What is the number of spiral galaxies in compact groups

The distribution of morphological types of galaxies in compact groups is studied on plates from the 6 m telescope. In compact groups there are 57 percent galaxies of late morphological types (S + Irr), 23 percent lenticulars (SO) and 20 percent elliptical galaxies. The morphological content of compact groups is very nearly the same as in loose groups. There is no dependence of galaxy morphology on density in all compact groups (and possibly in loose groups). Genuine compact groups form only 60 percent of Hickson's list

Charge-exchange resonances and restoration of the Wigner SU(4)-symmetry in heavy and superheavy nuclei

Energies of the giant Gamow-Teller and analog resonances - $E_{\rm G}$ and $E_{\rm A}$, are presented, calculated using the microscopic theory of finite Fermi system. The calculated differences $\Delta E_{\rm G-A}=E_{\rm G}-E_{\rm A}$ go to zero in heavier nuclei indicating the restoration of Wigner SU(4)-symmetry. The calculated $\Delta E_{\rm G-A}$ values are in good agreement with the experimental data. The average deviation is 0.30 MeV for the 33 considered nuclei for which experimental data is available. The $\Delta E_{\rm G-A}$ values were calculated for heavy and superheavy nuclei up to the mass number $A$= 290. Using the experimental data for the analog resonances energies, the isotopic dependence of the difference of the Coulomb energies of neighboring nuclei isobars analyzed within the SU(4)-approach for more than 400 nuclei in the mass number range of $A$ = 3 - 244. The Wigner SU(4)-symmetry restoration for heavy and superheavy nuclei is confirmed. It is shown that the restoration of SU(4)-symmetry does not contradict the possibility of the existence of the "island of stability" in the region of superheavy nuclei.Comment: 5 pages, 2 figure

DFT Study of Nitroxide Radicals. 1. Effects of solvent on structural and electronic characteristics of 4-amino-2,2,5,5-tetramethyl-3-imidazoline-N-oxyl

Imidazoline-based nitroxide radicals are often used as spin probes for medium acidity and polarity in different systems. In this work, using the density functional theory (DFT) approach, we have studied how physico-chemical characteristics (geometry, atomic charges and electron spin density distribution) of pH-sensitive spin label 4-amino-2,2,5,5-tetramethyl-3-imidazoline-N-oxyl (ATI) depend on protonation and aqueous surroundings. Our calculations demonstrate that ATI protonation should occur at the nitrogen atom of the imidazoline ring rather than at the amino group. Protonation of ATI leads to a decrease in a spin density on the nitrogen atom of the nitroxide fragment >N-O. For simulation of ATI hydration effects, we have constructed a water shell around a spin label molecule by means of gradual (step-by-step) surrounding of ATI with water molecules (n = 2-41). Calculated spin density on the nitrogen atom of the nitroxide fragment increased with an extension of a water shell around ATI. Both protonation and hydration of ATI caused certain changes in calculated geometric parameters (bond lengths and valence angles). Investigating how structural and energy parameters of a system ATI-(H2O)n depend on a number of surrounding water molecules, we came to the conclusion that a hydrogen-bonded cluster of n ≥ 41 water molecules could be considered as an appropriate model for simulation of ATI hydration effects.Comment: 30 pages, 11 figures, 6 table

Parabolic equations with the second order Cauchy conditions on the boundary

The paper studies some ill-posed boundary value problems on semi-plane for parabolic equations with homogenuous Cauchy condition at initial time and with the second order Cauchy condition on the boundary of the semi-plane. A class of inputs that allows some regularity is suggested and described explicitly in frequency domain. This class is everywhere dense in the space of square integrable functions.Comment: 7 page

On the Mapping of Time-Dependent Densities onto Potentials in Quantum Mechanics

The mapping of time-dependent densities on potentials in quantum mechanics is critically examined. The issue is of significance ever since Runge and Gross (Phys. Rev. Lett. 52, 997 (1984)) established the uniqueness of the mapping, forming a theoretical basis for time-dependent density functional theory. We argue that besides existence (so called v-representability) and uniqueness there is an important question of stability and chaos. Studying a 2-level system we find innocent, almost constant densities that cannot be constructed from any potential (non-existence). We further show via a Lyapunov analysis that the mapping of densities on potentials has chaotic regions in this case. In real space the situation is more subtle. V-representability is formally assured but the mapping is often chaotic making the actual construction of the potential almost impossible. The chaotic nature of the mapping, studied for the first time here, has serious consequences regarding the possibility of using TDDFT in real-time settings