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.     

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.     

Contributions to the determination of histamine rate by measuring out the histamine-orthophthalaldehyde complex in the absorption and fluorescence

Histamine is an important compound from a physiological point of view, but it is toxic since the absorption of low amounts of histamine can cause abdominal pains accompanied with vomiting. Why we have developed a new method for histamine analysis in order to improve Lerke and Bell method. From the absorption spectra, we showed that the stoichiometry of the complex histamine-orthophthalaldehyde (OPA) is 1:1. From the emission spectra, it was observed that the complex fluorescence is inhibited in acidic medium. In alkaline medium, an exaltation of fluorescence was observed, but the complex histamine-OPA was unstable. Nevertheless, kinetic study showed that good linear correlations between the fluorescence maxima of the formed complex and the histamine concentration could be obtained in this alkaline medium.     

Physicochemical Investigations on the Interaction of Surfactants and Salts with Polyvinylpyrrolidone in Aqueous Medium

Microcalorimetric investigations have been carried out onthe interaction of the surfactants sodium cholate, sodium deoxycholate, tetradecyltrimethylammonium bromide, cetyl(hexadecyl)trimethylammonium bromide, and p-tert-octylphenoxy polyoxy-ethylene ether (Triton X-100) and the salts potassium iodide, sodium benzoate, sodium bromide, and sodium salicylate with the neutral polymer polyvinylpyrrolidone (PVP). The enthalpy of dilution of the surfactants has been measured in the absence and presence of the polymer and the results are compared to determine the effect of PVP on the micellization of the surfactants and the energetics of the process. As well, the micellization activity of the surfactants in the presence of the polymer has been studied by conductometric and fluorimetric methods. The enthalpy of dilution of the salts has been measured to provide an understanding of the nature and magnitude of their interaction with PVP. Copyright 2001 Academic Press.     

Electrocatalytic oxidation of ascorbic acid and voltammetric determination with a ferrocene-modified platinum electrode

Ferrocene attached to the surface of a platinum electrode catalyses the electrochemical oxidation of ascorbic acid in acidic buffer solutions. The overpotential for ascorbic acid oxidation is decreased by 150 mV at pH 2.2 compared with reaction at bare platinum; and an increase in anodic current and decrease in cathodic current for the redox reaction of ferrocene occurs on addition of ascorbic acid to the solution. The ferrocene-modified electrode is useful for the voltammetric determination of ascorbic acid in natural fruit juices. The advantages result from the electrocatalytic effect and from the prevention of adsorption of inhibitory substances from solution.     

Zur regioselektiven nucleophilen Addition an 2,3-Dihydrobilatriene-abc

Donors are added regioselectively to position 10 of 2,3-dihydrobilatrienes-abc in a reversible reaction, which is complicated in case of strongly basic donors due to the easy deprotonation of the partially saturated ring. Compared to the bilatrienes-abc the addition equilibrium is retarded by about two orders of magnitude.