UNIT FRACTIONS AND THE ERDÖS-STRAUS CONJECTURE

This note considers some aspects of finite sums of unit fractions, including associated recurrence relations and conjectures in the context of experimental mathematics. Unit fractions provide a unifying theme

ON GOLDBACH'S CONJECTURE

This paper considers some aspects of Goldbach's conjecture as a conjecture and estimates the number of prime pairs in some intervals in order to portray a compelling picture of some of the computational issues generated by the conjecture

Natural Mathematics, the Fibonacci Numbers and Aesthetics in Art

The Mathematics of beauty and beauty in mathematics are important ingredients in learning in the liberal arts. The Fibonacci numbers play an important and useful role in this. This paper seeks to present and illustrate a grounding of visual aesthetics in natural mathematical principles, centered upon the Fibonacci numbers. The specific natural mathematical principles investigated are the Fibonacci numbers, the Fibonacci Spiral, and the Cosmic Bud

Generalized Fibonacci Numbers and Music

Mathematics and music have well documented historical connections. Just as the ordinary Fibonacci numbers have links with the golden ratio, this paper considers generalized Fibonacci numbers developed from generalizations of the golden ratio. It is well known that the Fibonacci sequence of numbers underlie certain musical intervals and compositions but to what extent are these connections accidental or structural, coincidental or natural and do generalized Fibonacci numbers share any of these connections

Some aspects of Fibonacci polynomial congruences

This paper formulates a definition of Fibonacci polynomials which is slightly different from the traditional definitions, but which is related to the classical polynomials of Bernoulli, Euler and Hermite. Some related congruence properties are developed and some unanswered questions are outlined. Keywords: Congruences, recurrence relations, Fibonacci sequence, Lucas sequences, umbral calculus

ARBITRARY ORDER RECURSIVE SEQUENCES AND ASSOCIATED CONTINUED FRACTIONS

The essential idea in this paper it to generalize and synthesize some of the pioneering ideas of Bernstein, Lucas and Horadam on generalizations of basic and primordial Fibonacci numbers and their arbitrary order generalizations and their relation to generalized continued fractions with matrices as the unifying elements

A randomized trial comparing skin antiseptic agents at Cesarean delivery

BACKGROUND: Preoperative skin antisepsis has the potential to decrease the risk of surgical-site infection. However, evidence is limited to guide the choice of antiseptic agent at cesarean delivery, which is the most common major surgical procedure among women in the United States. METHODS: In this single-center, randomized, controlled trial, we evaluated whether the use of chlorhexidine–alcohol for preoperative skin antisepsis was superior to the use of iodine–alcohol for the prevention of surgical-site infection after cesarean delivery. We randomly assigned patients undergoing cesarean delivery to skin preparation with either chlorhexidine–alcohol or iodine–alcohol. The primary outcome was superficial or deep surgical-site infection within 30 days after cesarean delivery, on the basis of definitions from the Centers for Disease Control and Prevention. RESULTS: From September 2011 through June 2015, a total of 1147 patients were enrolled; 572 patients were assigned to chlorhexidine–alcohol and 575 to iodine–alcohol. In an intention-to-treat analysis, surgical-site infection was diagnosed in 23 patients (4.0%) in the chlorhexidine–alcohol group and in 42 (7.3%) in the iodine–alcohol group (relative risk, 0.55; 95% confidence interval, 0.34 to 0.90; P = 0.02). The rate of superficial surgical-site infection was 3.0% in the chlorhexidine–alcohol group and 4.9% in the iodine–alcohol group (P = 0.10); the rate of deep infection was 1.0% and 2.4%, respectively (P = 0.07). The frequency of adverse skin reactions was similar in the two groups. CONCLUSIONS: The use of chlorhexidine–alcohol for preoperative skin antisepsis resulted in a significantly lower risk of surgical-site infection after cesarean delivery than did the use of iodine–alcohol. (Funded by the National Institutes of Health and Washington University School of Medicine in St. Louis; ClinicalTrials.gov number, NCT01472549.

Some identities of Gaussian binomial coefficients

In this paper, we present some identities of Gaussian binomial coefficients with respect to recursive sequences, Fibonomial coefficients, and complete functions by use of their relationships

The summer games

As part of a nationally funded project, we have developed and used \u27games\u27 as student centred teaching resources to enrich the capacity for design in beginning students in architecture, landscape architecture and urban design. Students are encouraged to learn inter-actively in a milieu characterised by self-directed play in a low-risk computer modelling environment. Recently thirteen upper year design students, six from Adelaide University (Adelaide, South Australia, Australia), five from Deakin University (Geelong, Victoria, Australia), and two from Victoria University, (Wellington, New Zealand) were commissioned over a ten-week period of the 2000-2001 Australian summer to construct a new series of games. This paper discusses the process behind constructing these games.This paper discusses six topical areas:&ndash; what is a game;&ndash; specific goals of the summer games;&ndash; the structure of a game;&ndash; the game-making process;&ndash; key findings from the production unit; and&ndash; future directions.<br /

Some identities of Gaussian binomial coefficients

In this paper, we present some identities of Gaussian binomial coefficients with respect to recursive sequences, Fibonomial coefficients, and complete functions by use of their relationships