A Euclidean interpretation of Dynkin diagrams and its relation to root systems

A simple metric property satisfied by bases of (finite, not necessarily reduced) root systems is used to define sets in Euclidean space that provide models for Dynkin diagrams and their positive semidefinite one-vertex extensions. The theory of root systems can be founded on the study of these Dynkin sets, and conversely the Dynkin sets representing connected diagrams can be characterized as the bases and extended bases of root systems. (By an extended base, we mean a base together with the lowest root of a given length.) In this correspondence the role of nonreduced root systems is natural and important.     

Entropy for Symbolic Dynamics with Overlapping Alphabets

We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces and show that it is equal to a limit of entropies of standard (non-overlapping) shifts when the underlying shift is of finite type. When a shift space with overlaps arises as a model for a discrete dynamical system with a finite set of overlapping neighborhoods, the entropy gives a lower bound for the topological entropy of the dynamical system.     

X-ray determination of the mean amplitudes of vibration and debye temperatures of some rare earth monochalcogenides

The x-ray diffraction intensities of Bragg reflections have been measured at room temperature for thulium selenide, samarium sulphide, samarium selenide and samarium telluride. On the basis of a common amplitude approximation, the Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. The values of the Debye temperatures and mean amplitudes of vibration are 176±16°K, 0·185 ± 0·017 Å (TmSe), 155 ± 7°K, 0·244 ± 0·012 Å (SmS), 153 ± 14°K, 0·221 ± 0·020 Å (SmSe) and 151 ± 20°K, 0·204 ± 0·027 Å (SmTe).     

Measurements of F2 and xF(nu)(3) - xF(nu;)(3) from CCFR nu(mu)-Fe and nu;(mu)-Fe Data in a Physics Model-Independent Way

We report on the extraction of the structure functions F2 and DeltaxF(3) = xF(nu)(3)-xF(nu;)(3) from CCFR nu(mu)-Fe and nu;(mu)-Fe differential cross sections. The extraction is performed in a physics model-independent (PMI) way. This first measurement of DeltaxF(3), which is useful in testing models of heavy charm production, is higher than current theoretical predictions. The ratio of the F2 (PMI) values measured in nu(mu) and mu scattering is in agreement (within 5%) with the predictions of next-to-leading-order parton distribution functions using massive charm production schemes, thus resolving the long-standing discrepancy between the two sets of data.     

Literatur

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