The self-assembly of [Cp(Bn)Fe(η(5)-P5)] (Cp(Bn) = η(5)-C5(CH2Ph)5) with CuBr2 leads to the formation of an unprecedented rugby ball-shaped supramolecule consisting of 24 units of the pentaphosphaferrocene and an extended CuBr framework, which does not follow the fullerene topology. The resulting scaffold of 312 noncarbon atoms reveals three different coordination modes of the cyclo-P5 ligand i...

Abstract The bounce of an oval shaped football may appear to be erratic but it can be described by simple laws of physics. Projected at an oblique angle without spin or with backspin, a football usually bounces backward if the top end points backward on impact. Projected with topspin, a football usually bounces forward. A football incident with topspin will sometimes bounce to a much larger hei...

In a well-known magic trick known as multiplying balls, conjurers fool their audience with the use of a semi-spherical shell, which the audience perceives as a complete ball [1]. Here, we report that this illusion persists even when observers touch the inside of the shell with their own finger. Even more intriguingly, this also produces an illusion of bodily self-awareness in which the finger f...

We show that the space Lip0(R) is the dual space of L(R;R)/N where N is the subspace of L(R;R) consisting of vector fields whose divergence vanishes identically. We prove that although the quotient space L(R;R)/N is weakly sequentially complete, the subspace N is not nicely placed in other words, its unit ball is not closed for the topology τm of local convergence in measure. We prove that if Ω...

In a series of papers, Burdzy et al. introduced the mirror coupling of reflecting Brownian motions in a smooth bounded domain D ⊂ Rd , and used it to prove certain properties of eigenvalues and eigenfunctions of the Neumann Laplaceian on D. In the present paper we show that the construction of the mirror coupling can be extended to the case when the two Brownian motions live in different domain...

A dynamical billiard is an idealization of the game of billiard, but where the table can have shapes other than the rectangular and even be multidimensional. We use only one billiard ball, and the billiard may even have regions where the ball is kept out. Formally, a dynamical billiard is a dynamical system where a massless and point shaped particle moves inside a bounded region. The particle i...

1T HE DUMBELL-DIFFUSION CELL described by Nobel (1) is made from a ball and socket joint, each end of which is formed into a bell-shaped flask. This cell is applicable to rapid testing of blood for the presence or absence of various toxic constituents. it allows diffusion, absorption, and i(lentiflcation reactions to proceed concurrently under a variety of conditions (Table 1). [sing this appar...

-Slash pine is the premier tree species on many sites throughout the South. Its ease of establishment and early growth, however, has extended its range to many sites where its performance has been less than ideal. For that reason, the acreage and volume of slash pine are declining. Nonetheless, it will continue to be the favored species on many sites where it is the most appropriate and product...

Hawaii has no native pines, but many species have been introduced as ornamental or potential timber trees. These species have been planted in environments that differ greatly from their natural habitat. This paper describes how the coordinated seasonal cycle of growth and flowering has been influenced by the climatic conditions these pines have encountered in Hawaii. Hawaii has no native pines,...