5,691 research outputs found

    What is the number of spiral galaxies in compact groups

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    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

    Parabolic equations with the second order Cauchy conditions on the boundary

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    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

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    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

    Quasi-Optimal Filtering in Inverse Problems

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    A way of constructing a nonlinear filter close to the optimal Kolmogorov - Wiener filter is proposed within the framework of the statistical approach to inverse problems. Quasi-optimal filtering, which has no Bayesian assumptions, produces stable and efficient solutions by relying solely on the internal resources of the inverse theory. The exact representation is given of the Feasible Region for inverse solutions that follows from the statistical consideration.Comment: 9 pages, 240 K
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