Cosine families and semigroups really differ

We reveal three surprising properties of cosine families, distinguishing them from semigroups of operators: (1) A single trajectory of a cosine family is either strongly continuous or not measurable. (2) Pointwise convergence of a sequence of equibounded cosine families implies that the convergence is almost uniform for time in the entire real line; in particular, cosine families cannot be perturbed in a singular way. (3) A non-constant trajectory of a bounded cosine family does not have a limit at infinity; in particular, the rich theory of asymptotic behaviour of semigroups does not have a counterpart for cosine families. In addition, we show that equibounded cosine families that converge strongly and almost uniformly in time may fail to converge uniformly.Adam Bobrowski and Wojciech Chojnack

Investigation of chlorine radical chemistry in the Eyjafjallajkull volcanic plume using observed depletions in non-methane hydrocarbons

As part of the effort to understand volcanic plume composition and chemistry during the eruption of the Icelandic volcano Eyjafjallajkull, the CARIBIC atmospheric observatory was deployed for three special science flights aboard a Lufthansa passenger aircraft. Measurements made during these flights included the collection of whole air samples, which were analyzed for non-methane hydrocarbons (NMHCs). Hydrocarbon concentrations in plume samples were found to be reduced to levels below background, with relative depletions characteristic of reaction with chlorine radicals (Cl). Recent observations of halogen oxides in volcanic plumes provide evidence for halogen radical chemistry, but quantitative data for free halogen radical concentrations in volcanic plumes were absent. Here we present the first observation-based calculations of Cl radical concentrations in volcanic plumes, estimated from observed NMHC depletions. Inferred Cl concentrations were between 1.3 × 10 and 6.6 × 10 Cl cm. The relationship between NMHC variability and local lifetimes was used to investigate the ratio between OH and Cl within the plume, with [OH]/[Cl] estimated to be ∼37. Copyright 2011 by the American Geophysical Union

On the Equivalence of Solutions for a Class of Stochastic Evolution Equations in a Banach Space

Acknowledgments: The author wishes to thank Professor Anna Chojnowska-Michalik and the referee for many helpful suggestions and comments.We study a class of stochastic evolution equations in a Banach space E driven by cylindrical Wiener process. Three different analytical concepts of solutions: generalised strong, weak and mild are defined and the conditions under which they are equivalent are given. We apply this result to prove existence, uniqueness and continuity of weak solutions to stochastic delay evolution equations. We also consider two examples of these equations in non-reflexive Banach spaces: a stochastic transport equation with delay and a stochastic delay McKendrick equation

The Impact of a 4th Generation on Mixing and CP Violation in the Charm System

We study D0-D0 mixing in the presence of a fourth generation of quarks. In particular, we calculate the size of the allowed CP violation which is found at the observable level well beyond anything possible with CKM dynamics. We calculate the semileptonic asymmetry a_SL and the mixing induced CP asymmetry eta_fS_f which are correlated with each other. We also investigate the correlation of eta_fS_f with a number of prominent observables in other mesonic systems like epsilon'/epsilon, Br(K_L -> pi0 nu nu), Br(K+ -> pi+ nu nu), Br(B_s ->mu+ mu-), Br(B_d -> mu+ mu-) and finally S_psi phi in the B_s system. We identify a clear pattern of flavour and CP violation predicted by the SM4 model: While simultaneous large 4G effects in the K and D systems are possible, accompanying large NP effects in the B_d system are disfavoured. However this behaviour is not as pronounced as found for the LHT and RSc models. In contrast to this, sizeable CP violating effects in the B_s system are possible unless extreme effects in eta_fS_f are found, and Br(B_s ->mu+ mu-) can be strongly enhanced regardless of the situation in the D system. We find that, on the other hand, S_psi phi > 0.2 combined with the measured epsilon'/epsilon significantly diminishes 4G effects within the D system.Comment: 22 pages, 23 figures, v2 (references added

Abel Symposia

Discrete Morse theory has recently lead to new developments in the theory of random geometric complexes. This article surveys the methods and results obtained with this new approach, and discusses some of its shortcomings. It uses simulations to illustrate the results and to form conjectures, getting numerical estimates for combinatorial, topological, and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics

An improved observable for the forward-backward asymmetry in B -> K* l+ l- and Bs -> phi l+ l-

We study the decay B -> K* l+ l- in the QCD factorization approach and propose a new integrated observable whose dependence on the form factors is almost negligible, consequently the non--perturbative error is significantly reduced and indeed its overall theoretical error is dominated by perturbative scale uncertainties. The new observable we propose is the ratio between the integrated forward--backward asymmetry in the [4,6] GeV^2 and [1,4] GeV^2 dilepton invariant mass bins. This new observable is particularly interesting because, when compared to the location of the zero of the FBA spectrum, it is experimentally easier to measure and its theoretical uncertainties are almost as small; moreover it displays a very strong dependence on the phase of the Wilson coefficient C_10 that is otherwise only accessible through complicated CP violating asymmetries. We illustrate the new physics sensitivity of this observable within the context of few extensions of the Standard Model, namely the SM with four generations, an MSSM with non--vanishing source of flavor changing neutral currents in the down squark sector and a Z' model with tree level flavor changing couplings.Comment: 19 pages, 7 figure