Mathematics Commons^™

Total Domination Dot Critical And Dot Stable Graphs., Stephanie Anne Marie Mcmahon

Electronic Theses and Dissertations

Two vertices are said to be identifed if they are combined to form one vertex whose neighborhood is the union of their neighborhoods. A graph is total domination dot-critical if identifying any pair of adjacent vertices decreases the total domination number. On the other hand, a graph is total domination dot-stable if identifying any pair of adjacent vertices leaves the total domination number unchanged. Identifying any pair of vertices cannot increase the total domination number. Further we show it can decrease the total domination number by at most two. Among other results, we characterize total domination dot-critical trees with total …

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Discrete Fractional Calculus And Its Applications To Tumor Growth, Sevgi Sengul

Masters Theses & Specialist Projects

Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real world problems. For instance, one can take the "difference" of any function, from 1st order up to the n-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make n- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractional calculus …

An Algorithm To Generate Two-Dimensional Drawings Of Conway Algebraic Knots, Jen-Fu Tung

Masters Theses & Specialist Projects

The problem of finding an efficient algorithm to create a two-dimensional embedding of a knot diagram is not an easy one. Typically, knots with a large number of crossings will not nicely generate two-dimensional drawings. This thesis presents an efficient algorithm to generate a knot and to create a nice two-dimensional embedding of the knot. For the purpose of this thesis a drawing is “nice” if the number of tangles in the diagram consisting of half-twists is minimal. More specifically, the algorithm generates prime, alternating Conway algebraic knots in O(n) time where n is the number of crossings …

Development Of A Discrete Mathematics Textbook And Guide For High School Teachers, Rebecca A. Stokes

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This project was to create the beginnings a textbook for teacher's to supplement instruction of a discrete mathematics course at the high school level. The development of the text was guided by past and current efforts to place discrete mathematics in high school curriculum. A review of the literature and experiences of instructors were viewed and analyzed to guide the construction of the textbook. The text was written with the goal to give teachers information about the topics of discrete mathematics, extra resources, lesson ideas , and optional worksheets for students. Several lessons were created and one was implemented in …

Classical Foundations For A Quantum Theory Of Time In A Two-Dimensional Spacetime, Nathan Thomas Carruth

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We consider the set of all spacelike embeddings of the circle S1 into a spacetime R1 × S1 with a metric globally conformal to the Minkowski metric. We identify this set and the group of conformal isometries of this spacetime as quotients of semidirect products involving diffeomorphism groups and give a transitive action of the conformal group on the set of spacelike embeddings. We provide results showing that the group of conformal isometries is a topological group and that its action on the set of spacelike embeddings is continuous. Finally, we point out some directions for future research.

Dancing With Heretics: Essays On Orthodoxy, Questioning And Faith, Darren M. Edwards

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

While much has been written about the conflicts, supposed or actual, between logic and faith, science and religion, few accounts of the personal turmoil these conflicts can cause exist. Likewise, many of these nonfiction accounts are written from a distinctly polarized place leaning either to science or faith.

In this thesis, I mix research and history with memoir and a sense of poetry to explore my personal experience with this conflict. At its outset, I hoped for this project to capture my struggle as an orthodox member of The Church of Jesus Christ of Latter-day Saints (LDS) in dealing with …

Dynamics Groups Of Asynchronous Cellular Automata, Michael Macauley, Jon Mccammond, Henning S. Mortveit

Publications

We say that a finite asynchronous cellular automaton (or more generally, any sequential dynamical system) is π-independent if its set of periodic points are independent of the order that the local functions are applied. In this case, the local functions permute the periodic points, and these permutations generate the dynamics group. We have previously shown that exactly 104 of the possible 2²³ = 256 cellular automaton rules are π-independent. In the article, we classify the periodic states of these systems and describe their dynamics groups, which are quotients of Coxeter groups. The dynamics groups provide information …

The Life Of Evariste Galois And His Theory Of Field Extension, Felicia N. Adams

Senior Honors Theses

Evariste Galois made many important mathematical discoveries in his short lifetime, yet perhaps the most important are his studies in the realm of field extensions. Through his discoveries in field extensions, Galois determined the solvability of polynomials. Namely, given a polynomial P with coefficients is in the field F and such that the equation P(x) = 0 has no solution, one can extend F into a field L with α in L, such that P(α) = 0. Whereas Galois Theory has numerous practical applications, this thesis will conclude with the examination and proof of the fact that it is impossible …

On The Numerical Range And Spectrum Of The Weighted Shift Operator In [Iota]², Gina-Louise Santamaria

Theses, Dissertations and Culminating Projects

In this paper, we examine the weighted shift operator in l² as described in Yoo & Rho [15], which is an example of what is known as a hyponormal weighted shift. Using the methods of Tam [13], in conjuction with properties of the weighted shift, we determine the numerical range of Yoo &; Rho’s unilateral weighted shift operator.

It is well-established that the spectrum of a bounded linear operator is always included in the closure of the numerical range. In particular, for a bounded linear operator, the point and compression spectra are contained within the numerical range itself [7]. …

Using Matrix Pencils To Solve Discrete Sturm-Liouville Problems With Nonlinear Boundary Conditions, Michael Kofi Wilson

Theses, Dissertations and Culminating Projects

This thesis deals with discrete second order Sturm-Liouville Boundary Value Problems (DSLBVP) where the parameter as part of the Sturm-Liouville difference equation appears nonlinearly in the boundary conditions. We focus on analyzing the case with cubic nonlinearity in the boundary condition. First, we describe the problem by a matrix equation with nonlinear variables such that solving the DSLBVP is equivalent to solving the matrix equation. Second, we formulate the problem as a nonlinear eigenvalue problem. We further reduce the problem to finding eigenvalues of a matrix pencil in the form A - X B . Under certain conditions, such a …

On Directionally Dependent Subdifferentials, Ivan Ginchev, Boris S. Mordukhovich

Mathematics Research Reports

In this paper directionally contextual concepts of variational analysis, based on dual-space constructions similar to those in [4, 5], are introduced and studied. As an illustration of their usefulness, necessary and also sufficient optimality conditions in terms of directioual subdifferentials are established, and it is shown that they can be effective in the situations where known optimality conditions in terms of nondirectional subdifferentials fail.

Analyzing Fractals, Kara Mesznik

Renée Crown University Honors Thesis Projects - All

For my capstone project, I analyzed fractals. A fractal is a picture that is composed of smaller images of the larger picture. Each smaller picture is self- similar, meaning that each of these smaller pictures is actually the larger image just contracted in size through the use of the Contraction Mapping Theorem and shifted using linear and affine transformations.

Fractals live in something called a metric space. A metric space, denoted (X, d), is a space along with a distance formula used to measure the distance between elements in the space. When producing fractals …

Time Series Models For Computing Activation In Fmri, Daniel W. Adrian, Ranjan Maitra, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Neutrosophic Physics: More Problems, More Solutions, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

When considering the laws of theoretical physics, one of the physicists says that these laws – the actual expressions of the laws of mathematics and logics being applied to physical phenomena – should be limited according to the physical meaning we attribute to the phenomena. In other word, there is an opinion that a theoretical physicist should put some limitations onto mathematics, in order to “reduce” it to the observed reality. No doubt, we can do it. However, if following this way, we would arrive at only mathematical models of already known physical phenomena. Of course, this might be useful …

Option Pricing And Stable Trading Strategies In The Presence Of Information Asymmetry, Anirban Dutta

Dissertations

Pricing derivatives is one of the central issues in mathematical finance. The seminal work of Black, Scholes and Merton has been the cornerstone of option pricing since their introduction in 1973. Their work influenced the pricing theory of other derivatives as well.

This derivative pricing theory has two primary shortcomings. Firstly, the theoretical pricing in such theories are not accompanied by a stable trading strategy. Secondly, they often assume that the market agents use a uniform model for the underlying instrument and that the market prices of the derivatives reveal all the information about the underlying instrument.

Theoreticians like Grossman …

Combinatorics And Topology Of Curves And Knots, Bailey Ann Ross

Boise State University Theses and Dissertations

The genus of a graph is the minimal genus of a surface into which the graph can be embedded. Four regular graphs play an important role in low dimensional topology since they arise from curves and virtual knot diagrams. Curves and virtual knots can be encoded combinatorially by certain signed words, called Gauss codes and Gauss paragraphs. The purpose of this thesis is to investigate the genus problem for these combinatorial objects: Given a Gauss word or Gauss paragraph, what is the genus of the curve or virtual knot it represents?

Developmental Understanding Of The Equals Sign And Its Effects On Success In Algebra, Ryan W. Brown

Boise State University Theses and Dissertations

For some students, the equals symbol is viewed as a directive to carry out a procedure, instead of a symbol expressing mathematical equivalence. The purpose of this study was to develop and to pilot a questionnaire to measure students’ understandings of relational equivalence as implied by their interpretations and use of the equals symbol. The results of this questionnaire were compared with student testing data with the goal of determining a correlation between understanding of symbolic equivalence and success in a typical algebra course. It was found that students who demonstrated an ability to define and articulate an appropriate meaning …

Stably Free Modules Over The Klein Bottle, Andrew Misseldine

Boise State University Theses and Dissertations

This paper is concerned with constructing countably many, non-free stably free modules for the Klein bottle group. The work is based on the papers “Stably Free, Projective Right Ideals" by J.T. Stafford (1985) and “Projective, Nonfree Modules Over Group Rings of Solvable Groups" by V. A. Artamonov (1981). Stafford proves general results that guarantee the existence of non-free stably frees for the Klein bottle group but has not made the argument explicit. Artamonov allows us to construct infinitely many non-free stably free modules. This paper will also construct presentations and sets of generators for these modules. This paper concludes with …

A Mathematical Model Of The Biofluidmechanics Of The Non-Newtonian Mucus Layer Of The Tear Film In The Human Eye, Douglas M. Platt

Theses, Dissertations and Culminating Projects

The human eye is a complicated and delicate organ. The structure of the eye is such that it provides for clear vision of the world. The cornea and conjunctiva at the front of the eye are avascular structures that require nutrients and moisture to be provided by the tear film. The tear film also provides for the removal of debris from the surface of the eye. The tear film has several layers: a lipid layer, an aqueous solution, and mucus. The optical clarity and structural uniformity of the tear film is maintained by the blinking motion of the eyelid. During …