536 research outputs found
Searching for a preferred direction with Union2.1 data
A cosmological preferred direction was reported from the type Ia supernovae
(SNe Ia) data in recent years. We use the Union2.1 data to give a simple
classification of such studies for the first time. Because the maximum
anisotropic direction is independent of isotropic dark energy models, we adopt
two cosmological models (CDM, CDM) for the hemisphere comparison
analysis and CDM model for dipole fit approach. In hemisphere
comparison method, the matter density and the equation of state of dark energy
are adopted as the diagnostic qualities in the CDM model and CDM
model, respectively. In dipole fit approach, we fit the fluctuation of distance
modulus. We find that there is a null signal for the hemisphere comparison
method, while a preferred direction () for the dipole fit method. This result indicates
that the dipole fit is more sensitive than the hemisphere comparison method.Comment: 8 pages, 2 figures, accepted for publication in MNRA
Analytical Solutions of Singular Isothermal Quadrupole Lens
Using analytical method, we study the Singular Isothermal Quadrupole (SIQ)
lens system, which is the simplest lens model that can produce four images. In
this case, the radial mass distribution is in accord with the profile of the
Singular Isothermal Sphere (SIS) lens, and the tangential distribution is given
by adding a quadrupole on the monopole component. The basic properties of the
SIQ lens have been studied in this paper, including deflection potential,
deflection angle, magnification, critical curve, caustic, pseudo-caustic and
transition locus. Analytical solutions of the image positions and
magnifications for the source on axes are derived. As have been found, naked
cusps will appear when the relative intensity of quadrupole to monopole is
larger than 0.6. According to the magnification invariant theory of the SIQ
lens, the sum of the signed magnifications of the four images should be equal
to unity \citep{dal98}. However, if a source lies in the naked cusp, the summed
magnification of the left three images is smaller than the invariant 1. With
this simple lens system, we study the situations that a point source infinitely
approaches a cusp or a fold. The sum of magnifications of cusp image triplet is
usually not equal to 0, and it is usually positive for major cusp while
negative for minor cusp. Similarly, the sum of magnifications of fold image
pair is usually neither equal to 0. Nevertheless, the cusp and fold relations
are still equal to 0, in that the sum values are divided by infinite absolute
magnifications by definition.Comment: 12 pages, 2 figures, accepted for publication in ApJ
Cusp Summations and Cusp Relations of Simple Quad Lenses
We review five often used quad lens models, each of which has analytical
solutions and can produce four images at most. Each lens model has two
parameters, including one that describes the intensity of non-dimensional mass
density, and the other one that describes the deviation from the circular lens.
In our recent work, we have found that the cusp and the fold summations are not
equal to 0, when a point source infinitely approaches a cusp or a fold from
inner side of the caustic. Based on the magnification invariant theory, which
states that the sum of signed magnifications of the total images of a given
source is a constant, we calculate the cusp summations for the five lens
models. We find that the cusp summations are always larger than 0 for source on
the major cusps, while can be larger or smaller than 0 for source on the minor
cusps. We also find that if these lenses tend to the circular lens, the major
and minor cusp summations will have infinite values, and with positive and
negative signs respectively. The cusp summations do not change significantly if
the sources are slightly deviated from the cusps. In addition, through the
magnification invariants, we also derive the analytical signed cusp relations
on the axes for three lens models. We find that both on the major and the minor
axes the larger the lenses deviated from the circular lens, the larger the
signed cusp relations. The major cusp relations are usually larger than the
absolute minor cusp relations, but for some lens models with very large
deviation from circular lens, the minor cusp relations can be larger than the
major cusp relations.Comment: 8 pages, 4 figures, accepted for publication in MNRA
Thoughts on Jinan's Establishment of the National Central City of China's Yellow River Basin
The national central city is not a single existence, and it must be based on the national-level urban agglomeration. At the same time, it must have superior geographical advantages and rich natural resources as the basis for development. Urban agglomeration promotes national central cities; on the contrary, national central cities can also drive the common development of urban agglomerations. During the National People’s Congress and National Committee of the Chinese People’s Political Consultative Conference this year, Jinan Municipal Government proposed to create a national central city in the Yellow River Basin as the development goal. In this article, the measures taken by Jinan Municipal Government to create the national central city of the Yellow River Basin are put forward, and the impact of the surrounding urban agglomeration on the development of Jinan is pointed out. Meanwhile, the opportunities and challenges that Jinan will bring to the surrounding urban agglomeration by establishing the national central city are elaborated
Magnification relations of quad lenses and applications on Einstein crosses
In this work, we mainly study the magnification relations of quad lens models
for cusp, fold and cross configurations. By dividing and ray-tracing in
different image regions, we numerically derive the positions and magnifications
of the four images for a point source lying inside of the astroid caustic.
Then, based on the magnifications, we calculate the signed cusp and fold
relations for the singular isothermal elliptical lenses. The signed fold
relation map has positive and negative regions, and the positive region is
usually larger than the negative region as has been confirmed before. It can
also explain that for many observed fold image pairs, the fluxes of the Fermat
minimum images are apt to be larger than those of the saddle images. We define
a new quantity cross relation which describes the magnification discrepancy
between two minimum images and two saddle images. Distance ratio is also
defined as the ratio of the distance of two saddle images to that of two
minimum images. We calculate the cross relations and distance ratios for nine
observed Einstein crosses. In theory, for most of the quad lens models, the
cross relations decrease as the distance ratios increase. In observation, the
cross relations of the nine samples do not agree with the quad lens models very
well, nevertheless, the cross relations of the nine samples do not give obvious
evidence for anomalous flux ratio as the cusp and fold types do. Then, we
discuss several reasons for the disagreement, and expect good consistencies for
more precise observations and better lens models in the future.Comment: 12 pages, 11 figures, accepted for publication in MNRA
The Magnification Invariant of Circularly-symmetric Lens Models
In the context of strong gravitational lensing, the magnification of image is
of crucial importance to constrain various lens models. For several commonly
used quadruple lens models, the magnification invariants, defined as the sum of
the signed magnifications of images, have been analytically derived when the
image multiplicity is a maximum. In this paper, we further study the
magnification of several disk lens models, including (a) exponential disk lens,
(b) Gaussian disk lens, (c) modified Hubble profile lens, and another two of
the popular three-dimensional symmetrical lens model, (d) NFW lens and (e)
Einasto lens. We find that magnification invariant does also exist for each
lens model. Moreover, our results show that magnification invariants can be
significantly changed by the characteristic surface mass density .Comment: 14 pages, 6 figures. Accepted for publication in RA
An Improved Upper Bound for SAT
We show that the CNF satisfiability problem can be solved
time, where is the number of clauses in the formula, improving the known
upper bounds given by Yamamoto 15 years ago and
given by Hirsch 22 years ago. By using an amortized technique and careful case
analysis, we successfully avoid the bottlenecks in previous algorithms and get
the improvement
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