Search

With rising healthcare costs and the rapid increase in remote physiologic monitoring and care delivery, there is an increasing need for economical, accurate, and non-invasive continuous measures of blood analytes. Based on radio frequency identification (RFID), a novel electromagnetic technology (the Bio-RFID sensor) was developed to non-invasively penetrate inanimate surfaces, capture data from individual radio frequencies, and convert those data into physiologically meaningful information and insights. Here, we describe groundbreaking proof-of-principle studies using Bio-RFID to accurately measure various concentrations of analytes in deionized water. In particular, we tested the hypothesis that the Bio-RFID sensor is able to precisely and non-invasively measure and identify a variety of analytes in vitro. For this assessment, varying solutions of (1) water in isopropyl alcohol; (2) salt in water, and (3) commercial bleach in water were tested, using a randomized double-blind trial design, as proxies for biochemical solutions in general. The Bio-RFID technology was able to detect concentrations of 2000 parts per million (ppm), with evidence suggesting the ability to detect considerably smaller concentration differences. [ABSTRACT FROM AUTHOR]

In 1749, Leonhard Euler solved a longstanding open problem in number theory, proving Fermat's 1640 conjecture that any prime number of the form 4 m + 1 can be written as the sum of two squares. This achievement overshadowed an equally impressive calculation that Euler devised at the same time, to test numbers for primality. In this article, we explore Euler's primality test, demonstrating its computational parity with trial division, at least for a class of testable numbers. Additionally, we will see that primality testing was one of Euler's lifelong interests, and was a topic he returned to time and again as an application of his number theory work. [ABSTRACT FROM AUTHOR]

INTRODUCTION: Health systems often emphasize technical skills to reduce iatrogenic injuries. Nontechnical skills such as clinical and communication skills are mostly overlooked or not readily retrievable from medical records. Our aim was to estimate the association of technical and nontechnical skills of endoscopists with indemnity payments to patients after endoscopic perforations. METHODS: This is an observational registry-based study of closed claims against gastroenterologists involved in endoscopic perforations. RESULTS: We analyzed 175 closed claims related to perforations, all of which involved allegations of improper performance of the endoscopic procedure. Inadequate communication (n 5 71, 41%) and clinical judgment (n 5 60, 34%) on the part of the endoscopists were observed. Inadequate communication and clinical judgment were associated with over 3-fold odds of indemnity payment (odds ratio [OR] 3.31; 95% confidence interval [CI], 1.46-7.48, and OR 3.18; 95% CI, 1.44-7.01, respectively). However, if there were nocommunication breakdown or clinical judgment issues and the only allegation was poor technical skill, the odds of indemnity payments were less than half of those cases (OR 0.43; 95% CI 0.15-0.80). There was no evidence of a statistically significant interaction among age, procedure type, trainee involvement, clinical severity, need for surgery, and procedure-related death. DISCUSSION: Weobserved that inadequate communication andclinical judgmentwere associated withindemnity payment, independent of the severity of clinical outcomes. On the other hand, cases wherein there was an allegation of poor technical skills alone, without communication breakdown or clinical judgment issues, were associated with favorable legal outcomes for the defendant. (See the Visual Abstract at http://links.lww.com/AJG/B568.). [ABSTRACT FROM AUTHOR]

This paper describes efforts by the author to engage and motivate students in undergraduate research by giving them a large audience and engaging the media in disseminating their work. I provide an introduction to public relations from the point of view of a mathematics professor, and describe some lessons I have learned in my own attempts to engage newsprint, radio, and television sources in stories about undergraduate research in mathematics. After describing some partially successful early attempts, the paper discusses a recent event in which undergraduate research in mathematics became, briefly, a “hot news item” in Central Washington. The paper concludes with some thoughts about the benefits of this type of work to our students and our profession. [ABSTRACT FROM AUTHOR]

The article discusses the qualitative trends in playwright William Shakespeare studies as examined by scholars Michael Taylor, Neema Parvini and R. S. White. It notes that data collected by the World Shakespeare Bibliography Online of book monographs, articles and computer software pertaining to the author required sorting in the taxonomies for scholarly content. The Modern Language Association International Bibliography is also cited for observing the rise in Shakespeare-centric publications.

This work describes the contributions of Leonhard Euler (1707-1783), the 18th- century physicist and mathematician, to the fields of articulatory and experimental phonetics. First the authors provide evidence for Euler's role in establishing the St. Petersburg Academy prize of 1780. Next, they consider a short and posthumously published work of Euler, the Meditatio de formatione vocum. It is shown that the Meditatio represents an early attempt to compare vowels in several languages, and includes a two-dimensional classification of vowels which anticipates in many ways the International Phonetic Alphabet vowel chart. [ABSTRACT FROM AUTHOR]

It is fairly well known that Darwin was inspired to formulate his theory of natural selection by reading Thomas Malthus's Essay on the Principle of Population. In fact, by reading Darwin's notebooks, we can even locate one particular sentence which started Darwin thinking about population and selection. What has not been done before is to explain exactly where this sentence - essentially Malthus's ideas about geometric population growth - came from. In this essay we show that eighteenth century mathematician Leonhard Euler is responsible for this sentence, and in fact forms the beginning of the logical chain which leads to the creation of the theory of natural selection. We shall examine the fascinating path taken by a mathematical calculation, the many different lenses through which it was viewed, and the path through which it eventually influenced Darwin. [ABSTRACT FROM AUTHOR]

The article discusses the study conducted to examine the reciprocal sum as a knowledge metric and also discusses its mathematical theory, computation and perfect numbers. Topics discussed include long and intimate connection of reciprocal sums with the number theory, using Euler's theorem for getting the better results of sum of reciprocals, and using partial summation as a powerful and versatile method for estimating the reciprocal sums.

This note has three goals. First, we discuss a presentation of Bertrand's paradox in a recent issue of Philosophia Mathematica, which we believe to be a subtle but important misinterpretation of the problem. We compare claims made about Bertrand with his 1889 Calcul des Probabilités. Second, we use this source to understand Bertrand's true intention in describing what we now call his paradox, comparing it both to another problem he describes in the same section and to a modern treatment. Finally, we briefly consider the importance of knowing when a specific example represents a general case. [ABSTRACT FROM AUTHOR]

The article analyzes the distribution of average playoffs found by playing a fixed number of St. Petersburg games. It examines the most popular experiment on the said game which is the results of the Compte de Buffon's playing the game 2048 times. It mentions that the St. Petersburg game is a probabilistic thought investigation which appears to have an infinite expected value, but which no person could be expected to pay much to play.

Two numbers m and n are considered amicable if the sum of their proper divisors, s( n) and s( m), satisfy s( n) == m and s( m) == n. In 1981, Pomerance showed that the sum of the reciprocals of all such numbers, P, is a constant. We obtain both a lower and an upper bound on the value of P. [ABSTRACT FROM AUTHOR]

Editor's Note: As of this issue, The College Mathematics Journal has published fifty completed volumes. To celebrate 50 years of continued excellence in publishing expository mathematics, pedagogical discussions, and more, we plan to use two pages in each of the five issues of 2020 to tell the story of one decade of the journal. Some of these pieces will be written by people who were personally involved with CMJ during that time, so watch this space for some familiar names! [ABSTRACT FROM AUTHOR]

The article presents information on the properties of Graeco-Latin squares enumerated by mathematician Leonhard Euler. Euler suggested that a Graeco-Latin square of size n could never exist for any n of the form 4k +2, although he was not able to prove it. A Latin square is an n-by-n array of n distinct symbols in which each symbol appears exactly once in each row and column. On the other hand a Graeco-Latin square is an n-by-n array of ordered pairs from a set of n symbols such that in each row and each column of the array, each symbol appears exactly once in each coordinate. In one of his papers on Graeco-Latin squares, Euler used magic squares, which are closely related to Graeco-Latin squares. Magic squares were constructed by using Graeco-Latin squares of orders 3, 4 and 5. He showed that a Graeco-Latin square of order n can be converted into a magic square by the use of an algorithm. One can construct Graeco-Latin squares of every order n except those values for which the prime factorization of n contains only a single factor of 2.

Background: Wearable long-duration low-intensity ultrasound is an emerging non-invasive and non-narcotic therapy for the daily treatment of musculoskeletal pain. The aim of this randomized, double-blind, placebo-controlled study was to examine whether long-duration low-intensity ultrasound was effective in treating pain and improving function in patients with knee osteoarthritis. Methods: Ninety patients with moderate to severe knee pain and radiographically confirmed knee osteoarthritis (Kellgren-Lawrence grade I/II) were randomized for treatment with active (n = 55) or placebo (n = 35) devices applied daily to the treated knee. Investigators and subjects were blinded to treatment groups. Ultrasound (3 MHz, 0.132 W/cm2, 1.3 W) was applied with a wearable device for 4 h daily for 6 weeks, delivering 18,720 J per treatment. The primary outcome was change in pain intensity (numeric rating scale) assessed prior to intervention (baseline) and after 6 weeks. Secondary outcomes of functional change were measured at baseline and after 6 weeks using the Western Ontario McMaster Osteoarthritis Questionnaire (n = 84), along with range of motion (flexion, extension) and isometric muscle strength (flexion, extension and rotation) tests on the injured knee in a small pilot subset (n = 17). Results: The study had a 93% retention rate, and there were no significant differences between the groups regarding demographic variables or baseline outcome measures. Patients treated with active therapy observed a significant mean NRS pain reduction over the 6-week study of 1.96 points for active (p < 0.0001), compared with a 0.85 points reduction for placebo (p = 0.13). The functional score was also significantly improved by 505 points for the active group over the 311-point improvement for placebo group compared to baseline (p = 0.02). In the pilot subset evaluated, rotational strength increased from baseline to 6 weeks (3.2 N, p = 0.03); however, no other measures were significant. Conclusions: Long-duration low-intensity ultrasound significantly reduced pain and improved joint function in patients with moderate to severe osteoarthritis knee pain. The clinical findings suggest that ultrasound may be used as a conservative non-pharmaceutical and non-invasive treatment option for patients with knee osteoarthritis. Additional research is warranted on non-weight bearing joints of the musculoskeletal system as well as extended treatment time frames and follow-up. Trial registration: NCT02083861, registered 11 March 2014, https://clinicaltrials.gov/ct2/show/results/NCT02083861 [ABSTRACT FROM AUTHOR]

A primitive set is one in which no element of the set divides another. Erdos conjectured that the sum ... taken over any primitive set A would be greatest when A is the set of primes. More recently, Banks and Martin have generalized this conjecture to claim that, if we let Nk represent the set of integers with precisely k prime factors (counted with multiplicity), then we have f(N1) > f(N2) > f(N3) > · · ·. The first of these inequalities was established by Zhang; we establish the second. Our methods involve explicit bounds on the density of integers with precisely k prime factors. In particular, we establish an explicit version of the Hardy-Ramanujan theorem on the density of integers with k prime factors. [ABSTRACT FROM AUTHOR]

This study investigates changes in instructor teaching tendencies, instructor's perception of impact on student learning and dispositions, and methods of implementation of Primary Source Projects (PSPs). PSPs are curricular modules designed to teach core mathematical topics from primary historical sources rather than from standard textbooks. In essence, they are a form of inquiry-based learning that incorporates the history of mathematics through original source texts. We provide an overview of results from two semesters of implementation reports and surveys administered at the beginning and end of the semester by instructors who implemented PSPs in their undergraduate mathematics classes. [ABSTRACT FROM AUTHOR]