Physical Sciences and Mathematics Commons^™

Analytic Besov Spaces And Invariant Subspaces Of Bergman Spaces, William T. Ross

Department of Math & Statistics Faculty Publications

In this paper, we examine the invariant subspaces (under the operator f -->z f) M of the Bergman space ^p_a (G\T) (where 1 < p < 2, G is a bounded region in C containing D, T is the unit circle, and D is the unit disk) which contain the characteristic functions x_D and x_G, i.e. the constant functions on the components of G\T. We will show that such M are in one-to-one correspondence with the invariant subspaces of the analytic Besov space AB_q (q is the conjugate index to p) and …

Nonstandard Analysis Based Calculus, Kathleen Renae Gibson

Theses Digitization Project

In the first part of the project the elementary development of an extended number system called Hyperreals is discussed. The second half of this project develops the basics of Nonstandard Analysis, including the theory of ultrafilters, and the formal construction of the Hyperreals.

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.

On Endomorphisms And Automorphisms Of Some Pure Subgroups Of The Baer-Specker Group, A. L.S. Corner, Brendan Goldsmith

Articles

The endomoprhism algebras of certain pure subgroups of the Baer-Specker group are investigated to answer a question of Irwin. Automorphism groups of these Abelian groups are investigated and a realization theme is established.

Characterization Of The Local Lipschitz Constant, M. W. Bartelt, J. J. Swetits

Mathematics & Statistics Faculty Publications

A characterization, using polynomials introduced by A. V. Kolushov, is given for the local Lipschitz constant for the best approximation operator in Chebyshev approximation from a Haar set. The characterization is then used to study the existence of uniform local Lipschitz constants.

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 …

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 …

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 …

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 …

Proof Without Words: Fair Allocation Of A Pizza, Stan Wagon, L. Carter

Stan Wagon, Retired

No abstract provided.

The Power Of Visualization: Notes From A Mathematica Course, Stan Wagon

Stan Wagon, Retired

No abstract provided.

A Mathematical Magic Trick, Stan Wagon

Stan Wagon, Retired

No abstract provided.

Foliations Transverse To Fibers Of Seifert Manifolds, Ramin Naimi

Ramin Naimi

No abstract provided.

Constructing Essential Laminations In 3-Manifolds Obtained By Surgery On 2-Bridge Knots, Ramin Naimi

Ramin Naimi

No abstract provided.

Clam Demography, Stan Wagon

Stan Wagon, Retired

No abstract provided.

Symmetrical Porosity Of Symmetrical Cantor Sets, M. Evans, P. Humke, Karen Saxe

Karen Saxe

No abstract provided.

Hexagons And Squares In A Passive Nonlinear Optical System, John Geddes, R.A. Indik, J.V. Moloney, Willie Firth

John B. Geddes

Pattern formation is analyzed and simulated in a nonlinear optical system involving all three space dimensions as well as time in an essential way. This system, counterpropagation in a Kerr medium, is shown to lose stability, for sufficient pump intensity, to a nonuniform spatial pattern. We observe hexagonal patterns in a self-focusing medium, and squares in a self-defocusing one, in good agreement with analysis based on symmetry and asymptotic expansions.

A Note On The Real Symmetric Eigenvalue, William F. Trench

William F. Trench

No abstract provided.

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 …