Digital Commons Network^™

Fermi Problems: Educated Guesses, John A. Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Galois Module Structure Of Ideals In Wildly Ramified Cyclic Extensions Of Degree P2, Gove Griffith Elder

Mathematics Faculty Publications

For L/K, any totally ramified cyclic extension of degree p2 of local fields which are finite extensions of the field of p-adic numbers, we describe the Zp[Gal(L/K)]-module structure of each fractional ideal of L explicitly in terms of the 4p+1 indecomposable Zp[Gal(L/K)]-modules classified by Heller and Reiner. The exponents are determined only by the invariants of ramification.

Spectral Properties Of Operators Having Dense Orbits, Valentin Matache

Mathematics Faculty Publications

In the following H will denote a separable, infinite-dimensional, complex Hilbert space. The term operator will always mean linear, bounded operator on H. By invariant subspace we mean closed, invariant linear manifold. For a given operator T, the set of all invariant subspaces of T will be denoted LatT, since obviously it is a lattice. The set of all operators commuting with T is denoted {T}'. A subspace will be called hyperinvariant for T if it is invariant under any operator in {T}'.

Estimating Transition Probabilities From Aggregate Samples Augmented By Haphazard Recaptures, D. L. Hawkins, Jerome Eisenfeld, C. P. Han

Mathematics Technical Papers - Archive

Transition probabilities provide a convenient summary of changes in a categorical trait over time in a population. The difficulties of estimating such probabilities based on only aggregate data from repeated sampling are well known. We give here a method for augmenting aggregate data with haphazard recapture data, which can dramatically improve the estimation precision of transition probabilities. The method requires a rather high sampling fraction to provide sufficient numbers of recaptures. It is based on a generalized nonlinear least squares strategy which yields transition probability estimates preserving their natural parameter space, and which are asymptotically efficient. The asymptotic theory is …

A Note On Reordering Ordered Topological Spaces And The Existence Of Continuous, Strictly Increasing Functions, Joe Mashburn

Mathematics Faculty Publications

The origin of this paper is in a question that was asked of the author by Michael Wellman, a computer scientist who works in artificial intelligence at Wright Patterson Air Force Base in Dayton, Ohio. He wanted to know if, starting with Rn and its usual topology and product partial order, he could linearly reorder every finite subset and still obtain a continuous function from Rⁿ into R that was strictly increasing with respect to the new order imposed on Rⁿ. It is the purpose of this paper to explore the structural characteristics of ordered topological spaces …

Singular Boundary Value Problems For Quasi-Differential Equations, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

Solutions are obtained of boundary value problems for Lny+f(x,L0y,…,Ln−2y), satisfying L2y(0)=Ln−1y(1)=0, 0≤i≤n−2, where Li, denotes the ith quasiderivative, and where f(x,y1,…,yn−1) has singularities at yi=0, 1≤i≤n−1.

Multipoint Boundary Value Problems For Functional Differential Equations, Paul W. Eloe, Johnny Henderson, Denise Taunton

Mathematics Faculty Publications

No abstract provided.

Positive Solutions For Higher Order Ordinary Differential Equations, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

Solutions that are positive with respect to a cone are obtained for the boundary value problem, u(n) + a(t)f(u) = 0, u(i)(0) = u(n−2)(1) = 0, 0 _ i _ n − 2, in the cases that f is either superlinear or sublinear. The methods involve application of a _xed point theorem for operators on a cone.

Behavior Of The Solutions To A Functional Equation Which Equates A Function's Inverse To Its Reciprocal, Robert Rudolph Anschuetz

Retrospective Theses and Dissertations

This thesis explores the behavior of solutions of the functional equation f-1(x)= 1/f(x) for x ε Dom(f), where f is a real-valued function of a real variable. It is quite common to mistake the notation f^-1, which means the inverse of f with respect to composition with the inverse of f with respect to multiplication, usually denoted by 1/f. This thesis shows that although f^-1 and 1/f are usually different function, they do indeed sometimes represent the same function. This thesis will also provide …

The Trace Of An Abelian Group:An Application To Digraphs, J. M. Burns, Brendan Goldsmith

Articles

The trace of a finite Abelian group is used to give a short proof of a result of Arlinghaus and Harary on the digraph number of such a group

Partial Least-Squares: Theoretical Issues And Engineering Applications In Signal Processing, Fredric M. Ham, Ivica Kostanic

Mathematics and System Engineering Faculty Publications

In this paper we present partial least-squares (PLS), which is a statistical modeling method used extensively in analytical chemistry for quantitatively analyzing spectroscopic data. Comparisons are made between classical least-squares (CLS) and PLS to show how PLS can be used in certain engineering signal processing applications. Moreover, it is shown that in certain situations when there exists a linear relationship between the independent and dependent variables, PLS can yield better predictive performance than CLS when it is not desirable to use all of the empirical data to develop a calibration model used for prediction. Specifically, because PLS is a factor …

Singularity Of Super-Brownian Local Time At A Point Catalyst, Donald A. Dawson, Klaus Fleischmann, Yi Li, Carl Mueller

Mathematics and Statistics Faculty Publications

No abstract provided.

Cardinal Invariants Concerning Functions Whose Sum Is Almost Continuous, Krzysztof Ciesielski

Faculty & Staff Scholarship

Let A stand for the class of all almost continuous functions from R to R and let A(A) be the smallest cardinality of a family F ⊆ R R for which there is no g: R → R with the property that f + g ∈ A for all f ∈ F. We define cardinal number A(D) for the class D of all real functions with the Darboux property similarly. It is known, that c < A(A) ≤ 2 c [10]. We will generalize this result by showing that the cofinality of A(A) is greater that c. Moreover, we will show that it is pretty much all that can be said about A(A) in ZFC, by showing that A(A) can be equal to any regular cardinal between c + and 2c and that it can be equal to 2c independently of the cofinality of 2c . This solves a problem of T. Natkaniec [10, Problem 6.1, p. 495]. We will also show that A(D) = A(A) and give a combinatorial characterization of this number. This solves another problem of Natkaniec. (Private communication.)

Nozzle Flow With Vibrational Nonequilibrium, John Gary Landry

Mathematics & Statistics Theses & Dissertations

Flow of nitrogen gas through a converging-diverging nozzle is simulated. The flow is modeled using the Navier-Stokes equations that have been modified for vibrational nonequilibrium. The energy equation is replaced by two equations. One equation accounts for energy effects due to the translational and rotational degrees of freedom, and the other accounts for the affects due to the vibrational degree of freedom. The energy equations are coupled by a relaxation time which measures the time required for the vibrational energy component to equilibrate with the translational and rotational energy components. An improved relaxation time is used in this thesis. The …

The Composition Of Operator-Valued Measurable Functions Is Measurable, Albert Badrikian, G. W. Johnson, Il Yoo

Department of Mathematics: Faculty Publications

Given separable Frechet spaces, E, F , and G , let L(E, F), L(F, G), and L(E, G) denote the space of continuous linear operators from E to F , F to G, and E to G, respectively. We topologize these spaces of operators by any one of a family of topologies including the topology of point-wise convergence and the topology of compact convergence. We will show that if (X, F) is any measurable space and both A: X → L(E, F) and B: X → L(F, G) are Borelian, then the operator composition BA: X → L(E, G) is …

Generalized Geynman Integrals: The 𝓛(L2, L2) Theory, Chull Park, David Skough

Department of Mathematics: Faculty Publications

In this paper we develop an 𝓛(L₂(R), L₂(R)) theory for the Feynman integral of functionals of general stochastic processes.

Uniformly Antisymmetric Functions And K5, Krzysztof Ciesielski

Faculty & Staff Scholarship

A function f from reals to reals (f:R-->R) is a uniformly antisymmetric function if there exists a gage function g:R-->(0,1) such that |f(x-h)-f(x+h)| is greater then or equal to g(x) for every x from R and 0R-->N, (see [K. Ciesielski, L. Larson, Uniformly antisymmetric functions, Real Anal. Exchange 19 (1993-94), 226-235]) while it is unknown whether such function can have a finite or bounded range. It is not difficult to show that there exists a uniformly antisymmetric function with an n-element range if and only if there exists a …

Numeric Transmission/Cultural Transition, Paul B. Pekarek

Honors Theses, 1963-2015

This thesis is a study of the computational methods and common use of mathematics during the Middle Ages. It also discusses the cultural transition that was associated with the numeric transition from the Roman numeral system to the Hindu-Arabic numeral system and the numeric systems' corresponding calculation methods in Christian Europe during the late Middle Ages and early Renaissance. I claim that the transition from Roman numerals to Hindu-Arabic numerals was a result of cultural influences. Furthermore, I show that the transition was steady and found its basis in preexisting forms of calculation. I also look at the influences that …

Rapid Rural Appraisal Of Household Adaptations To The Coastal Zone Of Ecuador, Jennifer A. Pereira

Marine Affairs Theses and Major Papers

It has become clear to those interested in development that the household is an integral institution linking the individual to the society and the environment. Understanding the functioning of this institution will facilitate improvements in planning, evaluation, and output of development projects. Development projects suffer from a lack of efficient research methods for collecting socioeconomic information regarding the household. It has been proposed that Rapid Rural Appraisal (RRA), a method of field work that is timely, flexible, and places an emphasis on local participation, may be an appropriate method for collecting these types of data. RRA was originally developed for …

Slow Motion In One-Dimensional Cahn-Morral Systems, Christopher P. Grant

Faculty Publications

In this paper we study one-dimensional Cahn-Morral systems, which are the multicomponent analogues of the Cahn-Hilliard model for phase separation and coarsening in binary mixtures. In particular, we examine solutions that start with initial data close to the preferred phases except at finitely many transition points where the data has sharp transition layers, and we show that such solutions may evolve exponentially slowly; i.e., if ε is the interaction length then there exists a constant C such that in exp(C/ε) units of time the change in such a solution is o(1). This corresponds to extremely slow coarsening of a multicomponent …

A Mathematical Model Of Cycle Chemotherapy, J. C. Panetta, J. Adam

Mathematics & Statistics Faculty Publications

A mathematical model is used to discuss the effects of cycle-specific chemotherapy. The model includes a constraint equation which describes the effects of the drugs on sensitive normal tissue such as bone marrow. This model investigates both pulsed and piecewise-continuous chemotherapeutic effects and calculates the parameter regions of acceptable dose and period. It also identifies the optimal period needed for maximal tumor reduction. Examples are included concerning the use of growth factors and how they can enhance the cell kill of the chemotherapeutic drugs.

Ensuring The Satisfaction Of A Temporal Specification At Run-Time, Grace Tsai, Matt Insall, Bruce M. Mcmillin

Mathematics and Statistics Faculty Research & Creative Works

A responsive computing system is a hybrid of real-time, distributed and fault-tolerant systems. In such a system, severe consequences can occur if the run-time behavior does not conform to the expected behavior or specifications. In this paper, we present a formal approach to ensure satisfaction of the specifications in the operational environment as follows. First we specify behavior of the systems using Interval Temporal Logic (ITL). Next we give algorithms for trace checking of programs in such systems. Finally, we present a fully distributed run-time evaluation system which causally orders the events of the system during its execution and checks …

Multiquadric Interpolation: Surface Fitting In Three-Dimensional Space, Michelle Ruse

Presidential Scholars Theses (1990 – 2006)

Using mathematics to solve a problem does not always yield a perfect or absolute answer but may instead yield an approximate solution. We can try to approximate the solution as precisely as possible by using the mathematical tools and skills that are available to us or we could try to discover new methods which would enable us to find good approximations. It is important that we have precise approximating tools to begin with, so that we may preserve as much accuracy as possible.

We can find such problems in the world around us. For instance, if we try to construct …

Right Angle Electrical Connector And Insertion Tool Therefor, Stephen L. Clark, Glenn J. Pontius

Mathematics and Statistics Faculty Research & Creative Works

Disclosed is a multi-row right angle connector and a press block for installing the connector on a mounting substrate without soldering the contact pins. The connector legs comprise "eye of the needle" compliant interfaces that make electrical contact with the interior surfaces of the substrate's plated through holes. The press block is designed for use with a four-row right angle receptacle and locates rows 2, 3, and 4 on respective true grid positions and serves as a means for transmitting force from an external press to the contact pin tails. The contact tails in rows 2, 3, and 4 have …

A General Theory Of Geodesics With Applications To Hyperbolic Geometry, Deborah F. Logan

UNF Graduate Theses and Dissertations

In this thesis, the geometry of curved surfaces is studied using the methods of differential geometry. The introduction of manifolds assists in the study of classical two-dimensional surfaces. To study the geometry of a surface a metric, or way to measure, is needed. By changing the metric on a surface, a new geometric surface can be obtained. On any surface, curves called geodesics play the role of "straight lines" in Euclidean space. These curves minimize distance locally but not necessarily globally. The curvature of a surface at each point p affects the behavior of geodesics and the construction of geometric …

Monte Carlo Methods For Confidence Bands In Nonlinear Regression, Shantonu Mazumdar

UNF Graduate Theses and Dissertations

Confidence Bands for Nonlinear Regression Functions can be found analytically for a very limited range of functions with a restrictive parameter space. A computer intensive technique, the Monte Carlo Method will be used to develop an algorithm to find confidence bands for any given nonlinear regression functions with a broader parameter space.

The logistic regression function with one independent variable and two parameters will be used to test the validity and efficiency of the algorithm. The confidence bands for this particular function have been solved for analytically by Khorasani and Milliken (1982). Their derivations will be used to test the …

Metode De Calcul În Analiza Matematică, Florentin Smarandache, C. Dumitrescu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

On The Relationship Between A Graph And The Cycle Graph Of Its Complement, Christian P. Lopez

Theses: Doctorates and Masters

From an arbitrary graph G, another graph called the cycle graph of G and denoted by C(G) can be derived. The cycle graph C(G) of G has as its vertices the chordless cycles of G and two vertices in C(G) are adjacent if and only if the corresponding chordless cycles have at least one edge in common.

Model And Design-Based Analysis Of Complex Surveys., Joydip Mitra Dr.

Doctoral Theses

We consider estimating the total Y of a variable y defined on a survey population. The survey is complex only in the sense that we admit sample selection with arbitrary probabilities. Our 'analysis' consists in examining efficacies of conf Idence intervals for the For this we need point estimators and or mean square error (MSE) variance { estimators, respectively say, total. the corresponding e and v. The distribution, resulting from repeated sampling, of the pivotal quantity d = (e-Y)/V 1s supposed to approximate that of standard normal deviate t or of Students t with (n-1) degrees of freedom, assuming large …

Computing Χ² Values, John F. Dooley, Daniel C. St Clair, William E. Bond

Mathematics and Statistics Faculty Research & Creative Works

Textbooks and courses on numerical algorithms contain numerous examples which lead students to believe that the algorithm of choice for computing the zeros of a function f1994 is Newton's algorithm. In many of these courses little or no time is spent in providing students with "real world" experiences where Newton's method fails. The work presented in this paper describes a slow convergence problem encountered while trying to use Newton to estimate values for the 2 distributions. The problem occurred while the authors were trying to implement a well-known machine learning algorithm from the field of artificial intelligence. The function being …