An asymptotic formula for the pion decay constant in a large volume

We derive an asymptotic formula à la Lüscher for the finite-volume correction to the pion decay constant: this is expressed as an integral over the 3π|A_μ|0 amplitude after proper subtraction of the pion pole contribution. We analyze the formula numerically at leading and next-to-leading order in the chiral expansion.     

Zur Charakterisierung der zyklischen Funktionen durch eine Funktionalgleichung

Ohne Zusammenfassung     

Quadrature of the circle in ancient Egypt

The mathematicians of ancient Egypt approximated the area of a circle by a square with astonishing accuracy. The way to find this approximation is not handed down. In this paper a conjecture is given which seems to be much more simple than earlier attempts.     

Refractive index and nonlinear optical properties of polyaniline derivatives

An investigation of the refractive index and third-order nonlinear optical susceptibility χ⁽³⁾ of two polypernigraniline derivatives, poly (4,4'-diphenylimine methine) (PDPIM) and poly (4,4'-diphenylimine p-heptyloxybenzylidene) (PDPIHB) reveals effects of molecular structure on the linear optical and nonlinear optical properties of conjugated polymers. The χ⁽³⁾ (?3ωω,ω,ω) of PDPIM was found to decrease relative to polypernigraniline, reflecting the observed decrease of the oscillator strength of the 2.2 eV absorption band when a methine carbon replaces one of the nitrogen atoms of pernigraniline repeat unti. The alkoxyphenylene side group substitution at the methine carbon in PDPIHB, however, significantly enhances the nonlinear optical response of PDPIHB while reducing the refractive index compared to PDPIM and polypernigraniline. The present results suggest that structural changes in conjugated polymers can be made in such a way as to enhance the nonlinear optical properties while modulating the linear optical properties. © 1994 John Wiley & Sons, Inc.     

Nicht-polytopale 3-Sphären mit 8 Ecken

Ohne Zusammenfassung