Topological density of ccc Boolean algebras--Every cardinality occurs

For every uncountable cardinal there is a ccc Boolean algebra whose topological density is .

     

Visible superradiance of excited F2 colour centres in LiF single crystals

Strong superradiation in the visible of optically excited F₂ colour centres in LiF X-rayed single crystal at room temperature was obtained.     

Heavy quark potential and quarkonia dissociation rates

Quenched lattice data for the interaction (in terms of heavy quark free energies) in the color-singlet channel at finite temperatures are fitted and used within the non-relativistic Schrödinger equation formalism to obtain binding energies and scattering phase shifts for the lowest eigenstates in the charmonium and bottomonium systems in a hot gluon plasma. The partial dissociation rate due to the Bhanot-Peskin process is calculated using different assumptions for the gluon distribution function, including free massless gluons, massive gluons, and massive damped gluons. It is demonstrated that a temperature dependent gluon mass has an essential influence on the heavy quarkonia dissociation, but that this process alone is insufficient to describe the heavy quarkonia dissociation rates.Arrival of the final proofs: 8 July 2005PACS: 12.38.Gc, 12.38.Mh, 14.40.GxD. Blaschke: Present address: GSI mbH, 64291 Darmstadt, Germany     

Auditory perception of sound source velocity

In this study we investigate the perception of the velocity of linearly moving sound sources passing in front of a listener. The binaural simulation of motion used in two psychoacoustical experiments includes changes in the overall sound pressure level, the Doppler effect, and changes in interaural time differences. These changes are considered as cues for the perception of velocity. The present experiments are an extension of the experiments performed by Lutfi and Wang [J. Acoust. Soc. Am. 106, 919-928 (1999)]. The results of Experiment I show that the differential velocity threshold is independent of the reference velocity (10, 20, 30, and 40 m/s), varying across listeners from 1.5 to 4.6 m/s. In Experiment II, a method based on the successive elimination of cues in compared pairs of signals was employed to estimate the weights of potential cues for velocity discrimination. The magnitudes of all underlying cues at thresholds are reported. The experimental results show the subject's preference for the Doppler cue and a weakest sensitivity to the cue related with interaural time differences. Finally, it was found that spatial differences in the source location at the endpoints of the motion trajectory are not a significant factor in the velocity discrimination task.     

Power residue problem on elliptic curves

Let E be an elliptic curve defined over a number field K, without complex multiplication, S a finite subset of E(K) and l a rational prime being good modulus for E/K. The main result of the paper asserts that if |S|l²+l and for almost all prime ideals P of _K S contains an element R satisfying R mod P = lQ with QE(_K/P) then S contains an element R which satisfies R=lQ with some QE(K). It improves the result of S.Wong [6], where the above statement is proved under the stronger assumption |S|l². Moreover we show that the bound |S|l²+l is optimal.     

Mercuric triflate catalyzed hydroxylative carbocyclization of 1,6-enynes

[reaction: see text] Hg(OTf)(2) exhibits remarkable catalytic activity for the hydroxylative cyclization of 1,6-enynes. The present procedure should involve a sequence of mercuration of a terminal alkyne, carbocyclization, hydration, and protodemercuration that regenerates the catalyst.     

On Transfer Operators for Continued Fractions with Restricted Digits

For any non-empty subset I of the natural numbers, let _I denotethose numbers in the unit interval whose continued fractiondigits all lie in I. Define the corresponding transfer operator for , where Re (rß) = _I is the abscissa of convergence of the series . When acting on a certain Hilbert space H_I, rß, weshow that the operator L_I, rß is conjugate to an integraloperator K_I, rß. If furthermore rß is real,then K_I, rß is selfadjoint, so that L_I, rß: H_I, rß H_I, rß has purely real spectrum.It is proved that L_I, rß also has purely real spectrumwhen acting on various Hilbert or Banach spaces of holomorphicfunctions, on the nuclear space C [0, 1], and on the Fréchetspace C [0, 1]. The analytic properties of the map rß L_I, rßare investigated. For certain alphabets I of an arithmetic nature(for example, I = primes, I = squares, I an arithmetic progression,I the set of sums of two squares it is shown that rß L_I, rß admits an analytic continuation beyond thehalf-plane Re rß > _I. 2000 Mathematics SubjectClassification 37D35, 37D20, 30B70.     

Molecular parameters describing intermolecular interactions in the electrooptical Kerr effect

Electrooptical Kerr effect has been studied in binary solutions of a dipolar liquid (-picoline, β-picoline) in a non-dipolar solvent (benzene, p-xylene) and 1,4-dioxane in the full range of concentrations of the dipolar component (0 ≤ f₂ ≤ 1). The experimental Kerr constant K_s of the solutions, refraction index n_s, density ρ_s and the dielectric constant ε_s have been measured and used for the calculation of the molar Kerr constants K_S^M within the Onsager local field model. Analysis of changes in the molar Kerr constants as a function of the solute concentration by fits of theoretical functions to the experimental ones has permitted a determination of the parameters characterizing intermolecular interactions in binary solutions.     

EPR and optical measurements of weakly doped LiNbO3: Er

Optical spectroscopy measurements of the congruent LiNbO₃ (LN) single crystals, weakly doped with Er (0.1–0.3 wt%) and Er (0.3 wt%) and Yb (0.5 wt%), have been carried out. The shape of the optical absorption and additional absorption bands registered after γ-irradiation suggests the presence of Er³⁺ ion pairs. EPR investigations were performed for LN single crystal doped with Er (0.1 wt%). Unusual behaviour of the temperature dependence of the intensity and linewidth of the main EPR line—corresponding to the fine transition of ^evenEr³⁺—ions, is reported. The main EPR line appears to be a superposition of several paramagnetic centres originating from isolated ^evenEr³⁺ ions and ^evenEr³⁺–^evenEr³⁺ pairs of ions. In low temperature region (below 20 K), the main EPR signal is dominated by signals arising from ^evenEr³⁺–^evenEr³⁺ pairs of ions. The inverse intensity of the EPR line at low temperature region fulfils the Curie–Weiss law and enabled to determine the Curie–Weiss constant Θ=1.5±0.5 K. The positive sign of Θ suggests that the ferromagnetic interactions arise in the system of ^evenEr³⁺–^evenEr³⁺ ion pairs in LN. Our results suggest that the distribution of Er ions in congruent LN is not homogeneous and Er impurity ions can form clusters in host lattice even in the case of weak erbium doping.