Physical Sciences and Mathematics Commons^™

Some Problem In Homogenization., M. Rajesh Dr.

Doctoral Theses

No abstract provided.

Abstracting Aristotle’S Philosophy Of Mathematics, John J. Cleary

Research Resources

In the history of science perhaps the most influential Aristotelian division was that

between mathematics and physics. From our modern perspective this seems like an unfortunate deviation from the Platonic unification of the two disciplines, which guided Kepler and Galileo towards the modern scientific revolution. By contrast, Aristotle’s sharp distinction between the disciplines seems to have led to a barren scholasticism in physics, together with an arid instrumentalism in Ptolemaic astronomy. On the positive side, however, astronomy was liberated from commonsense realism for the conceptual experiments of Aristarchus of Samos, whose heliocentric hypothesis was not adopted by later astronomers because …

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 …

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 …

An Ellam Scheme For Multidimensional Advection-Reaction Equations And Its Optimal-Order Error Estimate, Hong Wang, Xiquan Shi, Richard E. Ewing

Faculty Publications

We present an Eulerian-Lagrangian localized adjoint method (ELLAM) scheme for initial-boundary value problems for advection-reaction partial differential equations in multiple space dimensions. The derived numerical scheme is not subject to the Courant-Friedrichs-Lewy condition and generates accurate numerical solutions even if large time steps are used. Moreover, the scheme naturally incorporates boundary conditions into its formulation without any artificial outflow boundary conditions needed, and it conserves mass. An optimal-order error estimate is proved for the scheme. Numerical experiments are performed to verify the theoretical estimate.

Open To Reason, David L. Neuhouser

Books by Taylor faculty, staff, and administrators

Open to Reason is a comparison of the roles of reason, experience, imagination, intuition, faith, love, humility, and obedience in mathematics and religion.

Mathematics As Worship, David J. Stucki

Mathematics Faculty Scholarship

This paper treats worship in a broad, inclusive sense as the primary and necessary response of human beings to their creator. It provides a brief overview of the relationship between mathematics and theology from the Pythagoreans to the present. It argues that all knowledge is contingent upon faith and thus that contemplation of mathematical insights can lead to worship of God.

A Coin Flipping Game With Non Transitive Odds, Stacy Jurgens

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

Unit Sum Numbers Of Abelian Groups And Modules, Christopher Meehan

Doctoral

We discuss some open questions regarding the unit sum numbers of free modules of arbitrary infinite rank over commutative rings and, in particular, over principal ideal domains. The unit sum numbers of rational groups are then investigated: the importance of the rational prime 2 being an automorphism of the rational group is discussed and other results are achieved considering the number and distribution of rational primes which are, or are not, automorphisms of the group. We next prove the existence of rational groups with unit sum numbers greater than 2 but of finite value and we estimate an upper bound …

Artin-Schreier Families And 2-D Cycle Codes, Cem Guneri

LSU Doctoral Dissertations

We start with the study of certain Artin-Schreier families. Using coding theory techniques, we determine a necessary and sufficient condition for such families to have a nontrivial curve with the maximum possible number of rational points over the finite field in consideration. This result produces several nice corollaries, including the existence of certain maximal curves; i.e., curves meeting the Hasse-Weil bound.We then present a way to represent two-dimensional (2-D) cyclic codes as trace codes starting from a basic zero set of its dual code. This representation enables us to relate the weight of a codeword to the number of rational …

Depth-First Search Embedded Wavelet Algorithm For Hardware Implementation, Li-Minn Ang

Theses: Doctorates and Masters

The emerging technology of image communication over wireless transmission channels requires several new challenges to be simultaneously met at the algorithm and architecture levels. At the algorithm level, desirable features include high coding performance, bit stream scalability, robustness to transmission errors and suitability for content-based coding schemes. At the architecture level, we require efficient architectures for construction of portable devices with small size and low power consumption. An important question is to ask if a single coding algorithm can be designed to meet the diverse requirements. Recently, researchers working on improving different features have converged on a set of coding …

The Averaging Lemma, Ronald A. Devore, Guergana Petrova

Faculty Publications

No abstract provided.

On Logistic And Some New Discrimination Rules:Charecterizations,Inference And Application., Supratik Roy Dr.

Doctoral Theses

Introduction and Summary Consider the problem of classification of an observation into one of two specified populations. Fisher's classification rale, just as several other rules commonly used in practice, depends only on the ratio of the individual densities fi(x), i = 1,2. This led Cox (1966),/27) to model the "posterior odds" by a simple function. Specifically,Cox's logistic discrimination (LGD) rule is then based on the statistic a + 'ßx. This has the advantage that individual densities f.(x) need not be known and we only need to estimate the parameters a and B.Another advantage, which is claimed , is that the …

An Approximation To Miscible Fluid Flows In Porous Media With Point Sources And Sinks By An Eulerian-Lagrangian Localized Adjoint Method And Mixed Finite Element Methods, Hong Wang, Liang Dong, Richard E. Ewing, Stephen L. Lyons, Guan Qin

Faculty Publications

We develop an Eulerian–Lagrangian localized adjoint method (ELLAM)-mixed finite element method (MFEM) solution technique for accurate numerical simulation of coupled systems of partial differential equations (PDEs), which describe complex fluid flow processes in porous media. An ELLAM, which was shown previously to outperform many widely used methods in the context of linear convection-diffusion PDEs, is presented to solve the transport equation for concentration. Since accurate fluid velocities are crucial in numerical simulations, an MFEM is used to solve the pressure equation for the pressure and Darcy velocity. This minimizes the numerical difficulties occurring in standard methods for approximating velocities caused …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Mode Vertices And Mode Graphs., Jobriath Scott Kauffman

Electronic Theses and Dissertations

The eccentricity of a vertex, v, of a connected graph, G, is the distance to a furthest vertex from v. A mode vertex of a connected graph, G, is a vertex whose eccentricity occurs as often in the eccentricity sequence of G as the eccentricity of any other vertex. The mode of a graph, G, is the subgraph induced by the mode vertices of G. A mode graph is a connected graph for which each vertex is a mode vertex. Note that mode graphs are a generalization of self-centered graphs. This paper presents some …

Vertices In Total Dominating Sets., Robert Elmer Dautermann Iii

Electronic Theses and Dissertations

Fricke, Haynes, Hedetniemi, Hedetniemi, and Laskar introduced the following concept. For a graph G = (V,E), let rho denote a property of interest concerning sets of vertices. A vertex u is rho-good if u is contained in a {minimum, maximum} rho-set in G and rho-bad if u is not contained in a rho-set. Let g denote the number of rho-good vertices and b denote the number of rho-bad vertices. A graph G is called rho-excellent if every vertex in V is rho-good, rho-commendable if g > b > 0, rho-fair if g = b, and …

An Optimal-Order Error Estimate For An Ellam Scheme For Two-Dimensional Linear Advection-Diffusion Equations, Hong Wang

Faculty Publications

An Eulerian-Lagrangian localized adjoint method (ELLAM) is presented and an- alyzed for two-dimensional linear advection-diffusion partial differential equations (PDEs). An optimal-order error estimate in the L^2 norm and a superconvergence estimate in a discrete H^1 norm are derived. Numerical experiments are performed to verify the theoretical estimates.

Feature Evaluation, Classification And Rule Generation Using Fuzzy Sets And Neural Networks., Rajat Kumar De Dr.

Doctoral Theses

Pattern recognition and machine learning form a major area of research and develop- ment activity that encompasses the processing of pictorial and other non-numerical information obtained from the interaction between science, technology and society. A motivation for the spurt of activity in this field is the need for people to com- municate with the computing machines in their natural mode of communication. Another important motivation is that the scientists are also concerned with the idea of designing and making intelligent machines that can carry out certain tasks that we human beings do. The most salient outcome of these is the …

On Fractal Based Representation Of Image With Application To Image Processing., Suman Kumar Mitra Dr.

Doctoral Theses

The language of an image is universal. Images were the means of communicating infor- mation in ancient days. Even today, although people from different parts of the world speak in different languages, an image conveys almost the same universal meaning to all. With the rapid development of modern computer technologies and with the increasing attempt in getting information at ones finger tips, the importance of communication of information using images can not be ignored.Images are stored in computers in the form of a collection of bits representing pixels (picture elements). Pictures are to be digitized to store them in computers. …

Similarity Based Approximate Reasoning., Swapan Raha Dr.

Doctoral Theses

Many years of research in Artificial Intelligence, Cognitive Science and allied area reveal that the cognitive process of human reasoning deals with imprecise premises. As cognitive process of human reasoning is mainly concerned with the individual's perception, it is liable to be imprecise in nature. Precise traditional two-valued logic and/or multi-valued logics are not effective in handling such reasoning processes. This motivated Zadeh (109) to investigate how these impreciseness in human rea- soning could be modeled through some computable entities. In this regard, Zadeh has shown how such imprecise linguistic terms could be expressed through fuzzy sets over universes of …

Some Contribution To Reliability Analysis Of A Consecutive-K-Out-Of N: F System., Mohammad Khanjari Sadegh Dr.

Doctoral Theses

Present day technology has been characterized by development of complex systems or equipments containing a large number of subaystems and com- ponents. Reliability, as a buman attribute, has been praised for a very long time. For technical systems, however, the reliability concept has not been applied for more than about 50 years. Reliability is the concern of all scien- tists and engineers engaged in developing a system, from design, through the manufacturing, to its ultimate use. Reliability technology has a potentially wide range of application areas like safety or risk analysis, environmental protection, quality, optimization, maintenance, engineering design, etc.For a …

Quantum Stochastic Dilation Of Completely Positive Semigroups And Flows., Debashish Goswami Dr.

Doctoral Theses

The central theme of the present thesia is quantum stochastic dilation af semigroupe of completely panitive mapa on operator algebran. It is the sim of all mathemati- cal, or even all scientific theorics, to understand a given class of objects through a tanonical and simpler subclass of it. For example, abstract C"-algebras are studied through their conerete realisation as elgebra of operators, contractions on a Hilbert space by unitaries. Hilbert modules by the factorissble ones, to mention anly a few. In most af these caes, a general object of the relavant class is sociated with a canonical candidate of the …

Studies On Finite Linear Cellular Automata., Palash Sarkar Dr.

Doctoral Theses

Cellular Automata were originally proposed by John von Neumann as formal models of self reproducing organisms. The structure studied was mostly an ane and two dimensional infinite grida, though higher dimensions were also considered. Computation universality and other computation theoretic questions were considered important. See Burks [24] for a collection of essays on important problems on cellular automata during this period. Later physicists and biologists began to study cellular automsta for the purpose of modelling in their respective domains. In the present era, cellalar automata is being atudied from many widely different angles, and the relationship of these structurea to …

Uncertainity Principles On Some Lie Groups., Swagato Kumar Ray Dr.

Doctoral Theses

The uncertainty principles of Harmonic Analysis say that: a nonzero func- tion and its Fourier transform cannot both be sharply concen- trated. After the initial work on this phenomenon in 1920s, the last two decades witnessed a spurt of activity in this direction (we refer the reader to a very readable survey [FS]). One may notice two broad phases in this activity, the first concentrating on R where the notion of concentration is given different formulations to see whether the phenomenon still holds. In the later phase R is replaced by other commutative or noncommutative groups, or more generally by …

Generalised Bootstrap Techniques., Singdhansu Bhusan Chatterjee Dr.

Doctoral Theses

A typical problem in statistics is as follows: there is some observable data Xn = (X1,..., Xn), and a parameter of interest θ which is related in such a way to the distribution of Xn that meaningful conclusions about θ can be drawn based on Xn. Sometimes data Xn is observed keeping the objective parameter θ in mind, at other times the parameter appears while trying to model the observed data.Once the data is observed and the parameter fixed, the questions that have to be addressed are as follows:(I) How to estimate θ from the data Xn?(II) Given an estimator …