Extremely high energy hadron and gamma-ray families(3). Core structure of the halo of superfamily

The study of the core structure seen in the halo of Mini-Andromeda 3(M.A.3), which was observed in the Chacaltaya emulsion chamber, is presented. On the assumption that lateral distribution of darkness of the core is exponential type, i.e., D=D0exp(-R/r0), subtraction of D from halo darkness is performed until the cores are gone. The same quantity on cores obtained by this way are summarized. The analysis is preliminary and is going to be developed

Symmetry Reduction of Optimal Control Systems and Principal Connections

This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to obtain explicit expressions of the reduced system by exploiting the geometry. In particular, we show how to obtain a principal connection to be used in the reduction for various choices of symmetry groups, as opposed to assuming such a principal connection is given or choosing a particular symmetry group to simplify the setting. Our result synthesizes some previous works on symmetry reduction of nonlinear control and optimal control systems. Affine and kinematic optimal control systems are of particular interest: We explicitly work out the details for such systems and also show a few examples of symmetry reduction of kinematic optimal control problems.Comment: 23 pages, 2 figure

An empirical model to describe rapidity density and transverse momentum distributions

The distribution of rapidity density and transverse momentum is formulated empirically and analytically. It describes the data quite well over the wide energy range of √s = 22.4 – 7000 GeV

High capacitance carbon-based xerogel film produced without critical drying

This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in APPLIED PHYSICS LETTERS. 93(19):193112 (2008) and may be found at https://doi.org/10.1063/1.2976684 .ArticleAPPLIED PHYSICS LETTERS. 93(19):193112 (2008)journal articl