Edge Colourings of Graphs Avoiding Monochromatic Matchings of a Given Size

Let k and l be positive integers. With a graph G, we associate the quantity c(k,l)(G), the number of k-colourings of the edge set of G with no monochromatic matching of size l. Consider the function c(k,l) : N --> N given by c(k,l)(n) = max {c(k,l)(G): vertical bar V(G)vertical bar = n}, the maximum of c(k,l)(G) over all graphs G on n vertices. In this paper, we determine c(k,l)(n) and the corresponding extremal graphs for all large n and all fixed values of k and l.

The impact of structured teaching methods on the quality of education in Brazil

This paper estimates the impact of the use of structured methods on the quality of education for students in primary public school in Brazil. Structured methods encompass a range of pedagogical and managerial instruments applied in the educational system. In recent years, several municipalities in the state of Sao Paulo have contracted out private educational providers to implement these structured methods in their schooling systems. Their pedagogical proposal involves structuring of curriculum content, development of teacher and student textbooks, and the training and supervision of teachers anti instructors. Using a difference-in-differences estimation strategy, we find that the 4th- and 8th-grade students in the municipalities with structured methods performed better in Portuguese and mathematics than did students in municipalities not exposed to these methods. We find no differences in passing rates. A robustness test supports the assumption that there is no unobserved municipal characteristics associated with proficiency changes over time that may affect the results. (C) 2012 Elsevier Ltd. All rights reserved.

Definite integrals and operational methods

An operational method, already employed to formulate a generalization of the Ramanujan master theorem, is applied to the evaluation of integrals of various types. This technique provides a very flexible and powerful tool yielding new results encompassing different aspects of the special function theory. Crown Copyright (C) 2012 Published by Elsevier Inc. All rights reserved.