Q-complements on log surfaces

In this paper the log surfaces without \QQ-complement are classified. In particular, they are non-rational always. This result takes off the restriction in the theory of complements and allows one to apply it in the most wide class of log surfaces.Comment: Latex2e, 3 page

Comment on The Evidence for a Pentaquark and Kinematic Reflections

The Regge exchange model used by Dzierba et al. is shown to be questionable, since the pion pole term is not allowed. Hence the Regge amplitudes in their calculation are exaggerated. The amount of kinematic reflection in the mass spectrum of the (nK+) system, which is one decay channel of a possible pentaquark, is not well justified in the fitting procedure used by Dzierba et al., as shown by comparison with the (K+K-) invariant mass spectrum, which is one decay channel of the a_2 and f_2 tensor mesons. While kinematic reflections are still a concern in some papers that have presented evidence for the pentaquark, better quantitative calculations are needed to demonstrate the significance of this effect.Comment: Comment submitted to Phys. Rev. D (no figures

Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies

We studied the kink-antikink collision process for the "double sine-Gordon" (DSG) equation in 1+1 dimensions at different values of the potential parameter $R>0$. For small values of $R$ we discuss the problem of resonance frequencies. We give qualitative explanation of the frequency shift in comparison with the frequency of the discrete level in the potential well of isolated kink. We show that in this region of the parameter $R$ the effective long-range interaction between kink and antikink takes place.Comment: 9 pages, LaTeX, 4 figures (eps

The variation of the magnetic field of the Ap star HD~50169 over its 29 year rotation period

Context. The Ap stars that rotate extremely slowly, with periods of decades to centuries, represent one of the keys to the understanding of the processes leading to the differentiation of stellar rotation. Aims. We characterise the variations of the magnetic field of the Ap star HD 50169 and derive constraints about its structure. Methods. We combine published measurements of the mean longitudinal field of HD 50169 with new determinations of this field moment from circular spectropolarimetry obtained at the 6-m telescope BTA of the Special Astrophysical Observatory of the Russian Academy of Sciences. For the mean magnetic field modulus , literature data are complemented by the analysis of ESO spectra, both newly acquired and from the archive. Radial velocities are also obtained from these spectra. Results. We present the first determination of the rotation period of HD 50169, Prot = (29.04+/-0.82) y. HD 50169 is currently the longest-period Ap star for which magnetic field measurements have been obtained over more than a full cycle. The variation curves of both and have a significant degree of anharmonicity, and there is a definite phase shift between their respective extrema. We confirm that HD 50169 is a wide spectroscopic binary, refine its orbital elements, and suggest that the secondary is probably a dwarf star of spectral type M. Conclusions. The shapes and mutual phase shifts of the derived magnetic variation curves unquestionably indicate that the magnetic field of HD 50169 is not symmetric about an axis passing through its centre. Overall, HD 50169 appears similar to the bulk of the long-period Ap stars.Comment: 10 pages, 3 figures, accepted for publication in A&