La variazione seconda generalizzata nel caso dei punti terminali mobili e problemi sugli autovalori connessi

Suute. L'A. prendendo in esame un funzionaleJ[y] (l'integrale di una espressione quadratica iny ey′), pery variabile nell'insieme delle funzioni di classeC′ in un dato intervallo, mette in rilievo taluni problemi sugli autovalori inerenti a sistemi differenziali con condizioni quadratiche in due punti o generali condizioni lineari agli estremi, ed assegna, seguendo un procedimento assai semplice, una condizione espressiva e di facile applicazione che è necessaria e sufficiente: per l'esistenza del minimo diJ[y] e di autovaloricontenuti nell'intervallo (0, 1). Nel contempo dimostra l'esistenza di infiniti autovalori (con l'infinito come punto limite) pei menzionati sistemi, e, richiamandosi a precedenti studi, rileva la possibilità di estendere le superiori considerazioni al caso che si debba decidere dell'esistenza o no di autovalori contenuti in un intervallo assegnato (r ₁, r₂) e che il parametro figuri non linearmente.     

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.