A self-contained exposition is given of the topological and Galois-theoretic properties of the category of combinatorial 1-complexes, or graphs, very much in the spirit of Stallings [20]. A number of classical, as well as some new results about free groups are derived.

According to Dirac, fundamental laws of Classical Mechanics should be recovered by means of an ”appropriate limit” of Quantum Mechanics. In the same spirit it is reasonable to enquire about the fundamental geometric structures of Classical Mechanics which will survive the appropriate limit of Quantum Mechanics. This is the case for the symplectic structure. On the contrary, such geometric struc...

tance to infection. Ways of protecting the surrounding skin vary enormously and are largely a matter of individual preference. Some people think the regular use of soap, methylated spirit and talcum powder?although often considered completely outdated?is still the most effective preventive method. A lot of its success must be because of the massage that goes with it, carried out with a circular...

This article attempts to explain how Li Yu 李漁 (1611–80), China’s “first professional writer,” made himself indispensable to the literati culture upon which he socially and financially depended by writing, commenting on, and performing chuanqi傳奇, or plays in the characteristic Southern style. This article analyzes four plays based on Li’s own short stories and theorizes their appeal to seventeen...

In this paper, we study nonlocal gradients and their relationship to classical gradients. As the nonlocality vanishes we demonstrate the convergence of nonlocal gradients to their local analogue for Sobolev and BV functions. As a consequence of these localizations we give new characterizations of the Sobolev and BV spaces that are in the same spirit of Bourgain, Brezis, and Mironsecu’s 2001 cha...

The machine Gilbert Ryle expressed the scepticism of the age when he disparagingly referred to the traditional notion of man as composed of a spirit interacting with a brain as ‘the ghost in the machine’. For centuries dualism had been the prevalent view amongst philosophers, found embryonically in Plato and reaching its classical statement in Descartes. Man’s composite nature has also been ass...

Abstract. Given a doubling measure μ on R, it is a classical result of harmonic analysis that Calderón-Zygmund operators which are bounded in L(μ) are also of weak type (1, 1). Recently it has been shown that the same result holds if one substitutes the doubling condition on μ by a mild growth condition on μ. In this paper another proof of this result is given. The proof is very close in spirit...