Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras

Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic kinematical observables and represents it through operators on a suitable Hilbert space. In a second step, one implements the constraints. The main result of the paper concerns the representation theory of the kinematical algebra: We show that there is only one cyclic representation invariant under spatial diffeomorphisms.While this result is particularly important for loop quantum gravity, we are rather general: The precise definition of the abstract *-algebra of the basic kinematical observables we give could be used for any theory in which the configuration variable is a connection with a compact structure group. The variables are constructed from the holonomy map and from the fluxes of the momentum conjugate to the connection. The uniqueness result is relevant for any such theory invariant under spatial diffeomorphisms or being a part of a diffeomorphism invariant theory.     

Principle and applications of the protein-purification-parameter screening system

For the purification of a target protein, liquid chromatography is the method of choice, if its activity has to be maintained. The selection of optimum parameters will improve in proportion to the number of individual parameters varied in initial experiments. Here a fast screening method is described, which utilizes automated parallel chromatographic experiments in the batch mode in 96-well plates. The principle of this protein-purification-parameter screening (PPS) system is demonstrated with a mixture of four proteins. An application of PPS for the determination of a purification step of an angiotensin-II-generating enzyme from a crude tissue extract is shown.     

Solvent reduced wittig olefination reactions with halo containing conjugated phosphoranes

The Wittig reaction of carbaldehydes with alkoxycarbonylhalomethylidenetriphenylphosphoranes can be performed with ease in solventless systems. The analogous reaction of carbaldehydes with acylhalomethylidenetriphenylphosphoranes requires a small amount of solvent, such as chloroform, in order for the reaction to proceed. The products of the reaction are versatile precursors for further transformations, such as the Suzuki-Miyaura cross-coupling reaction.     

Dichlorocarbene Addition to

In contrast to the terminal phosphinidene complex PhPW(CO)(5) (2), which adds to [5]metacyclophane (1) in a 1,4-fashion, dichlorocarbene preferentially adds in a 1,2-fashion to the formal "anti-Bredt" type double bond of the aromatic ring of 1 to afford the norcaradiene 11b, which immediately rearranges to the bridged cycloheptatriene 12b and further by a [1,5] sigmatropic chlorine migration to the isomeric 13b as the first observable product. More slowly, the latter isomerizes via a dissociative mechanism to give 15b. A computational study supports the notion that the [1,5] chlorine migration in the rearrangement 12b --> 13b, for which an activation barrier of 70.2 kJ mol(-)(1) was calculated, is essentially concerted with minor charge separation. In contrast, the analogous [1,5] chlorine migration in the flat model compound 7,7-dichlorocycloheptatriene (12a) displays features of a dissociative pathway.     

Die quantitative Gewinnung kleinster Ionenmengen aus sehr großen Wassermassen

Zusammenfassung Ein Verfahren wird beschrieben, das auf der Grundlage der Gegenstrom-Ionenwanderung arbeitet und die quantitative Gewinnung kleinster Ionenmengen (z. B. radiochemischer Quantitäten) aus sehr großen Wassermassen ermöglicht. Durch eine kleine Laboranlage von etwa 250 W Leistung konnten pro Tag 0,51 Wasser durchgesetzt werden. Die Anlage wurde benutzt, um aus Regenwasser⁷Be zu extrahieren.

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The quantitative extraction of very small amounts of ions from very large amounts of water

Summary A process is described on the basis of counter-current electromigration for the quantitative preparing of very small quantities of ions (e. g. radiochemical quantities) from very large amounts of water. Through a small laboratory plant of 250 W electric power consumption we processed 0.5 t water/day. We used the apparatus for quantitative preparing of⁷Be from rain water.