Digital Commons Network^™

A General Expression For Hermite Expansions With Applications, Tom P. Davis

The Mathematics Enthusiast

Hermite polynomials arise when dealing with functions of normally distributed variables, and are commonly thought of as the analog of the simple polynomials on functions of regular variables. Therefore the Hermite expansion should be an analog of the Taylor expansion. Indeed there is a strong connection between the two – the general coefficient in the Hermite expansion is the weighted integral of the nth derivative, as compared to the nth derivative evaluated at zero in the case of Taylor. This fact can be used to derive the Hermite expansion for the integral and the derivative of a function. Furthermore, it …

The Tradition Of Large Integers In Historical Arithmetical Textbooks, Franka Miriam Bruckler, Vladimir Stilinovic

The Mathematics Enthusiast

After the Hindu-Arabic decimal positional system was introduced in Europe, throughout many centuries textbooks on elementary arithmetic, intended for beginners, had a more or less fixed organization of content, usually starting with chapters on numeration. These chapters, as a rule, contained one or more examples of large integers the purpose of which was simply to be named (read out loud), sometimes also vice versa. This tradition apparently began with the two first texts that significantly contributed to the spread of the decimal system in Europe—the Latin translations of al- Khwarizmi’s treatise on decimal arithmetic, and Leonardo’s Liber Abaci, containing examples …

Will They Automatically Work Together? Cooperation Among Non-Fools In Hobbes´S Leviathan, Karim Pluma

The Mathematics Enthusiast

Thomas Hobbes´s State of War is commonly imagined as a harrowing condition where hostile interactions are the rule and non-hostile encounters are the rare exception. However, while it is generally true that Hobbes purposely outlined his famed condition of anarchy as a condition of perennial conflict, it is also equally true that cooperative behavior was not uncommon. In fact, by only taking into account cooperative behavior, as presented in Leviathan, the anarchic humans leave the absolute uncertainties of the State of War and create the Commonwealth for their safety and well-being. Over the past fifty years or so, several exits …

An Examination Of The Factors And Characteristics That Contribute To The Success Of Putnam Fellows, Robert A. J. Stroud, Thomas C. Defranco

The Mathematics Enthusiast

The William Lowell Putnam Mathematical Competition is an intercollegiate mathematics competition for students in the United States and Canada and is regarded as the most prestigious and challenging mathematics competition in North America (Alexanderson, 2004; AMS, 2020; Grossman, 2002; Reznick, 1994; Schoenfeld, 1985). Students who earn the five highest scores on the examination are named Putnam Fellows. Since its inception in 1938, only 306 individuals have won the competition and a select few have won multiple times. Clearly, being named a Putnam Fellow is a remarkable achievement and therefore, understanding the factors and characteristics that contribute to their success is …

The Construction Of Figured Numbers In Geogebra Software Using Algebraic Properties, Francisco Evamar Barros, Francisco Regis Vieira Alves, Paula Maria Machado Cruz Catarino, Renata Teofilo De Sousa

The Mathematics Enthusiast

Figured numbers are sequences of natural numbers that, when represented by dots, form geometric configurations. The immediate sequence of figured numbers presents in its configuration the equilateral triangles, being the basis for finding several others, as long as a relationship between them is discovered. This article shows the construction of polygonal, stellar and three-dimensional figured numbers that can be constructed using the GeoGebra software as a resource to visualize the properties that relate these numbers to the triangular numbers. It is a way of observing the relationship that the figures shown have to each other, how we can understand the …

Tagging Opportunities To Learn: A Coding Scheme For Student Tasks, Janet Heine Barnett, Cihan Can, Daniel E. Otero

The Mathematics Enthusiast

This article describes the development of a coding scheme for analyzing mathematical tasks in Primary Source Projects (PSPs), curriculum materials based on primary historical sources designed for teaching standard topics from today’s undergraduate mathematics curriculum. Our scheme attends to social-cultural aspects of mathematical learning while focusing on the student actions expected as they work tasks. We exemplify our scheme with tasks drawn from a diverse set of PSPs and report results from its application to these projects. We conclude with comments on how our work can assist instructors, curriculum developers, and researchers, including those who are interested in other types …

On The Even Distribution Of Odd Primes: An On-Ramp To Mathematical Research, James Quinlan, Michael Todd Edwards

The Mathematics Enthusiast

The authors consider a conjecture by Chebyshev in 1853 on the distribution of odd primes among those that are one more than a multiple of four and those three more than a multiple of four—and use technology to explore the cardinality of these subsets. Generalizations are presented for student exploration along with several sources for more in-depth research.

The Chain Rule Does Not Have To Be A Pain Rule, Elizabeth Beeman, Jennifer Runge, Lauren Holden, Devon Maxwell, Yi-Yin (Winnie) Ko

The Mathematics Enthusiast

Relational and instrumental understanding of the Chain Rule can help teachers provide students a deeper and more meaningful calculus experience.

The Monty Brawl And Other Unexpected Consequences Of Mathematical Instruction, Francesco Beccuti

The Mathematics Enthusiast

No abstract provided.

Using Gardner's Three-Squares Problem For A Group Project In A Mathematical Problem Solving Module, Jonathan Hoseana

The Mathematics Enthusiast

Consider a 1 x 3 grid whose top-left vertex is connected to the bottom-right vertex of each of the unit squares. What is the sum of the three acute angles formed by the connecting segments with the unit squares' bases? This is the so-called three-squares problem, often attributed to Gardner. In a recent academic year, the author used a video on this problem, produced by the YouTube channel Numberphile, for a group project in a first-semester undergraduate module: Mathematical Problem Solving. The project involved collaborative writing on the problem and individual completion of a peer-assessment form. We report the outcomes …

Going Off On A Tangent: An Inclusion-Exclusion Identity, Aloysius Bathi Kasturiarachi

The Mathematics Enthusiast

Undergraduate research in tertiary education offers mathematics students a pathway to engage in high-impact practices. Using a simple sum equals product identity from number theory as a motivator, we build a series of inclusion-exclusion identities for convex polygons using the symmetry inherent in the tangent function. The techniques used are simple and accessible, illuminating and generalizable, in a manner that rejects a singular line of inquiry in favor of a plurality of mathematical ideas.

Investigating Problems Posed By Pre-Service Mathematics Teachers For The Four Operations In Fractions, Yasemin Kiymaz

The Mathematics Enthusiast

This study investigates 40 preservice middle school teachers’ problems posed for two given fractions. Pre-service teachers were asked to pose three problems (farea, length and set model) for each of the operations of addition, subtraction, multiplication and division with these fractions. 12 problems posed by each pre-service teacher were examined in terms of their suitability for the given operation, the targeted model and real life relevance. Errors in the posed problems were also examined. As a result of the analysis, it was observed that the model in which pre-service teachers were the most unsuccessful in posing problems was the set …

On Convincing Power Of Counterexamples, Orly Buchbinder, Rina Zazkis

The Mathematics Enthusiast

Despite plethora of research that attends to the convincing power of different types of proofs, research related to the convincing power of counterexamples is rather slim. In this paper we examine how prospective and practicing secondary school mathematics teachers respond to different types of counterexamples. The counterexamples were presented as products of students’ arguments, and the participants were asked to evaluate their correctness and comment on them. The counterexamples varied according to mathematical topic: algebra or geometry, and their explicitness. However, as we analyzed the data, we discovered that these distinctions were insufficient to explain why teachers accepted some counterexamples, …

A Role For Affect In The Future Of Mathematics Education (With Thoughts On Intelligence), Marcelo Almora Rios

The Mathematics Enthusiast

A Review of:

1. Alan Schoenfeld, Heather Fink, Alyssa Sayavedra, Anna Weltman, & Sandra Zuñiga-Ruiz’s (2023) Mathematics Teaching on Target, Routledge, 164pp. ISBN (HB): 978-1-0324-4167-2;

2. Alan Schoenfeld, Heather Fink, Sandra Zuñiga-Ruiz, Siqi Huang, Xinyu Wei, & Brantina Chirinda’s (2023) Helping Students Become Powerful Mathematics Thinkers, Routledge, 272pp. ISBN (HB): 978-1-0324-4168-9.

Shape Anisotropy-Governed High-Performance Nanomagnetosol For In Vivo Magnetic Particle Imaging Of Lungs, Saumya Nigam, Jeotikanta Mohapatra, Ashley V Makela, Hanaan Hayat, Jessi Mercedes Rodriguez, Aixia Sun, Elizabeth Kenyon, Nathan A Redman, Dana Spence, George Jabin, Bin Gu, Mohamed Ashry, Lorenzo F Sempere, Arijit Mitra, Jinxing Li, Jiahui Chen, Guo-Wei Wei, Steven Bolin, Brett Etchebarne, J Ping Liu, Christopher H Contag, Ping Wang

Faculty, Staff and Student Publications

Caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), coronavirus disease 2019 (COVID-19) has shown extensive lung manifestations in vulnerable individuals, putting lung imaging and monitoring at the forefront of early detection and treatment. Magnetic particle imaging (MPI) is an imaging modality, which can bring excellent contrast, sensitivity, and signal-to-noise ratios to lung imaging for the development of new theranostic approaches for respiratory diseases. Advances in MPI tracers would offer additional improvements and increase the potential for clinical translation of MPI. Here, a high-performance nanotracer based on shape anisotropy of magnetic nanoparticles is developed and its use in MPI imaging …

Circulating Tumor Dna And Radiological Tumor Volume Identify Patients At Risk For Relapse With Resected, Early-Stage Non-Small-Cell Lung Cancer, H T Tran, S Heeke, S Sujit, N Vokes, J Zhang, M Aminu, V K Lam, A Vaporciyan, S G Swisher, M C B Godoy, T Cascone, B Sepesi, D L Gibbons, J Wu, J V Heymach

Faculty, Staff and Student Publications

Background: Predicting relapse and overall survival (OS) in early-stage non-small-cell lung cancer (NSCLC) patients remains challenging. Therefore, we hypothesized that detection of circulating tumor DNA (ctDNA) can identify patients with increased risk of relapse and that integrating radiological tumor volume measurement along with ctDNA detectability improves prediction of outcome.

Patients and methods: We analyzed 366 serial plasma samples from 85 patients who underwent surgical resections and assessed ctDNA using a next-generation sequencing liquid biopsy assay, and measured tumor volume using a computed tomography-based three-dimensional annotation.

Results: Our results showed that patients with detectable ctDNA at baseline or after treatment and …

Macdiarmid The Spaceman: Extraterrestrial Space In Hugh Macdiarmid’S Poetry From Sangschaw To A Drunk Man Looks At The Thistle, Michael H. Whitworth

Studies in Scottish Literature

Looking at Hugh MacDiarmid’s Sangschaw (1925), Penny Wheep (1926), and A Drunk Man Looks at the Thistle (1926), this article considers MacDiarmid’s use of science, particularly astronomy, in the 1920s. It traces known and possible sources for his scientific knowledge in books and periodicals, especially The New Age. It examines the image of light travelling through space, found in popular astronomy works by Felix Eberty and Camille Flammarion. It also compares his conception of the earth as a moving object in space with that found in poems by Thomas Hardy.

New Discoveries On Protein Recruitment And Regulation During The Early Stages Of The Dna Damage Response Pathways, Kelly Waters, Donald E. Spratt

Chemistry

Maintaining genomic stability and properly repairing damaged DNA is essential to staying healthy and preserving cellular homeostasis. The five major pathways involved in repairing eukaryotic DNA include base excision repair (BER), nucleotide excision repair (NER), mismatch repair (MMR), non-homologous end joining (NHEJ), and homologous recombination (HR). When these pathways do not properly repair damaged DNA, genomic stability is compromised and can contribute to diseases such as cancer. It is essential that the causes of DNA damage and the consequent repair pathways are fully understood, yet the initial recruitment and regulation of DNA damage response proteins remains unclear. In this review, …

Diverse Hedge Funds, Yan Lu, Narayan Y. Naik, Melvyn Teo

Research Collection Lee Kong Chian School Of Business

Hedge fund teams with heterogeneous educational backgrounds, academic specializations, work experiences, genders, and races, outperform homogeneous teams after adjusting for risk and fund characteristics. An event study of manager team transitions, instrumental variable regressions, and an analysis of managers who simultaneously operate solo- and team-managed funds address endogeneity concerns. Diverse teams deliver superior returns by arbitraging more stock anomalies, avoiding behavioral biases, and minimizing downside risks. Moreover, diversity allows hedge funds to circumvent capacity constraints and generate persistent performance. Our results suggest that diversity adds value in asset management. Authors have furnished an Internet Appendix, which is available on the …

What Difference Do The New Factor Models Make In Portfolio Allocation?, Frank J. Fabozzi, Dashan Huang, Fuwei Jiang, Jiexun Wang

Research Collection Lee Kong Chian School Of Business

This paper compares the Hou-Xue-Zhang four-factor model with the Fama-French five-factor model from an investing perspective both in- and out-of-sample. Without margin requirements and model uncertainty, the Hou-Xue-Zhang model outperforms the Fama-French model. However, the outperformance could become negligible if an investor is subject to margin requirements and model uncertainty. The Hou-Xue-Zhang model shows similar power as the Fama-French model in describing the covariance matrix of asset returns. Overall, the two models do not make a difference for investing in a realistic setting.

An Overview Of The Second-Previous Memory Effect In The Strictlyalternating Donation Game, Mohamed Zayet, Essam El-Seidy, Amira Abdel-Malek, Aya Rabie

Basic Science Engineering

Game theory delves into the examination of strategic behaviour across diverse domains such as insurance, business, military, biology, andmore,with the aim of deriving optimal decisions. Recent research focusing on the alteration of memory in the donation game with simultaneous iterated rounds has spurred our interest in investigating this phenomenon within the realm of the strictly alternating donation game. This study proposes a novel decision-making approach, utilising the previous unit instead of the most recent one. Thescopenarrowsdownto16employedstrategies,each definedbyfinitetwo-stateautomata,whileaccountingforpotentialimplementationerrorsinthe computationofstrategypayoffs.Dominant strategies are determined by assessing the interaction payoffs among strategy pairs. This article centres on the calculation of equilibrium points among heteroclinic …

The Pacifican February 2024, University Of The Pacific

All Issues - Student Newspaper, The Pacifican, Pacific Weekly

No abstract provided.

Building A Sustainable Garch Model To Forecast Rubber Price: Modified Huber Weighting Function Approach, Intan Martina Md Ghani, Hanafi A Rahim

Baghdad Science Journal

The unstable and uncertain nature of natural rubber prices makes them highly volatile and prone to outliers, which can have a significant impact on both modeling and forecasting. To tackle this issue, the author recommends a hybrid model that combines the autoregressive (AR) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models. The model utilizes the Huber weighting function to ensure the forecast value of rubber prices remains sustainable even in the presence of outliers. The study aims to develop a sustainable model and forecast daily prices for a 12-day period by analyzing 2683 daily price data from Standard Malaysian Rubber Grade …

Investigate Spectroscopic Experimental And Theoretical Model For Hemoglobin Nanoscale Solution, Hanan Auda Naif, Asaad M. Abbas, Mahasin Fadhil Hadi Al-Kadhemy

Baghdad Science Journal

In the current study, haemoglobin analytes dissolved in a special buffer (KH2PO4(1M), K2HPO4(1M)) with pH of 7.4 were used to record absorption spectra measurements with a range of concentrations from (10-8 to 10-9) M and an absorption peak of 440nm using Broadband Cavity Enhanced Absorption Spectroscopy (BBCEAS) which is considered a simple, low cost, and robust setup. The principle work of this technique depends on the multiple reflections between the light source, which is represented by the Light Emitting Diode 3 W, and the detector, which is represented by the Avantes spectrophotomer. The optical cavity includes two high reflectivity ≥99% …

Comparative Study Of Gamma- Ray Shielding Parameters For Different Epoxy Composites, Amal A. El- Sawy, Eman Sarwat

Baghdad Science Journal

In the current work various types of epoxy composites were added to concrete to enhance its effectiveness as a gamma- ray shield. Four epoxy samples of (E/clay/B4C) S1, (E/Mag/B4C) S2, (EPIL) S3 and (Ep) S4 were used in a comparative study of gamma radiation attenuation properties of these shields that calculating using Mont Carlo code (MCNP-5). Adopting Win X-com software and Artificial Neural Network (ANN), µ/ρ revealed great compliance with MCNP-5. By applying (µ/ρ) output for gamma at different energies, HVL, TVL and MFP have been also estimated. ANN technique was simulated to estimate (µ/ρ) and dose rates. According to …

Estimating The Parameters Of Exponential-Rayleigh Distribution For Progressively Censoring Data With S- Function About Covid-19, Rihaam N. Shatti, Iden H. Al-Kinani

Baghdad Science Journal

The two parameters of Exponential-Rayleigh distribution were estimated using the maximum likelihood estimation method (MLE) for progressively censoring data. To find estimated values for these two scale parameters using real data for COVID-19 which was taken from the Iraqi Ministry of Health and Environment, AL-Karkh General Hospital. Then the Chi-square test was utilized to determine if the sample (data) corresponded with the Exponential-Rayleigh distribution (ER). Employing the nonlinear membership function (s-function) to find fuzzy numbers for these parameters estimators. Then utilizing the ranking function transforms the fuzzy numbers into crisp numbers. Finally, using mean square error (MSE) to compare the …

Forgotten Index And Forgotten Coindex Of Graphs, J. Senbaga Malar, A. Meenakshi

Baghdad Science Journal

F index is a connected graph, sum of the cubes of the vertex degrees. The forgotten topological index has been designed to be employed in the examination of drug molecular structures, which is extremely useful for pharmaceutical and medical experts in understanding the biological activities. Among all the topological indices, the forgotten index is based on degree connectivity on bonds. This paper characterized the forgotten index of union of graphs, join graphs, limits on trees and its complements, and accuracy is measured. Co-index values are analyzed for the various molecular structure of chemical compounds

Backdating #Metoo, Jessica K. Fink

Cardozo Law Review

The #MeToo movement radically altered the way that people think about workplace sexual harassment. For decades, women were expected to tolerate a broad range of sexualized conduct at work. However, the revelation of Harvey Weinstein’s misdeeds in late 2017, followed by the exposure of countless other bad actors, dramatically shifted the social narrative regarding appropriate workplace behavior. Conduct that employees once ignored or overlooked suddenly became the basis for vociferous objection; the perfunctory responses to harassment that many employers once adopted suddenly stood out as glaringly deficient.

While society has undergone great shifts in its understanding of and response to …

Girth-Based Administered Activity For Pediatric 99mtc-Dmsa Spect, Ye Li, Justin L Brown, Jingyan Xu, Junyu Chen, Michael Ghaly, Monet Dugan, Xinhua Cao, Yong Du, Frederic H Fahey, Wesley Bolch, George Sgouros, Eric C Frey

Faculty, Staff and Student Publications

Background: Pediatric molecular imaging requires a balance between administering an activity that will yield sufficient diagnostic image quality while maintaining patient radiation exposure at acceptable levels. In current clinical practice, this balance is arrived at by the current North American Consensus Guidelines in which patient weight is used to recommend the administered activity (AA).

Purpose: We have previously demonstrated that girth (waist circumference at the level of the kidneys) is better at equalizing image quality than patient weight for pediatric Tc-99m DMSA renal function imaging. However, the correlation between image quality (IQ), AA, and patient girth has not been rigorously …

Decentralized Autonomous Organizations: To Statutorily Organize Or Not?, David M. Grant, Eric M. Kirby, Steven Hawkins

Wyoming Law Review

This Article explores the evolving concept of decentralized autonomous organizations (DAOs) in the context of Web3 technology. It raises critical questions about whether DAOs truly represent a step forward in limiting liability in entity governance structures or if they risk centralizing the decentralized. The text discusses the potential of DAOs to address regulatory and tax challenges while also highlighting concerns about their legitimacy and security. It compares the governance structures of traditional entities to DAOs and contemplates the reasons for formal organization pursuant to state statute. The Article further delves into some of the statutory laws in specific states recognizing …