On-shell Extension of Distributions

We consider distributions on \({\mathbb{R}^{n}{\setminus}\{0\}}\) which satisfy a given set of partial differential equations and provide criteria for the existence of extensions to \({\mathbb{R}^n}\) that satisfy the same set of equations on \({\mathbb{R}^n}\) . We use the results to construct distributions satisfying specific renormalisation conditions in the Epstein and Glaser approach to perturbative quantum field theory. Contrary to other approaches, we provide a unified approach to treat Lorentz covariance, invariance under global gauge group and almost homogeneity, as well as discrete symmetries. We show that all such symmetries can be recovered by applying a linear map defined for all degrees of divergence. Using similar techniques, we find a relation between on-shell and off-shell time-ordered products involving higher derivatives of the fields.     

Rare-Earth Metal Diimide Complexes via Alkylaluminate Templating,Including a Ceric Derivative

Protonolysis of lanthanide tris(tetramethylaluminate)s with two equivalents of 2,6-diisopropylaniline affords La^III and Ce^III diimide compounds Ln[(μ-NC₆H₃iPr₂-2,6)₂AlMe₂](thf)₄ featuring a bidentate AlMe₂-linked diimido ligand. As revealed for the corresponding Ce(GaMe₄)₃-reaction, formation of the diimide complexes proceeds via tetrametallic complexes of the type [Ce{(μ-NC₆H₃iPr₂-2,6)(HNC₆H₃iPr₂-2,6)(MMe₃)}]₂ (Me=Al, Ga). Oxidation of the cerium(III) complex with hexachloroethane leads to a neutral Ce^IV diimide species. Partial protonolysis with phenylacetylene and hydrogenolysis via H₃SiPh give conclusive insights into the reactive coordination sites of such diimide complexes.     

Dissecting the activation of insulin degrading enzyme by inositol pyrophosphates and their bisphosphonate analogs

Inositol poly- and pyrophosphates (InsPs and PP-InsPs) are densely phosphorylated eukaryotic messengers, which are involved in numerous cellular processes. To elucidate their signaling functions at the molecular level, non-hydrolyzable bisphosphonate analogs of inositol pyrophosphates, PCP-InsPs, have been instrumental. Here, an efficient synthetic strategy to obtain these analogs in unprecedented quantities is described – relying on the use of combined phosphate ester-phosphoramidite reagents. The PCP-analogs, alongside their natural counterparts, were applied to investigate their regulatory effect on insulin-degrading enzyme (IDE), using a range of biochemical, biophysical and computational methods. A unique interplay between IDE, its substrates and the PP-InsPs was uncovered, in which the PP-InsPs differentially modulated the activity of the enzyme towards short peptide substrates. Aided by molecular docking and molecular dynamics simulations, a flexible binding mode for the InsPs/PP-InsPs was identified at the anion binding site of IDE. Targeting IDE for therapeutic purposes should thus take regulation by endogenous PP-InsP metabolites into account.

An efficient synthesis of non-hydrolyzable inositol pyrophosphate analogs was developed to subsequently investigate the regulation of insulin-degrading enzyme by these hyperphosphorylated signaling molecules.     

Thermodynamics of associated solutions: Henry's constants for nonpolar solutes in water

Hu, Y., Azevedo, D., Lüdecke, D. and Prausnitz, J., 1984. Thermodynamics of associated solutions: Henry's constants for nonpolar solutes in water. Fluid Phase Equilibria,17: 303–321.A systematic derivation is presented for the Helmholtz energy of a van der Waals fluid mixture whose nonideality is ascribed to both chemical and physical interactions; this derivation, applicable to all fluid densities, leads to an equation of state which contains chemical equilibrium constants in addition to the customary physical van der Waals constants a and b. Attention is given to the need for simplifying assumptions and to the variety of symplifying assumptions that can lead to useful results. A particular equation of state is used to correlate Henry's constants for nonpolar solutes in water over a wide temperature range. The correlation, however, is only partly successful, because a one-fluid van der Waals theory of mixtures is not satisfactory for mixtures containing molecules that differ appreciably in size, especially in the dilute region.     

Resolution of chiral, tetrahedral M4L6 metal-ligand hosts

The supramolecular metal-ligand assemblies of M416 stoichiometry are chiral (M = GaIII, AlIII, InIII, FeIII, TiIV, or GeIV, H41 = N,N'-bis(2,3-dihydroxybenzoyl)-1,5-diaminonaphthalene). The resolution process of delta delta delta delta- and lambda lambda lambda lambda-[M(4)1(6)]12- by the chiral cation S-nicotinium (S-nic+) is described for the Ga(III), Al(III), and Fe(III) assemblies, and the resolution is shown to be proton dependent. From a methanol solution of M(acac)3, H(4)1, S-nicI, and KOH, the delta delta delta delta-KH3(S-nic)7[(S-nic) subset M(4)1(6)] complexes precipitate, and the lambda lambda lambda lambda-K6(S-nic)5[(S-nic) subset M(4)1(6)] complexes subsequently can be isolated from the supernatant. Ion exchange enables the isolation of the (NEt4(+))(12), (NMe4(+))(12), and K+(12) salts of the resolved structures, which have been characterized by CD and NMR spectroscopies. Resolution can also be accomplished with 1 equiv of NEt4+ blocking the cavity interior, demonstrating that external binding sites are responsible for the difference in S-nic+ enantiomer interactions. Circular dichroism data demonstrate that the (NMe4(+))(12) and (NEt4(+))(12) salts of the resolved [Ga(4)1(6)]12- and [Al(4)1(6)]12- structures retain their chirality over extended periods of time (>20 d) at room temperature; heating the (NEt4(+))(12)[Ga(4)1(6)] assembly to 75 degrees C also had no effect on its CD spectrum. Finally, experiments with the resolved K(12)[Ga(4)1(6)] assemblies point to the role of a guest in stabilizing the resolved framework.     

Opportunities for measurements of astrophysical-relevant alpha-capture reaction rates at CRYRING@ESR

The heavy-ion storage ring CRYRING@ESR has recently been installed and commissioned at GSI as one of the first installations of the upcoming Facility for Antiproton and Ion Research (FAIR). It is designed to store highly charged ions in the energy range between 300 keV/u and about 10 MeV/u. It will incorporate a gas-jet target providing high-density jets of, among other gases, hydrogen and helium. This will allow to study alpha-capture reaction rates of astrophysical interest in the energy range of the Gamow window for core-collapse supernovae. Special interest comes from the long-lived radio-isotope ⁴⁴Ti (t_1/2 = 58.9 years), which is supposed to be produced in the alpha-rich freeze-out during such an event. The nucleosynthesis of this isotope is of great interest, as the amount of material produced can be estimated by direct observation in remnants of recent supernovae. The disagreements between the observations and the estimations from astrophysical models show the need of more experimental data for the production and consumption reactions in the energy range of a core-collapse supernova. In this article, we will describe the proposed method of injecting beams of ⁴⁴Ti into CRYRING@ESR and performing the actual reaction rate measurements.