On the scaling of the average multiplicity in hadron-hadron collisions

We show that, under rather general assumptions, the ratio of the average multiplicity to the cross section (rather than the average multiplicity itself) is expected to grow as Ins. We see that this ratio is already linear in lns at presently-available energy, and we extrapolate this linear dependence to predict the value of this ratio at higher energy.     

The automorphism-order in finite groups

The notion of automorphism-order is introduced as a generalization of elemental order in finite groups. Some theorems involving orders of elements are then generalized. Divisibility properties involving this concept are considered. Necessary and sufficient conditions for an abelian group to be represented by number-theoretic functions involving divisibility properties are given. Explicit formulas of these functions are also given.     

Integration over the group space of SUq(2), Clebsch-Gordan coefficients, and related identities

We calculate the Clebsch-Gordan coefficients of SUq(2) by a Woronowicz integration over the group manifold and obtain a representation differing from that reached by working with theq-group algebra. These apparently different results must agree, however, and their equivalence implies aq-identity. On lettingq = 1, we shall obtain two results of different structures for the Clebsch-Gordan coefficients of SU(2) and their equivalence similarly implies an identity among the usual binomial coefficients. With the same approach, one may extend the Woronowicz integral of the product of two irreducible representations to products of many irreducible representations.     

Massive gauge field in source theory. I

The vacuum polarization is calculated for a massive gauge field according to the methods of source theory. The spectral integral turns out to be convergent and the numerical coefficient, which is (1/3)(e²/4π²) in spinor electrodynamics, is here (3f/16)(g²/4π²) where f depends on the group and f = 1 for SU(2).     

Determination of the mechanism for resonant scattering in LaMnO3

The resonant multiple Bragg x-ray diffraction is used to study the forbidden (104) reflection in LaMnO3. Using the interference between the three-beam scattering and resonant scattering we can determine the phase of the resonant scattering. This phase is shown to be consistent with a model in which the resonant scattering is caused by the influence of the Mn-O bond length distortion rather than directly by the orbital ordering on the Mn 4p band structure.     

On generalized shock models for deteriorating systems

Standard assumptions in shock models are that failures of items are related either to the cumulative effect of shocks (cumulative models) or that they are caused by shocks that exceed a certain critical level (extreme shocks models). In this paper, we present useful generalizations of this setting to the case when an item is deteriorating itself, for example, when the boundary for the fatal shock magnitude is decreasing with time. Three stochastic failure models describing different impacts of shocks on items are considered. The cumulative effect of shocks is modeled in a way similar to the proportional hazards model. Explicit formulas for the corresponding survival functions are derived and several simple examples are considered. Copyright © 2012 John Wiley & Sons, Ltd.     

Two‐Color Valence‐to‐Core X‐ray Emission Spectroscopy Tracks Cofactor Protonation State in a Class I Ribonucleotide Reductase

Proton transfer reactions are of central importance to a wide variety of biochemical processes, though determining proton location and monitoring proton transfers in biological systems is often extremely challenging. Herein, we use two‐color valence‐to‐core X‐ray emission spectroscopy (VtC XES) to identify protonation events across three oxidation states of the O₂‐activating, radical‐initiating manganese–iron heterodinuclear cofactor in a class I‐c ribonucleotide reductase. This is the first application of VtC XES to an enzyme intermediate and the first simultaneous measurement of two‐color VtC spectra. In contrast to more conventional methods of assessing protonation state, VtC XES is a more direct probe applicable to a wide range of metalloenzyme systems. These data, coupled to insight provided by DFT calculations, allow the inorganic cores of the Mn^IVFe^IV and Mn^IVFe^III states of the enzyme to be assigned as Mn^IV(μ‐O)₂Fe^IV and Mn^IV(μ‐O)(μ‐OH)Fe^III, respectively.