No abstract

Rognes and Weibel used Voevodsky's work on the Milnor conjecture to deduce the strong Dwyer-Friedlander form of the Lichtenbaum-Quillen conjecture at the prime 2. In consequence (the 2-completion of) the classifying space for algebraic K-theory of the integers Z[1/2] can be expressed as a fiber product of wellunderstood spaces BO and BGL(F 3 ) + over BU . Similar results are now obtained for Hermitian K-theory and the classifying spaces of the integral symplectic and orthogonal groups. For the integers Z[1/2], this leads to computations of the 2-primary Hermitian Kgroups and affirmation of the Lichtenbaum-Quillen conjecture in the framework of Hermitian K-theory.Here Z ′ denotes the ring Z[1/2], F 3 the finite field with three elements, and, for F = R, C, BGL(F ) is the classifying space of the infinite general linear group GL(F ) with the usual topology. The symbol # indicates the 2-adic completion, and the map b the Brauer lift, corresponding to the fibring of Adams' map ψ 3 − 1 on BU = BGL(C). The remaining maps are induced from the obvious ring homomorphisms.The Dwyer-Friedlander formulation of the Lichtenbaum-Quillen conjecture for Z at the prime 2 is that the above square is homotopy cartesian [15]Conjecture 1.3, Proposition 4.2. This has been affirmed in work of Rognes and Weibel [48] -see [57]Corollary 8.Since the homotopy fiber of the map BGL(R) → BGL(C) is the homogeneous space GL(C)/GL(R), which has the homotopy type of Ω 7 (BGL(R)) by Bott periodicity [11], we may also write the homotopy fibration Ω 7 (BGL(R)) # −→ BGL(Z ′ ) + # −→ BGL(F 3 ) + # .

As a contribution to worldwide efforts towards a tobacco-free society, this paper considers the possibility of a long-term phasing-in of a total ban, by proposing that individuals born in or after the year 2000 have their supply of tobacco restricted. In conjunction, a survey that we have conducted in Singapore indicates strong public support (even among current smokers) for the proposal.

The tobacco-free generation proposal advocates legislation precluding the sale and supply of tobacco to individuals born after a certain year. The measure is aimed at overcoming defects with current youth access laws that suffer from rite-of-passage and mixed signalling effects. Since its introduction in 2010, the proposal has attracted international attention, highlighting a number of matters that the present short article discusses. Efficacy issues, including retailer compliance, supply by surrogates and illicit sales, are addressed in the broader setting of community adherence to legislation. Encouragement for the likelihood of successful implementation is provided by historical precedents. In principle objections, relating to choice and generational fairness, are considered against the criteria of consistency and proportionality. It is concluded that the measure's emphasis on the welfare of future generations and its regard for the interests of existing stakeholders provide a feasible opportunity for the ultimate eradication of tobacco supply in appropriate jurisdictions.

The fracture toughness (specific work of fracture) of the leaf of the dicotyledonous angiosperm, Calophyllum inophyllum L. (Guttiferae), which has a lamina with a reticulate venation comprising secondary and tertiary veins only, was investigated by cutting, notched tensile and punch-and-die tests. Toughness was found to depend on the presence of veins in the fracture path, with both tensile and cutting tests in agreement that fracture at right angles to secondary veins was 2.5-3.0 times as tough as fracture parallel to them. Values from tensile tests were smaller than those from cutting tests. The cutting method had the advantage of specifying the direction of fracture and of severing structures serially, allowing easy recognition of tough structures from force-displacement records. This showed that the fracture toughness of the lamina could be modelled by a ‘rule of mixtures’ whereby the veins (vascular bundles supported by sclerenchyma strands above and below), with a combined toughness of about 6000 J m -2 , are contrasted to other tissues - the mesophyll and the epidermis and its cuticle — which together probably have an average toughness of only 220-300 J m -2 . Bounds on the toughness of mature leaves are probably set close to these limits. However, we could not test all these tissues separately to confirm this. The model predicted the fracture toughness expected in a cylindrical punch-and-die test, which is the commonly used test in ecological studies. However, observed values from this test were twice those expected, which is mostly attributable to yielding of a large volume of mesophyll but also in part due to the debonding of secondary veins from the rest of the lamina. The results suggest that relevant classifications of leaves (sclerophyll, pachyphyll, etc.) should pay close attention to the venation of the leaf and the structure of these veins. It is proposed that the thickening of the walls of smaller veins to form a venous network is a defence against invertebrate herbivores.