New Results On Subtractive Magic Graphs,
2021
Centre College
New Results On Subtractive Magic Graphs, Matthew J. Ko, Jason Pinto, Aaron Davis
Rose-Hulman Undergraduate Mathematics Journal
For any edge xy in a directed graph, the subtractive edge-weight is the sum of the label of xy and the label of y minus the label of x. Similarly, for any vertex z in a directed graph, the subtractive vertex-weight of z is the sum of the label of z and all edges directed into z and all the labels of edges that are directed away from z. A subtractive magic graph has every subtractive edge and vertex weight equal to some constant k. In this paper, we will discuss variations of subtractive magic labelings on …
Directed Graphs Of The Finite Tropical Semiring,
2021
Dordt University
Directed Graphs Of The Finite Tropical Semiring, Caden G. Zonnefeld
Rose-Hulman Undergraduate Mathematics Journal
The focus of this paper lies at the intersection of the fields of tropical algebra and graph theory. In particular the interaction between tropical semirings and directed graphs is investigated. Originally studied by Lipvoski, the directed graph of a ring is useful in identifying properties within the algebraic structure of a ring. This work builds off research completed by Beyer and Fields, Hausken and Skinner, and Ang and Shulte in constructing directed graphs from rings. However, we will investigate the relationship (x, y)→(min(x, y), x+y) as defined by the operations of tropical algebra and applied to tropical semirings.
The Degeneration Of The Hilbert Metric On Ideal Pants And Its Application To Entropy,
2021
University of Michigan, Ann Arbor
The Degeneration Of The Hilbert Metric On Ideal Pants And Its Application To Entropy, Marianne Debrito, Andrew Nguyen, Marisa O'Gara
Rose-Hulman Undergraduate Mathematics Journal
Entropy is a single value that captures the complexity of a group action on a metric space. We are interested in the entropies of a family of ideal pants groups $\Gamma_T$, represented by projective reflection matrices depending on a real parameter $T > 0$. These groups act on convex sets $\Omega_{\Gamma_T}$ which form a metric space with the Hilbert metric. It is known that entropy of $\Gamma_T$ takes values in the interval $\left(\frac{1}{2},1\right]$; however, it has not been proven whether $\frac{1}{2}$ is the sharp lower bound. Using Python programming, we generate approximations of tilings of the convex set in the projective …
An Introduction To Fractal Analysis,
2021
Reed College
An Introduction To Fractal Analysis, Lucas Yong
Rose-Hulman Undergraduate Mathematics Journal
Classical analysis is not able to treat functions whose domain is fractal. We present an introduction to analysis on a particular class of fractals known as post-critically finite (PCF) self-similar sets that is suitable for the undergraduate reader. We develop discrete approximations of PCF self-similar sets, and construct discrete Dirichlet forms and corresponding discrete Laplacians that both preserve self-similarity and are compatible with a notion of harmonic functions that is analogous to a classical setting. By taking the limit of these discrete Laplacians, we construct continuous Laplacians on PCF self-similar sets. With respect to this continuous Laplacian, we also construct …
Irrational Philosophy? Kronecker's Constructive Philosophy And Finding The Real Roots Of A Polynomial,
2021
University of Missouri - Kansas City
Irrational Philosophy? Kronecker's Constructive Philosophy And Finding The Real Roots Of A Polynomial, Richard B. Schneider
Rose-Hulman Undergraduate Mathematics Journal
The prominent mathematician Leopold Kronecker (1823 – 1891) is often relegated to footnotes and mainly remembered for his strict philosophical position on the foundation of mathematics. He held that only the natural numbers are intuitive, thus the only basis for all mathematical objects. In fact, Kronecker developed a complete school of thought on mathematical foundations and wrote many significant algebraic works, but his enigmatic writing style led to his historical marginalization. In 1887, Kronecker published an extended version of his paper, “On the Concept of Number,” translated into English in 2010 for the first time by Edward T. Dean, who …
Infinite Peirce Distribution In The Algebra Of Compact Operators And Description Of Its Local Au-Tomorphisms,
2021
Andizhan State University
Infinite Peirce Distribution In The Algebra Of Compact Operators And Description Of Its Local Au-Tomorphisms, Farhodjon N. Arzikulov, Rejabboy Qo’Shaqov
Scientific Bulletin. Physical and Mathematical Research
In the present paper the infinite Peirce decomposition of the algebra 𝐾(𝐻) of com-pact operators on an infinite dimensional separable Gilbert space 𝐻 is constructed, using the norm of the algebra 𝐾(𝐻) and a maximal family of mutually or-thogonal minimal projections, i.e., self-adjoint,idempotent elements. The infinite Peirce decompo-sition on the norm of a 𝐶∗-algebra is also con-structed in 2012 by the first author. But, it turns, the condition, applied then, is not sufficient for the infi-nite Peirce decomposition on the norm constructed in 2012 to be an algebra. Therefore, in the present paper, the infinite Peirce decomposition on the norm …
The French Connection: Borda, Condorcet And The Mathematics Of Voting Theory,
2021
Colorado State University-Pueblo
The French Connection: Borda, Condorcet And The Mathematics Of Voting Theory, Janet Heine Barnett
General Education and Liberal Studies
No abstract provided.
Local And 2-Local Derivations On Octonion Algebras,
2021
Department of Mathematics, Nukus state pedagogical institute
Local And 2-Local Derivations On Octonion Algebras, Allayar Allambergenov
Karakalpak Scientific Journal
The present paper is devoted to study of local and 2-local derivations on octonion algebras. We shall give a general form of local derivations on the real octonion algebra \[{\mathbb{O}_\mathbb{R}}.\] This description implies that the space of all local derivations on \[{\mathbb{O}_\mathbb{R}}\] when equipped with Lie bracket is isomorphic to the Lie algebra \[\mathfrak{s}{\mathfrak{o}_7}(\mathbb{R})\] of all real skew-symmetric \[7 \times 7\]-matrices. We also consider \[2\]-local derivations on an octonion algebra \[{\mathbb{O}_\mathbb{F}}\] over an algebraically closed field \[\mathbb{F}\] of the characteristic zero and prove that every \[2\]-local derivation on \[{\mathbb{O}_\mathbb{F}}\] is a derivation. Further, we apply these results to similar problems …
What Is The Uncertainty Of The Result Of Data Processing: Fuzzy Analogue Of The Central Limit Theorem,
2021
The University of Texas at El Paso
What Is The Uncertainty Of The Result Of Data Processing: Fuzzy Analogue Of The Central Limit Theorem, Julio C. Urenda, Olga Kosheleva, Shahnaz Shahbazova, Vladik Kreinovich
Departmental Technical Reports (CS)
It is known that, due to the Central Limit Theorem, the probability distribution of the uncertainty of the result of data processing is, in general, close to Gaussian -- or to a distribution from a somewhat more general class known as infinitely divisible. We show that a similar result holds in the fuzzy case: namely, the membership function describing the uncertainty of the result of data processing is, in general, close to Gaussian -- or to a membership function from an explicitly described more general class.
Analysis Of Eeg Data Using Complex Geometric Structurization,
2021
Trinity University
Analysis Of Eeg Data Using Complex Geometric Structurization, Eddy A. Kwessi, L. J. Edwards
Mathematics Faculty Research
Electroencephalogram (EEG) is a common tool used to understand brain activities. The data are typically obtained by placing electrodes at the surface of the scalp and recording the oscillations of currents passing through the electrodes. These oscillations can sometimes lead to various interpretations, depending on, for example, the subject’s health condition, the experiment carried out, the sensitivity of the tools used, or human manipulations. The data obtained over time can be considered a time series. There is evidence in the literature that epilepsy EEG data may be chaotic. Either way, the Embedding Theory in dynamical systems suggests that time series …
So How To Make Group Decisions? Arrow's Impossibility Theorem 70 Years After,
2021
New Mexico State University
So How To Make Group Decisions? Arrow's Impossibility Theorem 70 Years After, Hung T. Nguyen, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In 1951, Kenneth Arrow proved that it is not possible to have a group decision making procedure that satisfies reasonable requirements like fairness. From the theoretical viewpoint, this is a great result -- well-deserving the Nobel Prize that was awarded to Professor Arrow. However, from the practical viewpoint, the question remains -- so how should we make group decisions? A usual way to solve this problem is to provide some reasonable heuristic ideas, but the problem is that different seemingly reasonable idea often lead to different group decision -- this is known, e.g., for different voting schemes. In this paper, …
Knot Theory In Virtual Reality,
2021
Western Kentucky University
Knot Theory In Virtual Reality, Donald Lee Price
Masters Theses & Specialist Projects
Throughout the study of Knot Theory, there have been several programmatic solutions to common problems or questions. These solutions have included software to draw knots, software to identify knots, or online databases to look up pre-computed data about knots. We introduce a novel prototype of software used to study knots and links by using Virtual Reality. This software can allow researchers to draw links in 3D, run physics simulations on them, and identify them. This technique has not yet been rigorously explored and we believe it will be of great interest to Knot Theory researchers. The computer code is written …
What Fuzzy And Quantum Computing Can Learn From The Success Of Deep Learning,
2021
Azerbaijan Technical University
What Fuzzy And Quantum Computing Can Learn From The Success Of Deep Learning, Shahnaz Shahbazova, Vladik Kreinovich
Departmental Technical Reports (CS)
How can we apply the ideas that made deep neural networks successful to other aspects of computing? For this purpose, we reformulate these ideas in a more general form -- and we show that this generalization also covers fuzzy and quantum computing. This enables us to suggest that similar ideas can be helpful for fuzzy and quantum computing as well. In this suggestion, we are encouraged by the fact that as we show, to some extent, these ideas are already helpful.
Why Quantum Techniques Are A Good First Approximation To Economic Phenomena, And What Next,
2021
The University of Texas at El Paso
Why Quantum Techniques Are A Good First Approximation To Economic Phenomena, And What Next, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
Somewhat surprisingly, several formulas of quantum physics -- the physics of micro-world -- provide a good first approximation to many social phenomena, in particular, to many economic phenomena, phenomena which are very far from micro-physics. In this paper, we provide three possible explanations for this surprising fact. First, we show that several formulas from quantum physics actually provide a good first-approximation description for many phenomena in general, not only to the phenomena of micro-physics. Second, we show that some quantum formulas represent the fastest way to compute nonlinear dependencies and thus, naturally appear when we look for easily computable models; …
Resilience Of Transportation Systems To Disasters,
2021
DePauw University
Resilience Of Transportation Systems To Disasters, Nangga (Ga Nan) Oirat, Suman Balasubramanian Phd
Annual Student Research Poster Session
We used graph theory's centrality measures to process the resiliency of rail stations in India. Centrality measures are the principles of processing, while Python is the tool of processing.
Big Cities: Air Pollution And Human Health,
2021
DePauw University
Big Cities: Air Pollution And Human Health, Natalie Michaels, Naima Shifa Phd
Annual Student Research Poster Session
Our project explores the growing issue of air pollution on urban environments throughout the United States. Through the use of the County Health Rankings data set, we investigated the connection amongst air pollution, health outcomes, and other socioeconomic and environmental risk factors.
Dynamic Parameter Estimation From Partial Observations Of The Lorenz System,
2021
CUNY Hunter College
Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng
Theses and Dissertations
Recent numerical work of Carlson-Hudson-Larios leverages a nudging-based algorithm for data assimilation to asymptotically recover viscosity in the 2D Navier-Stokes equations as partial observations on the velocity are received continuously-in-time. This "on-the-fly" algorithm is studied both analytically and numerically for the Lorenz equations in this thesis.
Smooth Global Approximation For Continuous Data Assimilation,
2021
CUNY Hunter College
Smooth Global Approximation For Continuous Data Assimilation, Kenneth R. Brown
Theses and Dissertations
This thesis develops the finite element method, constructs local approximation operators, and bounds their error. Global approximation operators are then constructed with a partition of unity. Finally, an application of these operators to data assimilation of the two-dimensional Navier-Stokes equations is presented, showing convergence of an algorithm in all Sobolev topologies.
Awegnn: Auto-Parametrized Weighted Element-Specific Graph Neural Networks For Molecules.,
2021
University of Kentucky
Awegnn: Auto-Parametrized Weighted Element-Specific Graph Neural Networks For Molecules., Timothy Szocinski, Duc Duy Nguyen, Guo-Wei Wei
Mathematics Faculty Publications
While automated feature extraction has had tremendous success in many deep learning algorithms for image analysis and natural language processing, it does not work well for data involving complex internal structures, such as molecules. Data representations via advanced mathematics, including algebraic topology, differential geometry, and graph theory, have demonstrated superiority in a variety of biomolecular applications, however, their performance is often dependent on manual parametrization. This work introduces the auto-parametrized weighted element-specific graph neural network, dubbed AweGNN, to overcome the obstacle of this tedious parametrization process while also being a suitable technique for automated feature extraction on these internally complex …
Effects Of Virtual Math Mentorships On Elementary Student Math Scores,
2021
Liberty University
Effects Of Virtual Math Mentorships On Elementary Student Math Scores, Tammy T. May
Doctoral Dissertations and Projects
The purpose of this quantitative, quasi-experimental study was to examine the relationship between college students’ virtual math mentorships and instruction on third grade students’ math academic success. College students in teacher preparation programs investigated deficiencies in third grade students’ competency of math concepts as specified by state standards, and they designed lessons to address these challenges through weekly virtual meetings. Third grade teachers wanted to provide additional math supports for their struggling students, and this partnership between the college students and the third graders was the foundation of this study at four Title 1 rural elementary schools. This research is …
