recent studies on wavelet transform and fractal modeling applied on mammograms for the detection of cancerous tissues indicate that microcalcifications and masses can be utilized for the study of the morphology and diagnosis of cancerous cases. it is shown that the use of fractal modeling, as applied to a given image, can clearly discern cancerous zones from noncancerous areas. in this paper, f...

It has been observed many times, both in the Monthly and elsewhere, that the set of all quotients of prime numbers is dense in the positive real numbers. In this short note we answer the related question: “Is the set of all quotients of Gaussian primes dense in the complex plane?” Quotient sets {s/t : s, t ∈ S} corresponding to subsets S of the natural numbers have been intensely studied in the...

Understanding the metabolic fate of small organic molecules is of fundamental importance to the successful design and development of drugs, nutritional supplements, cosmetics and agrochemicals [1,2]. In the current study we investigated how the products of metabolism differ from their parent molecules by analysing a large dataset of experimentally determined metabolic transformations (Figure 1)...

The underrepresentation of women in the mathematically-intensive sciences (hereafter, for brevity, referred to as the hard sciences) has been a concern in the United States for over half a century. After the women’s movement began in the 1960s, gender gaps in many professional fields decreased, and some even reversed dramatically. Currently women comprise about half the M.D’s, two-thirds of psy...

1. INTRODUCTION. In the beginning of the twelfth century CE, an interesting new geometry book appeared: The Book of Mensuration of the Earth and its Division, by Rabbi Abraham Bar Hiya (acronym RABH), a Jewish philosopher and scientist. This book is interesting both historically and mathematically. Its historical aspect is discussed in [3]. In this paper we consider the mathematical aspect. The...

One of the major events in the evolution of modern process thinking was the publication of Michael Porter’s book, Competitive Advantage, in 1985, which introduced the idea of the Value Chain. [2] (See Figure 1.) A value chain is the ultimate process of an organization. A value chain describes all of the activities that an organization undertakes to produce a product. The manager of the company ...

There are times when, in their haste to solve a particular problem, students (and their instructors) miss an opportunity to notice some interesting mathematics. For example, when calculus students are introduced to the derivatives of inverse trigonometric functions, they frequently run across a classic problem that goes something like this: There is a 6-foot tall picture on a wall, 2 feet above...

29 W e all want to change our appearance in some way. For example, makeup helps enhance appearance, although it primarily relates to the face. Many people try to change their moods by changing their accessories, clothes, and hairstyles. Some people even resort to plastic surgery to make permanent changes. We often observe behaviors that stem from a more radical desire for metamorphosis. For exa...

Although the Gross Domestic Product of the United States has been steadily rising since the 1950s, the gap between rich and poor is increasing (see Figure 1). John Kenneth Galbraith explained the importance of inequality when he stated, “People are poverty-stricken when their income, even if adequate for survival, falls markedly behind that of the community. Then they cannot have what the large...