Symmetric Hilbert spaces arising from species of structures

Symmetric Hilbert spaces such as the bosonic and the fermionic Fock spaces over some lsquo;one particle space’ are formed by certain symmetrization procedures performed on the full Fock space. We investigate alternative ways of symmetrization by building on Joyal's notion of a combinatorial species. Any such species F gives rise to an endofunctor of the category of Hilbert spaces with contractions mapping a Hilbert space to a symmetric Hilbert space with the same symmetry as the species F. A general framework for annihilation and creation operators on these spaces is developed, and compared to the generalised Brownian motions of R. Speicher and M. Bożejko. As a corollary we find that the commutation relation with admits a realization on a symmetric Hilbert space whenever f has a power series with infinite radius of convergence and positive coefficients. Received: 7 April 2000; in final form: 28 November 2000 / Published online: 19 October 2001     

Sliding spark spectroscopy

Summary A new analytical radiation source combined with fiber optics linked to a diode array detection device with modified software is described. The direct-reading spectrometer simultaneously covers the wavelength range 185–510 nm with a spectral resolution of <1.5 nm. Intense optical emission is observed when positionally stable high-current surface sparks supplied by a pulse-generator with definite discharge parameters (max. 800 Ampere/pulse) are sliding over compact non-conductive materials such as plastics, glasses, quartz filters or powder pellets. Substrate vaporization, ionization and excitation processes in the surface discharge plasma channel generate emission corresponding to neutral and ionic states. The spectra are essentially composed of lines emitted by the electrode material (e.g. copper, silver), from the substrate under investigation, radiation continuum as well as structured background from the surrounding air atmosphere. Due to the occurrence of emission lines of reactive fillers, inorganic pigments and stabilizers, a rapid multi-element screening method is demonstrated. A rapid identification system (mix-up test) of PVC or fire-retardant thermoplastics within one second has been realized from the atomic emission line intensity originating from the sputtered copper electrode material according to its increased volatility in the presence of chlorine (modified Beilstein test).Puls-Plasma-Technik GmbH, Dortmund     

A new polymorph of tetraphenyldiboroxane

A new polymorph of tetraphenyldiboroxane [or oxybis(diphenylborane)], C₂₄H₂₀B₂O, (Ia), has been found. It is monoclinic, like the already known form, (Ib), and can be refined in the same space group, namely P2₁/c, or in the equivalent setting P2₁/n. The molecular conformations of the two polymorphs differ in the rotations of two of the phenyl rings about the B—C bonds, leading to markedly different packing patterns and cell dimensions.     

Cyclic and telechelic ladder polymers derived from tetrahydroxytetramethylspirobisindane and 1,4‐dicyanotetrafluorobenzene

5,5′,6,6′‐Tetrahydroxy‐3,3,3′,3′‐tetramethylspirobisindane was polycondensed with 1,4‐dicyanotetrafluorobenzene in four different solvents at 70 °C. In dimethylformamide, N‐methylpyrrolidone, and sulfolane exclusively, cyclic polymers were detectable by matrix‐assisted laser desorption/ionization time‐of‐flight (MALDI‐TOF) mass spectrometry up to masses around 13,000 Da. In dimethyl sulfoxide, linear byproducts were also found. Higher temperatures caused degradation reactions catalyzed by potassium carbonate. Polycondensations performed with the addition of 4‐tert‐butyl catechol or 2,2′‐dihydroxy binaphthyl yielded linear telechelic oligomers. Equimolar mixtures of linear and cyclic ladder polymers were examined by MALDI‐TOF mass spectra to determine how the end groups and the cyclic structure influenced the signal‐to‐noise ratio. The results suggested a preferential detection of the linear chains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5344–5352, 2006