Riesz bounds of Wilson bases generated byB-splines

In this paper, we are concerned with biorthogonal Wilson bases having B-splines as well as powers of sinc functions as window functions. We prove properties of B-splines and exponential Euler splines and use these properties to estimate the Riesz bounds of the Wilson bases.     

Nanoscale skeletal nickel catalysts prepared via ‘bottom up’ method

NiAl nanoparticles are of considerable importance because of interest in examining the effects of size, surface area, and composition on their physical and catalytic properties. Recently, a new method for the ‘bottom up’ wet chemical preparation of nickel aluminides has been reported. The ability to leach the aluminum from this system provides an entrance to the preparation of skeletal‐type metal catalysts similar to those produced in Raney‐type systems. Furthermore, it is believed that these nanoparticulate catalysts should provide high surface areas and high activities, while the presence of aluminum within the bulk of these catalysts provides additional stability. Here, we present the results of studies conducted on this system which compare their properties and behavior with traditional bulk Raney nickel systems. Additionally, we show that we are able to alter the properties of these nanoparticles by changing the stoichiometric ratio of nickel and aluminum. The properties of all systems have been analyzed through the use of nitrogen adsorption, X‐ray diffraction, and elemental analysis. Finally, the catalysts generated have been compared for their activity in the hydrogenation of butyronitrile. Copyright © 2002 John Wiley & Sons, Ltd.     

Enantiopure N-Boc piperidine-2-ethanol for the synthesis of (+)- and (−)-dumetorine,and (+)- and (−)-epidihydropinidine

The convenient synthesis of both enantiomers of the piperidine alkaloids such as dumetorine and epidihydropinidine is described. Pure enantiomers of 2-(2-hydroxy-ethyl)-piperidine-1-carboxylic acid tert-butyl ester are used as a common starting material. The syntheses are based on a RCM reaction and on methylation of the piperidine ring according to Beak–Lee methodology, respectively.     

Future teachers’ professional knowledge on argumentation and proof: a case study from universities in three countries

In this paper, qualitative results of a case study about the professional knowledge in the area of argumentation and proof of future teachers from universities in three countries are described. Based on results of open questionnaires, data about the competencies these future teachers have in the areas of mathematical knowledge and knowledge of mathematics pedagogy are presented. The study shows that the majority of the future teachers at the participating universities situated in Germany, Hong Kong and Australia, were not able to execute formal proofs, requiring only lower secondary mathematical content, in an adequate and mathematically correct way. In contrast, in all samples there was evidence of at least average competencies of pedagogical content reflection about formal and pre-formal proving in mathematics teaching. However, it appears that possessing a mathematical background as mandated for teaching and having a high affinity with proving in mathematics teaching at the lower secondary level are not a sufficient preparation for teaching proof.     

Electrochemical Kinetic Characterization of Redox Mediated Glucose Oxidase Reactions: A Simplified Approach

One of the main drawbacks affecting first‐generation electrochemical biosensors in the analysis of real matrices is the interference of electroactive species present in the sample under investigation. Several approaches have been attempted to overcome this problem in the past ten years but the best results were achieved by using mediated based electrochemical biosensors. Despite this, the kinetic of the redox mediators‐enzymatic proteins interaction has not been studied deeply enough. In this work we have developed a theoretical‐methodological approach for the characterization of the kinetic of interaction between redox enzymes and substrates and/or redox mediators. Particularly, the interaction of glucose oxidase (GOx) with several commercially available redox mediators has been studied by means of amperometry and cyclic voltammetry. The main kinetic parameters for different mediators were exploited and discussed with the aim of finding the best mediator for a glucose biosensor to be used on real samples.     

Increasing engineering students' awareness to environment through innovative teaching of mathematical modelling

This article presents the results of two studies on using aninnovative pedagogical strategy in teaching mathematical modellingand applications to engineering students. Both studies are dealingwith introducing non-traditional contexts for engineering studentsin teaching/learning of mathematical modelling and applications:environment and ecology. The aims of using these contexts were:to introduce students to some of the techniques, methodologiesand principles of mathematical modelling for ecological andenvironmental systems; to involve the students in solving real-lifeproblems adjusted to their region emphasizing the aspects ofboth survival (short term) and sustainability (long term); toencourage students to pay attention to environmental issues.On one hand, the contexts are not directly related to engineering.On the other hand, the chances are that many graduates of engineeringwill deal with mathematical modelling of environmental systemsin one way or another in their future work because nearly everyengineering activity has an impact on the environment. The firststudy is a parallel study conducted in New Zealand and Germanysimultaneously with first-year students studying engineeringmathematics. The second study is a case study of the experimentalcourse Mathematical Modelling of Survival and Sustainabilitytaught to a mixture of year 2–5 engineering students inGermany by a visiting lecturer from New Zealand. The modelsused with the students from both studies had several specialfeatures. Analysis of students’ responses to questionnaires,their comments and attitudes towards the innovative approachin teaching are presented in the article.     

Synthesis of 5-trichloromethyl-Δ-1,2,4-oxadiazolines and their rearrangement into formamidine derivatives

A series of 5-trichloro-Δ⁴-1,2,4-oxadiazolines have been synthesised by 1,3-dipolar cycloaddition of nitrones to trichloroacetonitrile. These oxadiazolines rearrange into formamidine derivatives, via ring opening and a 1,2-aryl shift from carbon to the adjacent amino nitrogen. Both cycloaddition and rearrangement are facilitated when electron deficient nitriles and electron rich nitrones are used.