Ultrasonically tunable filter for ψ-rays

A new type of an ultra-narrow frequency transmission filter for ψ-rays is presented. The principle of its operation is based on the Mössbauer-sideband-spectroscopy [1–3]: A resonant absorber onto a thin piezo-electric polymer foil vibrates piston like at an ultrasonic frequency ω. At certain definite amplitudes the zero-order-sideband, i.e. the transition energy ω₀, is fully transmitted without any resonant absorption, whereas simultanously sidebands displaced by energies ±hhΩ from ω₀ are resonantly absorbed. Using several absorbers of this type in series having different frequencies a broadband filter for ψ-rays with a well defined transmission-profile can be designed. Symmetrically, on both sides of the central transmission window there exist resonant absorption bands. The energy width of these different bands is only limited by the possible ultrasonic frequencies and can be adjusted from 10^?o to 10^?5 eV. First experimental results using such an assembly of absorbers are presented. The limit of the efficiency of the filter, caused by non-resonant scattering is discussed.     

Kolloide Lösungen von praktisch unlöslichen Goldverbindungen und ihre Umwandlung in Goldsole

Ohne ZusammenfassungUebersetzt und bearbeitet von Wo. Ostwald und R. Köhler (Leipzig).     

Nonlinear Longitudinal Vibrations of Transversally Polarized Piezoceramics: Experiments and Modeling

Nonlinear behavior of piezoceramics at strong electric fields is a well-known phenomenon and is described by various hysteresis curves. On the other hand, nonlinear vibration behavior of piezoceramics at weak electric fields has recently been attracting considerable attention. Ultrasonic motors (USM) utilize the piezoceramics at relatively weak electric fields near the resonance. The consistent efforts to improve the performance of these motors has led to a detailed investigation of their nonlinear behavior. Typical nonlinear dynamic effects can be observed, even if only the stator is experimentally investigated. At weak electric fields, the vibration behavior of piezoceramics is usually described by constitutive relations linearized around an operating point. However, in experiments at weak electric fields with longitudinal vibrations of piezoceramic rods, a typical nonlinear vibration behavior similar to that of the USM-stator is observed at near-resonance frequency excitations. The observed behavior is that of a softening Duffing-oscillator, including jump phenomena and multiple stable amplitude responses at the same excitation frequency and voltage. Other observed phenomena are the decrease of normalized amplitude responses with increasing excitation voltage and the presence of superharmonics in spectra. In this paper, we have attempted to model the nonlinear behavior using higher order (quadratic and cubic) conservative and dissipative terms in the constitutive equations. Hamilton's principle and the Ritz method is used to obtain the equation of motion that is solved using perturbation techniques. Using this solution, nonlinear parameters can be fitted from the experimental data. As an alternative approach, the partial differential equation is directly solved using perturbation techniques. The results of these two different approaches are compared.     

Pyrazole analogues of porphyrins and oxophlorins

A series of porphyrin analogues with pyrazole rings replacing one of the usual pyrrole subunits have been synthesized. This was accomplished by reacting 1-phenyl, 1-methyl and 1-ethyl pyrazole-1,3-dicarbaldehydes with a tripyrrane in the presence of TFA, followed by an oxidation step. The initially formed phlorin product was sufficiently stable for the N-phenyl system to be isolated and characterized, although the related N-alkyl phlorin analogues were less stable. Attempts to dehydrogenate the intermediary phlorins with DDQ resulted in decomposition, but the N-alkylphlorins could be oxidized with 0.2% aqueous ferric chloride solutions. Although the phenyl-substituted phlorin could not be oxidized under these conditions, it did afford the pyrazoloporphyrin upon treatment with silver acetate under acidic conditions. Oxidations with silver acetate also afforded oxophlorin analogues where the oxo-linkage was selectively formed at the 5-position. The pyrazole-containing porphyrin analogues are cross-conjugated and exhibit only a small degree of diatropic character. The internal CH resonances were observed between 5.27 and 5.87 ppm, while the external meso-protons fell into a range of 6.84-7.88 ppm. The borderline overall aromatic character was attributed to dipolar resonance contributors. Protonation considerably increased the diatropicity and the diprotonated dications formed from these porphyrin analogues gave the internal CH resonance at upfield values of 2.65-3.20 ppm. The aromatic character was enhanced by the presence of an electron-donating alkyl substituent on the nitrogen compared to the phenyl-substituted species. The pyrazoloporphyrins reacted with nickel(II) acetate in DMF, or palladium(II) acetate in acetonitrile, to give the corresponding organometallic derivatives. The metal complexes showed increased diatropic character but protonation afforded nonaromatic cations. The oxophlorin analogues were also nonaromatic in the free base and protonated forms. This work extends our understanding of carbaporphyrinoid systems and provides the first detailed studies on pyrazole-containing porphyrin analogues.     

Kugo-Ojima confinement and QCD Green''s functions in covariant gauges

In Landau gauge QCD the Kugo-Ojima confinement criterion and its relations to the infrared behaviour of the gluon and ghost propagators are reviewed. It is demonstrated that the realization of this confinement criterion (which is closely related to the Gribov-Zwanziger horizon condition) results from quite general properties of the ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson-Schwinger equations provide an explicit example for the anticipated infrared behaviour. The results are in good agreement, also quantitatively, with corresponding lattice data obtained recently. The resulting running coupling approaches a fixed point in the infrared, (0) = 8.915/N_c. Solutions for the coupled system of Dyson-Schwinger equations for the quark, gluon and ghost propagators are presented. Dynamical generation of quark masses and thus spontaneous breaking of chiral symmetry takes place. In the quenched approximation the quark propagator functions agree well with those of corresponding lattice calculations. For a small number of light flavours the quark, gluon and ghost propagators deviate only slightly from the ones in quenched approximation. While the positivity violation of the gluon spectral function is manifest in the gluon propagator, there are no clear indications of analogous positivity violations for quarks so far.     

Spektraltheorie verwandter operationen

This is a résumé of A. Pietsch’s concept of related linear operators in the study of spectral properties and homomorphism theorems forp-bounded linear operators on Mackey-complete topological vector spaces. It turns out that many results proved by various authors in the setting of Mackey-complete topological vector spaces follow directly from the corresponding classical results by means of purely algebraic relations.