Approaches To Assessing Nutrient Coupling In Open Ocean Datasets, 2023 Humboldt State University

#### Approaches To Assessing Nutrient Coupling In Open Ocean Datasets, James M. Moore, Claire P. Till

*IdeaFest: Interdisciplinary Journal of Creative Works and Research from Cal Poly Humboldt*

Nutrient coupling describes a process where the biogeochemical cycles of two elements are linked by being incorporated similarly into biomass. This paper uses data from the GEOTRACES GP16 cruise (Eastern Pacific Zonal Transect) to investigate the relationship between certain macronutrients generally coupled to trace elements in terms of their oceanic distributions with the notable exception of in an oxygen minimum zone: cadmium-phosphate and zinc-silicate. There are many methods applied to oceanographic data to correlate analyte concentrations; while they are often presented independently in literature, here we attempt to use them in conjunction for a more thorough interpretation. By compiling 1) …

The Mean Sum Of Squared Linking Numbers Of Random Piecewise-Linear Embeddings Of $K_N$, 2023 University of Notre Dame

#### The Mean Sum Of Squared Linking Numbers Of Random Piecewise-Linear Embeddings Of $K_N$, Yasmin Aguillon, Xingyu Cheng, Spencer Eddins, Pedro Morales

*Rose-Hulman Undergraduate Mathematics Journal*

DNA and other polymer chains in confined spaces behave like closed loops. Arsuaga et al. \cite{AB} introduced the uniform random polygon model in order to better understand such loops in confined spaces using probabilistic and knot theoretical techniques, giving some classification on the mean squared linking number of such loops. Flapan and Kozai \cite{flapan2016linking} extended these techniques to find the mean sum of squared linking numbers for random linear embeddings of complete graphs $K_n$ and found it to have order $\Theta(n(n!))$. We further these ideas by inspecting random piecewise-linear embeddings of complete graphs and give introductory-level summaries of the ideas …

Differential Calculus: From Practice To Theory, 2023 Pennsylvania State University

#### Differential Calculus: From Practice To Theory, Eugene Boman, Robert Rogers

*Milne Open Textbooks*

*Differential Calculus: From Practice to Theory* covers all of the topics in a typical first course in differential calculus. Initially it focuses on using calculus as a problem solving tool (in conjunction with analytic geometry and trigonometry) by exploiting an informal understanding of differentials (infinitesimals). As much as possible large, interesting, and important historical problems (the motion of falling bodies and trajectories, the shape of hanging chains, the Witch of Agnesi) are used to develop key ideas. Only after skill with the computational tools of calculus has been developed is the question of rigor seriously broached. At that point, the …

Geometry In Spectral Triples: Immersions And Fermionic Fuzzy Geometries, 2023 Western University

#### Geometry In Spectral Triples: Immersions And Fermionic Fuzzy Geometries, Luuk S. Verhoeven

*Electronic Thesis and Dissertation Repository*

We investigate the metric nature of spectral triples in two ways.

Given an oriented Riemannian embedding i:X->Y of codimension 1 we construct a family of unbounded KK-cycles i!(epsilon), each of which represents the shriek class of i in KK-theory. These unbounded KK-cycles are further equipped with connections, allowing for the explicit computation of the products of i! with the spectral triple of Y at the unbounded level. In the limit epsilon to 0 the product of these unbounded KK-cycles with the canonical spectral triple for Y admits an asymptotic expansion. The divergent part of this expansion is known and …

Double Barrier Backward Doubly Stochastic Differential Equations, 2023 Pension Fund Management Division, Mitsubishi UFJ Trust and Banking Corporation, 1-4-5, Marunouchi, Chiyoda-ku, Tokyo, 100-8212, Japan

#### Double Barrier Backward Doubly Stochastic Differential Equations, Tadashi Hayashi

*Journal of Stochastic Analysis*

No abstract provided.

Symmetric Functions Algebras (Sfa) Iii: Stochastic And Constant Row Sum Matrices, 2023 Southern Illinois University, Carbondale, Illinois 62901, USA

#### Symmetric Functions Algebras (Sfa) Iii: Stochastic And Constant Row Sum Matrices, Philip Feinsilver

*Journal of Stochastic Analysis*

No abstract provided.

Math And Democracy, 2023 Juniata College

#### Math And Democracy, Kimberly A. Roth, Erika L. Ward

*Journal of Humanistic Mathematics*

Math and Democracy is a math class containing topics such as voting theory, weighted voting, apportionment, and gerrymandering. It was first designed by Erika Ward for math master’s students, mostly educators, but then adapted separately by both Erika Ward and Kim Roth for a general audience of undergraduates. The course contains materials that can be explored in mathematics classes from those for non-majors through graduate students. As such, it serves students from all majors and allows for discussion of fairness, racial justice, and politics while exploring mathematics that non-major students might not otherwise encounter. This article serves as a guide …

Dna Self-Assembly Of Trapezohedral Graphs, 2023 California State University - San Bernardino

#### Dna Self-Assembly Of Trapezohedral Graphs, Hytham Abdelkarim

*Electronic Theses, Projects, and Dissertations*

Self-assembly is the process of a collection of components combining to form an organized structure without external direction. DNA self-assembly uses multi-armed DNA molecules as the component building blocks. It is desirable to minimize the material used and to minimize genetic waste in the assembly process. We will be using graph theory as a tool to find optimal solutions to problems in DNA self-assembly. The goal of this research is to develop a method or algorithm that will produce optimal tile sets which will self-assemble into a target DNA complex. We will minimize the number of tile and bond-edge types …

An Extension Of The Complex–Real (C–R) Calculus To The Bicomplex Setting, With Applications, 2023 Chapman University

#### An Extension Of The Complex–Real (C–R) Calculus To The Bicomplex Setting, With Applications, Daniel Alpay, Kamal Diki, Mihaela Vajiac

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

In this paper, we extend notions of complex ℂ−ℝ-calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical real and complex least mean square algorithms.

Polynomial Density Of Compact Smooth Surfaces, 2023 Western University

#### Polynomial Density Of Compact Smooth Surfaces, Luke P. Broemeling

*Electronic Thesis and Dissertation Repository*

We show that any smooth closed surface has polynomial density 3 and that any connected compact smooth surface with boundary has polynomial density 2.

Multiplication Operators By White Noise Delta Functions And Associated Differential Equations, 2023 Universitá di Roma Tor Vergata, Via di Torvergata, Roma, Italy

#### Multiplication Operators By White Noise Delta Functions And Associated Differential Equations, Luigi Accardi, Un Cig Ji, Kimiaki Saitô

*Journal of Stochastic Analysis*

No abstract provided.

Random Variables With Overlapping Number And Weyl Algebras Ii, 2023 Missouri State University, Springfield, MO 65897, U.S.A.

#### Random Variables With Overlapping Number And Weyl Algebras Ii, Ruma Dutta, Gabriela Popa, Aurel Stan

*Journal of Stochastic Analysis*

No abstract provided.

An Explicit Construction Of Sheaves In Context, 2023 The Graduate Center, City University of New York

#### An Explicit Construction Of Sheaves In Context, Tyler A. Bryson

*Dissertations, Theses, and Capstone Projects*

This document details the body of theory necessary to explicitly construct sheaves of sets on a site together with the development of supporting material necessary to connect sheaf theory with the wider mathematical contexts in which it is applied. Of particular interest is a novel presentation of the plus construction suitable for direct application to a site without first passing to the generated grothendieck topology.

Operators Induced By Certain Hypercomplex Systems, 2023 Chapman University

#### Operators Induced By Certain Hypercomplex Systems, Daniel Alpay, Ilwoo Choo

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

In this paper, we consider a family {H_{t}}_{t∈R} of rings of hypercomplex numbers, indexed by the real numbers, which contain both the quaternions and the split-quaternions. We consider natural Hilbert-space representations {(C^{2}, π_{t})}_{t∈R} of the hypercomplex system {H_{t}}_{t∈R}, and study the realizations π_{t}(h) of hypercomplex numbers h ∈ H_{t}, as (2 × 2)-matrices acting on C^{2}, for an arbitrarily fixed scale t ∈ R. Algebraic, operator-theoretic, spectral-analytic, and free-probabilistic properties of them are considered.

A Hörmander–Fock Space, 2023 Chapman University

#### A Hörmander–Fock Space, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini, Daniele C. Struppa

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

In a recent paper we used a basic decomposition property of polyanalytic functions of order 2 in one complex variable to characterize solutions of the classical ∂-problem for given analytic and polyanalytic data. Our approach suggested the study of a special reproducing kernel Hilbert space that we call the Hörmander-Fock space that will be further investigated in this paper. The main properties of this space are encoded in a specific moment sequence denoted by η= (η_{n})_{n}≥0 leading to a special entire function E(z) that is used to express the kernel function of the Hörmander-Fock space. We …

Modelling Illiquid Stocks Using Quantum Stochastic Calculus: Asymptotic Methods, 2023 Memorial University of Newfoundland, St Johns, NL A1C 5S7, Canada

#### Modelling Illiquid Stocks Using Quantum Stochastic Calculus: Asymptotic Methods, Will Hicks

*Journal of Stochastic Analysis*

No abstract provided.

Modelling Nuclear Weapon Effects In Wargaming Using Monte Carlo Simulations, 2023 United States Military Academy

#### Modelling Nuclear Weapon Effects In Wargaming Using Monte Carlo Simulations, Tyler Guetzke, Alexander Withenbury, Zachary Dugger

*West Point Research Papers*

The United States Army’s interpretation of nuclear weapon effects needs change and modernization. Wargaming exercises are commonplace in today’s military, however, despite the growing threat of non-strategic nuclear weapons (NSNW), little has been done to inform battlefield commanders on their true effects. Our research seeks to develop a tool for commanders to easily interpret quantifiable effects of a NSNW. Utilizing Monte Carlo simulation, we are developing a new methodology to analyze NSNW effects. Our model allows a commander to calculate the expected unit strength following a NSNW strike which will aid in their operational decision making ability. The Monte Carlo …

Adaptive And Topological Deep Learning With Applications To Neuroscience, 2023 University of Tennessee, Knoxville

#### Adaptive And Topological Deep Learning With Applications To Neuroscience, Edward Mitchell

*Doctoral Dissertations*

Deep Learning and neuroscience have developed a two way relationship with each informing the other. Neural networks, the main tools at the heart of Deep Learning, were originally inspired by connectivity in the brain and have now proven to be critical to state-of-the-art computational neuroscience methods. This dissertation explores this relationship, first, by developing an adaptive sampling method for a neural network-based partial different equation solver and then by developing a topological deep learning framework for neural spike decoding. We demonstrate that our adaptive scheme is convergent and more accurate than DGM -- as long as the residual mirrors the …

Invariants Of 3-Braid And 4-Braid Links, 2023 United Arab Emirates University

#### Invariants Of 3-Braid And 4-Braid Links, Mark Essa Sukaiti

*Theses*

In this study, we established a connection between the Chebyshev polynomial of the first kind and the Jones polynomial of generalized weaving knots of type *W*(3,n,m).

Through our analysis, we demonstrated that the coefficients of the Jones polynomial of weaving knots are essentially the Whitney numbers of Lucas lattices which allowed us to find an explicit formula for the Alexander polynomial of weaving knots of type*W*(3,n).

In addition to confirming Fox’s trapezoidal conjecture, we also discussed the zeroes of the Alexander Polynomial of weaving knots of type *W*(3,n) as they relate to Hoste’s conjecture. In addition, …

Knot Equivalence, 2023 California State University, San Bernardino

#### Knot Equivalence, Jacob Trubey

*Electronic Theses, Projects, and Dissertations*

A knot is a closed curve in R3. Alternatively, we say that a knot is an embedding f : S1 → R3 of a circle into R3. Analogously, one can think of a knot as a segment of string in a three-dimensional space that has been knotted together in some way, with the ends of the string then joined together to form a knotted loop. A link is a collection of knots that have been linked together.

An important question in the mathematical study of knot theory is that of how we can tell when two knots are, or are …