The visibility of models: using technology as a bridge between mathematics and engineering

Engineering mathematics is traditionally conceived as a set of unambiguous mathematical tools applied to solving engineering problems, and it would seem that modern mathematical software is making the toolbox metaphor ever more appropriate. The validity of this metaphor is questioned and the case is made that engineers do in fact use mathematics as more than a set of passive tools— that mathematical models for phenomena depend critically on the settings in which they are used and the tools with which they are expressed. The perennial debate over whether mathematics should be taught by mathematicians or by engineers looks increasingly anachronistic in the light of technological change, and the authors suggest that it is more instructive to examine the potential of technology for changing the relationships between mathematicians and engineers, and for connecting their respective knowledge domains in new ways.     

Chermak–Delgado Lattice Extension Theorems

If G is a finite group with subgroup H, then the Chermak–Delgado measure of H (in G) is defined as |H||C _G (H)|. The Chermak–Delgado lattice of G, denoted 𝒞𝒟(G), is the set of all subgroups with maximal Chermak–Delgado measure; this set is a moduar sublattice within the subgroup lattice of G. In this paper we provide an example of a p-group P, for any prime p, where 𝒞𝒟(P) is lattice isomorphic to 2 copies of ?₂ (a quasiantichain of width 2) that are adjoined maximum-to-minimum. We introduce terminology to describe this structure, called a 2-string of 2-diamonds, and we also give two constructions for generalizing the example. The first generalization results in a p-group with Chermak–Delgado lattice that, for any positive integers n and l, is a 2l-string of n-dimensional cubes adjoined maximum-to-minimum and the second generalization gives a construction for a p-group with Chermak–Delgado lattice that is a 2l-string of ? _p+1 (quasiantichains, each of width p + 1) adjoined maximum-to-minimum.     

Properties of an h-Bernstein-like basis and curves

Blossoming is a useful technique to study bases and curve representations in computer-aided geometric design. Recently Simeonov et al. (Comput Aided Geom Des 28:549–565, 2011) have used a blossom generalization, namely the h-blossom, to derive new results about the h-Bernstein basis and h-Bézier curves that have previously been studied in approximation theory and computer-aided geometric design. This paper introduces a basis related to the h-Bernstein basis. There is a close relationship between this new basis and the h-Bernstein basis, between the new basis and the h-blossom, and between the new basis and “progressive” curves. This paper explores these relationships and uses them to derive properties both of the new basis itself, and of curves represented in terms of the new basis.     

Role of Context in Risk-Based Reasoning

In this article we report the influence of contextual factors on mathematics and science teachers' reasoning in risk-based decision-making. We examine previous research that presents judgments of risk as being subjectively influenced by contextual factors and other research that explores the role of context in mathematical problem-solving. Our own approach has been to develop carefully designed software tools that support the user to empathize with a hypothetical person, Deborah, who suffers from a medical condition. The tools were used by a group of teachers who were asked to help Deborah decide whether to have an operation that could cure the condition but which carries particular risks. In order to make this decision, the teachers were required to model the risks of the operation and also the lifestyle decisions that Deborah might make. We trace the teachers' efforts to coordinate judgments of likelihood and impact. The data emphasize the sensitivity of reasoning to matters of context; we set out in detail the various ways in which the process was affected by context.     

Separation of cold medicine ingredients using a precise MEKC method at elevated pH

An MEKC method was developed in order to separate a cold medicine formulation containing acetaminophen, ephedrine sulfate, doxylamine succinate, and dextromethorphan hydrobromide as active pharmaceutical ingredients. Because of their similar physical and chemical properties, it was a challenge to separate the basic compounds without sample pretreatment. In addition, the high content of alcohol and sucrose together with the variety of further excipients had to be considered. Thus, the complex matrix required several optimization steps. These included the search for the optimum pH and for a suitable sodium dodecyl sulfate concentration to avoid matrix-capillary wall interaction and to ensure precision. As a second developing step, an internal standard (benzocaine) was chosen to guarantee a high level of quantitative performance. An RSD% value of the peak areas between 1.0 and 2.0 was reached. The employed method development strategy can be generalized to similar separation approaches in the future.     

Evidence for non-chemical, non-electrical intercellular signaling in intestinal epithelial cells

Synchrony between mechanically separated biological systems is well known. We posed the question: can cells induce synchronous behavior in neighboring cells which are mechanically separated and which cannot communicate via chemical or electrical mechanisms. Caco-2 cell cultures were divided into three groups. "Inducer" cells were exposed to H(2)O(2). "Detector" cells were placed in separate containers near the inducer cells but were not exposed to H(2)O(2). Control cells were exposed to fresh media and were kept in a distant laboratory area. Samples were measured for total protein concentration, NFkappaB activation and structural changes, 10, 30 and 60 min after exposure respectively. Exposing inducer cells to H(2)O(2) resulted in a significant reduction in total protein content (-50%), an increase in nuclear NFkappaB activation (+38%), and structural damage (56%) compared to controls. There was a similar reduction in total protein content (-48%), increase in the nuclear fraction of NFkappaB (+35%) and structural damage (25%) in detector cells. These findings provide evidence in support of a non-chemical, non-electrical communication. This signaling system possibly plays a role in synchronous, stimulus-appropriate cell responses to noxious stimuli and may explain a number of cellular behaviors that are hard to explain based only on conventional cell signaling systems.