Orthogonal polynomial bases of the orthogonal and symplectic groups

The explicit construction of orthogonal polynomial bases of the orthogonal groups in a Gelfand-Cetlin basis is given. An indication how to compute orthogonal bases for the symplectic groups is presented.Invited talk at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–21, 1981.     

Ammonia‐Annealed TiO2 as a Negative Electrode Material in Li‐Ion Batteries: N Doping or Oxygen Deficiency?

Improving the chemical diffusion of Li ions in anatase TiO₂ is essential to enhance its rate capability as a negative electrode for Li‐ion batteries. Ammonia annealing has been used to improve the rate capability of Li₄Ti₅O₁₂. Similarly, ammonia annealing improves the Li‐ion storage performance of anatase TiO₂ in terms of the stability upon cycling and the C‐rate capability. In order to distinguish whether N doping or oxygen deficiencies, both introduced upon ammonia annealing, are more relevant for the observed improvement, a systematic electrochemical study was performed. The results suggest that the creation of oxygen vacancies upon ammonia annealing is the main reason for the improvement of the stability and C‐rate capability.     

Algorithms for Computing Generalized U(<Emphasis Type="Italic">N</Emphasis>) Racah Coefficients

Algorithms are developed for computing generalized Racah coefficients for the U(N) groups. The irreducible representations (irreps) of the U(N) groups, as well as their tensor products, are realized as polynomials in complex variables. When tensor product irrep labels as well as a given irrep label are specified, maps are constructed from the irrep space to the tensor product space. The number of linearly independent maps gives the multiplicity. The main theorem of this paper shows that the eigenvalues of generalized Casimir operators are always sufficient to break the multiplicity. Using this theorem algorithms are given for computing the overlap between different sets of eigenvalues of commuting generalized Casimir operators, which are the generalized Racah coefficients. It is also shown that these coefficients are basis independent. Mathematics Subject Classifications (2000) 22E70, 81R05, 81R40.     

Point-form quantum field theory and meson form factors

We comment on canonical quantization of relativistic field theories on a Lorentz-invariant surface of the form x ² = τ². By this choice of the quantization surface all components of the four-momentum operator become interaction dependent, whereas the generators of Lorentz transformations stay free of interactions – a feature characteristic for Dirac’s “point-form” of relativistic dynamics. In the sequel we demonstrate how field theoretical concepts may enter the framework of relativistic quantum mechanics. To this aim we employ a Poincaré-invariant approximation scheme, which allows to reduce a field theoretical many-body problem to a multichannel problem for a Bakamjian-Thomas-type mass operator. As an application of this multichannel formalism we will discuss the scattering of an electron by a (confined) quark-antiquark pair. It will be sketched how an electromagnetic meson form factor can be extracted from the one-photon exchange optical potential.     

Preparation of low temperature nano-structured ZnO and RhO2 on titanium substrates, and evaluation for phenol electro-catalytic oxidation

An approach based on a thermodynamical growth control concept of ZnO and RhO₂ nano-structured metal oxides on a titanium substrate for electro-catalytic oxidation of phenol is demonstrated. These nano-structured metal oxide materials prepared via a low temperature thin film growth technique were characterized by scanning electron microscopy. The effect of the method employed, i.e. three-dimensional arrays, could be clearly seen in the estimated values of surface roughness. The scanning electron technique confirmed the sizes of the metal titanium oxide materials in the nano range: The diameter of the ZnO rods ranges from 50–150 nanometers and the lengths from 1–2 μm. The diameters of RhO₂ showed oval structures from 10–100 nanometers. Thermogravimetric analyses showed that at 450 °C and 800 °C (the calcination temperature) no further structural changes occurred due to mass loss for ZnO and RhO₂ respectively. Cyclic voltammetry (CV) showed that both the Ti/ZnO and Ti/RhO₂ nano-structured electrodes can be used for phenol electro-catalytic oxidation and that the Ti/RhO₂ electrode can also be used as a sensor for the detection of phenol.     

Mono N,C,N-pincer complexes of titanium, vanadium and niobium. Synthesis, structure and catalytic activity in olefin polymerisation

Transmetallation of 4,4'-bis{(2,6-bis[(dimethylamino)methyl]phenylgold)diphenyl-phosphino}biphenyl (3) with MCl(4) (M = Ti, NbCl, V) in benzene gave the corresponding transition metal pincer complexes (4) and insoluble 4,4'-bis[P-(chloro gold(I))diphenylphosphino]biphenyl (2), which can be quantitatively recovered and recycled. Interestingly, 3 did not react with TiCl(3). However, reaction of 2,6-bis[(dimethylamino)methyl]phenyllithium (1) with TiCl(3) resulted in formation of the novel diaryltitanium(IV) compound 5 (16% yield), comprising one N,C,N-mer bound NCN-pincer ligand and a second NCN-pincer ligand that is rearranged from a 1,2,6-isomer to a 1,2,4 one. The latter NCN-ligand is dianionic and is bidentate bonded; one of the CH(2)NMe(2) substituents (para to C'(ipso)) is non-coordinated, while the second CH(2)NMe(2) group, after C-H activation of one of the Me groups, is η(2)-C,N-bonded to the titanium centre trans to C(ipso) of the mer-NCN ligand. The new NCN-pincer metal complexes 2,6-bis[(dimethylamino)methyl]phenylTiCl(3) (4a) and 2,6-bis[(dimethylamino)methyl]-phenylVCl(2) (4d) gave, after immobilization on MgCl(2)-based supports, very high activity in ethene polymerisation.