A Convenient Synthesis of 4-Hydroxybeno-(B)-Furan, (Karanjol)

The synthesis of karanjol from tetrahydro-(b)-furan intermediates is described.     

An Improves Method for the Cleavage of Methyl Esters

Synthetic organic chemists are continually looking for milder, more specific methods of effecting given transformations, and one such problem which recently arose in our laboratory involved ester cleavage. In particular, we sought a specific, wild, non-hydrolytic method for effecting teh ester - acid transformation under conditions which other acid or base sensitive functional groups would survive.     

Palladium-Catalyzed Coupling of L-Proline Acid Chloride with Vinylstannanes

Vinylstannanes were found to undergo a palladium-catalyzed coupling with L-N-protected proline acid chloride to produce the corresponding N-protected α'-amino-α,β-unsaturated ketones in moderate to good yield.     

Asking mathematical questions mathematically

It is proposed that the style and format of the questions used by lecturers and tutors profoundly influence students' conceptions of what mathematics is about and how it is conducted. By looking at reasons for asking questions, and becoming aware of different types of questions which mathematicians typically ask themselves, we can enrich students' experience of mathematics. Drawing on recent work by Watson and Mason stimulated by the ideas of Zygfryd Dyrszlag, the paper proposes that mathematical themes, powers, heuristics and activities generate a mathematical discourse which is not always represented in the questions students are asked, and that the real purpose of questions is to provoke students into construal, into constructing their own stories which constitute meaning and understanding, and which equip them for the future. The use of questions of whatever type depends on both scaffolding and fading their use with and in front of students, so that students internalize the questions into their own learning and doing of mathematics. The framework directed—prompted—spontaneous is proposed as an alternative to scaffolding—fading for informing interactions with students.     

Layer Communities in Multiplex Networks

Journal of Statistical Physics - Multiplex networks are a type of multilayer network in which entities are connected to each other via multiple types of connections. We propose a method, based on...     

Small embeddings for partial 5‐cycle systems

It has been conjectured that any partial 5‐cycle system of order u can be embedded in a 5‐cycle system of order v whenever v ≥ 3 u/ 2+1 and v ≡ 1 , 5 (mod 10) . The smallest known embeddings for any partial 5‐cycle system of order u is 10 u +5 . In this paper we significantly improve this result by proving that for any partial 5‐cycle system of order u ≥ 255 , there exists a 5‐cycle system of order at most (9 u +146) / 4 into which the partial 5‐cycle system of order u can be embedded. © 2011 Wiley Periodicals, Inc. J Combin Designs