17,035 research outputs found
The error and perturbation bounds for the absolute value equations with some applications
To our knowledge, so far, the error and perturbation bounds for the general
absolute value equations are not discussed. In order to fill in this study gap,
in this paper, by introducing a class of absolute value functions, we study the
error bounds and perturbation bounds for two types of absolute value equations
(AVEs): Ax-B|x|=b and Ax-|Bx|=b. Some useful error bounds and perturbation
bounds for the above two types of absolute value equations are presented. By
applying the absolute value equations, we also obtain the error and
perturbation bounds for the horizontal linear complementarity problem (HLCP).
In addition, a new perturbation bound for the LCP without constraint conditions
is given as well, which are weaker than the presented work in [SIAM J. Optim.,
2007, 18: 1250-1265] in a way. Besides, without limiting the matrix type, some
computable estimates for the above upper bounds are given, which are sharper
than some existing results under certain conditions. Some numerical examples
for the AVEs from the LCP are given to show the feasibility of the perturbation
bounds
Palatini formulation of gravity theory, and its cosmological implications
We consider the Palatini formulation of gravity theory, in which a
nonminimal coupling between the Ricci scalar and the trace of the
energy-momentum tensor is introduced, by considering the metric and the affine
connection as independent field variables. The field equations and the
equations of motion for massive test particles are derived, and we show that
the independent connection can be expressed as the Levi-Civita connection of an
auxiliary, energy-momentum trace dependent metric, related to the physical
metric by a conformal transformation. Similarly to the metric case, the field
equations impose the non-conservation of the energy-momentum tensor. We obtain
the explicit form of the equations of motion for massive test particles in the
case of a perfect fluid, and the expression of the extra-force, which is
identical to the one obtained in the metric case. The thermodynamic
interpretation of the theory is also briefly discussed. We investigate in
detail the cosmological implications of the theory, and we obtain the
generalized Friedmann equations of the gravity in the Palatini
formulation. Cosmological models with Lagrangians of the type and are investigated. These models lead to
evolution equations whose solutions describe accelerating Universes at late
times.Comment: 22 pages, no figures, accepted for publication in EPJC; references
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Palladium and silver abundances in stars with [Fe/H] > -2.6
Palladium (Pd) and silver (Ag) are the key elements for probing the weak
component in the rapid neutron-capture process (r-process) of stellar
nucleosynthesis. We performed a detailed analysis of the high-resolution and
high signal-to-noise ratio near-UV spectra from the archive of HIRES on the
Keck telescope, UVES on the VLT, and HDS on the Subaru Telescope, to determine
the Pd and Ag abundances of 95 stars. This sample covers a wide metallicity
range with -2.6 [Fe/H] +0.1, and most of them are dwarfs.
The plane-parallel LTE MAFAGS-OS model atmosphere was adopted, and the spectral
synthesis method was used to derive the Pd and Ag abundances from Pd I
{\lambda} 3404 {\AA} and Ag I {\lambda} 3280/3382 {\AA} lines. We found that
both elements are enhanced in metal-poor stars, and their ratios to iron show
flat trends at -0.6 < [Fe/H] < +0.1. The abundance ratios of [Ag/H] and [Pd/H]
are well correlated over the whole abundance range. This implies that Pd and Ag
have similar formation mechanisms during the Galactic evolution.Comment: 15 pages, 12 figures, accepted to A&
A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
We prove a general theorem on the relation between the bulk topological
quantum number and the edge states in two dimensional insulators. It is shown
that whenever there is a topological order in bulk, characterized by a
non-vanishing Chern number, even if it is defined for a non-conserved quantity
such as spin in the case of the spin Hall effect, one can always infer the
existence of gapless edge states under certain twisted boundary conditions that
allow tunneling between edges. This relation is robust against disorder and
interactions, and it provides a unified topological classification of both the
quantum (charge) Hall effect and the quantum spin Hall effect. In addition, it
reconciles the apparent conflict between the stability of bulk topological
order and the instability of gapless edge states in systems with open
boundaries (as known happening in the spin Hall case). The consequences of time
reversal invariance for bulk topological order and edge state dynamics are
further studied in the present framework.Comment: A mistake corrected in reference
Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
Journal ArticleWe propose models of two-dimensional paramagnetic semiconductors where the intrinsic spin Hall effect is exactly quantized in integer units of a topological charge. The model describes a topological insulator in the bulk and a "holographic metal" at the edge, where the number of extended edge states crossing the Fermi level is dictated by (exactly equal to) the bulk topological charge. We also demonstrate the spin Hall effect explicitly in terms of the spin accumulation caused by the adiabatic flux insertion
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