A Boolean algebra of characteristic subgroups of a finite group

We construct a “natural” sublattice L(G) of the lattice of all of those subgroups of a finite group G that contain the Frattini subgroup F(G){\Phi(G)} . We show that L(G) is a Boolean algebra, and that its members are characteristic subgroups of G. If F(G){\Phi(G)} is trivial, then L(G) is exactly the set of direct factors U of G such that U and G/U have no common nontrivial homomorphic image.     

Investigation of the thermal stability of Mg/Co periodic multilayers for EUV applications

Applied Physics A - We present the results of the characterization of Mg/Co periodic multilayers and their thermal stability for the EUV range. The annealing study is performed up to a temperature...     

Coherent population trapping of Bose-Einstein condensates: Detection of phase diffusion

Two Bose-Einstein condensates in different Zeeman sublevels can be decoupled from driving light fields in coherent population trapping. A condensate pair with a deterministic entanglement and a controllable value of the relative phase may be prepared by selecting the phase difference between the coherent light fields. The rate of the condensate phase diffusion may be determined from the two-photon resonant absorption of radiation. Received: 29 June 1998 / Revised: 10 October 1998 / Accepted: 19 October 1998     

Self pulsing in second harmonic generation

We consider nonlinear optical processes in a cavity maintained far from thermal equilibrium by external pumping. In second harmonic generation we predict a hard mode instability at a critical pump strength indicating the existence of undamped spiking similar to that in strongly pumped lasers. In subharmonic generation above the soft mode transition noted by Graham we predict the appearance of sidebands in the subharmonic spectrum.     

Production of squeezed states in a degenerate parametric amplifier

An analysis of the degenerate parametric amplifier including the quantisation of pump and signal modes is presented. It is shown that the fluctuations in one quadrature of the signal mode may be reduced at most by a factor of two. This is in contradistinction to analyses where the pump field is treated classically which overestimate the reduction in fluctuations possible.     

Artifacts in four-sector tandem mass spectrometry

Several types of artifacts were shown to be present in 4-sector tandem collision-induced dissociation (CID) mass spectra. In CID spectra of protonated peptides produced by liquid secondary-ion mass spectrometry (LSIMS), peaks corresponding to successive losses of matrix molecules from the precursor ion were observed. In addition, peaks corresponding to MH+ ions of smaller peptides that were also present in the sample/matrix mixture in greater abundance than the selected precursor ion were observed. Both of these types of artifact peaks were shown to originate from the 'peak-at-every-mass' chemical noise at the same nominal mass as that selected by the first 2 sectors (MS1). These noise ions are transmitted through to the collision cell and produce fragments that are analysed and detected in the next 2 sectors (MS2). A second, unrelated, kind of artifact was found to be due to decompositions in the second field-free region of MS2 in an EBEB geometry machine. These artifacts, which are detectable over only a very limited mass range when using a conventional single-point detector, can be present over a much greater mass range when an array detector is used and when the collision cell is floated above ground potential. A clear understanding of the origins of all peaks in a CID spectrum is important in order to have a firm foundation for interpretation, manual or computer-aided, of the spectra of unknown compounds.