Abstract Given $$d\in {\mathbb {N}}$$ d ? N , we prove that any polarized Enriques surface (over field k of characteristic $$p \ne 2$$ p ? 2 or with a smooth K3 cover) degree greater than $$12d^2$$ <mml...

We study the D-brane solutions to type IIB superstring in ten dimensions and find interpretation in terms of compactification of a twelve dimensional three-brane of (a specific) F-theory on a torus T 2. In this frame-work, there also exist a two-brane which may be argued to be equivalent to the three-brane by utilizing the electric-magnetic duality in eleven dimensions. In this context, we prop...

BACKGROUND Curriculum development in the health sciences usually entails a lengthy, in-depth review of most or all aspects of the curriculum. The review usually leads to the generation of a detailed report that is submitted to the Dean or executive committee of the faculty. Much has been written about the process of curriculum development but very little has been written about the important pro...

We exhibit twelve new primitive trinomials over GF(2) of record degrees 42 643 801, 43 112 609, and 74 207 281. In addition we report the first Mersenne exponent not ruled out by Swan’s theorem [10] — namely 57 885 161 — for which none primitive trinomial exists. This completes the search for the currently known Mersenne prime exponents. Primitive trinomials of degree up to 32 582 657 were repo...

The paper examines the research evidence for many of the issues that are perennially debated with respect to the education of gifted students. The first cluster of contentious topics focuses on how giftedness is recognized; the second on the social and emotional wellbeing of gifted children; and the third on educational provisions for gifted students. The preponderance of misconceptions on thes...

1 Lecture 1: Clouds–An Overview 3 1.1 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 What is a cloud? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Why are we interested in clouds? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Cloud classification schemes . . . . . . . . ....