Open Problems

Periodica Mathematica Hungarica -     

Formula 1 – A Mathematical Microworld with CAS: Analysis of Learning Opportunities and Experiences with Students

In this article we describe a mathematical microworld for investigating car motion on a racing course and its use with a group of grade 12 students. The microworld is concerned with the mathematical construction of courses and functions which describe car motion. It is implemented in the computer algebra system, Maple^®, which provides the means to represent courses and functions symbolically and graphically. We describe the learning opportunities offered by the microworld in relation to the research literature on functions. Various facets and layers of the function concept are addressed in the microworld, and we suggest how work in the microworld might help in overcoming some well-known misconceptions.This revised version was published online in September 2005 with corrections to the Cover Date.     

Future contributions toJournal of Crystallographic and Spectroscopic Research

Future contributions toJournal of Crystallographic and Spectroscopic Research     

On the geometries of the rational unfoldings of X k

With a view to applications to self-regulating dynamical processes in biology, we determine the geometric structure of what we call isotangent curves, i.e. curves parametrized by the slopes of their points. They come up naturally as bifurcation curves of rational unfoldings of X ^k, and we classify them according to degree and number of cusps. They, as well as their isotangent involute curves, turn up in simulations of these processes.     

Neutral oxygen atom density in the MESOX air plasma solar furnace facility

The density of neutral oxygen atoms in the MESOX set-up, one device of the PROMES-CNRS solar facilities, was determined by a fiber-optics catalytic probe (FOCP). Plasma was created in a flowing air within a quartz tube with the outer diameter of 5 cm by a 2.45 GHz microwave generator with the output power up to 1000 W. The flow of air was varied between 4 and 20 l/h. The O-atom density was found to increase monotonously with the increasing discharge power, and it decreased with the increasing flow rate. The degree of dissociation of oxygen molecules in the plasma column depended largely on the flow rate. At the air flow of 4 l/h it was about 80% but it decreased to about 20% at the flow of 20 l/h.     

Chain and Ring Phosphorus Compounds—Analogies between Phosphorus and Carbon Chemistry

Up to about 15 years ago compounds with a skeleton of phosphorus chains or rings were regarded as “exotic” in the field of nonmetal chemistry. Aside from a number of examples of molecules with two P atoms directly bonded to each other and a few sporadically discovered monocyclic ring compounds, only solids of undefined composition and structure were known. Since then the state of our knowledge in this sector has made considerable progress: between PH₃ and its derivatives on the one hand, and the high-molecular modifications of elementary phosphorus on the other, an unexpected variety of well defined compounds have been discovered, showing many similarities to the analogous compounds of carbon. However, surprises can still occur even with “small” phosphorus-containing molecules, as shown by the likewise recently discovered field of phosphorus three-membered ring compounds.