Digital Commons Network^™

Bergman Spaces On An Annulus And The Backward Bergman Shift, William T. Ross

Department of Math & Statistics Technical Report Series

In this paper, we will give a complete characterization of the invariant subspaces M (under ƒ → zƒ) of the Bergman space L^p_a(G), 1 < p < 2, G an annulus, which contain the constant function 1. As an application of this result, we will characterize the invariant subspaces of the adjoint of multiplication by z on the Dirichlet spaces D_q, q > 2, as well as the invariant subspaces of the backward Bergman shift ƒ → (ƒ – ƒ(0))/z on L^p_a(𝔻), 1 < p < 2.

Evolving Plane Curves By Curvature In Relative Geometries Ii, Michael E. Gage, Yi Li

Mathematics and Statistics Faculty Publications

In this paper we prove the existence of self-similar solutions to the anisotropic curve shortening equation.

Minimax-Optimal Strategies For The Best-Choice Problem When A Bound Is Known For The Expected Number Of Objects, Theodore P. Hill, D. P. Kennedy

Research Scholars in Residence

For the best-choice (or secretary) problem with an unknown number N of objects, minimax-optimal strategies for the observer and minimax distributions for N are derived under the assumption that N is a random variable with expected value at most M, where M is known. The solution is derived as a special case of the situation where N is constrained by Ef(N) ≤ M, where f is increasing with f(i)-f(i-1) convex.

Rational Cubic B-Spline Interpolation And Its Applications In Computer Aided Geometric Design, Kotien Wu

Mathematics & Statistics Theses & Dissertations

Because of the flexibility that the weights and the control points provide, NURBS have recently become very popular tools for the design of curves and surfaces. If the weights are positive then the NURB will lie in the convex hull of its control points and will not possess singularities. Thus it is desirable to have positive weights.

In utilizing a NURB a designer may desire that it pass through a set of data points {x_i} This interpolation problem is solved by the assigning of weights to each data point. Up to now little has been known regarding the …

Some Sampling Designs And Estimation Problems, Hassan Lakkis

Mathematics & Statistics Theses & Dissertations

In the first chapter we review some standard estimators in sampling from a finite population, and some design-based estimators in sampling from a continuous universe.

In concert with the theory initiated by professor Douglas Robson (personal communication) and later presented by Cordy (1993), we consider design-based variance estimation for probability sampling from a continuous and spatially distributed universe. Using this theory in chapter two, the sampling design of one random point from each cell of a translated grid is investigated and the problem of edge effects on estimation is illustrated with examples. Also in chapter four, standard systematic sampling methods …

Optimum Continuous Sampling Plans And A Few Other Sqc Problems., D Ghosh Dr.

Doctoral Theses

The wide acceptance of Statistics as a basic tool in technölogical growth, later recog- nised as a Key technology, gained ground with the pioneering work of Shewhart in 20s, introducing Statistical Quality Control (SQC) in manufacturing industry. Around the same time a solid statistical basis was being worked out for the ageold concepts of sampling inspection for industrial products. By 1930, acceptance sam- pling for lot by lot inspection was being applied in Western Electric Company and elsewhere. Since then statistical tools have been the major technical inputs of To- tal Quality Management which has spread far and wide as …

Pinching Theorems For Teardrops And Footballs Of Revolution, Joseph E. Borzellino

Mathematics

We give explicit optimal curvature pinching constants for the Riemannian (p, q)- football orbifolds under the assumption that they are realised as surfaces of revolution in ³. We show that sufficiently pinched sectional curvature assumptions imply that a (p, q)-football must be good.

Radially Symmetric Solutions To A Dirichlet Problem Involving Critical Exponents, Alfonso Castro, Alexandra Kurepa

All HMC Faculty Publications and Research

In this paper we answer, for N = 3,4, the question raised in [1] on the number of radially symmetric solutions to the boundary value problem -Δu(x) = λu(x) + u(x)|u(x)|^{4/(N-2)}, x ε B: = x ε R^N:{|x| < 1}, u(x)=0, x ε ∂B, where Δ is the Laplacean operator and λ>0. Indeed, we prove that if N = 3,4, then for any λ>0 this problem has only finitely many radial solutions. For N = 3,4,5 we show that, for each λ>0, the set of radially symmetric solutions is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.

Remarks On Automorphisms Of Subfactors, Phan Loi

Mathematics and Statistics Faculty Publications

We establish certain properties of automorphisms on an inclusion of AFD type II₁ factors with finite index and finite depth and discuss their applications to the classification problem of AFD type III subfactors, including a different proof of a result on subfactors with principal graph D_n.

A Hierarchy Of Nonlinear Evolution Equations And Finite-Dimensional Involutive Systems, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

A spectral problem and an associated hierarchy of nonlinear evolution equations are presented in this article. In particular, the reductions of the two representative equations in this hierarchy are given: one is the nonlinear evolution equation rl= - ar,- 2icu/3] r2] r which looks like the nonlinear Schrijdinger equation, the other is the generalized derivative nonlinear Schrijdinger equation rt= $ar,,- ialr12r- a/3(lr12r),- a j3I r I 2r,-2iap21r14r which is just a combination of the nonlinear Schrijdinger equation and two different derivative nonlinear Schrodinger equations [D. J. Kaup and A. C. Newell, J. Math. Phys. 19, 789 (1978); M. J. Ablowitz, …

The Crystalline Structure Of Mm3, A Derivative Of Dapsone, Tommie L. Heltcel

McCabe Thesis Collection

Dapsone is a drug which has recently been discovered as a potential treatment for the disease of leprosy. Many of the derivatives of dapsone have been sent to the United States by Dr. M. Muhundam and Professor M.S.R. Naidu of the Department of Chemistry, S.V. University, Tirupati, India, for structure analysis. One such derivative is (E)-3-[2-[(4-Chlorophenyl) sulphonyl] ethenyl]-4H-l-benzopyran-4-one, which will hereafter be referred to as MM3. MM3 was synthesized and the initial data for the structural analysis taken in the departments of Physics and Chemistry at S.V. University, Tirupati, India. The drug has been found to have a high antibacterial …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Creation And Simulation Of A Model For A Discrete Time Buffer System With Interrupted Poisson Arrivals And Uncorrelated Server Interruptions, Susanne Naegele-Jackson

Masters Theses & Specialist Projects

A mathematical model for a discrete-time buffer system with both arrival and server interruptions is developed. In this model fixed-size packets arrive at the buffer according to a Poisson distribution and are stored there until they can be transmitted over the output channel. Service times are constant and the buffer is assumed to be of infinite size. Both arrival stream as well as the service of the packets are subjected to random interruptions described by Bernoulli processes, where the interruption process of the Poisson input stream is uncorrelated to the interruptions of the output line. Expressions are derived for the …

Classification Characteristics Of Som And Art2, J. Aleshunas, D. St. Clair, W. Bond

Computer Science Technical Reports

Artificial neural network algorithms were originally designed to model human neural activities. They attempt to recreate the processes involved in such activities as learning, short term memory, and long term memory. Two widely used artificial neural network algorithms are the Self-Organizing Map (SOM) and the Adaptive Resonance Theory (ART2). Each was designed to simulate a particular biological neural activity. Both can be used as unsupervised data classifiers.

This paper compares performance characteristics of two unsupervised artificial neural network architectures; the SOM and the ART2 networks. The primary factors analyzed were classification accuracy, sensitivity to data noise, and sensitivity to the …

An Inverse Approach To A Probability Model For Fractured Networks, Stacy G. Vail

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A common problem in science and engineering applications deals with finding information about a system where only limited information is known. One example of this problem is determining the geometry of an aquifer or oil reservoir based on well tests taken at the site. The Conditional Coding Method attacks this type of problem. This method uses the Simulated Annealing Algorithm in conjunction with a probability model which generates possible solutions based on a uniform random number list. The Annealing Algorithm generates a conditional probability distribution on all possible solutions generated by the probability model, conditioned on the observed data set. …

Average Genus Of The Cube, Jody Koenemann

Honors Theses

In recent years, there has been interest in the mathematical community in a rapidly developing branch of theoretical mathematics known as random topological graph theory. This new area of mathematics explores the different ways in which certain graphs can be imbedded in given surfaces. The random nature of the new branch results when one also imposes a random distribution on set of all imbeddings of a fixed graph, via the orientation of the edges at each vertex. Using the technique of J. Edmonds, developed in 1960, this paper explores the imbeddings for the graph Q₃ using a particular group …

Third Order Degree Regular Graphs, Leslie D. Hayes

Honors Theses

A graph G is regular of degree d if for every vertex v in G there exist exactly d vertices at distance 1 from v. A graph G is kth order regular of degree d if for every vertex v in G, there exist exactly d vertices at distance k from v. In this paper, third order regular graphs of degree 1 with small order are characterized.

Retiling A Colored Hexagonal Plane, Kari Kelton

Mahurin Honors College Capstone Experience/Thesis Projects

No abstract provided.

Using The Id3 Symbolic Classification Algorithm To Reduce Data Density, Barry Fiachsbart, Daniel C. St. Clair, Jeff Holland

Mathematics and Statistics Faculty Research & Creative Works

Effective data reduction is mandatory for modeling complex domains. The work described here demonstrates how to use a symbolic classifier algorithm from machine learning to effectively reduce large amounts of data. The algorithm, Quirdan's ID3, uses input data records and corresponding classifications to produce a decision tree. The resulting tree can be used to classify previously unseen inputs. Alternatively, the attributes found in the tree can be used as the basis to develop other system modeling techniques such as neural networks or mathematical programming algorithms. This approach has been used to effectively reduce data from a large complex domain. The …

Classification Characteristics Of Som And Art2, J. J. Aleshunas, Daniel C. St. Clair, William E. Bond

Mathematics and Statistics Faculty Research & Creative Works

Artificial neural network algorithms were originally designed to model human neural activities. They attempt to recreate the processes involved in such activities as learning, short term memory, and long-term memory. Two widely used unsupervised artificial neural network algorithms are the Self-Organizing Map (SOM) and Adaptive Resonance Theory (ART2). Each was designed to simulate a particular biological neural activity. Both can be used as unsupervised data classifiers. This paper compares performance characteristics of two unsupervised artificial neural network architectures; the SOM and the ART2 networks. The primary factors analyzed were classification accuracy, sensitivity to data noise, and sensitivity of the algorithm …

Generating Indexing Functions Of Regularly Sparse Arrays For Array Compilers, Scott Thibault, Lenore Mullin, Matt Insall

Computer Science Technical Reports

There are many applications involving arrays that contain non-zero components in regular geometric partitions. These include triangular, diagonal, tridiagonal, banded, etc. When computing with this type of arrays, they are usually stored in a packed form and computations are performed with only the non-zero components. This packed form requires an indexing function that maps an index of the array to an index of the packed lexico-graphically stored array. This paper presents a method of describing regular partitions and of automatically generating an indexing function from that description. These methods enable an array compiler to compile array operations on these type …

A Construction Of Difference Sets In High Exponent 2-Groups Using Representation Theory, James A. Davis, Ken Smith

Department of Math & Statistics Faculty Publications

Nontrivial difference sets in groups of order a power of 2 are part of the family of difference sets called Menon difference sets (or Hadamard), and they have parameters (2^2d+2, 2^2d+1 ±2^d, 2^2d±2^d). In the abelian case, the group has a difference set if and only if the exponent of the group is less than or equal to 2^d+2. In [14], the authors construct a difference set in a nonabelian group of order 64 and exponent 32. This paper generalizes that result to …

Monads And Realcompactness, Sergio Salbany, Todor D. Todorov

Mathematics

We give a quantifier free characterization of realcompactness and ordered realcompactness in terms of monads. We also present simple proofs of some topological facts concerning realcompact spaces.

A Special Class Of Almost Disjoint Families, Thomas E. Leathrum

Dartmouth Scholarship

The collection of branches (maximal linearly ordered sets of nodes) of the tree ${}^{<\omega}\omega$ (ordered by inclusion) forms an almost disjoint family (of sets of nodes). This family is not maximal -- for example, any level of the tree is almost disjoint from all of the branches. How many sets must be added to the family of branches to make it maximal? This question leads to a series of definitions and results: a set of nodes is {\it off-branch} if it is almost disjoint from every branch in the tree; an {\it off-branch family} is an almost disjoint family of off-branch sets; ${\frak o}=\min\{|{\Cal O}|: {\Cal O}$ is a maximal off-branch family$\}$. Results concerning $\frak o$ include: (in ZFC) ${\frak a}\leq{\frak o}$, and (consistent with ZFC) $\frak o$ is not equal to any of the standard small cardinal invariants $\frak b$, $\frak a$, $\frak d$, or ${\frak c}=2^\omega$. Most of these consistency results use standard forcing notions -- for example, $Con({\frak b}={\frak a}<{\frak o}={\frak d}={\frak c})$ comes from starting with a model of $ZFC+CH$ and adding $\omega_2$-many Cohen reals. Many interesting open questions remain, though -- for example, $Con({\frak o}<{\frak d})$.

Markov Dilation Of Nonconservative Quantum Dynamical Semigroups And Quantum Boundary Theory., B. V. Rajarama Bhat Dr.

Doctoral Theses

In classical probability theory, based on Kolmogorov consistency theorem, one can associate a Markov process to any one parameter semigroup of stochastic matrices or transition probability operators. It is indeed the foundation for the theory of Markov processes. Here a quantum version of this theorem has been established. This effectively answers some of the questions raised by P. A. Meyer in his book (see page 220 of (Me).It is widely agreed upon that irreversible dynamics in the quantum setting is de- scribed by contractive semigroups of completely positive maps on C" algebras ([Kr). (AL]). In other words these semigroups, known …

The Prime Decomposition Of Knotted Periodic Orbits In Dynamical Systems, Michael C. Sullivan

Articles and Preprints

Templates are used to capture the knotting and linking patterns of periodic orbits of positive entropy flows in 3 dimensions. Here, we study the properties of various templates, especially whether or not there is a bound on the number of prime factors of the knot types of the periodic orbits. We will also see that determining whether two templates are different is highly nontrivial.

Extrapolating Human Probability Judgment, Daniel N. Osherson, Edward E. Smith, Tracy S. Myers, Eldar Shafir, Michael Stob

University Faculty Publications and Creative Works

We advance a model of human probability judgment and apply it to the design of an extrapolation algorithm. Such an algorithm examines a person's judgment about the likelihood of various statements and is then able to predict the same person's judgments about new statements. The algorithm is tested against judgments produced by thirty undergraduates asked to assign probabilities to statements about mammals.

Discrete Singularity Method And Its Application To Incompressible Flows., S K. Venkatesan Dr.

Doctoral Theses

The smooth flow of a fluid has sprung many surprises. A flow which at an instant of time is quite regular and orderly could produce on the slightest of disturbance a complex bewildering varieties of flows, broadly termed as turbulence. Direct numerical simulation of the Navier-Stokes equations have shown that it is quite possible that these turbulent flows are solutions of the Navier-Stokes equations. In fact it is by now well recognized that many non-linear systems produce chaos quite similar to turbulence. However the large number of scales and their complex interactions involved make turbulence difficult to understand. Direct numerical …

Stability Of Cereal Crop Yields' Performance: An Econometric Analysis For India And Andhra Pradesh., A. Ganesh Kumar Dr.

Doctoral Theses

Agriculture is an importannt sector of the economy in many developing countries. Of late, in many countries, this sector Is believed to be suffering from unstable performance, especially where the modern (Green Revolutlon) technology has been widely adopted. The issue of stability of agricul tura! performance is one of international concern. This thesis is about the performance of cereal crop yiel ds in India.Importance of Agriculture in the Indian Economy.Agriculture is an important sector Aooounting for more than 30% of the countrys national 1988-89, the performance of agriculture, both as nateriais for industrla! producelon ponsumption demand, determines of the Indian …

Three Aspects Of Industrial Dualism In A Developing Economy., Malbika Roy Dr.

Doctoral Theses

The concept of duali sm which has remained central to the study of the by of economic development, was first developed process Lewis(1954) and then further extended by Fel and Ranis(1966). Lewis concelved of a developing economy as one typically consisting of two sectors: a modern sector identified with industry, and a traditional sector identified with agriculture. Resources flow from the traditional to the modern sector whlle the process of development continues. As a consequence, the modern sector grows and the traditional sector shrinks. Some of the other development economists used other facets of dualism. Harris-Todaro(1970) explained the process of …