or borders …

Optimum Estimators And Strategies In Survey Sampling., M. K. Ramakrishnan Dr.

Doctoral Theses

This thesis consists of nine chapters. In the first chapter we give the basic concepts and definitions and also a broad review of the literature related to the problems considered in this thesis. The second and third chapters are devoted to a detailed modified comparison of sampling with and without replacement, for the case of equal and unequal probability sampling respectively. In the fourth and fifth chapters we discuss the criteria of hyper-admissibility and linear suf2iciency for the choice of an optimum estimator for a given sampling design. The succeeding three chapters have as their main objective the central problem …