Physical Sciences and Mathematics Commons^™

On Some Optimal Tests In Finite Mixtures: Constructions And Applications., Chandranath Pal Dr.

Doctoral Theses

Mixtures of distributions are now-a-days playing very important roles in both theoretical and applied statistics. There is an abundance of real-life situations where mixture distributions are being extensively used for modelling data and drawing inference. Several books and monographs on mixtures have so far been published, e.g., Everitt and Hand (1981), Titterington et al. (1985), McLachlan and Basford (1988), McLachlan (1997) etc., which cover a wide area on different aspects of mixture distributions and their applications. The book by Titterington et al. (1985, pp. 16-21), in particular, contains a comprehensive list of references on direct applications of finite mixtures in …

The Structure And Stability Of Expanding And Converging Near-Stoichiometric Flames, Raymond Addabbo

Dissertations

The stability of expanding and converging premixed flames is investigated theoretically. These configurations are inherently unsteady and represent simple examples of positively (expanding) and negatively (converging) stretched flames. A new model is employed in this study that incorporates both hydrodynamic and diffusional-thermal effects. The model expands earlier works by incorporating variable transport properties, variations in the mixture strength and a more realistic dependence on viscosity.

The expanding flame is shown to remain stable at small radii provided the thermal diffusivity exceeds the mass diffusivity of the deficient reactant. However, once the flame achieves a critical size, a cellular instability appears, …

Asymptotic Methods In Applied Waveguide Problems, Helen Martynov

Dissertations

Some of the most challenging problems in acoustics and electromagnetics involve the study of scattered fields in waveguides caused by targets of elaborate shape. The complexity of the resulting scattered field depends on the geometry of the scatterer, and exact solutions exist only for the simple geometries.

The asymptotic methods developed in this dissertation give the approximate solutions for the scattered fields in two practically important geometries: an object placed inside a stratified waveguide, and a waveguide with multiple abrupt width transitions. The solutions for these geometries are obtained by approximating the field near the target or junction by the …

An Individual-Based Approach To Population Dynamics With Applications To Sockeye Salmon And Iteroparous Organisms, Cynthia Moira Krohn

Doctoral Dissertations

Individual-based models have been used to study the population dynamics of semelparous and iteroparous organisms. The rst model, developed for sockeye salmon ( On-corhynchus nerka), was based on the physiology of the individual and incorporated into a population model via a McKendrick-von Foerster type partial di
erential equation. Cycles of population abundance historically found in the Fraser River system were recreated through model simulations. Explanations for the appearance of the cycling were investigated and tested. The results showed that density- and size-dependent mortality were not necessary for cycling to appear, however their inclusion or exclusion in combination with the type …

Cost Domination In Graphs, David John Erwin

Dissertations

Let G be a connected graph having order at least 2. A function f : V (G) —> {0 , 1 , . . . , diam G} for which f ( v ) < e(v) for every vertex v of G is a cost function on G. A vertex v with f ( v ) > 0 is an f-dominating vertex, and the set Vj~ = {v 6 V(G) : f(v) > 0} of f-dominating vertices is the f-dominating set. An /-dominating vertex v is said to f-dominate every vertex u with d(n, v) < f(u ), while …

A Dynamical Model Of The Distributed Interaction Of Intracellular Signals, Adrienne C.N. James

Dissertations

A major goal of modern cell biology is to understand the regulation of cell behavior in the reductive terms of all the molecular interactions. This aim is made explicit by the assertion that understanding a cell's response to stimuli requires a full inventory of details. Currently, no satisfactory explanation exists to explain why cells exhibit only a relatively small number of different behavioral modes.

In this thesis, a discrete dynamical model is developed to study interactions between certain types of signaling proteins. The model is generic and "connectionist" in nature and incorporates important concepts from the biology. The emphasis is …

Efficient Inversion Methods In Underwater Acoustics, Xiaoqun Ma

Dissertations

This dissertation describes efficient methods developed and implemented for source localization and sound speed and bottom depth estimation using sound propagation in the ocean. The proposed inversion techniques are based on the linearization of the generally non-linear inverse problem of parameter estimation in underwater acoustics. These techniques take into account properties of the ocean environment and are accurate in their estimation results without being prohibitively computationally intensive. For the inversion, select ray paths are taken into account: the direct, first surface bounce, and first bottom bounce. Ray travel time derivatives with respect to parameters that affect path arrival times are …

Some Aspects Of Banks And Financial Markets In Emerging Economics., Gurbachan Singh Dr.

Doctoral Theses

Liquidity and Bank RunsThe policy of deposit insurance in the banking sector has succeeded in pre- venting bank runs but it has encouraged moral haxard (Kane, 1985 and 1989). This has increased the cost of capital. So the government and/or the central bank need to regulate (Flannery, 1982). In chapter 2, we ask the question - Is there an alternative to deposit insurance? What is the role of equity capital in this context? Is full insurance optimal?The seminal paper on bank runs by Diamond and Dybvig (1983) argues that a lack of deposit insurance leads to muitiple Nash equilibria, including …

The Modern Mathematics Classroom: A Collection Of Virtual Manipulatives For Teachers And Students, David Stowell

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

An important assumption in the implementation of the National Council of Teachers of Mathematics (NCTM) Standards 2000 is that the mathematics classroom is a place where students are actively involved in the learning process. One way to foster such a learning environment is by using manipulatives. By their nature, manipulatives make the learning of mathematics a discovery-based activity. As computer use increases in the classroom, virtual manipulatives will become more important as instructional tools. Virtual manipulatives offer advantages over their traditional versions. Most important is their dynamic nature. Their dynamic capabilities provide two main benefits. First, the number of potential …

Generalized Minimum Penalized Hellinger Distance Estimation And Generalized Penalized Hellinger Deviance Testing For Generalized Linear Models: The Discrete Case, Huey Yan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this dissertation, robust and efficient alternatives to quasi-likelihood estimation and likelihood ratio tests are developed for discrete generalized linear models. The estimation method considered is a penalized minimum Hellinger distance procedure that generalizes a procedure developed by Harris and Basu for estimating parameters of a single discrete probability distribution from a random sample. A bootstrap algorithm is proposed to select the weight of the penalty term. Simulations are carried out to compare the new estimators with quasi-likelihood estimation. The robustness of the estimation procedure is demonstrated by simulation work and by Hapel's α-influence curve. Penalized minimum Hellinger deviance tests …

Generalizations Of The Zero-Divisor Graph Of A Ring, Shane Patrick Redmond

Doctoral Dissertations

Let R be a commutative ring with 1, and let Z(R) denote the set of zero­divisors of R. We define an undirected graph Γ(R) with vertices Z(R)* = Z(R) - {0}, where distinct vertices x and y of R are connected if and only if xy = 0. This graph is called the zero-divisor graph of R. We extend the definition of the zero-divisor graph to a noncommutative ring in several ways. Next, given a commutative ring R and ideal Ι of R, we introduce the notion of an …

Some Problem In Homogenization., M. Rajesh Dr.

Doctoral Theses

No abstract provided.

Engineering Production Function And Choice Of Technique., N. S. S. Narayana Dr.

Doctoral Theses

This study deala wi th the selection of technological al ternaid ves of production, a problom referred to as choice of techninues" in ecommie theory. Selection of an appropriate technique (or a technolo gical al ternative) haa to be Bede with ro spe et to speci fied objectives and avail phle reDurces. Selection of proper techniques from smong many avall ablo el ternatives ha boen one of the min tasks whilu planni ng for econonio development. Generally develooping co untries like India are handi capped by problema of BCerci ty of on-lebour reaources, abundant labour force, lini ted foreign-aid, 1inited …

Stochastic Comparision And Dependence Among Order Statistics,Spacing And Concomitants Of Order Statistics., Baha-Eldin Khaledi Dr.

Doctoral Theses

The simplest and the most common way of comparing two random variables is through their means and variances. It may happen that in some cases the median of X is larger than the median of Y, while the mean of X is smaller than the mean of Y. However, this confusion will not arise if the random variables are stochastically ordered. Similarly, the same may happen if one would like to compare the variability of X with that of Y based only on numerical measures of variability. Besides, these characteristics of distributions might not exist in some cases. In most …

Mapping Quantitative Trait Loci In Humans: Some Statistical Contributions., Saurabh Ghosh Dr.

Doctoral Theses

Maty qualitative tralts - such an, milk yield la cows, blood pressure in lumans --are known to be determined primarly, though zot exclusively, by inherited genetic luctora. It ls the of coasklerable impartance to identify chromosontal locations of tho genes that control a quantitative character. Linkage analysis (Ou 1990), which deals with the deduction of linkagn and estimation of recombination fractions among the loci controlling a qualitative/quantitative character and major loci wkoo poertions are knows aprfori, is widely used for localisation of gens. Although statistical methodologies for magplag gemen determining dichotomos qualitative charactes in humans aro well-developed, the demicrant of …

Boolean Functions With Important Cryptographic Properties., Subhamoy Maitra Dr.

Doctoral Theses

In this thesis we concentrate on properties of cryptographically significant Boolean functions.The techniques are mainly combinstorial and provide new resulta on enumeration and construction of such functions. Initially we concentrate on a partieular subset of Boolean functions called the symmetric Boolean functions. A closed form expression for the Walsh transform of an arbitrary symmetric Boolean function is presented. We completely characterize the symmetric functions with maximum nonlinearity and show that the maximum nonlinearity of n-variable symmetrie function can be 2n-1-2[n-1l2], Moreover, new classes of symmetric balanced and symmetric correlation immune functions are considered.We provide a randomised heuristic to construct balanced …

Contributions To Random Interactions And Dynamical Systems., Santanu Chakraborty Dr.

Doctoral Theses

In recent years random iterations of maps on Polish spaces has gained prominence. They are. nice examples of Markov processes whose invariant measures can be used in Computer imaging (see Berger ( 1). They also arise as random perturabations of deterministic dynamical systems.Let S be a Polish space with its Borel a-field. Let r be a collection of Borel maps from S to S. Let P be a probability on r. Then starting with a point z in S, we choose a map yn er according to the law P and move to ya(x). Then we choose 2 € r …

Multi-Mode Cavity Effects In The Microwave Heating Of A Ceramic Slab, Stuart J. Walker

Dissertations

In order to gain insight into hot spot development in microwave heated ceramics, a partially insulated, two dimensional ceramic slab situated in a TE_M01 cavity is modeled in the small Biot number limit. If the electrical conductivity is an exponential function of temperture and E₀ is the strength of the incident mode, then the relationship between the spatially uniform, steady state leading order temperature, v₈, and E₀¹ is characterized by the well known bi-stable, or S shaped, response curve. The steady state second order temperature, v₁, is described by a boundary …

Analysis Of Discrete Dynamical System Models For Competing Species, Jerry J. Chen

Dissertations

A discrete version of the Lotka-Volterra (LV) differential equations for competing population species is analyzed in detail, much the same way as the discrete form of the logistic equation has been investigated as a source of bifurcation phenomena and chaotic dynamics. Another related system, namely, the Exponentially Self Regulating (ESR) population model, is also thoroughly analyzed. It is found that in addition to logistic dynamics - ranging from the very simple to manifestly chaotic regimes in terms of the governing parameters - the discrete LV model and the ESR model exhibit their own brands of bifurcation and chaos that are …

Topological Conjugacy And Rigidity Of Affine Actions., Siddhartha Bhattacharya Dr.

Doctoral Theses

The main theme of this thesis is topological classiication of aline Hows on homogeneous spaces and rigidity of equivariant continuous maps between such dows. Both these aspects have been extensively studied in the literature for subgroup actions (cf. [Be), [B-Dj and [Wi) and for automorphism flows of the cyclic group (cf. [Ar]. [K-R] and [C-S). We will consider similar questions in more general situations. A detailed outline is given below. For a topological group T, by a r-flow we mean pair (X,p), where X is a opological space and p is a continuous action of I on X. For any …

Routing Algorithms For Channels, Switchboxes And Mcm's In Vlsi Layout Design., Sandip Das Dr.

Doctoral Theses

The term Very Large Scale Integration (VLSI) reflects the capability of semi- conductor industry to fabricate a complex electronic circuit consisting of millions of components on a single silicon substrate. The growth of semiconductor technol- ogy in recent years has been described by "Moore's law", enunciated in the late 1960s, which projected quadrupling of components in a chip in every three to four years. Several factors contributed to this tremendous growth : (i) reduction of line width of the basic device and interconnection wires due to the development of high- resolution lithographic techniques and improved processing capabilities, (ii) increase in …

Constructing Regular Ramanujan Graphs Via Graph Extension, Sage Michelle Accardo

Honors Theses

No abstract provided.

A Multigrid Method For Elliptic Grid Generation Using Compact Schemes, Balaji S. Iyangar

Doctoral Dissertations

Traditional iterative methods are stalling numerical processes, in which the error has relatively small changes from one iteration to the next. Multigrid methods overcome the limitations of iterative methods and are computationally efficient. Convergence of iterative methods for elliptic partial differential equations is extremely slow. In particular, the convergence of the non-linear elliptic Poisson grid generation equations used for elliptic grid generation is very slow. Multigrid methods are fast converging methods when applied to elliptic partial differential equations. In this dissertation, a non-linear multigrid algorithm is used to accelerate the convergence of the non-linear elliptic Poisson grid generation method. The …

Reliability Studies Of The Skew Normal Distribution, Nicole Dawn Brown

Electronic Theses and Dissertations

It has been observed in various practical applications that data do not conform to the normal distribution, which is symmetric with no skewness. The skew normal distribution proposed by Azzalini(1985) is appropriate for the analysis of data which is unimodal but exhibits some skewness. The skew normal distribution includes the normal distribution as a special case where the skewness parameter is zero. In this thesis, we study the structural properties of the skew normal distribution, with an emphasis on the reliability properties of the model. More specifically, we obtain the failure rate, the mean residual life function, and the reliability …

Using Generalized Linear Models With A Mixed Random Component To Analyze Count Data, Jungah Jung

Electronic Theses and Dissertations

Many discrete response variables have counts as possible outcomes. Poisson regression has been recognized as an important tool for analyzing count data. This technique includes the simple Poisson generalized linear model and mixtures of independent Poisson models as special cases. Generalized linear models have been found useful in many statistical analysis. Count data analyzed under such models often exhibit overdispersion. In many practical circumstances the restriction that the mean and variance are equal is not realistic. Especially, when there is overdispersion in the data, a conditional negative binomial mixed model, given some random effects, could be an attractive alternative. This …

Scintillation Behind The Collecting Lens Of A Receiver, Clarissa A. Fleming Russell

Retrospective Theses and Dissertations

One of the negative effects that a laser beam experiences as it propagates through the atmosphere is intensity fluctuations or scintillation. Because scintillation-- as it pertains to laser radar and laser satellite communication systems-- is the main subject of this research, the assumption of an optical element ( such as a Gaussian lens) along the propagation path in front of the detector is valid. The mathematical addition of optical elements to the propagation path is treated using the ABCD ray matrix method. The expression for scintillation is derived, analyzed, and numerically calculated for positions to the left and right of …

Identities For The Multiple Polylogarithm Using The Shuffle Operation, Ji Hoon Ryoo

Electronic Theses and Dissertations

At the beginning of my research, I understood the shuffle operation and iterated integrals to make a new proof-method (called a combinatorial method). As a first work, I proved an combinatorial identity 2 using a combinatorial method. While proving it, I got four identities and showed that one of them is equal to an analytic identity 1 which is found at the paper [2] written by David M. Bradley and Doug Bowman. Furthermore, I derived an formula involving nested harmonic sums. Using Maple (a mathematical software), I found a new combinatorial identity 3 and derived two formulas: One is related …

Analysis Of A Non-Replicated Split-Split Plot Experiment, Emily Simmons Sim

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

A major obstacle in the analysis of experimental data, in many situations, is the lack of "true" or "complete" replication. In some disciplines, researchers are very aware of the importance of replication and the methods for correctly replicating an experiment. In other subject areas, however, researchers are less aware of what it means to properly replicate an experiment. Due to this lack of awareness, many non-replicated experiments are carried out every year. For many of these non-replicated experiments, there is no satisfactory statistical analysis.

The subject of this report is the analysis of two non-replicated experiments in environmental engineering. First, …

The Renner Monoids And Cell Decompositions Of The Classical Algebraic Monoids, Zhenheng Li

Digitized Theses

The Renner monoids, cross section lattices and cell decompositions of the classical algebraic monoids are studied.

The Renner monoid is extremely important in the theory of reductive algebraic monoids. It is well know that the Renner monoid [Special characters omitted.] of M_n (K ) is the monoid of all zero-one matrices which have at most one entry equal to one in each row and column, i.e., [Special characters omitted.] consists of injective partial maps on a set of n elements. We obtain that the Renner monoids of the symplectic algebraic monoids and special orthogonal algebraic monoids turn out …

Mathematical Models Of Quiescent Solar Prominences, Iain Mckaig

Mathematics & Statistics Theses & Dissertations

Magnetic fields in the solar atmosphere suspend and insulate dense regions of cool plasma known as prominences. The convection zone may be the mechanism that both generates and expels this magnetic flux through the photosphere in order to make these formations possible. The connection is examined here by modeling the convection zone as both one-dimensional, then more realistically, two-dimensional.

First a Dirichlet problem on a semi-infinite strip is solved using conformal mapping and the method of images. The base of the strip represents the photosphere where a current distribution can be given as a boundary condition, and the strip extends …