Transition metal complexes bearing a 2,2-bis(3,5-dimethylpyrazol-1-yl)propionate ligand: one methyl more matters

The new N,N,O ligand 2,2-bis(3,5-dimethylpyrazol-1-yl)propionic acid (2,2-Hbdmpzp) (2) and its transition metal complexes [Mn(2,2-bdmpzp)(CO)(3)] (3), [Re(2,2-bdmpzp)(CO)(3)] (4), [Cu(2,2-bdmpzp)(2)] (5), and [Ru(2,2-bdmpzp)Cl(L)(PPh(3))] [L = PPh(3) (6), N(2) (7), CO (8a/b), SO(2) (9a/b)] have been synthesized, characterized and compared to analogous complexes bearing a bis(3,5-dimethylpyrazol-1-yl)acetic acid. It was found that the additional methyl group has a remarkable influence on the stability and reactivity of transition metal complexes.     

Cu(I) catalysed cyclopropanation with enantiopure scorpionate type ligands derived from (+)-camphor or (-)-menthone

One-pot syntheses of three new enantiopure heteroscorpionate ligands derived from (+)-camphor or (-)-menthone are described. The ligands are obtained by reacting pyrazoles derived from (+)-camphor or (-)-menthone with sodium hydride and thionyl chloride. Subsequent reactions with pyridine and various aldehydes afford the tripod ligands in multi-gram amounts. Especially the menthopyrazole based ligand 6 showed encouraging ee values up to 69% in the Cu(I) catalysed enantioselective cyclopropanation of styrene with ethyl diazoacetate.     

Fischer–Tropsch Chemistry at Room Temperature?

The unique catalytic activity of vanadium nitrogenase suggests a new direction for the direct production of biofuels from CO with either synthetic catalysts or nitrogenase-containing bacteria. The reduction of CO by V?nitrogenase to light hydrocarbons shows striking similarities to the established Fischer-Tropsch process; however, the enzyme does not use H(2) directly for this reaction. ADP=adenosine diphosphate, ATP= adenosine triphosphate.     

OnE 10 and the DDF construction

An attempt is made to understand the root spaces of Kac Moody algebras of hyperbolic type, and in particularE ₁₀, in terms of a DDF construction appropriate to a subcritical compactified bosonic string. While the level-one root spaces can be completely characterized in terms of transversal DDF states (the level-zero elements just span the affine subalgebra), longitudinal DDF states are shown to appear beyond level one. In contrast to previous treatments of such algebras, we find it necessary to make use of a rational extension of the self-dual root lattice as an auxiliary device, and to admit non-summable operators (in the sense of the vertex algebra formalism). We demonstrate the utility of the method by completely analyzing a non-trivial level-two root space, obtaining an explicit and comparatively simple representation for it. We also emphasize the occurrence of several Virasoro algebras, whose interrelation is expected to be crucial for a better understanding of the complete structure of the Kac Moody algebra.Supported by Konrad-Adenauer-Stiftung e.V.This article was processed by the author using the Latex style filepljour1 from Springer-Verlag.     

Neutrino mass effect on the nuclear muon capture

Multipole expansion of the partial transition amplitude in the nuclear muon capture with massive lefthanded Dirac neutrino has been derived. The multipole amplitudes for the partial nuclear transitions are given as the explicit functions of the neutrino mass parameter. As an example, the capture rate, the recoil asymmetry and the neutrino polarization are investigated in terms of these multipole amplitudes. The transversal neutrino polarization provides a connection between theT-violation and the neutrino mass: ifT-odd component in the neutrino polarization is observed, then neutrino must be a massive particle. It turns out that in the capture rate and recoil polarization, the effects due to very small neutrino mass can be proportional to the square ratio of the neutrino mass to its momentum, while the neutrino transversal polarization is proportional to this ratio only. Under the recent limits on the muon neutrino mass, the observable effects inthe partial transition may be below the order of ?10^?3.     

Monte Carlo simulation of SU(2) gauge theory with fermions on a four-dimensional lattice

After integration over the fermions in an SU(2) lattice gauge theory, the effective fermionic action may be expressed as a sum over all possible closed gauge field loops with corresponding weight factors. We approximate this sum and perform a Monte Carlo simulation of a coupled fermion-gauge system on a 4⁴ lattice. We compare our results for 〈S_eff〉 and $\text{〈}\text{ψ}\text{ψ〉}$ for different values of the gauge field coupling β and fermion coupling κ with the free fermion theory on a lattice. 〈S_eff〉 turns out to be quite small for $\text{κ?}\text{1}\text{8}$.     

N = 8 supergravity

The complete structure of N = 8 supergravity is presented with an optional local SO(8) invariance. The SO(8) gauge interactions break E₇ invariance, but leave the local SU(8) unaffected. Exploiting E₇ × SU(8) invariance and using explicit lowest order results, we first derive the complete action and transformation laws. Subsequently, we introduce local SO(8) invariance and prove the consistency of the theory. Possible implications of our results are discussed.     

Geometry of coset spaces and massless modes of the squashed seven-sphere in supergravity

We derive some general results for Killing vectors on arbitrary coset manifolds and explicitly exhibit the squashed seven-sphere as the coset space Sp₄×Sp₂/Sp₂×Sp₂. Using these results, we then analyze the zero-mass sector of supergravity of the squashed S⁷ and argue that it is not interpretable as a spontaneously broken version of N=8 supergravity. We also point out the existence of a new solution which combines squashing and torsion.