On transfer operators for continued fractions with restricted digits

For any non-empty subset I of the natural numbers, let {Lambda}I denote those numbers in the unit interval whose continued fraction digits all lie in I. Define the corresponding transfer operator Formula. for Formula, where Re (rß) = {theta}I is the abscissa of convergence of the series Formula. When acting on a certain Hilbert space HI, rß, we show that the operator LI, rß is conjugate to an integral operator KI, rß. If furthermore rß is real, then KI, rß is selfadjoint, so that LI, rß : HI, rß -> HI, rß has purely real spectrum. It is proved that LI, rß also has purely real spectrum when acting on various Hilbert or Banach spaces of holomorphic functions, on the nuclear space C{omega} [0, 1], and on the Fréchet space C{infty} [0, 1]. The analytic properties of the map rß ↦ LI, rß are investigated. For certain alphabets I of an arithmetic nature (for example, I = primes, I = squares, I an arithmetic progression, I the set of sums of two squares it is shown that rß ↦ LI, rß admits an analytic continuation beyond the half-plane Re rß > {theta}I

Resonance structure in the Li^- photodetachment cross section

We report on the first observation of resonance structure in the total cross section for the photodetachment of Li^-. The structure arises from the autodetaching decay of doubly excited ^1P states of Li^- that are bound with respect to the 3p state of the Li atom. Calculations have been performed for both Li^- and H^- to assist in the identification of these resonances. The lowest lying resonance is a symmetrically excited intrashell resonance. Higher lying asymmetrically excited intershell states are observed which converge on the Li(3p) limit.Comment: 4 pages, 2 figure, 19 references, RevTeX, figures in ep

The Li Overabundance of J37: Diffusion or Accretion?

In September 2002 the discovery of a super Li-rich F-dwarf (J37) in NGC 6633, an iron poor analogue of the better studied Hyades and Praecepe open clusters, was announced. This unique star was thought to be the smoking gun for the action of diffusion, models of which predict a narrow "Li-peak" at approximately the correct temperature. However, with more detailed studies into J37s abundance pattern this star provides firm evidence for the accretion of planetesimals or other material from the circumstellar environment of new born stars. Thanks to the specific predictions made about the behaviour of Be abundances, (the most striking of which being no Be in super-Li-rich dwarfs subject to diffusion) the opposing diffusion/accretion predictions can be tested. Initial modelling of the Be line indicates that J37 is as Be rich as it is Li rich; log N(Be) = 2.25 +/- 0.25, and so is broadly consistent with an accretion-fuelled enhancement. However, that both Li and Be are enhanced by much more than the iron-peak elements (as determined in previous studies) suggests that diffusion also plays a role in increasing the abundances of Li and Be specifically. Furthermore, a new data set from the UVES/UT2 combination has allowed the elemental abundance of Iron to be measured, and the set of preliminary stellar parameters determined; Teff ~ 7340 K, log g ~ 4.1, microturbulence ~ 4.3 km/s, [Fe/H] ~ 0.50. This again provides distinct evidence for the effects of accretion in J37 and requires a new synthesis of the Be doublet.Comment: 5 pages, 2 figures. Poster presented at IAU Symposium 224 "The A Star Puzzle", 7-13 July 2004, Poprad, Slovaki

The Synthesis and Characterization of New, Robust Titanium (IV) Scorpionate Complexes

Titanium complexes possessing sterically encumbered ligands have allowed for the preparation of reactive moieties (imido, alkylidene and alkylidyne species) relevant to reactions such as olefin polymerization and alkyne hydroamination. For this reason, we have targeted robust scorpionate ancillary ligands to support reactive titanium centers. Thus, a series of titanium complexes were synthesized using an achiral oxazoline-based scorpionate ligand, tris(4,4-dimethyl-2-oxazolinyl)phenyl borate [To^M^]^-^ as well as the related chiral ligand, tris(4-isopropyl-2-oxazolinyl)phenyl borate [To^P^]^-^. The complex [Ti(κ^3^- To^M^)Cl~3~] was prepared in moderate yield (43%) by the rapid (<1 min at room temperature) reaction of Li[To^M^] and TiCl~4~ in methylene chloride; this new compound was characterized by ^1^H NMR spectroscopy as the expected C~3v~-symmetric species. One route to Ti (IV) alkyls involves salt metathesis; accordingly, syntheses of [To^M^]Ti alkyl complexes by interaction of [Ti(κ^3^-To^M^)Cl~3~] and one or three equivalents of alkylating agents, such as benzyl potassium (KCH~2~C~6~H~5~), trimethylsilylmethyl
lithium (LiCH~2~Si(CH~3~) ~3~), or neopentyl lithium (LiCH~2~C(CH~3~)~3~) are currently under investigation. The complexes [Ti(=NBut) (κ~3~-To^M^)(Cl)(Bu^t^py)] (Bu^t^py=4 tert-butylpyridine) and [Ti(=NBu^t^) (κ~3~-To^P^)(Cl)(Bu^t^py)] were synthesized by reaction of the known Ti imido [Ti(=NBu^t^)(Cl)~2~(Bu^t^py)~2~] with Li[To^M^] or Li[To^P^], respectively, by stirring overnight in methylene chloride at ambient temperature. The complexes were identified using ^1^H NMR spectroscopy, ^1^H-^13^C HMQC and ^1^H-^15^N HMBC correlation experiments

Come by the wind: Li Fan's story in Bunyun election

Der Artikel beschreibt die Erfahrungen des chinesischen Politikwissenschaftlers Li Fan im Zusammenhang mit der ersten direkten Wahl, die in der Gemeinde Buyun in der VR China abgehalten wurde. Li Fan dokumentiert die Abläufe und beurteilt die Bedeutung dieser Wahlen, die weltweit stark beachtet worden sind. Eine vorangestellte kurze Einleitung von C. Göbel und A. Senz ordnet die Wahlen in den Kontext politischer Reformprozesse im heutigen China ein. --