Mathematics Commons^™

Developing Optimization Techniques For Logistical Tendering Using Reverse Combinatorial Auctions, Jennifer Kiser

Electronic Theses and Dissertations

In business-to-business logistical sourcing events, companies regularly use a bidding process known as tendering in the procurement of transportation services from third-party providers. Usually in the form of an auction involving a single buyer and one or more sellers, the buyer must make decisions regarding with which suppliers to partner and how to distribute the transportation lanes and volume among its suppliers; this is equivalent to solving the optimization problem commonly referred to as the Winner Determination Problem. In order to take into account the complexities inherent to the procurement problem, such as considering a supplier’s network, economies of scope, …

Developments In Multivariate Post Quantum Cryptography., Jeremy Robert Vates

Electronic Theses and Dissertations

Ever since Shor's algorithm was introduced in 1994, cryptographers have been working to develop cryptosystems that can resist known quantum computer attacks. This push for quantum attack resistant schemes is known as post quantum cryptography. Specifically, my contributions to post quantum cryptography has been to the family of schemes known as Multivariate Public Key Cryptography (MPKC), which is a very attractive candidate for digital signature standardization in the post quantum collective for a wide variety of applications. In this document I will be providing all necessary background to fully understand MPKC and post quantum cryptography as a whole. Then, I …

Dynamics Of Paramagnetic And Ferromagnetic Ellipsoidal Particles In Shear Flow Under A Uniform Magnetic Field, Christopher A. Sobecki, Jie Zhang, Yanzhi Zhang, Cheng Wang

Mathematics and Statistics Faculty Research & Creative Works

We investigate the two-dimensional dynamic motion of magnetic particles of ellipsoidal shapes in shear flow under the influence of a uniform magnetic field. In the first part, we present a theoretical analysis of the rotational dynamics of the particles in simple shear flow. By considering paramagnetic and ferromagnetic particles, we study the effects of the direction and strength of the magnetic field on the particle rotation. The critical magnetic-field strength, at which particle rotation is impeded, is determined. In a weak-field regime (i.e., below the critical strength) where the particles execute complete rotations, the symmetry property of the rotational velocity …

Equations Of Multi-Rees Algebras, Babak Jabbar Nezhad

Graduate Theses and Dissertations

In this thesis we describe the defining equations of certain multi-Rees algebras. First, we determine the defining equations of the multi-Rees algebra $R[I^{a_1}t_1,\dots,I^{a_r}t_r]$ over a Noetherian ring $R$ when $I$ is an ideal of linear type. This generalizes a result of Ribbe and recent work of Lin-Polini and Sosa. Second, we describe the equations defining the multi-Rees algebra $R[I_1^{a_1}t_1,\dots,I_r^{a_r}t_r]$, where $R$ is a Noetherian ring containing a field and the ideals are generated by a subset of a fixed regular sequence.

The 2-Domination Number Of A Caterpillar, Presley Chukwukere

Electronic Theses and Dissertations

A set D of vertices in a graph G is a 2-dominating set of G if every vertex in V − D has at least two neighbors in D. The 2-domination number of a graph G, denoted by γ₂(G), is the minimum cardinality of a 2- dominating set of G. In this thesis, we discuss the 2-domination number of a special family of trees, called caterpillars. A caterpillar is a graph denoted by P_k(x₁, x₂, ..., x_k), where x_i is the number of leaves attached to the ith vertex …

The Expected Number Of Patterns In A Random Generated Permutation On [N] = {1,2,...,N}, Evelyn Fokuoh

Electronic Theses and Dissertations

Previous work by Flaxman (2004) and Biers-Ariel et al. (2018) focused on the number of distinct words embedded in a string of words of length n. In this thesis, we will extend this work to permutations, focusing on the maximum number of distinct permutations contained in a permutation on [n] = {1,2,...,n} and on the expected number of distinct permutations contained in a random permutation on [n]. We further considered the problem where repetition of subsequences are as a result of the occurrence of (Type A and/or Type B) replications. Our method of enumerating the Type A replications causes double …

On Some Metaphysical Problems Of Many Worlds Interpretation Of Quantum Mechanics, Florentin Smarandache, Victor Christianto, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

Despite its enormous practical success, many physicists and philosophers alike agree that the quantum theory is full of contradictions and paradoxes which are difficult to solve consistently. Even after 90 years, the experts themselves still do not all agree what to make of it. The area of disagreement centers primarily around the problem of describing observations. Formally, the socalled quantum measurement problem can be defined as follows: the result of a measurement is a superposition of vectors, each representing the quantity being observed as having one of its possible values. The question that has to be answered is : how …

Partially-Ordered Multi-Type Algebras, Display Calculi And The Category Of Weakening Relations, Peter Jipsen, Fei Liang, M. Andrew Moshier, Apostolos Tzimoulis

Mathematics, Physics, and Computer Science Faculty Articles and Research

"We define partially-ordered multi-type algebras and use them as algebraic semantics for multi-type display calculi that have recently been developed for several logics, including dynamic epistemic logic [7], linear logic[10], lattice logic [11], bilattice logic [9] and semi-De Morgan logic [8]."

Fast Adjustable Npn Classification Using Generalized Symmetries, Xuegong Zhou, Lingli Wang, Peiyi Zhao, Alan Mishchenko

Mathematics, Physics, and Computer Science Faculty Articles and Research

NPN classification of Boolean functions is a powerful technique used in many logic synthesis and technology mapping tools in FPGA design flows. Computing the canonical form of a function is the most common approach of Boolean function classification. In this paper, a novel algorithm for computing NPN canonical form is proposed. By exploiting symmetries under different phase assignments and higher-order symmetries of Boolean functions, the search space of NPN canonical form computation is pruned and the runtime is dramatically reduced. The algorithm can be adjusted to be a slow exact algorithm or a fast heuristic algorithm with lower quality. For …

A Formulation Of L-Isothermic Surfaces In Three-Dimensional Minkowski Space, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

The Cartan structure equations are used to study space-like and time-like isothermic surfaces in three-dimensional Minkowski space in a unified framework. When the lines of curvature of a surface constitute an isothermal system, the surface is called isothermic. This condition serves to define a system of one-forms such that, by means of the structure equations, the Gauss-Codazzi equations for the surface are determined explicitly. A Lax pair can also be obtained from these one-forms for both cases, and, moreover, a nonhomogeneous Schrödinger equation can be associated with the set of space-like surfaces.

Brun's 1920 Theorem On Goldbach's Conjecture, James A. Farrugia

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One form of Goldbach’s Conjecture asserts that every even integer greater than 4is the sum of two odd primes. In 1920 Viggo Brun proved that every sufficiently large even number can be written as the sum of two numbers, each having at most nine prime factors. This thesis explains the overarching principles governing the intricate arguments Brun used to prove his result.

Though there do exist accounts of Brun’s methods, those accounts seem to miss the forest for the trees. In contrast, this thesis explains the relatively simple structure underlying Brun’s arguments, deliberately avoiding most of his elaborate machinery and …

Canonical Coordinates On Lie Groups And The Baker Campbell Hausdorff Formula, Nicholas Graner

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Lie Groups occur in math and physics as representations of continuous symmetries and are often described in terms of their Lie Algebra. This thesis is concerned with finding a concrete description of a Lie group given its associated Lie algebra. Several calculations toward this end are developed and then implemented in the Maple Differential Geometry package. Examples of the calculations are given.

Frontiers For Young Minds: Call For Contributions, Jeremy L. Martin

Journal of Humanistic Mathematics

Frontiers for Young Minds, available at https://kids.frontiersin.org/, is a free, open-access scientific journal with articles written by scientists with an audience of children and young teens (ages 8-15). A distinctive feature of the journal is that submitted articles are reviewed not by the author's peers, but by kids themselves, working under the guidance of experts. The mathematics community is invited to submit articles, both on original research and on classic topics.

When Mercy Seasons Justice, Basant K B

Journal of Humanistic Mathematics

This is based on the simple mathematical concept of ratio, which tends to get more intricate the more one thinks about it.

The Rubbish Researchers Puzzle, Michael W. Lucht

Journal of Humanistic Mathematics

The Rubbish Researchers Puzzle is a humorous short story about the Blue-Eyed Islanders Puzzle, cultural insensitivity in logic problems, and the quality of research.

A Mother's Math Is Never Done, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Untitled, Marion D. Cohen

Journal of Humanistic Mathematics

No abstract provided.

Mathematical Motherhood, Marylesa Howard

Journal of Humanistic Mathematics

No abstract provided.

Breastmilk And Theorems, Bonnie Jacob

Journal of Humanistic Mathematics

Breastmilk and Theorems is a poem that traces a mother’s journey breastfeeding her baby over the course of the baby’s first months of life, while mentally working on proving a theorem.

Wondering, Joanne Growney

Journal of Humanistic Mathematics

This 15-line poem speaks of the ways that motherhood (in contrast with fatherhood) might limit creativity and publication. The lines of the poem have syllable counts that follow the Fibonacci Numbers: 1-1-2-3-5-8-13-21-13-8-5-3-2-1-1.

Super Mamas: A Real Life Story Of Everyday Super Heroes, Emille Lawrence

Journal of Humanistic Mathematics

Bridging the gap between the world of motherhood and the world of academia can seem like a heroic feat. This essay acknowledges and celebrates a community of super women doing this every day. The Math Mamas Facebook group was formed in 2016 and today boasts over five hundred members. It provides its members a platform to commiserate about the challenges and celebrate the wins, big or small, whichever is appropriate whenever.

Balancing An Academic Career In Mathematics With Motherhood And Life's Other Passions, Deena R. Schmidt

Journal of Humanistic Mathematics

I became a mother while a postdoctoral fellow, and solved my two-body problem shortly thereafter becoming a tenure-track professor in mathematics and statistics. My plan to have a second child came with an unexpected bonus: I had identical twin girls, and this happened during my second year on the tenure-track. Finding anything resembling a work-life balance has been extremely challenging since then. Many days I struggle just to cover the basics at work and home, let alone finding time for other passions in life --- in my case, dance has been my creative outlet since childhood and an essential part …

Optimizing Maternal And Tenure Clocks: A Mathematical Proof, Tara T. Craig

Journal of Humanistic Mathematics

This essay shares my journey to solving the problem of timing, specifically as it applies to having a child on my journey towards a career as a mathematician in academia. I share some of the challenges I faced during pregnancy and the first few years of motherhood, which coincided with my first few years as an assistant professor of mathematics.

College Dropout To College Professor, Deborah L. Gochenaur, Rose I. Verbos

Journal of Humanistic Mathematics

Being a college dropout wasn’t something to be proud of; it just happened. Life doesn’t always turn out the way we want or expect. Yet, it is often how we deal with defeat that defines us – figuring out when to lick our wounds and when to come back fighting. It took a few years to redefine my dream, start a family, and seem to move forward, but the ache for more was always in the back of my mind. Could I succeed at something at which I had already failed? Going back to school at a community college at …

Rational Points On Surfaces And In Life, Amanda Knecht

Journal of Humanistic Mathematics

This essay collects together examples of instances where I should have advocated for myself more as a mother and examples of how I have advocated for my children. Theses stories come from a mathematician who gave birth to two children while on the tenure track in an older department with only one tenured woman.

Four Times Exceptional: Reflections On Motherhood And Teaching College Mathematics, Maria Fung

Journal of Humanistic Mathematics

This essay discusses the challenges of mothering four very different children--one adopted, one gifted, one anxious and one dyslexic child--and the impact of this experience on teaching mathematics at the college level.

Arrival At The Same Point: My Long, Winding, And Not-So-Circular Path To Professor, Melissa B. Hanzsek-Brill

Journal of Humanistic Mathematics

This is my story of the constant struggle between wanting both mathematics and motherhood, and realizing I could have it all but not all at once.The story involves earning degrees, securing a tenure-track position only to resign two years later, and then, through a gauntlet of adjunct and fixed-term positions, applying for and accepting another tenure-track position at the same institution, finally arriving back at the same point on the path I had been on sixteen years earlier. I walked this long, winding, and ultimately no-so-circular path while becoming and being a mother of four. It is my hope that …

Beautiful Madness: Math And Motherhood --- Can You Have It All?, Abigail Wacher

Journal of Humanistic Mathematics

I am a tenure-track assistant professor, and I have a beautiful three-year old boy and a husband who I love. My life today is within epsilon of the future I imagined while I was in university and contemplating a career in mathematics. Getting here, however, took longer than I thought. Along the way I often felt I was under pressure to choose between my career and having a family. I never made this choice and, although my pregnancy and my son did interfere with my career, I would not have it any other way. This is the story of how …

Mommy Brain And The Mommy Mathematician, Bonnie Jacob

Journal of Humanistic Mathematics

Is mommy brain real? Are pregnant women and mothers ditzier than non-mothers? If mommy brain is a real phenomenon, what are the implications for women mathematicians whose careers depend on their mental agility? While anecdotes and references to the phenomenon in pop culture abound, concrete evidence is decidedly murky. In this article, I discuss some of the recent research on so-called mommy brain. I delve into the implications of its alleged existence, particularly for mother-mathematicians. I include perspectives of several mother-mathematicians on the consequences of mommy brain … or its perceived existence.

Don't Ask The Baby To Do Calculus: Thoughts From An Early-Career Math Mama, Caitlin Krul

Journal of Humanistic Mathematics

I very recently became a math mama. In my desperate search for patterns and structure in those first few weeks, my husband told me, "She's only three weeks old; we can't expect her to be doing calculus homework." I suppose he was right. I am working towards tenure and finding a new balance between teaching and family, all while trying to not lose sight of who I am. My personal challenges range from the logistics of being a nursing mother in a shared office to feelings of being seen as less adequate in my job if I present myself as …