Towards a superstatistical SU(2) Yang-Mills EoS

We study an SU(2) lattice gauge field system on a 10⁴ symmetric and on a 10³ × 2 asymmetric lattice in order to learn about the equation of state.     

On the invariant faces associated with a cone-preserving map

For an nonnegative matrix , an isomorphism is obtained between the lattice of initial subsets (of ) for and the lattice of -invariant faces of the nonnegative orthant . Motivated by this isomorphism, we generalize some of the known combinatorial spectral results on a nonnegative matrix that are given in terms of its classes to results for a cone-preserving map on a polyhedral cone, formulated in terms of its invariant faces. In particular, we obtain the following extension of the famous Rothblum index theorem for a nonnegative matrix: If leaves invariant a polyhedral cone , then for each distinguished eigenvalue of for , there is a chain of distinct -invariant join-irreducible faces of , each containing in its relative interior a generalized eigenvector of corresponding to (referred to as semi-distinguished -invariant faces associated with ), where is the maximal order of distinguished generalized eigenvectors of corresponding to , but there is no such chain with more than members. We introduce the important new concepts of semi-distinguished -invariant faces, and of spectral pairs of faces associated with a cone-preserving map, and obtain several properties of a cone-preserving map that mostly involve these two concepts, when the underlying cone is polyhedral, perfect, or strictly convex and/or smooth, or is the cone of all real polynomials of degree not exceeding that are nonnegative on a closed interval. Plentiful illustrative examples are provided. Some open problems are posed at the end.

     

On families of quadratic surfaces having fixed intersections with two hyperplanes

We investigate families of quadrics all of which have the same intersection with two given hyperplanes. The cases when the two hyperplanes are parallel and when they are nonparallel are discussed. We show that these families can be described with only one parameter and describe how the quadrics are transformed as the parameter changes. This research was motivated by an application in mixed integer conic optimization. In that application, we aimed to characterize the convex hull of the union of the intersections of an ellipsoid with two half-spaces arising from the imposition of a linear disjunction.     

Effect of atmospheric pressure variations on the <Superscript>222</Superscript>Rn activity concentration in the air of a wine cellar

We have measured the variation of atmospheric pressure and of ²²²Rn activity concentration in the air of a wine cellar with an AlphaGAURD type ionization chamber radon monitor. We have found that the ²²²Rn activity concentration varies inversely with pressure. To explain this behavior we have done model calculations. We have compared the results of model calculations with the results of experimental measurements, and we have found that the model is capable to reproduce some part of the variation of ²²²Rn activity concentration.     

HPTLC Investigation of a Ring-Like Discoloration of Pedunculate Oak (Quercus robur L.) Heartwood

JPC – Journal of Planar Chromatography – Modern TLC - Discoloration of industrially important woods causes substantial economic loss. Although color defects are not always associated...