Mass Structured Systems with Boundary Delay: Oscillations and the Effect of Selective Predation

We study equilibrium and oscillatory solutions of a general mass structured system with a boundary delay. Such delays may be derived from systems with a separate egg class. Analytical calculations reveal existence criteria for non-trivial steady states. We further explore parameter space using numerical methods. The analysis is applied to a typical mass structured slug population model revealing oscillations, pulse solutions and irregular dynamics. However, robustly defined isolated cohorts, of the form sometimes suggested by experimental data, do not naturally emerge. Nonetheless, disordered, leapfrogging local maxima do result and may be enhanced by selective predation.     

Extendibility of bilinear forms on banach sequence spaces

We study Hahn-Banach extensions of multilinear forms defined on Banach sequence spaces. We characterize c ₀ in terms of extension of bilinear forms, and describe the Banach sequence spaces in which every bilinear form admits extensions to any superspace.     

In Situ Generation of ArCu from CuF2 Makes Coupling of Bulky Aryl Silanes Feasible and Highly Efficient

A bimetallic system of Pd/CuF₂, catalytic in Pd and stoichiometric in Cu, is very efficient and selective for the coupling of fairly hindered aryl silanes with aryl, anisyl, phenylaldehyde, p‐cyanophenyl, p‐nitrophenyl, or pyridyl iodides of conventional size. The reaction involves the activation of the silane by Cu^II, followed by disproportionation and transmetalation from the Cu^I(aryl) to Pd^II, upon which coupling takes place. Cu^III formed during disproportionation is reduced to Cu^I(aryl) by excess aryl silane, so that the CuF₂ system is fully converted into Cu^I(aryl) and used in the coupling. Moreover, no extra source of fluoride is needed. Interesting size selectivity towards coupling is found in competitive reactions of hindered aryl silanes. Easily accessible [PdCl₂(IDM)(AsPh₃)] (IDM = 1,3‐dimethylimidazol‐2‐ylidene) is by far the best catalyst, and the isolated products are essentially free from As or Pd (<1 ppm). The mechanistic aspects of the process have been experimentally examined and discussed.     

Identity, Leibniz's Law and Non-transitive Reasoning

Arguments based on Leibniz's Law seem to show that there is no room for either indefinite or contingent identity. The arguments seem to prove too much, but their conclusion is hard to resist if we want to keep Leibniz's Law. We present a novel approach to this issue, based on an appropriate modification of the notion of logical consequence.