A nonterminating 8φ7 summation for the root system Cr

Using multiple q-integrals and a determinant evaluation, we establish a nonterminating ₈φ₇ summation for the root system C_r. We also give some important specializations explicitly.     

Proton–neutron structure of the N=52 nucleus Zr

Following the successful identification of mixed-symmetric one- and two-phonon states in the N=52 nuclei ⁹⁴Mo and ⁹⁶Ru, we have performed a photon scattering experiment on the N=52 isotone ⁹²Zr. Experimental data and shell model calculations show that both, single particle and collective degrees of freedom are present in the low-lying levels of ⁹²Zr. The second excited quadrupole state shows the signatures of the one-phonon mixed-symmetric 2⁺ state, while calculations and data indicate an almost pure neutron configuration for the 2⁺₁ state, in contradiction with the F-spin symmetric limit. Furthermore, two strong dipole excitations, which are candidates for the two-phonon quadrupole–octupole coupled E1 excitation and for the mixed-symmetric 1⁺ two-phonon state, were observed.     

Geometrical forms of Abelès'' equations involving film thickness

Abelès' equations (in terms of ₁; ₂ and optical film thickness x) for all the eight optical functions (R_s; R_p; T_s; T_p; F_s; F_p; X_s and X_p) have been expressed in the form of equations representing standard geometrical three-dimensional figures. X_s and X_p are represented by plane surfaces whilst the remainder are skew cones. Translated into the n; k notation; X_s and X_p generate hyperboloids whilst the remainder produce paraboloids whose cross-sections are parts of figures of eight.     

Coupling routes to hexafluoro-1,3-butadiene, substituted-1,3-fluorine-containing butadienes and fluorinated polyenes

Hexafluoro-1,3-butadiene was readily prepared via a variety of self-coupling processes, such as Cu(0) mediated self-coupling of iodotrifluoroethene, Pd(0) catalyzed coupling of iodotrifluoroethene with the trifluorovinylzinc reagent, and CuBr₂ mediated coupling of the trifluorovinylzinc reagent. Perfluoro-2,3-dimethyl-1,3-butadiene was readily synthesized by the reaction of pentafluoropropenyl-2-zinc reagent with either CuBr₂ or FeCl₃. Alternatively, perfluoro-2,3-dimethyl-1,3-butadiene was prepared by oxidation of the pentafluoropropenyl-2-copper reagent with dioxygen. Cu(0) mediated coupling of an (E)-substituted ,β-difluoro-β-iodostyrene provided the first useful route to a (Z)(Z)-1,4-diaryl-1,3-tetrafluorobutadiene. Extension of the Cu(0) mediated coupling methodology to a perfluorodienyl iodide demonstrated a useful stereospecific route to perfluoropolyenes.     

Herz spaces and summability of Fourier transforms

A general summability method is considered for functions from Herz spaces K^α_p,r (?^d ). The boundedness of the Hardy–Littlewood maximal operator on Herz spaces is proved in some critical cases. This implies that the maximal operator of the θ ‐means σ^θ _T f is also bounded on the corresponding Herz spaces and σ^θ _T f → f a.e. for all f ∈ K^{–d /p} _p,∞ (?^d ). Moreover, σ^θ _T f (x) converges to f (x) at each p ‐Lebesgue point of f ∈ K^{–d /p} _p,∞ (?^d ) if and only if the Fourier transform of θ is in the Herz space K^{d /p} _{p ′,1} (?^d ). Norm convergence of the θ ‐means is also investigated in Herz spaces. As special cases some results are obtained for weighted L_p spaces. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adsorption and oxidation of purine bases and their derivatives on electrodes modified with carbon nanotubes

The electrochemical behavior of nitrogen bases and their derivatives is studied on electrodes modified with carbon nanotubes. On these electrodes, the strong adsorption of purines and their oxidation is observed at potentials in the vicinity of +0.8 V for guanine and +1.0 V (vs. Ag/AgCl) for guanine nucleosides/nucleotides and adenine. At more positive potentials, the high background current prevents the detection of adenine nucleotides and pyrimidines. The peculiarities of oxidation of the most easily detectable DNA components, namely, guanine and deoxyguanosinemonophosphate, on modified electrodes are elucidated and the corresponding reaction scheme is proposed. The results can be used in the development of biosensors based on electroactive properties of nucleic acids and their components.     

New approach of fragment charge correlations in Xe+Sn central collisions

A previous analysis of the charge (Z) correlations in the ΔZ−Z plane for ¹²⁹Xe+^natSn central collisions at 32 MeV/n has shown an enhancement in the production of equally sized fragments (low ΔZ) which was interpreted as an evidence for spinodal decomposition. However, the signal is weak and rises the question of the estimation of the uncorrelated yield. After a critical analysis of its robustness, we propose in this paper a new technique to build the uncorrelated yield in the charge correlation function. The application of this method to ¹²⁹Xe+^natSn central collision data at 32, 39, 45 and 50 MeV/n does not show any particular enhancement of the correlation function in any ΔZ bin.