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We have investigated the pitch angle ($\psi$) of the spiral arms of galaxies in the Hubble Space Telescope COSMOS field. The sample consists of 102 face-on galaxies with a two-armed pattern at a mean redshift $\langle z \rangle \approx 0.5$. The typical values of $\psi$ in the spiral arms of distant galaxies are shown to be close to those for nearby spiral galaxies. Within one galaxy the scatter of $\psi$ for different arms is, on average, half the mean pitch angle. In the $z$ range from 1 to 0 we have found a tendency for $\psi$ to decrease. Our analysis of the $\psi$ distributions in galaxies at different redshifts is consistent with the assumption that in most of the galaxies at $z \leq 0.5$ the spiral arms are tidal in origin or they arose from transient recurrent instabilities in their disks., Comment: 8 pages, 7 figures

A regular method is suggested for constructing vortex-like solutions with cylindrical symmetry in the Skyrme-Einstein chiral model. The method is based on the expansion of metric and field functions in power series with respect to the two small parameters entering the model. The length mass density of the vortex is estimated., Comment: 9 pages

A regular method for constructing vortex-like solutions with cylindrical symmetry to the equations of the SU(2) Skyrme chiral model is proposed. A numerical estimate for the length density of mass is given.