Zener diode function generator requires no external reference voltage

Function generator utilizing parallel impedance networks with zener diodes produces functions which are discontinuous in slope. The function generated appears at the output of the parallel network in the form of a voltage varying in time

5-[4'-(2,2,5,5-Tetramethyl-3-pyrroline-1-oxyl-3-carbonyl)biphenyl-4-ylethynyl]-2,3,7,8,12,13,17,18-octaethylporphyrinato}copper(II) benzene solvate : corrigendum

In the paper by Bolte [Acta Cryst. (2006), E62, m1609-m1610], the chemical name in the title and the chemical diagram are incorrect. The correct title is {5-[4'-(2,2,5,5-Tetramethyl-3-pyrroline-1-oxyl-3-carbonyloxy)biphenyl-4-ylethynyl]-2,3,7,8,12,13,17,18-octaethylporphyrinato}copper(II) benzene solvate' and the correct diagram is given below

(1R,2S)-Methyl 1-(4-chloro-phen-yl)-3-oxo-1,2,3,4-tetra-hydro-cyclo-penta-[b]indole-2-carboxyl-ate 0.2-hydrate

The title compound, C(19)H(14)ClNO(3)·0.2H(2)O, crystallizes with five mol-ecules and a disordered water mol-ecule in the asymmetric unit. Four of the five mol-ecules form hydrogen-bonded dimers via N-H⋯O hydrogen bonds towards another symmetry-independent mol-ecule, whereas the fifth mol-ecule forms a hydrogen-bonded dimer with its symmetry equivalent, also via N-H⋯O hydrogen bonds. The dihedral angle between the planes of the fused benzene ring and the five-membered ring to which it is attached is 79.45 (13), 49.00 (15), 72.49 (16), 81.91 (18) and 76.38 (16)° for the five mol-ecules in the asymmetric unit

Semiclassical limits for the QCD Dirac operator

We identify three semiclassical parameters in the QCD Dirac operator. Mutual coupling of the different types of degrees of freedom (translational, colour and spin) depends on how the semiclassical limit is taken. We discuss various semiclassical limits and their potential to describe spectrum and spectral statistics of the QCD Dirac operator close to zero virtuality.Comment: 34 pages, 1 figur

The spin contribution to the form factor of quantum graphs

Following the quantisation of a graph with the Dirac operator (spin-1/2) we explain how additional weights in the spectral form factor K(\tau) due to spin propagation around orbits produce higher order terms in the small-\tau asymptotics in agreement with symplectic random matrix ensembles. We determine conditions on the group of spin rotations sufficient to generate CSE statistics.Comment: 9 page