1,678 research outputs found
Correctors for some nonlinear monotone operators
In this paper we study homogenization of quasi-linear partial differential
equations of the form -\mbox{div}\left( a\left( x,x/\varepsilon _h,Du_h\right)
\right) =f_h on with Dirichlet boundary conditions. Here the
sequence tends to as
and the map is periodic in monotone in
and satisfies suitable continuity conditions. We prove that
weakly in as where
is the solution of a homogenized problem of the form -\mbox{div}\left(
b\left( x,Du\right) \right) =f on We also derive an explicit
expression for the homogenized operator and prove some corrector results,
i.e. we find such that in
Lower and upper estimates on the excitation threshold for breathers in DNLS lattices
We propose analytical lower and upper estimates on the excitation threshold
for breathers (in the form of spatially localized and time periodic solutions)
in DNLS lattices with power nonlinearity. The estimation depending explicitly
on the lattice parameters, is derived by a combination of a comparison argument
on appropriate lower bounds depending on the frequency of each solution with a
simple and justified heuristic argument. The numerical studies verify that the
analytical estimates can be of particular usefulness, as a simple analytical
detection of the activation energy for breathers in DNLS lattices.Comment: 10 pages, 3 figure
Some homogenization and corrector results for nonlinear monotone operators
This paper deals with the limit behaviour of the solutions of quasi-linear
equations of the form \ \ds -\limfunc{div}\left(a\left(x, x/{\varepsilon
_h},Du_h\right)\right)=f_h on with Dirichlet boundary conditions.
The sequence tends to and the map is
periodic in , monotone in and satisfies suitable continuity
conditions. It is proved that weakly in , where is the solution of a homogenized problem \
-\limfunc{div}(b(x,Du))=f on . We also prove some corrector results,
i.e. we find such that in
Far-from-constant mean curvature solutions of Einstein's constraint equations with positive Yamabe metrics
In this article we develop some new existence results for the Einstein
constraint equations using the Lichnerowicz-York conformal rescaling method.
The mean extrinsic curvature is taken to be an arbitrary smooth function
without restrictions on the size of its spatial derivatives, so that it can be
arbitrarily far from constant. The rescaled background metric belongs to the
positive Yamabe class, and the freely specifiable part of the data given by the
traceless-transverse part of the rescaled extrinsic curvature and the matter
fields are taken to be sufficiently small, with the matter energy density not
identically zero. Using topological fixed-point arguments and global barrier
constructions, we then establish existence of solutions to the constraints. Two
recent advances in the analysis of the Einstein constraint equations make this
result possible: A new type of topological fixed-point argument without
smallness conditions on spatial derivatives of the mean extrinsic curvature,
and a new construction of global super-solutions for the Hamiltonian constraint
that is similarly free of such conditions on the mean extrinsic curvature. For
clarity, we present our results only for strong solutions on closed manifolds.
However, our results also hold for weak solutions and for other cases such as
compact manifolds with boundary; these generalizations will appear elsewhere.
The existence results presented here for the Einstein constraints are
apparently the first such results that do not require smallness conditions on
spatial derivatives of the mean extrinsic curvature.Comment: 4 pages, no figures, accepted for publication in Physical Review
Letters. (Abstract shortenned and other minor changes reflecting v4 version
of arXiv:0712.0798
Physical Properties of OSIRIS-REx Target Asteroid (101955) 1999 RQ36 derived from Herschel, ESO-VISIR and Spitzer observations
In September 2011, the Herschel Space Observatory performed an observation
campaign with the PACS photometer observing the asteroid (101955) 1999 RQ36 in
the far infrared. The Herschel observations were analysed, together with ESO
VLT-VISIR and Spitzer-IRS data, by means of a thermophysical model in order to
derive the physical properties of 1999 RQ36. We find the asteroid has an
effective diameter in the range 480 to 511 m, a slightly elongated shape with a
semi-major axis ratio of a/b=1.04, a geometric albedo of 0.045 +0.015/-0.012,
and a retrograde rotation with a spin vector between -70 and -90 deg ecliptic
latitude. The thermal emission at wavelengths below 12 micron -originating in
the hot sub-solar region- shows that there may be large variations in roughness
on the surface along the equatorial zone of 1999 RQ36, but further measurements
are required for final proof. We determine that the asteroid has a
disk-averaged thermal inertia of Gamma = 650 Jm-2s-0.5K-1 with a 3-sigma
confidence range of 350 to 950 Jm-2s-0.5K-1, equivalent to what is observed for
25143 Itokawa and suggestive that 1999 RQ36 has a similar surface texture and
may also be a rubble-pile in nature. The low albedo indicates that 1999 RQ36
very likely contains primitive volatile-rich material, consistent with its
spectral type, and that it is an ideal target for the OSIRIS-REx sample return
mission.Comment: Accepted for publication in Astronomy & Astrophysics, 9 pages, 7
figure
Detailed Spectroscopic and Photometric Analysis of DQ White Dwarfs
We present an analysis of spectroscopic and photometric data for cool DQ
white dwarfs based on improved model atmosphere calculations. In particular, we
revise the atmospheric parameters of the trigonometric parallax sample of
Bergeron et al.(2001), and discuss the astrophysical implications on the
temperature scale and mean mass, as well as the chemical evolution of these
stars. We also analyze 40 new DQ stars discovered in the first data release of
the Sloan Digital Sky Survey.Comment: 6 pages,3 figures, 14th European Workshop on White Dwarfs, ASP
Conference Series, in pres
Persistent clinical efficacy and safety of anti-tumour necrosis factor \textgreeka therapy with infliximab in patients with ankylosing spondylitis over 5 years: evidence for different types of response
Background: There is insufficient evidence for the long-term efficacy and safety of anti-tumour necrosis factor therapy in patients with ankylosing spondylitis (AS). This is the first report on the treatment with infliximab over 5 years.Methods: As part of a multicentre randomised trial, 69 patients with active AS at baseline (BL) have been continuously treated with infliximab (5 mg/kg i.v. every 6 weeks)---except for a short discontinuation after 3 years (FU1). The primary outcome of this extension was remission according to the ASsessment in Ankylosing Spondylitis (ASAS) criteria at the end of year 5 of the study (FU2).Results: Of the 43 patients who completed year 3, 42 agreed to continue, 38 of which (90.5%) finished year 5 (55% of 69 initially). Partial clinical remission was achieved in 13 of 38 patients (34.2%) at FU1 and FU2. At FU2, the mean Bath Ankylosing Spondylitis Disease Activity Index (BASDAI) was 2.5±1.9 (BL:6.4, FU1:2.5). BASDAI values <4 were seen in 79% of patients at both, FU1 and FU2. ASAS 20% and 40% responses were seen in 32 (84%) and 24 (63%) patients at FU2, respectively. Most patients classified as non-responders at FU2 were part-time responders, as all but one patient achieved an ASAS 20% response at least once within the last 2 years. Three types of responders were identified. No major side effects occurred during years 4 and 5 of infliximab therapy.Conclusions: Infliximab is safe and efficacious in AS patients over 5 years. The majority of the patients remained on treatment and had rather persistent levels of low disease activity. Different response types could be identified
Detection of Chlamydia trachomatis-DNA in synovial fluid: evaluation of the sensitivity of different DNA extraction methods and amplification systems
Lagrange Multipliers in Infinite-Dimensional Systems, Methods of
International audienceThis entry will describe Lagrange multipliers method using a formulation which is valid for infinite-dimensional dynamical systems. The method of Lagrange multipliers is employed to deal with systems subject to constraints. The theoretical foundations of this method are presented, and a proof of the main theorem is illustrated for the relevant case of constraints defined on a Banach vector space
- âŠ