It is increasingly clear that children’s excessive consumption of products high in added (or extrinsic) sugar causes obesity and obesity-related health problems like type 2 diabetes, cardiovascular disease, and metabolic syndrome. Less clear is how best to address this problem through public health policy. In contrast to policies that might conflict with adult’s right to self-determination — fo...

Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained through a low-dimensional maximum principle in the limit N-->infinity (where N, or N(d) with d> or =1, is proportional to the number of types). In order to extend...

The sugar cane industry represents one of the most important economic sectors in Brazil. It produces sugar and ethanol for the internal and external markets. Also, thermal and electric energy are produced for the own factory consumption, using sugar cane bagasse as fuel in cogeneration plants. Almost all the sugar cane factories in Brazil are self-sufficient in terms of energy supply and in the...

In this note we introduce a notion of essentially-Euclidean normed spaces (and convex bodies). Roughly speaking, an n-dimensional space is λ-essentially-Euclidean (with 0 < λ < 1) if it has a [λn]dimensional subspace which has further proportionally dimensional Euclidean subspaces of any proportion. We consider a space X1 = (Rn, ‖ · ‖1) with the property that if a space X2 = (Rn, ‖ · ‖2) is “no...

For f in L∞, the space of essentially bounded Lebesgue measurable functions on the unit circle, ∂D, the Toeplitz operator with symbol f is the operator Tf on the Hardy space H2 of the unit circle defined by Tfh = P (fh). Here P denotes the orthogonal projection in L2 with range H2. There are many fascinating problems about Toeplitz operators ([3], [6], [7] and [20]). In this paper we shall conc...

The Lake: Alice, Bertha, and Claudia live around Forest Lake, at some distance from each other. The ecosystem is sensitive, in particular to the solvent they have been using when painting their boats, and the lake is faring badly. Until recently, they had no way of knowing that the solvent would have this effect, but they just learned that it is in fact killing the fish in the lake, and that th...