Angular correlations in the decaysB→VV using heavy quark symmetry

We calculate branching ratios and the polarization in the decay ofB mesons to two vector mesons using heavy quark symmetries to evaluate the current matrix elements.     

Differentiability of continuous homomorphisms between smooth loops

It is a well-known fact that a continuous homomorphism between Lie groups is analytic. We prove a similar result (Thm. 1.8) for continuous homomorphisms of differentiable left or right loops in section 1 of this paper. Section 2 deals with images and kernels of such homomorphisms. Again, the results obtained are quite analogous to the Lie group case. The paper ends with applications of Theorem 1.8. For example, it turns out that the group of continuous automorphisms of a smooth generalized polygon is a Lie transformation group with respect to the compact-open topology.     

Quaternionic Killing Spinors

In [17] we proved a lower bound for the spectrum of the Dirac operator on quaternionic Kähler manifolds. In the present article we study the limiting case, i.e. manifolds where the lower bound is attained as an eigenvalue. We give an equivalent formulation in terms of a quaternionic Killing equation and show that the only symmetric quaternionic Kähler manifolds with smallest possible eigenvalue are the quaternionic projective spaces.     

Single jet photoproduction at HERA in next-to-leading order QCD

We present results for next-to-leading order calculations of single jet inclusive cross sections by resolved photons inep-collisions at HERA. The dependence on the jet recombination cut and on the choice of the renormalization and factorization scales is studied in detail.     

On the stability of the polaron in one dimensional disordered systems

A one-dimensional disordered system of electrons described by a tight binding model interacting with vibrational degrees of freedom (in harmonic approximation) is considered. A stable configuration is determined by a numerical minimization of the total energy which is based on the adiabatic approximation. The behaviour of the electron density (charge density wave) and the density of states is analysed. The localization properties are investigated as well. In contrast to the corresponding disordered system with vanishing electron-phonon coupling the present model has an energy gap. The formation of the gap and the polaron band is shown to be quite different for both onsite and intersite types of coupling terms. For large disorder, the lattice distortion and the gap disappear if only the vibrational contribution to the intersite coupling is important. They increase, however, if only the vibrational contribution to the site energies is taken into account. In both cases the localization length decreases upon increasing the electron-phonon coupling energy. The results are discussed with respect to low dimensional organic materials and amorphous semiconductors.     

Reductive Insertion of Elemental Chalcogens into Boron–Boron Multiple Bonds

The syntheses of sulfur‐ and selenium‐bridged cyclic compounds containing boron stabilized by N‐heterocyclic carbenes (NHCs) have been achieved by the reductive insertion of elemental chalcogens into boron–boron multiple bonds. The three pairs of bonding electrons between the boron atoms in the triply bonded diboryne enabled six‐electron reduction reactions, resulting in the formation of [2.2.1]‐bicyclic systems wherein bridgehead boron atoms are spanned by three chalcogen bridges. A similar reaction using a diborene (boron–boron double bond) resulted in the reductive transfer of both pairs of bonding electrons to three sulfur atoms, yielding a NHC‐stabilized trisulfidodiborolane. The demonstration of these six‐ and four‐electron reductions lends support to the presence of three and two pairs of bonding electrons between the boron atoms of the diboryne and diborene, respectively, a fact that may be useful in future discussions on bond order.     

The Synthesis of B2(SIDip)2 and its Reactivity Between the Diboracumulenic and Diborynic Extremes

A new compound with the formula L‐B₂‐L wherein the stabilizing ligand (L) is 1,3‐bis[diisopropylphenyl]‐4,5‐dihydroimidazol‐2‐ylidene (SIDip) has been synthesized, isolated, and characterized. The π‐acidity of the SIDip ligand, intermediate between the relatively non‐acidic IDip (1,3‐bis[diisopropylphenyl]imidazol‐2‐ylidene) ligand and the much more highly acidic CAAC (1‐[2,6‐diisopropylphenyl]‐3,3,5,5‐tetramethylpyrrolidin‐2‐ylidene) ligand, gives rise to a compound with spectroscopic, electrochemical, and structural properties between those of L‐B₂‐L compounds stabilized by CAAC and IDip. Reactions of all three L‐B₂‐L compounds with CO demonstrate the differences caused by their respective ligands, as the π‐acidities of the CAAC and SIDip carbenes enabled the isolation of bis(boraketene) compounds (L(OC)B‐B(CO)L), which could not be isolated from reactions with B₂(IDip)₂. However, only B₂(IDip)₂ and B₂(SIDip)₂ could be converted into bicyclic bis(boralactone) compounds.     

Ansa‐Bridged Bis(benzene) Titanium Complexes

Taking advantage of an improved synthesis of [Ti(η⁶‐C₆H₆)₂], we report here the first examples of ansa‐bridged bis(benzene) titanium complexes. Deprotonation of [Ti(η⁶‐C₆H₆)₂] with nBuLi in the presence of N,N,N′,N′′,N′′‐pentamethyldiethylenetriamine (pmdta) leads to the corresponding 1,1′‐dilithio salt [Ti(η⁶‐C₆H₅Li)₂] ? pmdta that enables the preparation of the first one‐ and two‐atom‐bridged complexes by simple salt metathesis. The ansa complexes were fully characterized (NMR spectroscopy, UV/Vis spectroscopy, elemental analysis, and X‐ray crystallography) and further studied electrochemically and computationally. Moreover, [Ti(η⁶‐C₆H₆)₂] is found to react with the Lewis base 1,3‐dimethylimidazole‐2‐ylidene (IMe) to give the bent sandwich complex [Ti(η⁶‐C₆H₆)₂(IMe)].