Mathematics Commons^™

The Formal Presentation Language Of Mathematics And Communication Ethics, Marshall Gordon

Journal of Humanistic Mathematics

Mathematics employs a formal language where symbols, verbs, and nouns serve to express terms, concepts, and rules that concatenate to definitions, problem-solving procedures, and proofs. Taken together these constitute the expository language of mathematics found in journals, textbooks, and demonstrations. As a communication given to informing, there are epistemological and ethical considerations that deserve examination. For in keeping with the commitment to an aesthetic of concision promulgated by tradition, the formal presentation language and style of mathematics, while valuable in furthering the body of knowledge, provides only the conclusion of an inquiry, completely excluding the language of investigation that informed …

Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel

Journal of Humanistic Mathematics

Almost exactly fifty years ago, Friedrich Kambartel, in his classic essay “Ethics and Mathematics,” did pioneering work in an intellectual environment that almost self-evidently assumed a strict separation of the two fields. In our first section we summarize and discuss that classical paper. The following two sections are devoted to complement and contrast Kambartel’s picture. In particular, the second section is devoted to ethical aspects of the indirect and direct mathematization of modern societies. The final section gives a short categorization of various philosophical positions with respect to the rationality of ethics and the mutual relation between ethics and mathematics.

Special Issue -- Ethics In Mathematics: Foreword, Catherine Buell, Victor Piercey

Journal of Humanistic Mathematics

No abstract provided.

Doughnuts And Ice Cream Cones: Sweet Mathematics, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Quantization For A Probability Distribution Generated By An Infinite Iterated Function System, Lakshmi Roychowdhury, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Quantization for probability distributions concerns the best approximation of a d-dimensional probability distribution P by a discrete probability with a given number n of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on ℝ. For such a probability measure P, an induction formula to determine the optimal sets of n-means and the nth quantization error for every natural number n is given. In addition, using the induction formula we give some results and observations about the optimal sets of n-means for all n ≥ 2.

The Dope Distance Is Sic: A Stable, Informative, And Computable Metric On Ordered Merge Trees, Jose Arbelo, Antonio Delgado, Charley Kirk, Zach Schlamowitz

Mathematics Summer Fellows

When analyzing time series data, it is often of interest to categorize them based on how different they are. We define a new dissimilarity measure between time series: Dynamic Ordered Persistence Editing (DOPE). DOPE satisfies metric properties, is stable to noise, is as informative as alternative approaches, and efficiently computable. Satisfying these properties simultaneously makes DOPE of interest to both theoreticians and data scientists alike.

Left-Separation Of Ω1, Lukas Stuelke, Adrienne Stanley Ph.D.

Summer Undergraduate Research Program (SURP) Symposium

A topological space is left-separated if it can be well-ordered so that every initial segment is closed. Here, we show that all countable ordinal numbers are left-separated. We then prove that a similar method could not work for ω₁ , using the pressing-down lemma¹ . We finish by showing that a left-separating well-ordering on ω₁ necessarily leads to a contradiction.

Rendezvous Numbers Of Compact And Connected Spaces, Kevin Demler, Bill Wood Ph.D.

Summer Undergraduate Research Program (SURP) Symposium

The concept of a rendezvous number was originally developed by O. Gross in 1964, and was expanded upon greatly by J. Cleary, S. Morris, and D. Yost in 1986. This number exists for every metric space, yet very little is known about it, and it’s exact value for most spaces is not known. Furthermore, it’s exact value is difficult to calculate, and in most cases we can only find bounds for the value. We focused on their arguments using convexity and applied it to shapes in different metrics and graphs. Using sets of points that stood out (vertices, midpoints) as …

Computing Well-Structured Subgraphs In Geometric Intersection Graphs., Satyabrata Jana Dr.

Doctoral Theses

For a set of geometric objects, the associative geometric intersection graph is the graph with a vertex for each object and an edge between two vertices if and only if the corresponding objects intersect. Geometric intersection graphs are very important due to their theoretical properties and applicability. Based on the different geometric objects, several types of geometric intersection graphs are defined. Given a graph G, an induced (either vertex or edge) subgraph H ⊆ G is said to be an well-structured subgraph if H satisfies certain properties among the vertices in H. This thesis studies some well-structured subgraphs finding problems …

The Construction And Estimation Of Hidden Semi-Markov Models, Kurdstan Abdullah, John Van Der Hoek

Journal of Stochastic Analysis

No abstract provided.

Random Walks In The Quarter Plane: Solvable Models With An Analytical Approach, Harshita Bali, Enrico Au-Yeung

DePaul Discoveries

Initially, an urn contains 3 blue balls and 1 red ball. A ball is randomly chosen from the urn. The ball is returned to the urn, together with one additional ball of the same type (red or blue). When the urn has twenty balls in it, what is the probability that exactly ten balls are blue? This is a model for a random process. This urn model has been extended in various ways and we consider some of these generalizations. Urn models can be formulated as random walks in the quarter plane. Our findings indicate that for a specific type …

Propuestas Y Resultados De Investigación Transmoderna, Translocal Y Digital Desde Jóvenes Semilleristas, Xiomara Gonzalez Gaitan

Institucional

En el presente libro se recopilan las propuestas, avances y resultados de los proyectos en curso de los Semilleros de Investigación de la Universidad de Cundinamarca (Colombia), que se presentaron en el «II Encuentro de Semilleros de Investigación: ciencia, tecnología e innovación en la era digital» en su versión de 2020. Publicamos estos proyectos con la intención de difundir el conocimiento y como muestra del esfuerzo y del alcance de la labor investigadora de los semilleristas de la Universidad de Cundinamarca. Esperamos que los lectores encuentren en estas propuestas caminos para resolver problemas o inspiración para construir nuevas propuestas de …

Work In Progress: The Rica Project: Rich, Immediate Critique Of Antipatterns In Student Code, Leo C. Ureel Ii, Laura Brown, Jon Sticklen, Michelle E. Jarvie-Eggart, Mary Benjamin

Michigan Tech Publications, Part 1

Rich, relevant, and immediate student feedback is a core ingredient supporting effective student learning. Feedback is particularly important for introductory computing courses where novice programmers are still learning the basic syntax and semantics of a programming language. Our project is aimed at detecting poor solutions to common problems, termed antipatterns, in student code and providing feedback that guides the student to better solutions. This paper discusses the first year of the project, specifically, the development of a Code Critiquer to detect antipatterns in student code and generate appropriate feedback. This important first step sets-up the project to advance knowledge about …

On Superoscillations And Supershifts In Several Variables, Yakir Aharonov, Fabrizio Colombo, Andrew N. Jordan, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen

Mathematics, Physics, and Computer Science Faculty Articles and Research

The aim of this paper is to study a class of superoscillatory functions in several variables, removing some restrictions on the functions that we introduced in a previous paper. Since the tools that we used with our approach are not common knowledge we will give detailed proof for the case of two variables. The results proved for superoscillatory functions in several variables can be further extended to supershifts in several variables.

The Thermodynamics Of A Stochastic Geometry Model With Applications To Non-Extensive Statistics, O.K. Kazemi, A. Pourdarvish, J. Sadeghi

Journal of Stochastic Analysis

No abstract provided.

Radio Number Of Hamming Graphs Of Diameter 3, Jason Devito, Amanda Niedzialomski, Jennifer Warren

Theory & Applications of Graphs

For G a simple, connected graph, a vertex labeling f:V(G) → Z+ is called a radio labeling of G if it satisfies |f(u)-f(v)|≥ diam(G)+1-d(u,v) for all distinct vertices u,v ∈ V(G). The radio number of G is the minimal span over all radio labelings of G. If a bijective radio labeling onto {1,2,…|V(G)|} exists, G is called a radio graceful graph. We determine the radio number of all diameter 3 Hamming graphs and show that an infinite subset of them is radio graceful.

Oer Ancient Egyptian Numerals And Arithmetic Activity, Cynthia Huffman Ph.D.

Faculty Submissions

Many people are fascinated with ancient Egypt. The amazing, unique culture influenced many other civilizations and cultures. If you study the history of math, you will see how this influence included mathematics. Ancient Egypt also lasted an incredibly long time – over 3000 years. According to Egyptologist Bob Brier, “No civilization lasted so long, contributed so much, or repeatedly amazed as did ancient Egypt.”

In this Open Educational Resource activity, students will have the opportunity to learn about ancient Egyptian numerals and basic arithmetic. For motivation, the setting is a scribal school with each student using a clipboard, paper, and …

On The Integer-Antimagic Spectra Of Non-Hamiltonian Graphs, Wai Chee Shiu, Richard M. Low

Theory & Applications of Graphs

Let A be a nontrivial abelian group. A connected simple graph G = (V, E) is A-antimagic if there exists an edge labeling f: E(G) → A \ {0} such that the induced vertex labeling f+: V(G) → A, defined by f+(v) = Σ {f(u,v): (u, v) ∈ E(G)}, is a one-to-one map. In this paper, we analyze the group-antimagic property for Cartesian products, hexagonal nets and theta graphs.

Restrained Reinforcement Number In Graphs, Kazhal Haghparast, Jafar Amjadi, Mustapha Chellali, Seyed Mahmoud Sheikholeslami

Theory & Applications of Graphs

A set S of vertices is a restrained dominating set of a graph G=(V,E) if every vertex in V\ S has a neighbor in S and a neighbor in V\S. The minimum cardinality of a restrained dominating set is the restrained domination number γ_r(G). In this paper we initiate the study of the restrained reinforcement number r_r(G) of a graph G defined as the cardinality of a smallest set of edges F ⊆ E( ‾G) for which γ_r(G + F) < γ_r(G), where ‾G denotes the complement graph of G. …

Bbt Acoustic Alternative Top Bracing Cadd Data Set-Norev-2022jun28, Bill Hemphill

STEM Guitar Project’s BBT Acoustic Kit

This electronic document file set consists of an overview presentation (PDF-formatted) file and companion video (MP4) and CADD files (DWG & DXF) for laser cutting the ETSU-developed alternate top bracing designs and marking templates for the STEM Guitar Project’s BBT (OM-sized) standard acoustic guitar kit. The three (3) alternative BBT top bracing designs in this release are
(a) a one-piece base for the standard kit's (Martin-style) bracing,
(b) 277 Ladder-style bracing, and
(c) an X-braced fan-style bracing similar to traditional European or so-called 'classical' acoustic guitars.

The CADD data set for each of the three (3) top bracing designs includes …

Artificial Neural Network Concepts And Examples, Harcharan Kabbay

Theses

Artificial Neural Networks have gained much media attention in the last few years. Every day, numer- ous articles on Artificial Intelligence, Machine Learning, and Deep Learning exist. Both academics and business are becoming increasingly interested in deep learning. Deep learning has innumerable uses, in- cluding autonomous driving, computer vision, robotics, security and surveillance, and natural language processing. The recent development and focus have primarily been made possible by the convergence of related research efforts and the introduction of APIs like Keras. The availability of high-speed compute resources such as GPUs and TPUs has also been instrumental in developing deep learning …

The Cartesian Analytical Solutions For The N-Dimensional Compressible Navier-Stokes Equations With Density-Dependent Viscosity, Engui Fan, Zhijun Qiao, Manwai Yuen

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we prove the existence of general Cartesian vector solutions u=b(t)+A(t)x for the N-dimensional compressible Navier-Stokes equations with density-dependent viscosity, based on the matrix and curve integration theory. Two exact solutions are obtained by solving the reduced systems.

On P-Competition Graphs Of Loopless Hamiltonian Digraphs Without Symmetric Arcs And Graph Operations, Kuniharu Yokomura, Morimasa Tsuchiya

Theory & Applications of Graphs

For a digraph D, the p-competition graph C_p(D) of D is the graph satisfying the following: V(C_p(D))=V(D), for x,y ∈ V(C_p(D)), xy ∈ E(C_p(D)) if and only if there exist distinct p vertices v₁, v₂, ..., v_p ∈ V(D) such that x → v_i, y → v_i ∈ A(D) for each i=1,2, ..., p.

We show the H₁ ∪ H₂ is a p-competition graph of a loopless digraph without symmetric arcs for p ≥ 2 , where …

Harmonious Labelings Via Cosets And Subcosets, Jared L. Painter, Holleigh C. Landers, Walker M. Mattox

Theory & Applications of Graphs

In [Abueida, A. and Roblee, K., More harmonious labelings of families of disjoint unions of an odd cycle and certain trees, J. Combin. Math. Combin. Comput., 115 (2020), 61-68] it is shown that the disjoint union of an odd cycle and certain paths is harmonious, and that certain starlike trees are harmonious using properties of cosets for a particular subgroup of the integers modulo m, where m is the number of edges of the graph. We expand upon these results by first exploring the numerical properties when adding values from cosets and subcosets in the integers modulo m. …

On The Total Set Chromatic Number Of Graphs, Mark Anthony C. Tolentino, Gerone Russel J. Eugenio, Mari-Jo P. Ruiz

Theory & Applications of Graphs

Given a vertex coloring c of a graph, the neighborhood color set of a vertex is defined to be the set of all of its neighbors’ colors. The coloring c is called a set coloring if any two adjacent vertices have different neighborhood color sets. The set chromatic number χ_s(G) of a graph G is the minimum number of colors required in a set coloring of G. In this work, we investigate a total analog of set colorings; that is, we study set colorings of the total graph of graphs. Given a graph G = (V, E) …

Geodesic Bipancyclicity Of The Cartesian Product Of Graphs, Amruta V. Shinde, Y.M. Borse

Theory & Applications of Graphs

A cycle containing a shortest path between two vertices u and v in a graph G is called a (u,v)-geodesic cycle. A connected graph G is geodesic 2-bipancyclic, if every pair of vertices u,v of it is contained in a (u,v)-geodesic cycle of length l for each even integer l satisfying 2d + 2 ≤ l ≤ |V(G)|, where d is the distance between u and v. In this paper, we prove that the Cartesian product of two geodesic hamiltonian graphs is a geodesic 2-bipancyclic graph. As a consequence, we show that for n …

Total Colouring Of New Classes Of Subcubic Graphs, Sethuraman G, Velankanni Anthonymuthu

Theory & Applications of Graphs

The total chromatic number of a graph G, denoted χ”(G), is the least number of colours needed to colour the vertices and the edges of G such that no incident or adjacent elements (vertices or edges) receive the same colour. The popular Total Colouring Conjecture (TCC) posed by Behzad states that, for every simple graph G, χ”(G) ≤ Δ(G)+2. In this paper, we prove that the total chromatic number for a family of subcubic graphs called cube connected paths and also for a class of subcubic graphs having the property that the vertices are covered by independent …

Quantization Of The Poisson Type Central Limit Theorem (1), Yungang Lu

Journal of Stochastic Analysis

No abstract provided.

Finding Approximate Pythagorean Triples (And Applications To Lego Robot Building), Ronald I. Greenberg, Matthew Fahrenbacher, George K. Thiruvathukal

Computer Science: Faculty Publications and Other Works

This assignment combines programming and data analysis to determine good combinations of side lengths that approximately satisfy the Pythagorean Theorem for right triangles. This can be a standalone exercise using a wide variety of programming languages, but the results are useful for determining good ways to assemble LEGO pieces in robot construction, so the exercise can serve to integrate three different units of the Exploring Computer Science high school curriculum: "Programming", "Computing and Data Analysis", and "Robotics". Sample assignment handouts are provided for both Scratch and Java programmers. Ideas for several variants of the assignment are also provided.