An algorithm for automatic checking of exercises in a dynamic geometry system: iGeom

One of the key issues in e-learning environments is the possibility of creating and evaluating exercises. However, the lack of tools supporting the authoring and automatic checking of exercises for specifics topics (e.g., geometry) drastically reduces advantages in the use of e-learning environments on a larger scale, as usually happens in Brazil. This paper describes an algorithm, and a tool based on it, designed for the authoring and automatic checking of geometry exercises. The algorithm dynamically compares the distances between the geometric objects of the student`s solution and the template`s solution, provided by the author of the exercise. Each solution is a geometric construction which is considered a function receiving geometric objects (input) and returning other geometric objects (output). Thus, for a given problem, if we know one function (construction) that solves the problem, we can compare it to any other function to check whether they are equivalent or not. Two functions are equivalent if, and only if, they have the same output when the same input is applied. If the student`s solution is equivalent to the template`s solution, then we consider the student`s solution as a correct solution. Our software utility provides both authoring and checking tools to work directly on the Internet, together with learning management systems. These tools are implemented using the dynamic geometry software, iGeom, which has been used in a geometry course since 2004 and has a successful track record in the classroom. Empowered with these new features, iGeom simplifies teachers` tasks, solves non-trivial problems in student solutions and helps to increase student motivation by providing feedback in real time. (c) 2008 Elsevier Ltd. All rights reserved.

Aerobic oxidation of monoterpenic alcohols catalyzed by ruthenium hydroxide supported on silica-coated magnetic nanoparticles

Ruthenium hydroxide supported on silica-coated magnetic nanoparticles was shown to be an efficient heterogeneous catalyst for the liquid-phase oxidation of a wide range of alcohols using molecular oxygen as a sole oxidant in the absence of co-catalysts or additives. The material was prepared through the loading of the amino modified support with ruthenium(III) ions from an aqueous solution of ruthenium(III) chloride followed by treatment with sodium hydroxide to form ruthenium hydroxide species. Characterizations suggest that ruthenium hydroxide is highly dispersed on the support surface, with no ruthenium containing crystalline phases being detected. Various carbonylic monoterpenoids important for fragrance and pharmaceutical industries can be obtained in good to excellent yields starting from biomass-based monoterpenic alcohols, such as isobomeol, perillyl alcohol, carveol, and citronellol. The catalyst undergoes no metal leaching and can be easily recovered by the application of an external magnet and re-used. (C) 2011 Elsevier Inc. All rights reserved.