Strong Cardinals and Sets of Reals in Lω1(ℝ)

We generalize results of [3] and [1] to hyperprojective sets of reals, viz. to more than finitely many strong cardinals being involved. We show, for example, that if every set of reals in L_ω (?) is weakly homogeneously Souslin, then there is an inner model with an inaccessible limit of strong cardinals.     

Bayesian methods for parameter estimation in effective field theories

We demonstrate and explicate Bayesian methods for fitting the parameters that encode the impact of short-distance physics on observables in effective field theories (EFTs). We use Bayes’ theorem together with the principle of maximum entropy to account for the prior information that these parameters should be natural, i.e., O(1) in appropriate units. Marginalization can then be employed to integrate the resulting probability density function (pdf) over the EFT parameters that are not of specific interest in the fit. We also explore marginalization over the order of the EFT calculation, M, and over the variable, R, that encodes the inherent ambiguity in the notion that these parameters are O(1). This results in a very general formula for the pdf of the EFT parameters of interest given a data set, D. We use this formula and the simpler “augmented χ²” in a toy problem for which we generate pseudo-data. These Bayesian methods, when used in combination with the “naturalness prior”, facilitate reliable extractions of EFT parameters in cases where χ² methods are ambiguous at best. We also examine the problem of extracting the nucleon mass in the chiral limit, M₀, and the nucleon sigma term, from pseudo-data on the nucleon mass as a function of the pion mass. We find that Bayesian techniques can provide reliable information on M₀, even if some of the data points used for the extraction lie outside the region of applicability of the EFT.     

Inside Cover: A Spherical Molecule with a Carbon‐Free Ih‐C80 Topological Framework (Angew. Chem. Int. Ed. 27/2009)

Template‐controlled self‐assembly of discrete molecular pentaphosphaferrocene and CuCl units was used to form the first entirely carbon‐free molecule that has C₈₀ topology and encapsulates a carborane unit. In their Communication on page 5046 ff. , M. Scheer and co‐workers report the synthesis and characterization of this impressive supramolecular compound, which displays an electronic interaction between the carborane and the spherical host molecule. C blue, Fe olive, P pink, Cl green, C gray, B/C orange, H white.

     

Hadronic Parity Violation in Few-Nucleon Systems

The weak interaction between quarks induces a parity-violating component in the interactions between nucleons, which is typically suppressed by a factor of \({\approx 10^{-7}}\) compared to the dominant parity-conserving part. Because of the short range of the weak interactions, it provides a unique probe of the strong dynamics that confine quarks into nucleons. An experimental program to map out this weak component of the nuclear force is underway at a number of facilities, including the Spallation Neutron Source at Oak Ridge National Laboratory. The corresponding observables are related to few-nucleon processes at very low energies, at which pionless effective field theory provides a reliable and model-independent theoretical approach to hadronic parity violation. Results in two- and three-nucleon systems, the role of parity-violating three-nucleon forces, and possible extensions to other few-nucleon systems are discussed.     

Zur Bestimmung des Schwefels im Eisen

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Notiz über Crotonaldoxim und Allylcyanid

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