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Articles 1801 - 1830 of 8400
Full-Text Articles in Physical Sciences and Mathematics
Fibonacci-Inspired Spiral Quilts, Kathleen Offenholley, Sk Collins, David Radcliffe
Fibonacci-Inspired Spiral Quilts, Kathleen Offenholley, Sk Collins, David Radcliffe
Journal of Humanistic Mathematics
This article provides insight into the mathematics and designs of quilts inspired by Fibonacci and logarithmic spirals. We introduce the history and development of the Fibonacci number sequence and how to hand-draw a Fibonacci spiral. Further, we explain the relationship between the Fibonacci spiral and logarithmic spirals, the advantages of using logarithmic spirals to create designs, and how to produce digital spiral designs using Desmos, a free web-based graphing calculator. Finally, we discuss methods for designing spiral quilts or other triangle and spiral designs (such as collage or other media) and derive a formula for calculating the apex angles of …
Badass Women, Richard Delaware
Badass Women, Richard Delaware
Journal of Humanistic Mathematics
In this true story, one mathematics major supports another in an unexpected way.
Intuitive Explanations In Mathematical Education, Jerzy Pogonowski
Intuitive Explanations In Mathematical Education, Jerzy Pogonowski
Journal of Humanistic Mathematics
I discuss the role of intuitive explanations in the learning, teaching, and popularization of mathematics. Several examples of such explanations are presented, related to linguistic explanations, perception, empirical models, and internal explanations inside mathematics itself. I emphasize the fact that intuitive explanations in a sense transgress mere mathematical arguments. I also discuss in brief the role of paradox resolution in mathematical education.
Bootstraps And Scaffolds: What A Cognitive-Historical Analysis Of The Complex Number System Reveals About Numerical Cognition, Charles R. Card, Gary G. Miller
Bootstraps And Scaffolds: What A Cognitive-Historical Analysis Of The Complex Number System Reveals About Numerical Cognition, Charles R. Card, Gary G. Miller
Journal of Humanistic Mathematics
The following investigation is a cognitive-historical analysis of the conceptual development of complex numbers. The history of this development spans nearly two millennia, from the earliest appearance of the square root of a negative quantity in the calculations of Heron of Alexandra (1st Century CE) to the full flowering of complex numbers in the first half of the 19th Century. The approach used for this analysis is Nersessian's, including her formulations of model-based reasoning and mental models. Additional aspects of the analysis feature the prominent roles played by process representations, including object-process complementarities, and by core numerical systems. Our analysis …
Building Communities Of Care For Equity, Justice, And Culturally Responsive Practice In Mathematics Education, Nicole Fletcher, B Waid
Building Communities Of Care For Equity, Justice, And Culturally Responsive Practice In Mathematics Education, Nicole Fletcher, B Waid
Journal of Humanistic Mathematics
Teaching is widely considered one of the “caring professions,” but conceptualizations of care and how care is put into practice in education are not universal. In this article, we draw from a range of perspectives on care that integrate supportive interpersonal relationships, high expectations, and culturally relevant theories of critical care, as well as Queer Theory and Disability Justice, to explore the application of these ideas in mathematics education. We identify key elements for building communities of care in mathematics education contexts: co-constructing community agreements, redefining participation, shifting traditional power structures, collaborative problem solving, and building networks of care beyond …
The Braids On Your Blanket, Michelle Cheng, Robert Uwe Laugwitz
The Braids On Your Blanket, Michelle Cheng, Robert Uwe Laugwitz
Journal of Humanistic Mathematics
In this expository essay, we introduce some elements of the study of groups by analysing the braid pattern on a knitted blanket. We determine that the blanket features pure braids with a minimal number of crossings. Moreover, we determine polynomial invariants associated to the links obtained by closing the braid patterns of the blanket.
Mathematical Models And Pedagogy Of Marxist Political Economy, Christopher Perez
Mathematical Models And Pedagogy Of Marxist Political Economy, Christopher Perez
Journal of Humanistic Mathematics
How can we teach people about the economics of labor and exploitation in mathematics courses? We define a mathematical model for describing the relationships embodied by commodities and labor. We then use this model to illustrate the exploitative nature of profit and the tendency for catastrophic chain-reactions that lead to market crashes. Lastly, we discuss applications to pedagogy in mathematics courses using a simplified version of the model.
What Is An Imaginary Number? The Plane And Beyond, Andrew W. Powell
What Is An Imaginary Number? The Plane And Beyond, Andrew W. Powell
Journal of Humanistic Mathematics
In this article I argue that i is a quantity associated with the two-dimensional real number plane, whether as a vector, a bi-vector, a point or a transformation (rotation). This position provides a foundation for the complex numbers and accounts for complex numbers in some equations of applied mathematics and physics. I also argue that complex numbers are fundamentally geometrical and can be described by geometric algebra, and that moreover the meaning of complex numbers in physics varies with dimension and geometry of the manifold.
Language Analysis Via The Run And Flattened Statistics On Permutations, Jennifer Elder, Pamela E. Harris, Anthony Simpson
Language Analysis Via The Run And Flattened Statistics On Permutations, Jennifer Elder, Pamela E. Harris, Anthony Simpson
Journal of Humanistic Mathematics
A permutation π in Sn can be decomposed into its runs π = τ1τ2 . . . τk, where a run of π is a maximal contiguous subsequence whose elements are in increasing order. If the first values of each run are in increasing order, then π is said to be flattened. Motivated by the study of flattened permutations, we study the words in the Danish, German, English, Spanish, French, Italian, Dutch, and Norwegian languages. In each language considered, our work provides the following: a list of the longest flattened words, histograms for the proportion …
Millions, Billions, Or Trillions: How To Partition Large Numbers Into Friendly Figures, Eryn Michelle Maher, Ha Nguyen, Cynthia Sanchez Tapia
Millions, Billions, Or Trillions: How To Partition Large Numbers Into Friendly Figures, Eryn Michelle Maher, Ha Nguyen, Cynthia Sanchez Tapia
Journal of Humanistic Mathematics
Communicating and making sense of large numbers — millions, billions, and trillions — is a persistent struggle in our society. Using large numbers is a learning requirement for elementary school children, but even adults struggle with it. Hence supporting future teachers in developing their own understanding of the concepts is valuable. To construct, enact, and revise an educational experience for preservice teachers, we apply three frameworks of teaching mathematics for social justice tasks, high cognitive demand tasks, and productive mathematics discussion. The context uses United States educational and defense spending, the national budget, and the gross domestic product. Preservice teachers …
The Modern Geometrician: Euclidean Construction For Digital Paper, Deborah A. Kent, David J. Muraki
The Modern Geometrician: Euclidean Construction For Digital Paper, Deborah A. Kent, David J. Muraki
Journal of Humanistic Mathematics
The emphasis on traditional hand-drawn compass and straight-edge geometrical constructions has been reduced in the core narrative of most current curricula. In response to this trend, this paper presents a virtual toolkit for producing precision geometrical figures within the popular note-taking app, Notability. These graphical procedures employ the app's stylus-based input and shape tools (for lines, circles and squares) to offer a modern take on classical geometrical construction. These procedures are adaptations of familiar textbook methods, necessary because the app's circle-drawing tool behaves differently from a standard compass. Beyond the familiar canon of elementary Euclidean constructions, such as angle bisectors …
Sociomathematical Norms And Automated Proof Checking In Mathematical Education: Reflections And Experiences, Merlin Carl
Sociomathematical Norms And Automated Proof Checking In Mathematical Education: Reflections And Experiences, Merlin Carl
Journal of Humanistic Mathematics
According to a widely held view, mathematical proofs are essentially (indications of) formal derivations, and thus in principle mechanically checkable (this view is defended, for example, by Azzouni [3]). This should in particular hold for the kind of simple proof exercises typically given to students of mathematics learning to write proofs. If that is so, then automated proof checking should be an attractive option for math education at the undergraduate level. An opposing view would be that mathematical proofs are social objects and that what constitutes a mathematical proof can thus not be separated from the social context in which …
My Own Private World Of Non-Ordinary Associative Arithmetics, Marion D. Cohen
My Own Private World Of Non-Ordinary Associative Arithmetics, Marion D. Cohen
Journal of Humanistic Mathematics
A binary operation # on Z+ is said to be an associative arithmetic if both # and its iteration — the binary operation ∗ defined recursively by: x∗1 = x and x∗y = [x ∗ (y − 1)]#x — are associative. E. Rosinger [6] showed that under reasonable conditions an associative arithmetic must be ordinary addition. However, in the general case, there are associative arithmetics that are not ordinary addition. This paper gives examples of these as well as results towards a structure theorem for associative arithmetics. The paper also describes the role that this particular math problem has played …
Picturing Mathematics (Education) In New Ways, Mark Huber, Gizem Karaali
Picturing Mathematics (Education) In New Ways, Mark Huber, Gizem Karaali
Journal of Humanistic Mathematics
No abstract provided.
Enhancing Fuel Injection System Reliability Through Weibull Family Functions Analysis, Ali Nouri Qarahasanlou, Abbas Barabadi, Meisam Saleki, Ali Rahimazar, Parisa Rezakhania, Masoume Gholamia
Enhancing Fuel Injection System Reliability Through Weibull Family Functions Analysis, Ali Nouri Qarahasanlou, Abbas Barabadi, Meisam Saleki, Ali Rahimazar, Parisa Rezakhania, Masoume Gholamia
Journal of Sustainable Mining
The efficient operation of heavy machinery is crucial to the success of mining and civil construction operations. To guarantee this performance, equipment performance is assessed using the Reliability Index, which analyzes failures to study the ability of a system to carry out its intended functions under predetermined conditions. On the other hand, the failure rate and operational environmental condition (such as management decisions, maintenance performance, etc., that are defined as “risk factors”) over the life cycle of industrial systems pose a significant challenge to reliability analysis. This paper proposes an approach to address these challenges by extending Weibull family functions …
Excited State Processes In Radical Elaborated Platinum Donor-Acceptor Complexes, Sangita Paudel
Excited State Processes In Radical Elaborated Platinum Donor-Acceptor Complexes, Sangita Paudel
Chemistry and Chemical Biology ETDs
Organo-transition metal complexes are being widely studied to understand their photophysical properties for their wide range of applications as efficient emitters in organic light emitting diodes (OLEDs), light emitting electrochemical cells (LEECs), etc. Cyclometalated organo-transition metal complexes such as cyclometalated square planar platinum(II) complexes are becoming suitable candidates for such applications because of their highly efficient luminescence. Understanding the excited properties of such complexes is useful in designing highly efficient and color tunable phosphors with desired excited state lifetimes. We aim to explore the influence of radical substituents on electronic structure, luminescence quantum efficiencies, and excited state lifetimes by synthesizing …
Health And Environmental Pollution: A Literature Review, Elsa Yuniarti, Levi Anatolia S.M. Exposto, Indang Dewata, Fitra Arya Dwi Nugraha, Alfitri Alfitri
Health And Environmental Pollution: A Literature Review, Elsa Yuniarti, Levi Anatolia S.M. Exposto, Indang Dewata, Fitra Arya Dwi Nugraha, Alfitri Alfitri
Kesmas
This study aimed to review various studies focusing on pollution that could adversely affect health, including sources, types, and mitigation efforts. The data used were obtained through a search on the Scopus website using the keywords "Health" AND "Pollution" from 2016 to 2023. Using these two keywords, 72 titles and abstracts of papers were successfully found. The results of this literature review were then analyzed with the assistance of NVivo 12 Pro, which grouped the findings based on their impact on health, reasons for pollution, types of pollution, and preventive measures. It was identified that the most common disease was …
Maximizing Generative Ai Benefits With Task Creativity And Human Validation, Charu Sinha, Veselina P. Vracheva, Cristina Nistor
Maximizing Generative Ai Benefits With Task Creativity And Human Validation, Charu Sinha, Veselina P. Vracheva, Cristina Nistor
Business Faculty Articles and Research
Much of the existing literature on generative AI applications is conflicting, with findings suggesting that investing in AI will lead to better organizational outcomes but also pointing out that incorporating AI may be a wasteful even counterproductive initiative. We develop a conceptual frame-work to characterize generative AI benefits based on the types of tasks that generative AI may be used for in management. Our work suggests that task creativity plays a key role in successful generative AI outcomes, but human validation - the extent to which a human engages in a supervisory role - is required to reap the benefits. …
Increasing The Robustness Of Machine Learning By Adversarial Attacks, Gourab Mukhopadhyay
Increasing The Robustness Of Machine Learning By Adversarial Attacks, Gourab Mukhopadhyay
Theses and Dissertations
By perturbation or physical attacks any machine can be fooled into predicting something else other than the intended output. There are training data based on which the model is trained to predict unknown things. The objective was to create noises and shades of different levels on the images and do experiments for measuring accuracy and making the model classify the traffic signs. When it comes to adding shades to the pictures, pixels were modified for three different layers of the pictures. The experiment also shows that with the shadows getting deeper, the accuracies drop significantly. Here, some changes in pixels …
Castor Oil-Based Polyurethane Adhesives: Effect Of Cross-Linker On The Bond Strength, Mayankkumar Chaudhary
Castor Oil-Based Polyurethane Adhesives: Effect Of Cross-Linker On The Bond Strength, Mayankkumar Chaudhary
Electronic Theses & Dissertations
Adhesives are important for binding diverse materials, promoting structural integrity and functional versatility in countless daily life applications. An enormous obstacle remains in the development of polyurethane (PU) adhesives exhibiting excellent bonding strength. Designing a chain extender with appropriate molecular structures is critical to improving the bonding strength of PU-based adhesives. In this work, PU-based adhesive was prepared using castor-oil-based polyol (COP) and diisocyanate. The bonding strength of the adhesive was improved by adding chain extenders such as N, N-bis(2-hydroxyethyl) thiophene-2,5-dicarboxamide (ETP) and N, N-Bis(2-hydroxyethyl)-terephthalamide (ETAM). The modified adhesive showed high bonding strength after the addition of chain extenders due …
Suitability Assessment Of Groundwater Quality For Drinking Purposes, Md. Zahidul Islam, M. G. Mostafa
Suitability Assessment Of Groundwater Quality For Drinking Purposes, Md. Zahidul Islam, M. G. Mostafa
Journal of Environmental Science and Sustainable Development
The groundwater status of Northwestern Bangladesh is a complex and challenging issue due to its arid and semi-arid climates, increasing population, overexploitation for domestic and irrigation purposes, lack of adequate rainfall, and limited water resources. The study aimed to assess the suitability and health risk of groundwater quality for drinking purposes. A total of one hundred groundwater samples were collected from shallow tubewells in two seasons, the monsoon (MON) and post-monsoon (POM), in northwestern Bangladesh (Ganges River basin) and analyzed using standard methods of analysis (Atomic adsorption spectrometry, UV-visible spectrometry, graphite, ion chromatography). The trends of predominant cations were Ca2+ …
Nilpotent Global Centers Of Generalized Polynomial Kukles System With Degree Three, Hebai Chen, Zhaosheng Feng, Rui Zahg
Nilpotent Global Centers Of Generalized Polynomial Kukles System With Degree Three, Hebai Chen, Zhaosheng Feng, Rui Zahg
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper, we study and characterize the nilpotent global centers of a generalized polynomial Kukles system with degree three. A sufficient and necessary condition of global centers is established under certain parametric conditions.
New Empirical Formulae For Some (P,Γ) Reactions Of Astrophysical S-Factor And Thermonuclear Reaction Rates, Mohammed Issa Hussein
New Empirical Formulae For Some (P,Γ) Reactions Of Astrophysical S-Factor And Thermonuclear Reaction Rates, Mohammed Issa Hussein
Polytechnic Journal
The study utilized weighted averages of cross sections in millibarn for (p,γ) reactions of 74Ge, 88Sr, 89Y, 90Zr, and 107Ag medium target elements from the EXFOR nuclear data library and compares them with evaluated from TALYS 1.95 nuclear model code. These averages were employed to develop empirical formulas for the astrophysical S-factor, covering proton energies up to 5 MeV, and thermonuclear reaction rates up to 20×109 K T9 (T9 is the temperature in units of 109K). Polynomial formulas have been utilized to accurately model the calculated astrophysical S-factor and thermonuclear …
Aplicación De La Serie De Fourier En La Eliminación De Armónicos Musicales Para Obtener Un Tono Puro, Kelly Johana Infante Beltrán, Néstor Orlando Forero Díaz, Adalberto Pardo Rodríguez
Aplicación De La Serie De Fourier En La Eliminación De Armónicos Musicales Para Obtener Un Tono Puro, Kelly Johana Infante Beltrán, Néstor Orlando Forero Díaz, Adalberto Pardo Rodríguez
Educación
Este libro explora la relación entre las matemáticas y la música a través de la aplicación de la serie de Fourier para eliminar armónicos y obtener tonos puros, fundamentales tanto en la audiometría médica como en la afinación de instrumentos musicales. Utilizando herramientas como Matlab y Sonic Visualiser, se analiza la pureza de las cuerdas de la guitarra clásica, destacando la importancia de esta técnica en diversos campos, desde la acústica hasta la medicina. El estudio incluye un simulador en Matlab para eliminar armónicos y una comparación de frecuencias específicas, mostrando cómo la comprensión de la serie de Fourier enriquece …
Short-Time Fourier Transform And Superoscillations, Daniel Alpay, Antonino De Martino, Kamal Diki, Daniele C. Struppa
Short-Time Fourier Transform And Superoscillations, Daniel Alpay, Antonino De Martino, Kamal Diki, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we investigate new results on the theory of superoscillations using time-frequency analysis tools and techniques such as the short-time Fourier transform (STFT) and the Zak transform. We start by studying how the short-time Fourier transform acts on superoscillation sequences. We then apply the supershift property to prove that the short-time Fourier transform preserves the superoscillatory behavior by taking the limit. It turns out that these computations lead to interesting connections with various features of time-frequency analysis such as Gabor spaces, Gabor kernels, Gabor frames, 2D-complex Hermite polynomials, and polyanalytic functions. We treat different cases depending on the …
The Role Of Sensing Modalities In Shaping Collective Motion And Group Behavior, Poorendra P. Ramlall
The Role Of Sensing Modalities In Shaping Collective Motion And Group Behavior, Poorendra P. Ramlall
Doctoral Dissertations and Master's Theses
Collective behavior refers to the coordinated movements that emerge from simple interactions between individuals within a group. Traditionally, researchers have modeled these interactions assuming individuals can sense their surroundings in all directions, like having eyes all around their heads. While this is a useful simplification, it does not capture the diverse ways animals actually sense the world. In this thesis, we take inspiration from the natural world, particularly from animals like bats and dolphins that use a combination of hearing and sight to navigate their environments. We explore how combining these sensory cues in a three-dimensional space affects the way …
Visualization Of Species Tree Likelihood Under The Multispecies Coalescent Model, Jaimasan Sutton
Visualization Of Species Tree Likelihood Under The Multispecies Coalescent Model, Jaimasan Sutton
Mathematics & Statistics ETDs
A commonly used tool for evolutionary biologists is a phylogenetic tree that represents the ancestry of a set of species and the evolution of traits. Statistical models can be used to predict the probabilities of gene trees which represent ancestral relationships of genes sampled from species. Because of this, we are able to represent the likelihood of a species tree, which represents the evolutionary history of a set of species, as a function of the counts of gene tree topologies, where each gene tree represents the ancestry of a specific genetic locus for multiple species. Because we can represent these …
Assessing Consequences And Relevant Thresholds Of Seismic Events In Puerto Rico To Aid The Future Creation Of Consequence-Driven Scenarios, Yahaira D. Alvarez-Gandia
Assessing Consequences And Relevant Thresholds Of Seismic Events In Puerto Rico To Aid The Future Creation Of Consequence-Driven Scenarios, Yahaira D. Alvarez-Gandia
Geography ETDs
Puerto Rico frequently experiences damaging earthquakes due to its location on the northeastern margin of the Caribbean Plate. Its unique combination of factors, including high population, informal construction practices, and environmental risks, such as tsunamis or landslides, create a heightened risk of loss of life and property. Within this context, earthquake scenarios are vital communication, mitigation, and preparedness tools. They provide the opportunity to think critically about possible alternatives to reduce the risks and impacts of these unpredictable events. As an initial step for integrated earthquake scenario development, this study uses semi-structured interviews and the analysis of government reports to …
Secondary Electron Yield Of Metals, Alloys, And Metal Oxides From First Principles Based Monte Carlo Simulations, Raul E. Gutierrez
Secondary Electron Yield Of Metals, Alloys, And Metal Oxides From First Principles Based Monte Carlo Simulations, Raul E. Gutierrez
Electrical and Computer Engineering ETDs
Density Functional Theory (DFT) based Monte Carlo (MC) simulations of the Sec-
ondary Electron Yield (SEY) of metals, alloys, and metal oxides are performed to
find material properties that could help reduce or influence the multipactor effect.
In order to accurately model the SEY of materials, knowledge of the frequency- and
momentum-dependent Energy Loss Function (qDepELF) is required. The qDepELF
is difficult to determine from experiment; however, it can be calculated from first
principles. The DFT-MC approach for simulating the secondary electron genera-
tion, propagation, and emission processes is described herein. Material properties,
which are calculated using DFT and used …