542 research outputs found
The inverse spectral problem for the discrete cubic string
Given a measure on the real line or a finite interval, the "cubic string"
is the third order ODE where is a spectral parameter. If
equipped with Dirichlet-like boundary conditions this is a nonselfadjoint
boundary value problem which has recently been shown to have a connection to
the Degasperis-Procesi nonlinear water wave equation. In this paper we study
the spectral and inverse spectral problem for the case of Neumann-like boundary
conditions which appear in a high-frequency limit of the Degasperis--Procesi
equation. We solve the spectral and inverse spectral problem for the case of
being a finite positive discrete measure. In particular, explicit
determinantal formulas for the measure are given. These formulas generalize
Stieltjes' formulas used by Krein in his study of the corresponding second
order ODE .Comment: 24 pages. LaTeX + iopart, xypic, amsthm. To appear in Inverse
Problems (http://www.iop.org/EJ/journal/IP
Fibrils from Designed Non-Amyloid-Related Synthetic Peptides Induce AA-Amyloidosis during Inflammation in an Animal Model
Background: Mouse AA-amyloidosis is a transmissible disease by a prion-like mechanism where amyloid fibrils act by seeding. Synthetic peptides with no amyloid relationship can assemble into amyloid-like fibrils and these may have seeding capacity for amyloid proteins. Principal Findings: Several synthetic peptides, designed for nanotechnology, have been examined for their ability to produce fibrils with Congo red affinity and concomitant green birefringence, affinity for thioflavin S and to accelerate AAamyloidosis in mice. It is shown that some amphiphilic fibril-forming peptides not only produced Congo red birefringence and showed affinity for thioflavin S, but they also shortened the lag phase for systemic AA-amyloidosis in mice when they were given intravenously at the time of inflammatory induction with silver nitride. Peptides, not forming amyloid-like fibrils, did not have such properties. Conclusions: These observations should caution researchers and those who work with synthetic peptides and thei
The Degasperis-Procesi equation with self-consistent sources
The Degasperis-Procesi equation with self-consistent sources(DPESCS) is
derived. The Lax representation and the conservation laws for DPESCS are
constructed. The peakon solution of DPESCS is obtained.Comment: 15 page
On the tau-functions of the Degasperis-Procesi equation
The DP equation is investigated from the point of view of
determinant-pfaffian identities. The reciprocal link between the
Degasperis-Procesi (DP) equation and the pseudo 3-reduction of the
two-dimensional Toda system is used to construct the N-soliton solution of the
DP equation. The N-soliton solution of the DP equation is presented in the form
of pfaffian through a hodograph (reciprocal) transformation. The bilinear
equations, the identities between determinants and pfaffians, and the
-functions of the DP equation are obtained from the pseudo 3-reduction of
the two-dimensional Toda system.Comment: 27 pages, 4 figures, Journal of Physics A: Mathematical and
Theoretical, to be publishe
Type Ia Supernova Explosion Models
Because calibrated light curves of Type Ia supernovae have become a major
tool to determine the local expansion rate of the Universe and also its
geometrical structure, considerable attention has been given to models of these
events over the past couple of years. There are good reasons to believe that
perhaps most Type Ia supernovae are the explosions of white dwarfs that have
approached the Chandrasekhar mass, M_ch ~ 1.39 M_sun, and are disrupted by
thermonuclear fusion of carbon and oxygen. However, the mechanism whereby such
accreting carbon-oxygen white dwarfs explode continues to be uncertain. Recent
progress in modeling Type Ia supernovae as well as several of the still open
questions are addressed in this review. Although the main emphasis will be on
studies of the explosion mechanism itself and on the related physical
processes, including the physics of turbulent nuclear combustion in degenerate
stars, we also discuss observational constraints.Comment: 38 pages, 4 figures, Annual Review of Astronomy and Astrophysics, in
pres
Projective dynamics and first integrals
We present the theory of tensors with Young tableau symmetry as an efficient
computational tool in dealing with the polynomial first integrals of a natural
system in classical mechanics. We relate a special kind of such first
integrals, already studied by Lundmark, to Beltrami's theorem about
projectively flat Riemannian manifolds. We set the ground for a new and simple
theory of the integrable systems having only quadratic first integrals. This
theory begins with two centered quadrics related by central projection, each
quadric being a model of a space of constant curvature. Finally, we present an
extension of these models to the case of degenerate quadratic forms.Comment: 39 pages, 2 figure
Constrained Simulations of the Real Universe: the Local Supercluster
We present cosmological simulations which closely mimic the real Universe
within 100Mpc of the Local Group. The simulations, called Constrained
Simulations, reproduce the large-scale density field with major nearby
structures, including the Local Group, the Coma and Virgo clusters, the Great
Attractor, the Perseus-Pices, and the Local Supercluster, in approximately
correct locations. The MARK III survey of peculiar velocities of the observed
structures inside 80Mpc/h sphere is used to constrain the initial conditions.
Fourier modes on scales larger then 5Mpc/h are dominated by the constraints,
while small scale waves are random. The main aim of this paper is the structure
of the Local Supercluster (LSC; 30Mpc/h around the Virgo cluster) and the Local
Group environment. We find that at the current epoch most of the mass
(7.5e14Msun/h) of the LSC is located in a filament roughly centered on the
Virgo cluster and extending over 40Mpc/h. The simulated Local Group (LG) is
located in an adjacent smaller filament, which is not a part of the main body
of the LSC, and has a peculiar velocity of 250kms toward the Virgo cluster. The
peculiar velocity field in the LSC region is complicated and is drastically
different from the field assumed in the Virgocentric infall models. The
peculiar velocity flow in the vicinity of the LG in the simulation is ``cold'':
the peculiar line-of-sight velocity dispersion within 7Mpc/h of the LG is less
than 60km/s, comparable to the observed velocity dispersion of nearby galaxies.Comment: 22 pages, 9 figures, submitted to ApJ, high resolution version is
available at http://astro.nmsu.edu/~aklypin/HOFFMA
Midterm results of the Ross procedure in children: an appraisal of the subannular implantation with interrupted sutures technique
OBJECTIVES: The support of the pulmonary autograft root by the fibromuscular left ventricular outflow tract is emphasized to address the concern related to the dilatation of the pulmonary autograft structures in the paediatric population.
METHODS: This retrospective study analyses the outcomes of 75 children who were operated between 1998 and 2012 with the subannular interrupted sutures technique at a median age of 10.2 years (range, 5.3 months–18.0 years). Median follow-up time was 5.2 years (range, 3 days–13.2 years).
RESULTS: There were no deaths, but there were 3 reinterventions on the autograft for regurgitation and 2 resections of left ventricular outflow tract obstruction. There was no significant autograft stenosis, and freedom from moderate-to-severe regurgitation was 95% (95% confidence interval: 89–100) and 88% (95% confidence interval: 77–99) at 5 and 10 years, respectively. Median z-scores at the latest follow-up examination were, at the annulus, 0.31 [interquartile range (IQR) = −0.81 to 1.2]; at the sinus of Valsalva, 2.7 (IQR = 1.5–3.5); and at the sinotubular junction, 3.1 (IQR = 1.7–4.2). The correlation between z-scores and time after the operation was negative at the level of the annulus (r = −0.29, P = 0.034) but positive at the level of the sinus (r = +0.37, P = 0.005) and the sinotubular junction (r = +0.26, P = 0.068). The median rate of change in the z-score at the annulus was low, 0.065 z-score/year (IQR = −0.13 to 0.43).
CONCLUSIONS: The subannular interrupted sutures implantation technique is associated with acceptable risks and, in the midterm, delivers limited annular dilatation, autograft regurgitation and delayed need for autograft reintervention
Projective dynamics and classical gravitation
Given a real vector space V of finite dimension, together with a particular
homogeneous field of bivectors that we call a "field of projective forces", we
define a law of dynamics such that the position of the particle is a "ray" i.e.
a half-line drawn from the origin of V. The impulsion is a bivector whose
support is a 2-plane containing the ray. Throwing the particle with a given
initial impulsion defines a projective trajectory. It is a curve in the space
of rays S(V), together with an impulsion attached to each ray. In the simplest
example where the force is identically zero, the curve is a straight line and
the impulsion a constant bivector. A striking feature of projective dynamics
appears: the trajectories are not parameterized.
Among the projective force fields corresponding to a central force, the one
defining the Kepler problem is simpler than those corresponding to other
homogeneities. Here the thrown ray describes a quadratic cone whose section by
a hyperplane corresponds to a Keplerian conic. An original point of view on the
hidden symmetries of the Kepler problem emerges, and clarifies some remarks due
to Halphen and Appell. We also get the unexpected conclusion that there exists
a notion of divergence-free field of projective forces if and only if dim V=4.
No metric is involved in the axioms of projective dynamics.Comment: 20 pages, 4 figure
When Is a Principal Charged With an Agent’s Knowledge?
Question: Detecting species presence in vegetation and making visual assessment of abundances involve a certain amount of skill, and therefore subjectivity. We evaluated the magnitude of the error in data, and its consequences for evaluating temporal trends. Location: Swedish forest vegetation. Methods: Vegetation data were collected independently by two observers in 342 permanent 100-m2 plots in mature boreal forests. Each plot was visited by one observer from a group of 36 and one of two quality assessment observers. The cover class of 29 taxa was recorded, and presence/absence for an additional 50. Results: Overall, one third of each occurrence was missed by one of the two observers, but with large differences among species. There were more missed occurrences at low abundances. Species occurring at low abundance when present tended to be frequently overlooked. Variance component analyses indicated that cover data on 5 of 17 species had a significant observer bias. Observer-explained variance was < 10% in 15 of 17 species. Conclusion: The substantial number of missed occurrences suggests poor power in detecting changes based on presence/absence data. The magnitude of observer bias in cover estimates was relatively small, compared with random error, and therefore potentially analytically tractable. Data in this monitoring system could be improved by a more structured working model during field work.Original publication: Milberg, P., Bergstedt, J., Fridman, J., Odell, G & Westerberg, L., Systematic and random variation in vegetation monitoring data, 2008, Journal of Vegetation Science, (19), 633-644. http://dx.doi.org/10.3170/2008-8-18423. Copyright: Opulus Press, http://www.opuluspress.se/index.ph
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