4,822 research outputs found
Nonexistence of self-similar singularities for the 3D incompressible Euler equations
We prove that there exists no self-similar finite time blowing up solution to
the 3D incompressible Euler equations. By similar method we also show
nonexistence of self-similar blowing up solutions to the divergence-free
transport equation in . This result has direct applications to the
density dependent Euler equations, the Boussinesq system, and the
quasi-geostrophic equations, for which we also show nonexistence of
self-similar blowing up solutions.Comment: This version refines the previous one by relaxing the condition of
compact support for the vorticit
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Ipilimumab and Nivolumab in Rare Tumors S1609: Neuroendocrine-Response.
The Cosmic Lens All-Sky Survey parent population - I. Sample selection and number counts
We present the selection of the Jodrell Bank Flat-spectrum (JBF) radio source
sample, which is designed to reduce the uncertainties in the Cosmic Lens
All-Sky Survey (CLASS) gravitational lensing statistics arising from the lack
of knowledge about the parent population luminosity function. From observations
at 4.86 GHz with the Very Large Array, we have selected a sample of 117
flat-spectrum radio sources with flux densities greater than 5 mJy. These
sources were selected in a similar manner to the CLASS complete sample and are
therefore representative of the parent population at low flux densities. The
vast majority (~90 per cent) of the JBF sample are found to be compact on the
arcsecond scales probed here and show little evidence of any extended radio jet
emission. Using the JBF and CLASS complete samples we find the differential
number counts slope of the parent population above and below the CLASS 30 mJy
flux density limit to be -2.07+/-0.02 and -1.96+/-0.12, respectively.Comment: 10 pages, 4 figures, accepted for publication in MNRA
School Counseling Toward a Mission of “IB for All”
Although the International Baccalaureate Organization (IBO) recognizes the importance of school counselors, there is limited guidance about the expectations and roles of school counselors in serving the diverse needs of students in IB schools. With the IBO’s movement toward a mission of “IB for All” to address equitable access to academic rigor, this also aligns with school counselors’ ethical responsibilities as advocates, collaborators, and leaders to promote access and equity for all students. The authors (a) highlight the work of one school counseling program that developed and implemented initiatives, using the U.S.-based ASCA National Model (ASCA, 2019a) as a framework, to increase access to the IB program for diverse students and families; and (b) articulate the potential roles of school counselors in promoting students’ academic, social and emotional, and postsecondary development and trajectories from grades nine through 12 in the IB Middle Years and Diploma Programs
Gravitational Lensing by Power-Law Mass Distributions: A Fast and Exact Series Approach
We present an analytical formulation of gravitational lensing using familiar
triaxial power-law mass distributions, where the 3-dimensional mass density is
given by . The deflection angle and magnification factor are
obtained analytically as Fourier series. We give the exact expressions for the
deflection angle and magnification factor. The formulae for the deflection
angle and magnification factor given in this paper will be useful for numerical
studies of observed lens systems. An application of our results to the Einstein
Cross can be found in Chae, Turnshek, & Khersonsky (1998). Our series approach
can be viewed as a user-friendly and efficient method to calculate lensing
properties that is better than the more conventional approaches, e.g.,
numerical integrations, multipole expansions.Comment: 24 pages, 3 Postscript figures, ApJ in press (October 10th
HST Observations of the Gravitationally Lensed Cloverleaf Broad Absorption Line QSO H1413+1143: Modeling the Lens
We investigate gravitational lens models for the quadruply-lensed Cloverleaf
BAL QSO H1413+1143 based on the HST WFPC/WFPC2 astrometric and photometric data
of the system by Turnshek et al. and the HST NICMOS-2 data by Falco et al. The
accurate image positions and the dust-extinction-corrected relative
amplifications, along with a possible detection of the lensing galaxy in the
infrared, permit more accurate lens models than were previously possible. While
more recent models are qualitatively consistent with the HST data, none of the
previous models considered the dust-extinction-corrected relative
amplifications of the image components. We use the power-law elliptical mass
model to fit the HST data. We find that a single elliptical galaxy perturbed by
an external shear can fit the image positions within the observational
uncertainties; however, the predicted relative magnifications are only roughly
consistent with the observational relative amplifications. We find that a
primary galaxy combined with a secondary galaxy in the vicinity of the
Cloverleaf or a cluster centered (south-)west of the Cloverleaf can fit both
the image positions and relative amplifications within the observational
uncertainties. We discuss future observations which could be used to test
and/or further constrain lens models of the Cloverleaf.Comment: 23 pages (in aaspp.sty) including 5 tables and 3 figures, Accepted
for publication in the Astrophysical Journa
On formation of a locally self-similar collapse in the incompressible Euler equations
The paper addresses the question of existence of a locally self-similar
blow-up for the incompressible Euler equations. Several exclusion results are
proved based on the -condition for velocity or vorticity and for a range
of scaling exponents. In particular, in dimensions if in self-similar
variables and u \sim \frac{1}{t^{\a/(1+\a)}}, then the blow-up
does not occur provided \a >N/2 or -1<\a\leq N/p. This includes the
case natural for the Navier-Stokes equations. For \a = N/2 we exclude
profiles with an asymptotic power bounds of the form |y|^{-N-1+\d} \lesssim
|u(y)| \lesssim |y|^{1-\d}. Homogeneous near infinity solutions are eliminated
as well except when homogeneity is scaling invariant.Comment: A revised version with improved notation, proofs, etc. 19 page
B0850+054: a new gravitational lens system from CLASS
We report the discovery of a new gravitational lens system from the CLASS
survey. Radio observations with the VLA, the WSRT and MERLIN show that the
radio source B0850+054 is comprised of two compact components with identical
spectra, a separation of 0.7 arcsec and a flux density ratio of 6:1. VLBA
observations at 5 GHz reveal structures that are consistent with the
gravitational lens hypothesis. The brighter of the two images is resolved into
a linear string of at least six sub-components whilst the weaker image is
radially stretched towards the lens galaxy. UKIRT K-band imaging detects an
18.7 mag extended object, but the resolution of the observations is not
sufficient to resolve the lensed images and the lens galaxy. Mass modelling has
not been possible with the present data and the acquisition of high-resolution
optical data is a priority for this system.Comment: 5 pages, 4 figures, accepted for publication in MNRA
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