On the Finiteness Problem for Automaton (Semi)groups

This paper addresses a decision problem highlighted by Grigorchuk, Nekrashevich, and Sushchanskii, namely the finiteness problem for automaton (semi)groups. For semigroups, we give an effective sufficient but not necessary condition for finiteness and, for groups, an effective necessary but not sufficient condition. The efficiency of the new criteria is demonstrated by testing all Mealy automata with small stateset and alphabet. Finally, for groups, we provide a necessary and sufficient condition that does not directly lead to a decision procedure

Nonlinear evolution of dark matter and dark energy in the Chaplygin-gas cosmology

The hypothesis that dark matter and dark energy are unified through the Chaplygin gas is reexamined. Using generalizations of the spherical model which incorporate effects of the acoustic horizon we show that an initially perturbative Chaplygin gas evolves into a mixed system containing cold dark matter-like gravitational condensate.Comment: 11 pages, 3 figures, substantial revision, title changed, content changed, added references, to appear in JCA

First M87 Event Horizon Telescope Results. VII. Polarization of the Ring

In 2017 April, the Event Horizon Telescope (EHT) observed the near-horizon region around the supermassive black hole at the core of the M87 galaxy. These 1.3 mm wavelength observations revealed a compact asymmetric ring-like source morphology. This structure originates from synchrotron emission produced by relativistic plasma located in the immediate vicinity of the black hole. Here we present the corresponding linear-polarimetric EHT images of the center of M87. We find that only a part of the ring is significantly polarized. The resolved fractional linear polarization has a maximum located in the southwest part of the ring, where it rises to the level of similar to 15%. The polarization position angles are arranged in a nearly azimuthal pattern. We perform quantitative measurements of relevant polarimetric properties of the compact emission and find evidence for the temporal evolution of the polarized source structure over one week of EHT observations. The details of the polarimetric data reduction and calibration methodology are provided. We carry out the data analysis using multiple independent imaging and modeling techniques, each of which is validated against a suite of synthetic data sets. The gross polarimetric structure and its apparent evolution with time are insensitive to the method used to reconstruct the image. These polarimetric images carry information about the structure of the magnetic fields responsible for the synchrotron emission. Their physical interpretation is discussed in an accompanying publication

Neutron-Rich [sup 62,64,64]Fe Show Enhanced Collectivity: The Washout of N\u2009=\u200940 in Terms of Experiment, Valence Proton Symmetry and Shell Model

Probing shell structure at a large neutron excess has been of particular interest in recent times. Neutron-rich nuclei between the proton shell closure Z=20 and Z=28 offer an exotic testing ground for shell evolution. The development of the N=40 gap between neutron fp and 1 g(9/2) shells gives rise to highly interesting variations of collectivity for nuclei in this region. While Ni-68 shows double magic properties in level energies and transition strength, this was not observed in neighbouring nuclei. Especially neutron-rich Fe isotopes proved particularly resistant to calculational approaches using the canonical valence space (fpg) resulting in important deviations of the predicted collectivity. Only an inclusion of the d(5/2)-orbital could solve the problem [1]. Hitherto no transition strengths for Fe-66 have been reported. We determined B(E2, 2(1)(+) -> 0(1)(+)) values from lifetimes measured with the recoil distance Doppler-shift method using the Cologne plunger for radioactive beams at National Superconducting Cyclotron Laboratory at Michigan State University. Excited states were populated by projectile Coulomb excitation for Fe-62,Fe-64,Fe-66. The data show a rise in collectivity for Fe isotopes towards N=40. Results [2] are interpreted by means of modified version of the Valence Proton symmetry [3] and compared to shell model calculation using a new effective interaction recently developed for the fpgd valence space [4]