Die sterischen Bedingungen der Fragmentierungsreaktion III. Teil. Stereoisomere 4-, 5- und 7-Decahydrochinolyl-toluolsulfonate Fragmentierungsreaktionen, 16. Mitteilung

In a heterolytic fragmentation reaction of the type a-b-c-d-X → a - b + c = d + : X the geometry of the d - X bond and that of the electron-donating group a relative to the b - c bond are critical. This follows from a study of solvolysis rates and products of stereoisomeric 1-methyl-4-, -5- and -7-decahydroquinolyl p-toluenesulphonates in 80 Vol.% ethanol.     

Unambiguous identification of three beta-decaying isomers in 70Cu

Using resonant laser ionization, beta-decay studies, and for the first time mass measurements, three beta-decaying states have been unambiguously identified in 70Cu. A mass excess of -62 976.1(1.6) keV and a half-life of 44.5(2) s for the (6-) ground state have been determined. The level energies of the (3-) isomer at 101.1(3) keV with T(1/2)=33(2) s and the 1+ isomer at 242.4(3) keV with T(1/2)=6.6(2) s are confirmed by high-precision mass measurements. The low-lying levels of 70Cu populated in the decay of 70Ni and in transfer reactions compare well with large-scale shell-model calculations, and the wave functions appear to be dominated by one proton-one neutron configurations outside the closed Z=28 shell and N=40 subshell. This does not apply to the 1+ state at 1980 keV which exhibits a particular feeding and deexcitation pattern not reproduced by the shell-model calculations.     

Field Theory on Kappa-spacetime

A general formalism is developed, that allows the construction of field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime is replaced by a quantum group. This formalism is demonstrated for the -deformed Poincaré algebra and its quantum space. The algebraic setting is mapped to the algebra of functions of commuting variables with a suitable -product. Fields are elements of this function algebra. As an example, the Klein-Gordon equation is defined and derived from an action.     

Bioorganometallic chemistry: biocatalytic oxidation reactions with biomimetic NAD/NADH co-factors and [Cp*Rh(bpy)H] for selective organic synthesis

The biocatalytic, regioselective hydroxylation of 2-hydroxybiphenyl to the corresponding catechol was accomplished utilizing the monooxygenase 2-hydroxybiphenyl 3-monooxygenase (HbpA). The necessary natural 1,4-dihydronicotinamde adenine dinucleotide (NADH) co-factor for this biocatalytic process was replaced by a biomimetic co-factor, N-benzyl-1,4-dihydronicotinamide, 1b. The interaction between the flavin (FAD) containing HbpA enzyme and the corresponding biomimetic NADH compound, N-benzyl-1,4-dihdronicotinamide, 1b, for hydride transfer, was shown to readily occur. The in situ recycling of the reduced NADH biomimic 1b from 1a was accomplished with [Cp*Rh(bpy)H](Cl); however, productive coupling of this regeneration reaction to the enzymatic hydroxylation reaction was not totally successful, due to a deactivation process concerning the HbpA enzyme peripheral groups; i.e., -SH or -NH₂ possibly reacting with the precatalyst, [Cp*Rh(bpy)(H₂O)](Cl)₂, and thus inhibiting the co-factor regeneration process. The deactivation mechanism was studied, and a promising strategy of derivatizing these peripheral -SH or -NH₂ groups with a polymer containing epoxide was successful in circumventing the undesired interaction between HbpA and the precatalyst. This latter strategy allowed tandem co-factor regeneration using 1a or 2a, [Cp*Rh(bpy)(H₂O)](Cl)₂, and formate ion, in conjunction with the polymer bound, FAD containing HbpA enzyme to provide the catechol product.     

A new approach to helical primary structures of four-membered rings: (P)- and (M)-tetraspiro[3.0.0.0.3.2.2.2]hexadecane

A new approach to helical primary structures of four-membered rings uses a cycloaddition of a trimethylenketeniminium salt to suitable tailored methylenecyclobutanes to assemble the desired carbon framework. The results are short and effective syntheses of (M)-trispiro[3.0.0.3.2.2]tridecane [(M)-5], and (P)- and (M)-tetraspiro[3.0.0.0.3.2.2.2]hexadecane [(P)- and (M)-24]. Unlike helices of three-membered rings, the specific rotation decreases, as the length of the helix increases.     

Extendable Cycles in Multipartite Tournaments

An n-partite tournament is an orientation of a complete n-partite graph. If D is a strongly connected n-partite (n3) tournament, then we shall prove that every partite set of D has at least one vertex which lies on a cycle C_m of each length m for such that V(C₃)V(C₄)V(C_n), where V(C_m) is the vertex set of C_m for . This result extends those of Bondy [2], Guo and Volkmann [4], Gutin [6], Moon [8], and Yeo [12].Final version received: June 9, 2003     

Cumulants are universal homomorphisms into Hausdorff groups

This is a contribution to the theory of sums of independent random variables at an algebraico-analytical level: Let Prob denote the convolution semigroup of all probability measures on with all moments finite, topologized by polynomially weighted total variation. We prove that the cumulant sequence regarded as a function from Prob into the additive topological group ofall real sequences, is universal among continuous homomorphisms from Prob into Hausdorff topological groups, in the usual sense that every other such homomorphism factorizes uniquely through . An analogous result, referring to just the first cumulants,holds for the semigroup of all probability measures with existing rth moments. In particular, there is no nontrivial continuous homomorphism from the convolution semigroup of all probability measures, topologized by the total variation metric, into any Hausdorff topological group.Mathematics Subject Classification (2000): 60B15, 60E10, 60G50     

Power-law tail distributions and nonergodicity

We establish an explicit correspondence between ergodicity breaking in a system described by power-law tail distributions and the divergence of the moments of these distributions.     

The mass of 22Mg

Mass measurements with a relative precision of better than 1.5 x 10(-8) were performed on 22Mg and its reaction partners 21Na and 22Na with the ISOLTRAP Penning trap mass spectrometer at CERN, yielding the mass excesses D(22Mg)=-399.92(27) keV, D(21Na)=-2184.71(21) keV, and D(22Na)=-5181.56(16) keV. The importance of these results is twofold. First, a comparative half-life (Ft value) has been obtained for the superallowed beta decay of 22Mg to further test the conserved-vector-current hypothesis. Second, the resonance energy for the 21Na proton capture reaction has been independently determined, allowing direct comparisons of observable gamma radiation in nova explosions with the yield expected from models.     

Electron delocalization in cross-conjugated p-phenylenevinylidene oligomers

The synthesis, structure, and electronic properties of a series of cross-conjugated p-phenylenevinylidene oligomers with one to four double bonds are reported. The X-ray crystal structure of the compound with two double bonds reveals a nonplanar conformation with torsion angles about the C(phenylene)-C(vinylidene) and C(phenyl)-C(vinylidene) formal single bonds of 39.5(2) degrees and 30.5(2) degrees, respectively. Admixture of quinoid character in the ground state is observed. Infrared and Raman spectroscopy do not provide a clear picture of the degree of electron delocalization in the series, since the C=C stretching mode does not adequately reflect the C=C bond order and has a local nature. In contrast, electronic spectra and electrochemical data, as well as AM1 and PPP/SCF calculations, reveal that the cross-conjugated compounds basically behave as linearly pi-conjugated systems in the sense that molecular orbitals are delocalized over the entire structure and systematically change in energy. The electronic interaction between the repeating units is, however, not very strong, which has the consequence that spatial extension of the molecular orbitals does not lead to a red shift of the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) electronic transition. This is related to the feature that the modest narrowing of the HOMO-LUMO gap with the chain length is accompanied by a relatively large reduction of electron repulsion. This finding implies that care should be taken in the use of electronic spectra for the evaluation of conjugation phenomena.