Canonical Quantum Gravity on the Space of Vassiliev Invariants

I review some recent results on canonicalquantum gravity in the spin network representation. Aset of ambient isotopy spin network invariants isintroduced. These invariants are the natural extensionto spin networks of the Vassiliev invariants. Itis shown that this set is loop differentiable in thesense of distributions. The quantum gravity constraintsare written in terms of loop derivatives. It is explicitly shown that Vassiliev invariantssolve the diffeomorphism constraint. The regularizedAshtekar Hamiltonian constraint is studied, and itsaction on valence-four Vassiliev invariantsdiscussed.     

The application of the sulphide contraction to the synthesis of some simple pyrrolidine alkaloids

The alkaloids (±)-hygrine, (±)-dehydrodarlinine, (±)-dehydrodarlingianine, and (±)-N-methylruspolinone have been synthesised by selective reduction of vinylogous amides formed by sulphide contraction of the salts prepared by reaction of N-methyl-2-thiopyrrolidone with the appropriate bromomethyl ketones.     

Permanganate oxidation of 3-methyl-4-nitro-5-styrilisoxazole: a correction

In contrast with a previous report, permanganate oxidation of the title compound $\text{3}$ gives the nitroisoxazolone $\text{8}$ and not 3-methyl-4- nitroisoxazole-5-carboxylic acid $\text{2}$; a reaction pathway, involving the spirocyclisation of the carboxylate $\text{10}$, is suggested.     

Autour des algèbres de Bernstein

Sans résuméTravail subventionné par Dirección de Investigación, Universidad de La Frontera, Temuco. Chile et CONICYT.     

Synthesis and crystal structure of bis(dimethylthioacetonedicarboxylate)nickel(II)

Summary The title compound has been synthesized and characterized. The crystal structure has been determined by single-crystal x-ray analysis from diffractometer data, and refined to R= 0.063 for 1889 observed reflections. Crystals are monoclinic, space group P2₁/n, witha=21.97(2),b=8.21(1),c=10.44(1) A, and =101.87(3), and Z=4. Both ligands are coordinated to nickel through sulphur and one oxygen atom to realize thecis form of the complex in the square planar coordination geometry. Bond distances are: Ni-S, 2.14(1), Ni-O, 1.87(1) and 1.90(1) Å. Each nickel atom also forms two close contacts with oxygen atoms from adjacent molecules.     

Decision support systems for water management: The Lake Como case study

We review an application-oriented study on the management of Lake Como, a natural multipurpose reservoir in Northern Italy. The emphasis is on the Decision Support System that resulted from this study and which is now being used by the manager to take his decisions on the amount of water to be released each day from the lake. The decision support system is based on the optimal solutions of complex multiobjective mathematical programming problems.     

Towards sympathetic cooling of trapped ions with laser-cooled Mg + ions for mass spectrometry and laser spectroscopy

Sympathetic cooling by laser cooled Mg ions has been proposed as a method for fast cooling of highly charged ions to a very low temperature. The paper describes the construction of the solid state laser system at 279.63 nm required for laser cooling of the Mg ions. The laser system is composed of a fiber laser at 1,118.54 nm and two successive second harmonic generation (SHG) ring cavities for frequency quadrupling. In the first SHG cavity, non-critical phase matching of a lithium triborate (LBO) crystal is used for doubling from 1,118.54 to 559.27 nm. The second SHG cavity uses critical phase matching of a β-barium borate (BBO) crystal for doubling from 559.27 to 279.63 nm. With the aid of Boyd–Kleinmann theory, optimum experimental parameters are calculated and used for an efficient SHG. Besides this, the paper intends to be a shortcut for practical applications of the Boyd–Kleinmann theory for SHG.     

Bilinear paraproducts revisited

Boundedness properties for bilinear paraproducts on several function spaces are presented. The methods are based on the realization of paraproducts as bilinear Calderón‐Zygmund operators and the molecular character‐ization of function spaces. This provides a unified approach for the study of paraproducts, recovering some know results and establishing several new (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)