On the exceptional series,and its descendantsLa série exceptionnelle,et sa descendance

Many of the striking similarities which occur for the adjoint representation of groups in the exceptional series (cf. [1–3]) also occur for certain representations of specific reductive subgroups. The tensor algebras on these representations are easier to describe (cf. [4,5,7]), and may offer clues to the original situation.The subgroups which occur form a Magic Triangle, which extends Freudenthal's Magic Square of Lie algebras. We describe these groups from the perspective of dual pairs, and their representations from the action of the dual pair on an exceptional Lie algebra. To cite this article: P. Deligne, B.H. Gross, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 877–881.     

Effect of photoinitiator on photopolymerization of inorganic–organic hybrid polymers (ORMOCER®)

Inorganic–organic hybrid polymers have been developed and tested for evaluation in optical and electrical applications. Although hybrid inorganic–organic polymers can be synthesized by sol–gel chemistry at first, the physical properties of hybrid inorganic–organic polymers are changed during thin film-making processes, that is, photocuring and thermal curing. To investigate the effect of photoinitiator on the material properties during processing, a model system containing methacrylic groups as organically polymerizable units was selected. The conversion of CC double bond of methacrylic groups depending on some kinds of photoinitiator quantities was characterized by Fourier transform infrared spectroscopy. It was confirmed to correlate the degree of CC double bond conversion with the refractive indices. Thermodynamically, the enthalpy of the photopolymerization of hybrid polymer was investigated by UV–DSC. UV–DSC spectra showed the exothermic nature of photopolymerization of ORMOCER® to be in dependence of photoinitiator quantities. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1979–1986, 2004     

Field optimized initial state based control of photodissociation

A new scheme for controlling photodissociation through preparation of a variationally optimized linear superposition of field free vibrational eigenstates is applied for selective control of IBr and HI dissociation. The dependence of photodissociation on various field parameters and initial conditions is examined to investigate the mechanistic basis of selective control. The parametric equations of motion approach for determining vibrational dynamics as a function of field parameters without having to solve the time dependent Schrödinger equation explicitly for each field parameter separately is outlined and its use to identify field characteristics which will provide the requisite population mix represented by the optimal linear superposition of vibrational states is advocated.     

Numerical propagation of partially coherent laser beams through optical systems

The propagation of partially coherent beams through optical systems is computed numerically in one transverse dimension. The optical system is divided into different elementary segments, through which the propagation of light can be calculated by appropriate operators, working on the coherence function or the Wigner distribution function respectively. For the necessary changes between these two functions describing the partially coherent beams, the use of the remarkable z-transform seems to be an advantage. With this algorithm the grid and the resolution in the spatial frequency domain can be arbitrarily chosen in contrast to the usual Fourier transform, the influence of phase aberrations on the focusability of Gauss-Schell model beams is discussed as an application example of the numerical model. With the help of this tool, practical beam guiding systems can be simulated for use with multimode laser radiation.     

Origins and structures of background ions produced by fast-atom bombardment of glycerol

Accurate mass measurements were used to assign elemental compositions and tandem mass spectrometry was used to characterize the peak-at-every-mass background ions produced by kiloelectron-volt-particle bombardment of neat fast-atom bombardment matrices. The majority of the background ions observed in the mass spectrum of neat glycerol was identified. On the basis of the experiments with glycerol, a theory for the formation of background ions is presented. Results are discussed according to the chemical and physical changes that ygoe;on-volt-particle bombardment produces in the matrix.