Pieces of eight!

Eight Pieces Cannot Cover a Chess Board

The problem of maximising the number of squares on a chess board which can be attacked by a configuration of the eight main pieces was first posed in 1849. We report on a computer search which proves that at most 63 squares can be simultaneously attacked, and we give results for other variations of the problem. Our search technique, which pruned the space of2.27x 10 positions to 1.03 x 10, is o...

Pieces of Eight: Semiselfdual Lattices and a New Foundation for the Theory of Conway and Mathieu Groups

We give a new and easy construction of the largest groups of Mathieu and Conway, as the full automorphism groups of the Golay code and Leech lattice, respectively. In addition we get a new uniqueness proof for the Leech lattice and the Golay code. The main technique is intensive use of semiselfdual sublattices: instead of rank 1 lattices as the basis for coordinate concepts, we use scaled versi...

Cultural and Social Enigmas: Missing Pieces of Food Security

   The growing attention in food security has suggested many approaches to develop a society free from hunger and malnutrition. Methodological approaches are mostly used to overcome the challenges of food security, but food insecurity is more than mere availability and access to food. Cultural and social dimensions and their intricacies to achieve food security are mostly missing from the lite...

Two Pieces by Dewey 1 Running head : TWO PIECES BY DEWEY Reflections on Two Pieces

Focus: Missing Pieces

Stem Cells and Cancer: The Medical Mystery of the 21st Century Cancer, which is characterized by abnormal cell proliferation that leads to uncontrolled tumor growth, is a leading cause of death worldwide (7.4 million deaths in 2004). Scientists have focused on the biological mechanism of tumor formation in an attempt to develop well-informed, effective cancer treatments that slow or halt the pr...