Let R be a commutative ring. Unless indicated otherwise, all modules are R-modules and all tensor products are taken over R, so we abbreviate ⊗R to ⊗. A bilinear function out of M1 × M2 turns into a linear function out of the tensor product M1 ⊗ M2. In a similar way, a multilinear function out of M1 × · · · ×Mk turns into a linear function out of the k-fold tensor product M1 ⊗ · · · ⊗Mk. We wil...

The Unitary Executive offers a powerful case for the historical pedigree of the unitary executive theory. Offering an account of presidential practice stemming from George Washington to George W. Bush, the book seeks to ground unitary executive theory with exhaustive historical evidence. Although the authors do not purport to present a history of the presidency, they do provide important and co...

Scientists working in areas that are (rightly or wrongly) socially contentious might benefit by perusing readers' comments lodged on online newspaper websites after the appearance of announcements in their fields. On many occasions, they would find not only approving sentiments but also a surprising degree of hostility. The recent announcement of draft sequence coverage of the wheat genome prov...

This work is devoted to proving that, given an integer $x \ge 2$, there are infinitely many perfect powers, coprime with $x$, having exactly $k 3$ non-zero digits in their base $x$ representation, except for the case $x=2, k=4$, which a known finiteness result by Corvaja and Zannier holds.

The natural notion of categoricity, as it was discovered in the 1930's, is degenerate for first order languages, since only a finite structure can be described up to isomorphism by its first order theory. This has led to a new notion of categoricity. A theory is said to be categorical in a power if it has a model of this power which is unique up to isomorphism. Morley has proved, answering the ...

The investigation of the asymptotic behaviour of various parameters of powers of a fixed graph leads to many fascinating problems, some of which are motivated by questions in information theory, communication complexity, geometry and Ramsey theory. In this survey we discuss these problems and describe the techniques used in their study which combine combinatorial, geometric, probabilistic and l...

In this paper, we prove that for any positive integers k, n with k ≥ 2, the graph P k n is a divisor graph if and only if n ≤ 2k + 2, where P k n is the k power of the path Pn. For powers of cycles we show that C n is a divisor graph when n ≤ 2k + 2, but is not a divisor graph when n ≥ 2k + bk2 c+ 3, where C k n is the k th power of the cycle Cn. Moreover, for odd n with 2k + 2 < n < 2k + bk2 c...

In 1988, Golumbic and Hammer characterized powers of cycles, relating them to circular-arc graphs. We extend their results and propose several further structural characterizations for both powers of cycles and powers of paths. The characterizations lead to linear-time recognition algorithms of these classes of graphs. Furthermore, as a generalization of powers of cycles, powers of paths, and ev...