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Multigrid Acceleration Of Time-Dependent Solutions Of Navier-Stokes Equations, Sarafa Oladele Ibraheem

Mechanical & Aerospace Engineering Theses & Dissertations

Recent progress in Computational Fluid Dynamics is encouraging scientists to look at fine details of flow physics of problems in which natural unsteady phenomena have hitherto been neglected. The acceleration methods that have proven very successful in steady state computations can be explored for time dependent computations. In this work, an efficient multigrid methods is developed to solve the time-dependent Euler and Navier-Stokes equations. The Beam-Warming ADI method is used as the base algorithm for time stepping calculations. Application of the developed algorithm proved very efficient in selected steady and unsteady test problems. For instance, the inherent unsteadiness present in …

Invariant Manifolds Of A Toy Climate Model, Michael Toner

Mathematics & Statistics Theses & Dissertations

According to astronomical theory, ice ages are caused by variations in the Earth's orbit. However, ice core data shows strong fluctuations in ice volume at a low frequency not significantly present in orbital variations. To understand how this might occur, the dynamics of a two dimensional nonlinear differential equation representing glacier/temperature interaction of an idealized climate was studied. Self sustained oscillation of the autonomous equation was used to model the internal mechanisms that could produce these fluctuations. Periodic parametric modulation of a damped internal oscillation was used to model periodic climate response at double the external modulation period. Both phenomena …

An Algorithm For Suslin's Stability Theorem, Cynthia Huffman Ph.D.

Faculty Submissions

In 1977, A.A. Suslin proved that Em (R), the subgroup of the general linear group GLm(R) which is generated by the elementary matrices, is equal to the special linear group SLm (R), whenever R is a polynomial ring in n variables over a field and m is at least three. This dissertation contains an algorithmic proof of this result which is now known as Suslin's Stability Theorem, thus providjng an algorithm for factoring a polynomial matrix with determinant one into a product of elementary matrices. There are three key parts to the algorithm: reduction to a special case by using …

Statistical Analysis Of Survival Data, Rexanne Marie Bruno

UNF Graduate Theses and Dissertations

The terminology and ideas involved in the statistical analysis of survival data are explained including the survival function, the probability density function, the hazard function, censored observations, parametric and nonparametric estimations of these functions, the product limit estimation of the survival function, and the proportional hazards estimation of the hazard function with explanatory variables.

In Appendix A these ideas are applied to the actual analysis of the survival data for 54 cervical cancer patients.

A Relationship Between The Fibonacci Sequence And Cantor's Ternary Set, John David Samons

UNF Graduate Theses and Dissertations

The Fibonacci sequence and Cantor's ternary set are two objects of study in mathematics. There is much theory published about these two objects, individually. This paper provides a fascinating relationship between the Fibonacci sequence and Cantor's ternary set. It is a fact that every natural number can be expressed as the sum of distinct Fibonacci numbers. This expression is unique if and only if no two consecutive Fibonacci numbers are used in the expression--this is known as Zekendorf's representation of natural numbers. By Zekendorf's representation, a function F from the natural numbers into [0,0.603] will be defined which has the …

The Recurrence Relation Of B-Wavelets, Rumi Kumazawa '94

Honors Projects

Our goal is to construct smooth wavelet functions. In constructing such wavelet functions, we need a smooth scaling function to begin with. B-spline functions are suitable as our scaling function because they are piecewise polynomials with compact supports and are relatively smooth. B-wavelet functions are just dilations and translations of these B-spline functions. In addtion, we can find a recurrence relation of the B-spline functions with different order. Hence B-wavelets of any order can be constructed successively from the lower order ones.

A Partial "Squeezing Theorem" For A Particular Class Of Many-Valued Logics, Stephen Michael Walk

Dissertations and Theses @ UNI

The problem to be studied for this thesis was that of whether the usual statement calculus is a suitable formal system for every many-valued logic in a particular collection of logics. The logics in question are those that fall between the usual two-valued logic and a modified form of the Lukasiewicz-Tarski three-valued logic.

Since this betweenness relationship was an original concept and appeared nowhere in the literature, the first goal in the research plan was to define this relationship precisely. Preliminary concepts included truth value mapping and forgivingness of logics, concepts that, like betweenness, are original to this paper and …

On Cohesion Stable Graphs, Virginia Rice, Richard D. Ringeisen

Mathematics & Statistics Faculty Publications

The cohesion of a graph was introduced to model vulnerability of a graph relative to the neighborhoods of its vertices. We are concerned in this paper with the changes in this parameter when an edge is deleted. In particular, after displaying some results on stability under edge destruction, we go on to display various infinite classes of cohesion stable graphs. Several ways in which graphs or parts of graphs may be combined to produce stable graphs are also presented, along with a look at what cannot be stated at this time.

Modelling Time Series Using Time Varying Coefficient Autoregressive Models : With Application To Several Data Sets, Retno Maharesi

Theses: Doctorates and Masters

In this thesis the state space approach and the Kalman recursions are used for modelling univariate time series data. The models that are examined in this thesis are time varying Coefficient Autoregressive models, which can be represented in state space form. The coefficients are assumed to change according to a stationary process, a non-stationary process or a random process. In order to be able to estimate these changing unknown coefficients, they will be treated as state variables and the equation describing the changes of the state variables will be given by the state equation. The model can then be expressed …

Quantile-Locating Functions And The Distance Between The Mean And Quantiles, D. Gilat, Theodore P. Hill

Research Scholars in Residence

Given a random variable X with finite mean, for each 0 < p < 1, a new sharp bound is found on the distance between a p-quantile of X and its mean in terms of the central absolute first moment of X. The new bounds strengthen the fact that the mean of X is within one standard deviation of any of its medians, as well as a recent quantile-generalization of this fact by O'Cinneide.

A Non-Homogeneous, Spatio-Temporal, Wavelet Multiresolution Analysis And Its Application To The Analysis Of Motion, Thomas J. Burns

Theses and Dissertations

This research presents a multiresolution wavelet analysis tool for analyzing motion in time sequential imagery. A theoretical framework is developed for constructing an L2R wavelet multiresolution analysis from three non-identical spatial and temporal L2R wavelet multiresolution analyses. This framework provides the flexibility to tailor the spatio-temporal frequency characteristics of the three dimensional wavelet filter to match the frequency behavior of the analyzed signal. An unconventional, discrete multiresolution wavelet decomposition algorithm is developed which yields a rich set of independent spatio-temporally oriented frequency channels for analyzing, the size and speed characteristics of moving objects. Unlike conventional wavelet decomposition methods, this algorithm …

Interaction Of Price And Technology In The Presence Of Structural Specificities:An Analysis Of Crop Production In Kerala., Delampady Narayana Dr.

Doctoral Theses

The present study attempts to understand the agricultural economy of Kerala in terms of the structural characteristics specific to the state. This approach requires such aspects to be incorporated in the analysis, and also entails a shift from certain accepted modes of thinking and statistical treatment used in the analysis of field crops.The specificities arise from certain distinctive features on the demand and supply sides'. On the demand side, there is substi tution between rice and tapioca, and the two crops constitute the food group. The rest of the crops form the non-food group, and there is no substitution among …

On Image Segmentation Using Neural Networks And Fuzzy Sets., Ashish Ghosh Dr.

Doctoral Theses

During the last five decades or even more a large number of researchers are trying to design intelligent systems to perform tasks at which human beings are more efficient at present. One of the most important behavioral tasks in which human beings show their expertise is image analysis or recognition; where a large amount of pictorial data is processed in a very small amount of time (called real time). Widespread attempts have been made to develop intelligent systems (under different names, like pattern recognition system, image under- standing system, computer vision system etc.) for pictorial pattern analysis and recognition. The …

Splitting Theorems In Recursion Theory, Rod G. Downey, Michael Stob

University Faculty Publications and Creative Works

A splitting of an r.e. set A is a pair A1, A2 of disjoint r.e. sets such that A1 ∪ A2 = A. Theorems about splittings have played an important role in recursion theory. One of the main reasons for this is that a splitting of A is a decomposition of A in both the lattice, ε, of recursively enumerable sets and in the uppersemilattice, R, of recursively enumerable degrees (since A1 ≤T A, A2 ≤T A and A ≤T A1 ⊕ A2). Thus splitting theor ems have been used to obtain results about the structure of ε, the structure …

Reconstruction Of Multiple Cracks From Experimental, Electrostatic Boundary Measurements, Kurt M. Bryan, Valdis Liepa, Michael Vogelius

Mathematical Sciences Technical Reports (MSTR)

We demonstrate the viability of using Electrical Impedance Tomography (EIT) for the reconstruction of multiple macroscopic cracks in a conductive medium.

Tangential And Normal Euler Numbers, Complex Points, And Singularities Of Projections For Oriented Surfaces In Four-Space, Thomas Banchoff, Frank A. Farris

Mathematics and Computer Science

For a compact oriented smooth surface immersed in Euclidean four-space (thought of as complex two-space), the sum of the tangential and normal Euler numbers is equal to the algebraic number of points where the tangent plane is a complex line. This follows from the construction of an explicit homology between the zero-chains of complex points and the zero-chains of singular points of projections to lines and hyperplanes representing the tangential and normal Euler classes.

Controllability And Stabilizability Of Coupled Strings With Control Applied At The Coupled Points, Lop-Fat Ho

Mathematics and Statistics Faculty Publications

Controllability and stabilizability of a system of coupled strings with control applied at the coupled points is studied. By investigating the properties of certain exponential series, it is shown that the system is approximate controllable if and only if related systems of uncoupled strings do not share a common eigenvalue. A sufficient condition for exact controllability is also obtained in terms of the Riesz basis properties of those exponential series.

Stacking Ellipses -- Revisited, Calvin Jongsma

Faculty Work Comprehensive List

Response to the article “Stacking Ellipses” by Richard E. Pfiefer in The College Mathematics Journal, Vol. 22, No. 4 (Sep., 1991), pp. 312-313.

New Constructions Of Menon Difference Sets, K. T. Arasu, James A. Davis, Jonathan Jedwab, Surinder K. Sehgal

Department of Math & Statistics Faculty Publications

Menon difference sets have parameters (4N², 2N² − N, N² − N). These have been constructed for N = 2^a3^b, 0 ⩽ a,b, but the only known constructions in abelian groups require that the Sylow 3-subgroup be elementary abelian (there are some nonabelian examples). This paper provides a construction of difference sets in higher exponent groups, and this provides new examples of perfect binary arrays.

On Markov Processes Charecterised Via Martingale Problem., Abhay G. Bhatt Dr.

Doctoral Theses

Martingale approach to the study of finite dimensional diffusions was initiated by Stroock-Varadhan, who coined the term martingale problem. Their success led to a similar approach being used to study Markov processes occuring in other areas such as infinite particle systems, branching processes, genetic models, density dependent population processes, random evolutions etc.Suppose X is a Markov process corresponding to a semigroup (T)e20 with generator L. Then all the information about X is contained in L. We also have thatMf(t) := f(X(t)) – ∫t0 Lf(X(s))dsis a martingale for every f ∈ D(L). i.e. X is a solution to the martingale problem …

A Run-Time Decision Procedure For Responsive Computing Systems, Grace Tsai, Matt Insall, Bruce M. Mcmillin

Computer Science Technical Reports

A responsive computing system is a hybrid of real-time, distributed and fault-tolerant systems. In such a system, severe consequences will occur if the logical and physical specifications of the system are not met. In this paper, we present a logic, Interval Temporal Logic (ITL), to specify responsive systems and give decision procedures to verify properties of the system at run-time as follows. First, we collect, during execution, events occurring in the system to represent a distributed computation. Next, we specify properties of the system using ITL formulas. Finally, we apply the decision procedures to determine satisfaction of the formulas. Thus, …

Imsa Math Journal: A Resource Notebook For High School Mathematics, Illinois Math And Science Academy

IMSA Math Journal

Welcome to the second issue of the IMSA Math Journal, an official publication of the Illinois Mathematics and Science Academy. The purpose of the IMSAMJ i s to communicate through mathematics with both students and teachers. Some of our goals include:

• Presenting teaching insights, lessons, problems.
• Sharing mathematical ideas, mathematical teaching ideas, observations, approaches, connections, extensions, generalizations of interest to students and teachers of mathematics.
• Featuring mathematics problems for both in the classroom and outside the classroom, i.e. math contests, math competitions, etc.
• Discussing and sharing the role of technology including calculators and computers in the instruction and learning of …

On Revelation Transforms That Characterize Probability Distributions, Stefanka Chukova, Boyan N. Dimitrov, Jean Pierre Dion

Mathematics Publications

A characterization of exponential, geometric and of distributions with almost-lack-of-memory property, based on the revelation transform of probability distributions and relevation of random variables is discussed. Known characterizations of the exponential distribution on the base of relevation transforms given by Grosswald et al. [4], and Lau and Rao [7] are obtained under weakened conditions and the proofs are simplified. A characterization the class of almost-lack-of-memory distributions through the relevation is specified.

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

The Lazer Mckenna Conjecture For Radial Solutions In The Rn Ball, Alfonso Castro, Sudhasree Gadam

All HMC Faculty Publications and Research

When the range of the derivative of the nonlinearity contains the first k eigenvalues of the linear part and a certain parameter is large, we establish the existence of 2k radial solutions to a semilinear boundary value problem. This proves the Lazer McKenna conjecture for radial solutions. Our results supplement those in [5], where the existence of k + 1 solutions was proven.

Harmonic-Analysis Of Fractal Measures Induced By Representations Of A Certain C*-Algebra, Palle Jorgensen, Steen Pedersen

Mathematics and Statistics Faculty Publications

We describe a class of measurable subsets Ω in R^d such that L²(Ω) has an orthogonal basis of frequencies e_λ(x) = e^i2πλ.x(x ε Ω) indexed by λ ∈ Λ ⊂ R^d. We show that such spectral pairs (Ω, Λ) have a self-similarity which may be used to generate associated fractal measures μ with Cantor set support. The Hilbert space L²(μ) does not have a total set of orthogonal frequencies, but a harmonic analysis of mu may be built instead from a natural representation of the Cuntz …

A Note On New Semi-Regular Divisible Difference Sets, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

We give a construction for new families of semi-regular divisible difference sets. The construction is a variation of McFarland's scheme [5] tor noncyclic difference sets.

Joint Venture And Bargaining., Prabal Ray Chaudhuri Dr.

Doctoral Theses

My dissertation deals with some problems in theoretical economics. The five essays in this thesis can be classified under the broad categories of industrial organization and game theory.Part I of the thesis comprises three chapters. These deal with some issues in the area of joint ventures and technology transfer. Chapter 2 investigates the relationship between technological dissimilarity and joint venture success. The third chapter explores some policy issues related to joint product development. Chapter 4 examines the relative efficacy of centralized and decentralized bargaining schemes in technology transfer.In part II I examine some issues in bargaining theory. The fifth chapter …

Constructing An Interval Temporal Logic For Real-Time Systems, Grace Tsai, Matt Insall, Bruce M. Mcmillin

Computer Science Technical Reports

A real-time system is one that involves control of one or more physical devices with essential timing requirements. Examples of these systems are command and control systems, process control systems, flight control systems, and the space shuttle avionics systems. The characteristics of these systems are that severe consequences will occur if the logical and physical timing specifications of the systems are not met.

Formal specification and verification are among the techniques to achieve reliable software for real-time systems, in which testing may be impossible or too dangerous to perform. This paper presents a modal logic, Interval Temporal , built upon …

Approximation Methods For Singular Diffusions Arising In Genetics, Nacer E. Abrouk

Mathematical Sciences Technical Reports (MSTR)

Stochastic models in population genetics leading to diffusion equations are considered. When the drift and the square of the diffusion coefficients are polynomials, an infinite system of ordinary differential equations for the moments of the diffusion process can be derived using the Martingale property. An example is provided to show how the classical Fokker-Planck Equation approach may not be appropriate for this derivation. A Gauss-Galerkin method for approximating the laws of the diffusion, originally proposed by Dawson (1980), is examined. In the few special cases for which exact solutions are known, comparison shows that the method is accurate and the …