4,503 research outputs found
Uniqueness of radial solutions for the fractional Laplacian
We prove general uniqueness results for radial solutions of linear and
nonlinear equations involving the fractional Laplacian with for any space dimensions . By extending a monotonicity
formula found by Cabre and Sire \cite{CaSi-10}, we show that the linear
equation in has at most one radial and
bounded solution vanishing at infinity, provided that the potential is a
radial and non-decreasing. In particular, this result implies that all radial
eigenvalues of the corresponding fractional Schr\"odinger operator
are simple. Furthermore, by combining these findings on
linear equations with topological bounds for a related problem on the upper
half-space , we show uniqueness and nondegeneracy of ground
state solutions for the nonlinear equation in for arbitrary space dimensions and all
admissible exponents . This generalizes the nondegeneracy and
uniqueness result for dimension N=1 recently obtained by the first two authors
in \cite{FrLe-10} and, in particular, the uniqueness result for solitary waves
of the Benjamin--Ono equation found by Amick and Toland \cite{AmTo-91}.Comment: 38 pages; revised version; various typos corrected; proof of Lemma
8.1 corrected; discussion of case \kappa_* =1 in the proof of Theorem 2
corrected with new Lemma A.2; accepted for publication in Comm. Pure. Appl.
Mat
Diagnosing space telescope misalignment and jitter using stellar images
Accurate knowledge of the telescope's point spread function (PSF) is
essential for the weak gravitational lensing measurements that hold great
promise for cosmological constraints. For space telescopes, the PSF may vary
with time due to thermal drifts in the telescope structure, and/or due to
jitter in the spacecraft pointing (ground-based telescopes have additional
sources of variation). We describe and simulate a procedure for using the
images of the stars in each exposure to determine the misalignment and jitter
parameters, and reconstruct the PSF at any point in that exposure's field of
view. The simulation uses the design of the SNAP (http://snap.lbl.gov)
telescope. Stellar-image data in a typical exposure determines secondary-mirror
positions as precisely as . The PSF ellipticities and size, which
are the quantities of interest for weak lensing are determined to and accuracies respectively in each exposure,
sufficient to meet weak-lensing requirements. We show that, for the case of a
space telescope, the PSF estimation errors scale inversely with the square root
of the total number of photons collected from all the usable stars in the
exposure.Comment: 20 pages, 6 figs, submitted to PAS
Tradescantia bioassays as monitoring systems for environmental mutagenesis: a review.
Since the early studies on the genetic effects of chemical and physical agents, species and clones of Tradescantia have been used as experimental subjects, by virtue of a series of favorable genetic characteristics. Bearing just six pairs (2n = 12) of large, easily observable chromosomes, cells from almost every part of the plant, from the root tips to the developing pollen tube, yield excellent material for cytogenetic studies. As a consequence of the intensive use of Tradescantia in genetic studies, a series of genetic characteristics have been found that offer opportunities for the detection of agents affecting the stability of the genome. At least five such characteristics have been selected as endpoints for the establishment of assays to evaluate mutagenesis. Three of these, root-tip mitosis, pollen-tube, and microspore mitosis are essentially chromosome aberration assays, wherein one observes and evaluates the visible damage in the chromosomes. A fourth, the stamen-hair mutation assay (Trad-SHM), is a point mutation mitotic assay based on the expression of a recessive gene for flower color in heterozygous plants. The fifth assay is a cytogenetic test based on the formation of micronuclei (Trad-MCN) that result from chromosome breakage in the meiotic pollen mother cells. This article examines the characteristics and fundamentals of the Trad-MCN and the Trad-SHM assays and reviews the results obtained to date with these systems in the assessment of environmental mutagenesis
Relativistic Harmonic Oscillator
We study the semirelativistic Hamiltonian operator composed of the
relativistic kinetic energy and a static harmonic-oscillator potential in three
spatial dimensions and construct, for bound states with vanishing orbital
angular momentum, its eigenfunctions in compact form, i. e., as power series,
with expansion coefficients determined by an explicitly given recurrence
relation. The corresponding eigenvalues are fixed by the requirement of
normalizability of the solutions.Comment: 14 pages, extended discussion of result
Quantized reduction as a tensor product
Symplectic reduction is reinterpreted as the composition of arrows in the
category of integrable Poisson manifolds, whose arrows are isomorphism classes
of dual pairs, with symplectic groupoids as units. Morita equivalence of
Poisson manifolds amounts to isomorphism of objects in this category.
This description paves the way for the quantization of the classical
reduction procedure, which is based on the formal analogy between dual pairs of
Poisson manifolds and Hilbert bimodules over C*-algebras, as well as with
correspondences between von Neumann algebras. Further analogies are drawn with
categories of groupoids (of algebraic, measured, Lie, and symplectic type). In
all cases, the arrows are isomorphism classes of appropriate bimodules, and
their composition may be seen as a tensor product. Hence in suitable categories
reduction is simply composition of arrows, and Morita equivalence is
isomorphism of objects.Comment: 44 pages, categorical interpretation adde
What do aquaporin knockout studies tell us about fluid transport in epithelia?
The investigation of near-isosmotic water transport in epithelia goes back over 100 years; however, debates over mechanism and pathway remain. Aquaporin (AQP) knockouts have been used by various research groups to test the hypothesis of an osmotic mechanism as well as to explore the paracellular versus transcellular pathway debate. Nonproportional reductions in the water permeability of a water-transporting epithelial cell (e.g., a reduction of around 80–90 %) compared to the reduction in overall water transport rate in the knockout animal (e.g., a reduction of 50–60 %) are commonly found. This nonproportionality has led to controversy over whether AQP knockout studies support or contradict the osmotic mechanism. Arguments raised for and against an interpretation supporting the osmotic mechanism typically have partially specified, implicit, or incorrect assumptions. We present a simple mathematical model of the osmotic mechanism with clear assumptions and, for models based on this mechanism, establish a baseline prediction of AQP knockout studies. We allow for deviations from isotonic/isosmotic conditions and utilize dimensional analysis to reduce the number of parameters that must be considered independently. This enables a single prediction curve to be used for multiple epithelial systems. We find that a simple, transcellular-only osmotic mechanism sufficiently predicts the results of knockout studies and find criticisms of this mechanism to be overstated. We note, however, that AQP knockout studies do not give sufficient information to definitively rule out an additional paracellular pathway
Uniqueness and Nondegeneracy of Ground States for in
We prove uniqueness of ground state solutions for the
nonlinear equation in , where
and for and for . Here denotes the fractional Laplacian
in one dimension. In particular, we generalize (by completely different
techniques) the specific uniqueness result obtained by Amick and Toland for
and in [Acta Math., \textbf{167} (1991), 107--126]. As a
technical key result in this paper, we show that the associated linearized
operator is nondegenerate;
i.\,e., its kernel satisfies .
This result about proves a spectral assumption, which plays a central
role for the stability of solitary waves and blowup analysis for nonlinear
dispersive PDEs with fractional Laplacians, such as the generalized
Benjamin-Ono (BO) and Benjamin-Bona-Mahony (BBM) water wave equations.Comment: 45 page
Quantum pathology of static internal imperfections in flawed quantum computers
Even in the absence of external influences the operability of a quantum
computer (QC) is not guaranteed because of the effects of residual one- and
two-body imperfections. Here we investigate how these internal flaws affect the
performance of a quantum controlled-NOT (CNOT) gate in an isolated flawed QC.
First we find that the performance of the CNOT gate is considerably better when
the two-body imperfections are strong. Secondly, we find that the largest
source of error is due to a coherent shift rather than decoherence or
dissipation. Our results suggest that the problem of internal imperfections
should be given much more attention in designing scalable QC architectures
THE PREVALENCE AND CAUSE OF NON-CONTACT INJURY MECHANISMS IN U.S. MEN’S RUGBY-7S
The aim of this study was to prospectively report non-contact injury incidence and causes in U.S. men’s Rugby-7s players (n=446) over 2010-2015, using the Rugby Injury Survey & Evaluation (RISE) methodology. Non-contact injuries (time-loss 25%; medical attention 75%) had higher rates among backs (62%; 28.4/1000ph) than forwards (38%; 23.2/1000ph; RR:1.22; p=0.05). Non-contact injuries resulted in an average of 48.7days (d) absence from sport (classic non-contact 48.1d; other non-contact 77.0d). Acute injuries (85%) were most common during attempts to elude a tackle (31%) and in running/open play (48% overall; from 35% in 2010, 41% in 2011, 52% in 2012, 43% in 2013, 46% in 2014, 70% in 2015). Most non-contact injuries (44%) occurred during the first two tournament matches. These results provide much needed data on Rugby-7s, impacting emerging countries
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