Real Brauer characters

In this paper, we determine the structure of finite groups with a small number of real-valued irreducible Brauer characters.     

The fundamental theorem of mutual insurance

The essence of mutual insurance is the notion that re-distributing risk in a pool of risks is more beneficial than taking the risk alone. Interpreting ‘more beneficial’ as an increase in utility and considering sequences of exchangeable risks, we are able to formalize this notion from the policyholder’s perspective and demonstrate its validity for various alternative preference functionals (e.g., expected utility, Choquet expected utility, and distortion risk measures). To obtain this result, we exploit that for a sequence of exchangeable risks the corresponding sequence of arithmetical averages is a reversed martingale.We conclude that pooling risks is fundamental for understanding the mechanisms of insurance because it favourably affects the utility of policyholders, and we refer to this phenomenon as the ‘utility-improving effect of risk pooling’. Moreover, we demonstrate that the utility of the policyholder is (strictly) increasing with the size of the risk pool.     

Water-Assisted Concerted Proton-Electron Transfer at Co(II)-Aquo Sites in Polyoxotungstates With Photogenerated RuIII(bpy)33+ Oxidant

The cobalt substituted polyoxotungstate [Co₆(H₂O)₂(α-B-PW₉O₃₄)₂(PW₆O₂₆)]¹⁷⁻ ( Co6 ) displays fast electron transfer (ET) kinetics to photogenerated Ru^III(bpy)₃³⁺, 4 to 5 orders of magnitude faster than the corresponding ET observed for cobalt oxide nanoparticles. Mechanistic evidence has been acquired indicating that: (i) the one-electron oxidation of Co6 involves Co(II) aquo or Co(II) hydroxo groups (abbreviated as Co6(II) −OH ₂ and Co6(II) −OH, respectively, whose speciation in aqueous solution is associated to a pK_a of 7.6), and generates a Co(III)−OH moiety ( Co6(III) −OH), as proven by transient absorption spectroscopy; (ii) at pH>pK_a, the Co6(II) −OH→Ru^III(bpy)₃³⁺ ET occurs via bimolecular kinetics, with a rate constant k close to the diffusion limit and dependent on the ionic strength of the medium, consistent with reaction between charged species; (iii) at pH <pK_a, the process involves Co6(II) − OH₂ → Co6(III)−OH transformation and proceeds via a multiple-site, concerted proton electron transfer (CPET) where water assists the transfer of the proton, as proven by the absence of effect of buffer base concentrations on the rate of the ET and by a H/D kinetic isotope in a range of 1.2–1.4. The reactivity of water is ascribed to its organization on the surface of the polyanionic scaffold through hydrogen bond networking involving the Co(II)−OH₂ group.     

Spectral Element Discretization of the Circular Driven Cavity. Part IV: The Navier-Stokes Equations

This paper deals with the spectral element discretization of the Navier-Stokes equations in a disk with discontinuous boundary data, which is known as the driven cavity problem. The numerical treatment does not involve any regularization of these data. Relying on a variational formulation in the primitive variables of velocity and pressure, we describe a discretization of these equations and derive error estimates in appropriate weighted Sobolev spaces. We propose an algorithm to solve the nonlinear discrete system and present numerical experiments to verify its efficiency.