On the finiteness of the classifying space for the family of virtually cyclic subgroups

Given a group G, we consider its classifying space for the family of virtually cyclic subgroups. We show for many groups, including for example, one-relator groups, acylindrically hyperbolic groups, 3-manifold groups and CAT(0) cube groups, that they do not admit a finite model for this classifying space unless they are virtually cyclic. This settles a conjecture due to Juan-Pineda and Leary for these classes of groups

GRB 060206: hints of precession of the central engine?

Aims. The high-redshift (z=4.048) gamma-ray burst GRB 060206 showed unusual behavior, with a significant rebrightening by a factor of ~4 at about 3000 s after the burst. We argue that this rebrightening implies that the central engine became active again after the main burst produced by the first ejecta, then drove another more collimated jet-like ejecta with a larger viewing angle. The two ejecta both interacted with the ambient medium, giving rise to forward shocks that propagated into the ambient medium and reverse shocks that penetrated into the ejecta. The total emission was a combination of the emissions from the reverse- and forward- shocked regions. We discuss how this combined emission accounts for the observed rebrightening. Methods. We apply numerical models to calculate the light curves from the shocked regions, which include a forward shock originating in the first ejecta and a forward-reverse shock for the second ejecta. Results. We find evidence that the central engine became active again 2000 s after the main burst. The combined emission produced by interactions of these two ejecta with the ambient medium can describe the properties of the afterglow of this burst. We argue that the rapid rise in brightness at ~3000 s in the afterglow is due to the off-axis emission from the second ejecta. The precession of the torus or accretion disk of the central engine is a natural explanation for the departure of the second ejecta from the line of sight

GRB 060206: Evidence of Precession of Central Engine

The high-redshift (z = 4.048) gamma-ray burst GRB 060206 showed unusual behavior, with a significant re-brightening about 3000 s after the burst. We assume that the central engine became active again 2000 s after the main burst and drove another more collimated off-axis jet. The two jets both interacted with the ambient medium and contributed to the whole emission. We numerically fit this optical afterglow from the two jets using the forward-shock model and the forward-reverse shock model. Combining with the zero time effect, we suggest that the fast rise at ~3000 s in the afterglow was due to the off-axis emission from the second jet. The precession of the torus or accretion disk of the gamma ray burst engine is the natural explanation for the symmetry axes of these two jets not to lie on the same line

Asteroseismology of the δ\delta Scuti star HD 50844

Aims. We aim to probe the internal structure and investigate more detailed information of the $\delta$ Scuti star HD 50844 with asteroseismology. Methods. We analyse the observed frequencies of the $\delta$ Scuti star HD 50844 obtained by Balona (2014), and search for possible multiplets based on the rotational splitting law of g-mode. We tried to disentangle the frequency spectra of HD 50844 by means of the rotational splitting only. We then compare them with theoretical pulsation modes, which correspond to stellar evolutionary models with various sets of initial metallicity and stellar mass, to find the best-fitting model. Results. There are three multiplets including two complete triplets and one incomplete quintuplet, in which mode identifications for spherical harmonic degree $l$ and azimuthal number $m$ are unique. The corresponding rotational period of HD 50844 is found to be 2.44$^{+0.13}_{-0.08}$ days. The physical parameters of HD 50844 are well limited in a small region by three modes identified as nonradial ones ($f_{11}$, $f_{22}$, and $f_{29}$) and by the fundamental radial mode ($f_{4}$). Our results show that the three nonradial modes ($f_{11}$, $f_{22}$, and $f_{29}$) are all mixed modes, which mainly represent the property of the helium core. The fundamental radial mode ($f_{4}$) mainly represents the property of the stellar envelope. In order to fit these four pulsation modes, both the helium core and the stellar envelope must be matched to the actual structure of HD 50844. Finally, the mass of the helium core of HD 50844 is estimated to be 0.173 $\pm$ 0.004 $M_{\odot}$ for the first time. The physical parameters of HD 50844 are determined to be $M=$ 1.81 $\pm$ 0.01 $M_{\odot}$, $Z=$ 0.008 $\pm$ 0.001. $T_{\rm eff}=$ 7508 $\pm$ 125 K, log$g=$ 3.658 $\pm$ 0.004, $R=$ 3.300 $\pm$ 0.023 $R_{\odot}$, $L=$ 30.98 $\pm$ 2.39 $L_{\odot}$.Comment: 11 pages, 7 figures, 6 tables, accepted for publication in A&

Novel dynamical effects and glassy response in strongly correlated electronic system

We find an unconventional nucleation of low temperature paramagnetic metal (PMM) phase with monoclinic structure from the matrix of high-temperature antiferromagnetic insulator (AFI) phase with tetragonal structure in strongly correlated electronic system $BaCo_{0.9}Ni_{0.1}S_{1.97}$. Such unconventional nucleation leads to a decease in resistivity by several orders with relaxation at a fixed temperature without external perturbation. The novel dynamical process could arise from the competition of strain fields, Coulomb interactions, magnetic correlations and disorders. Such competition may frustrate the nucleation, giving rise to a slow, nonexponential relaxation and "physical aging" behavior.Comment: 5 pages, 4 figure

Dynamics of ultra-intense circularly polarized solitons under inhomogeneous plasmas

The dynamics of the ultra-intense circularly polarized solitons under inhomogeneous plasmas are examined. The interaction is modeled by the Maxwell and relativistic hydrodynamic equations and is solved with fully implicit energy-conserving numerical scheme. It is shown that a propagating weak soliton can be decreased and reflected by increasing plasma background, which is consistent with the existing studies based on hypothesis of weak density response. However it is found that ultra-intense soliton is well trapped and kept still when encountering increasing background. Probably, this founding can be applied for trapping and amplifying high-intensity laser-fields.Comment: 4 pages, 3 figures, submitted to Phys. Plasma

The size of the largest fluctuations in a market model with Markovian switching

This paper considers the size of the large fluctuations of a stochastic differential equation with Markovian switching. We concentrate on processes which obey the Law of the Iterated Logarithm, or obey upper and lower iterated logarithm growth bounds on their almost sure partial maxima. The results are applied to financial market models which are subject to random regime shifts. We prove that the security exhibits the same long-run growth properties and deviations from the trend rate of growth as conventional geometric Brownian motion, and also that the returns, which are non-Gaussian, still exhibit the same growth rate in their almost sure large deviations as stationary continuous-time Gaussian processes

Research on 2×2 MIMO Channel with Truncated Laplacian Azimuth Power Spectrum

Multiple-input multiple-output (MIMO) Rayleigh fading channel with truncated Laplacian azimuth power spectrum (APS) is studied. By using the power correlation matrix of MIMO channel model and the modified Jakes simulator, into which with random phases are inserted, the effect of the azimuth spread (AS), angle of departure (AOD) and angle of arrival (AOA) on the spatial correlation coefficient and channel capacity are investigated. Numerical results show that larger AS generates smaller spatial correlation coefficient amplitude, while larger average AOD or AOA produces larger spatial correlation coefficient amplitude. The average capacity variation is comprehensively dominated by the average AOD, AOA and AS