A characterization of the \Sigma_1-definable functions of KP\omega + (uniform\; AC)

The subject of this paper is a characterization of the -definable set functions of Kripke-Platek set theory with infinity and a uniform version of axiom of choice: . This class of functions is shown to coincide with the collection of set functionals of type 1 primitive recursive in a given choice functional and . This goal is achieved by a G?del Dialectica-style functional interpretation of and a computability proof for the involved functionals. Received October 9, 1996     

Conformal field algebras with quantum symmetry from the theory of superselection sectors

According to the theory of superselection sectors of Doplicher, Haag, and Roberts, field operators which make transitions between different superselection sectors—i.e. different irreducible representations of the observable algebra—are to be constructed by adjoining localized endomorphisms to the algebra of local observables. We find the relevant endomorphisms of the chiral algebra of observables in the minimal conformal model with central chargec=1/2 (Ising model). We show by explicit and elementary construction how they determine a representation of the braid groupB which is associated with a Temperley-Lieb-Jones algebra. We recover fusion rules, and compute the quantum dimensions of the superselection sectors. We exhibit a field algebra which is quantum group covariant and acts in the Hilbert space of physical states. It obeys local braid relations in an appropriate weak sense.     

The 2-length of the hughes subgroup

For a finite groupG and some prime powerp ⁿ , the -subgroup is defined by . Meixner proved that ifG is a finite solvable group and for somen≧1, then the Fitting length of is bounded by 4n. In the following note it is shown that the 2-length of is at mostn. This result cannot be derived from Meixner’s paper, since his result implies only that the 2-length is bounded by 2n.     

Some trends in the development of microplasmas for spectrochemical analysis

The development of microplasmas for spectrochemical analysis by optical methods is discussed. Recent achievements in miniaturization are highlighted, especially for three types of plasmas, namely high-frequency plasmas, dc-discharges and microwave plasmas. The potentials of each of these groups of plasmas as sources for atomic emission spectrometry are discussed. Literature citations and experiments indicate that the plasmas are also very useful as atom reservoirs for atomic absorption spectrometry. Methods of sampling, including feeding with gas chromatography effluents, the use of electrothermal vaporization, and the evolution of gaseous species (as shown for the case of Hg vapor), are discussed as prominent interfaces to make use of these sources for elemental analysis.     

Extending the scope of enantiomer separation by capillary supercritical fluid chromatography on immobilized polysiloxane-anchored permethyl-β-cyclodextrin (Chirasil-Dex)

Immobilized polysiloxane-anchored permethyl-β-cyclodextrin (Chirasil-Dex) with a cyclodextrin content of approximately 30 % by weight, previously employed as a versatile chiral stationary phase for the separation of enantiomers by GC, has been used for the separation of enantiomers by capillary supercritical fluid chromatography (SFC). A considerable number of racemates could be resolved, e.g. aromatic alcohols, amino alcohols (TFA derivatives), and underivatized acids. Many pharmaceutical compounds were among those analyzed, including several NSAIDs (e.g. ibuprofen and ketoprofen), a steroidal drug (nor-gestrel), a barbiturate (hexobarbital), and others. Among the racemates resolved were many which cannot be analyzed by GC owing to low volatility or decomposition at elevated temperatures. For two racemates, analysis temperature and mobile phase density were systematically varied to give constant analysis times or capacity factors k. Low temperatures (ca 60 °C) yielded the best separation in term of separation factor, α, or resolution, R_s, even though higher densities had to be used. In comparison with GC, capillary SFC was able to furnish higher separation factors and similar resolution. The applicability of capillary SFC for the analysis of mixtures of cyclodextrin derivatives, e.g. those used in the synthesis of Chirasil-Dex, was, furthermore, demonstrated.     

Macrocyclization on the fullerene core: Direct regio- and diastereoselective multi-functionalization of [60]fullerene,and synthesis of fullerene-dendrimer derivatives

The macrocyclization between buckminsterfullerene, C₆₀, and bis-malonate derivatives in double Bingel reaction provides a versatile and simple method for the preparation of covalent bis-adducts of C₆₀ with high regio- and diastereoselectivity. A combination of spectral analysis, stereochemical considerations, and X-ray crystallography (Fig. 2) revealed that out of the possible in-in, in-out, and out-out stereoisomers, the reaction of bis-malonates linked by o-, m-, or p-xylylene tethers afforded only the out-out ones (Scheme 1). In contrast, the use of larger tethers derived from 1,10-phenanthroline also provided a first example, (±)- 19 (Scheme 2), of an in-out product. Starting from optically pure bis-malonate derivatives, the new bis-functionalization method permitted the diastereoselective preparation of optically active fullerene derivatives (Schemes 4 and 5) and, ultimately, the enantioselective preparation (enantiomeric excess ee > 97%) of optically active cis-3 bis-adducts whose chirality results exclusively from the addition pattern (Fig. 6). The macrocyclic fixation of a bis-malonate with an optically active, 9,9′-spirobi[9H-fluorene]-derived tether to C₆₀ under generation of 24 and ent- 24 with an achiral addition pattern (Scheme 4) was found to induce dramatic changes in the chiroptical properties of the tether chromophore such as strong enhancement and reversal of sign of the Cotton effects in the circular dichroism (CD) spectra (Figs. 4 and 5). By the same method, the functionafized bis-adducts 50 and 51 (Schemes 10 and 11) were prepared as initiator cores for the synthesis of the fullerene dendrimers 62 , 63 , and 66 (Schemes 12 and 13) by convergent growth. Finally, the new methodology was extended, to the regio- and diastereoselective construction of higher cyclopropanated adducts. Starting from mono-adduct 71 , a clipping reaction provided exclusively the all-cis-2 tris-adduct (±)- 72 (Scheme 14), whereas the similar reaction of bis-adduct 76 afforded the all-cis-2 tetrakis-adduct 77 (Scheme 15). Electrochemical investigations by steady-state voltammetry (Table 2) in CH₂Cl₂ (+0.1M Bu₄NPF₆) showed that all macroeyciic bis(methano)fullerenes underwent multiple reduction steps, and that regioisomerism was not much influencing the redox potentials, All cis-2 bis-adducts gave an instable dianion which decomposed during the electrochemical reduction. In CH₂Cl₂, the redox potential of the fullerene core in dendrimers 62, 63 , and 66 is not affected by differences in size and density of the surrounding poly(ether-amide) dendrons. The all-cis-2 tris- and tetrakis(meihano)fullercnes (±) -72 and 77 , respectively, are reduced at more negative potential than previously reported all-e tris- and tetrakis-adducts with methane bridges that are also located along an equatorial belt. This indicates a larger perturbation of the original fullerene π-chromophore and a larger raise in LUMO energy in the former derivatives.     

Accurate ab initio determination of the van der Waals interaction in the X 2Σ+ ground state of LiHe

Accurate quantum-chemical ab initio calculations have been performed at the SCF and CEPA (coupled electron pair approximation) levels for the van der Waals interaction in the X ² Σ ⁺ ground state of LiHe. An extended basis set has been used and the counterpoise correction for the basis set superposition error (BSSE) has been applied. The calculated potential energy curve has a very shallow minimum at 11.56 a ₀ with a well depth of only 1.49 cm^?1. This is too small to allow for a bound vibrational level. The analysis of the results shows that the interaction mainly consists of the Pauli repulsion between Li(1s ²2s) and He (1s ²), which is decaying exponentially, and the attractive London dispersion energy. Van der Waals coefficients C₆, C₈, and C₁₀ have been determined by a least squares fit to the long-range part of the calculated potential curve.     

Ab initio calculations of small hydrides including electron correlation

Five different structures of CH₅ ⁺ and one structure of CH₅ ^– are calculated using a gaussian basis both in the SCF approximation and with the inclusion of electron correlation in the independent electron pair approximation (IEPA). While on SCF level the C _sstructure of CH₅ ⁺ has to lowest energy, the energy difference between the C _sand C _2vstructures becomes negligible if correlation is included. In contrast to this the approach of a proton to CH₄ at large and intermediate distances is most favorable towards a corner of the CH₄ tetrahedron which means a structure. The decomposition of CH₅ ⁺ into CH₃ ⁺ and H₂ requires 20kcal/mol on SCF level and 40 kcal/mol if correlation is included.