Product of matrical discs

We determine the matrical disc with minimal radius for the set of products XY when X and Y run over a (possibly distinct) matrical disc, respectively. Also we determine the union of the numerical ranges W(XY).     

Synthesis and complexation of a novel cyclophane

A novel cyclophane, 17, 17, 40, 40-tetramethyl-7, 30-dinitro-1, 10, 24, 33-tetraoxa[2.2.1.2.2.1] metaparaparametaparaparacyclophane, was synthesized by 2:2 cyclization of 3,5-bis(bromomethyl)nitrobenzene, derived from 3,5-dimethylnitrobenzene, and bisphenol A. The cyclophane was found to form 1:1 complex with benzene.     

Experiments on plasma heating in the lower hybrid frequency range

Experimental results of lower hybrid heating in a small tokamak are described. When rf power is applied, a high energy tail of ions is produced, whether or not there is a lower hybrid resonance layer (LHR layer) in the plasma column, though bulk ion heating is not observed. The electron temperature in the plasma surface increases, while the electrons in the center lose their energy, which is related to an impurity ion flux diffusing from the outside of the plasma.     

Transcendence of the values of infinite products in several variables

The aim of this paper is to prove the transcendence of certain infinite products. As applications, we get necessary and sufficient conditions for transcendence of the value of $\Pi_{k=0}^{\infty}(1+a_{k}^{(1)}{z_{1}r^{k}}+\cdot\cdot\cdot+a_{k}^{(m)}{z_{m}r^{k}})$ at appropriate algebraic points, where r ≥ 2 is an integer and {a_n ⁽ⁱ⁾}_{n≥ 0} (1 ≤ i ≤ m) are suitable sequences of algebraic numbers.     

Optimized perturbation theory in quantum electrodynamics

The optimized perturbation expansions, Grunberg's fastest apparent convergence and Stevenson's principle of minimal sensitivity, are applied to some low-energy QED quantities. The optimization does not disturb the experimentally established values, and, at higher orders, its effects are in the direction of reducing small differences between theoretical and experimental values.