68 research outputs found
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
Dynamics of a thin shell in the Reissner-Nordstrom metric
We describe the dynamics of a thin spherically symmetric gravitating shell in
the Reissner-Nordstrom metric of the electrically charged black hole. The
energy-momentum tensor of electrically neutral shell is modelled by the perfect
fluid with a polytropic equation of state. The motion of a shell is described
fully analytically in the particular case of the dust equation of state. We
construct the Carter-Penrose diagrams for the global geometry of the eternal
black hole, which illustrate all possible types of solutions for moving shell.
It is shown that for some specific range of initial parameters there are
possible the stable oscillating motion of the shell transferring it
consecutively in infinite series of internal universes. We demonstrate also
that this oscillating type of motion is possible for an arbitrary polytropic
equation of state on the shell.Comment: 17 pages, 7 figure
Graviton production in the scaling of a long-cosmic-string network
In a previous paper [1] we considered the possibility that (within the
early-radiation epoch) there has been (also) a short period of a significant
presence of cosmic strings. During this radiation-plus-strings stage the
Universe matter-energy content can be modelled by a two-component fluid,
consisting of radiation (dominant) and a cosmic-string fluid (subdominant). It
was found that, during this stage, the cosmological gravitational waves (CGWs)
- that had been produced in an earlier (inflationary) epoch - with comoving
wave-numbers below a critical value (which depends on the physics of the
cosmic-string network) were filtered, leading to a distorsion in the expected
(scale-invariant) CGW power spectrum. In any case, the cosmological evolution
gradually results in the scaling of any long-cosmic-string network and, hence,
after a short time-interval, the Universe enters into the late-radiation era.
However, along the transition from an early-radiation epoch to the
late-radiation era through the radiation-plus-strings stage, the
time-dependence of the cosmological scale factor is modified, something that
leads to a discontinuous change of the corresponding scalar curvature, which,
in turn, triggers the quantum-mechanical creation of gravitons. In this paper
we discuss several aspects of such a process, and, in particular, the
observational consequences on the expected gravitational-wave (GW) power
spectrum.Comment: 12 pages, 2 figures, accepted for publication in Physical Review
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
Selective dynamical imaging of interferometric data
Recent developments in very long baseline interferometry (VLBI) have made it possible for the Event Horizon
Telescope (EHT) to resolve the innermost accretion flows of the largest supermassive black holes on the sky. The
sparse nature of the EHT’s (u, v)-coverage presents a challenge when attempting to resolve highly time-variable
sources. We demonstrate that the changing (u, v)-coverage of the EHT can contain regions of time over the course
of a single observation that facilitate dynamical imaging. These optimal time regions typically have projected
baseline distributions that are approximately angularly isotropic and radially homogeneous. We derive a metric of
coverage quality based on baseline isotropy and density that is capable of ranking array configurations by their
ability to produce accurate dynamical reconstructions. We compare this metric to existing metrics in the literature
and investigate their utility by performing dynamical reconstructions on synthetic data from simulated EHT
observations of sources with simple orbital variability. We then use these results to make recommendations for
imaging the 2017 EHT Sgr A* data sethttp://iopscience.iop.org/2041-8205Physic
An Investigation on Manufacturing of the Straight Bevel Gear Using End Mill by CNC Milling Machine
Influence of Margin Designs on Crack Initiation of High Translucency Monolithic Zirconia Crowns
Effect of virtual articulator settings on occlusal morphology of CAD/CAM restorations.
PURPOSE: Determinants of mandibular movements, like condylar inclination and incisal guidance, should be considered in the fabrication of restorations in occlusion to prevent posterior excursive occlusal interferences. The aim of this study was to investigate differences in the occlusal morphology of the right mandibular molar resulting from high, average, and low values of settings for determinants of anteroposterior and transverse mandibular movement using a virtual articulation model. MATERIAL AND METHODS: The articulation functionalities of computer integrated restorative technology by imaging and new acquisition (CYRTINA, Oratio B.V., Zwaag, The Netherlands) were used as a tool to examine the potential effect of determinants of mandibular movement on occlusal molar design. High, average, and low values for condylar guide inclination, incisal guide angle, and intercuspal contact area (antero-posterior determinants) and laterotrusion, mandibular lateral translation and intercuspal contact area (transverse determinants) were introduced and differences in molar morphology studied. The latter was done by comparing mesiodistal and buccolingual sections of the occlusal designs. These interocclusal differences were quantified as differences in frequency of occlusal distance intervals in an interocclusal range of 1 mm, measured from the occlusal surface of the molar model. The vertical distance with which a standard crown in occlusion had to be corrected to avoid interferences was calculated. RESULTS: Among all parameters, the ipsilateral and contralateral mandibular lateral translation, sagittal condylar guide inclination, the ipsilateral laterotrusion and the incisal guide angle give substantial occlusal surface corrections. The high setting for the ipsilateral mandibular lateral translation required most correction. CONCLUSION: High and low setting values of mandibular movement determinants require considerable adaptation of the occlusal surface of a crown to prevent occlusal disturbance
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