836 research outputs found
H\"older estimates for parabolic operators on domains with rough boundary
We investigate linear parabolic, second-order boundary value problems with
mixed boundary conditions on rough domains. Assuming only boundedness and
ellipticity on the coefficient function and very mild conditions on the
geometry of the domain, including a very weak compatibility condition between
the Dirichlet boundary part and its complement, we prove H\"older continuity of
the solution in space and time.Comment: 1 figur
Communicating Mental Illness in the Black American Community
Human-human interactions are of central relevance for the success in professional and occupational environments, which also substantially influence quality of life. This is especially true in the case of individuals with high-functioning autism (HFA), who experience deficits in social cognition that often lead to social exclusion and unemployment. Despite good education and high motivation, individuals with HFA do not reach employment rates that are substantially higher than 50 %. This is an alarmingly high rate of unemployment considering that the United Nations have recently emphasized the inclusion of handicapped persons as a mandatory human right. To date, the specific needs of autistic persons with respect to their working environment are largely unexplored. It remains moreover an open question how support systems and activities, including newly developed communication devices for professional environments of individuals with HFA, should look like. The German health and social care systems are not adequately prepared for the proper support of this population. This leads us to suggest that supported employment programs should be developed for adults with HFA that specifically address their needs and requirements. Such programs should comprise (1) the adequate assessment of HFA, including a neuropsychological profile and an individual matching of persons' preferences with requirements of the working place, (2) on-the-job coaching activities that include systematic communication and interaction training, and (3) instruction of non-autistic peers, including colleagues and supervisors, about weaknesses and strengths of HFA
Local freedom in the gravitational field
In a cosmological context, the electric and magnetic parts of the Weyl
tensor, E_{ab} and H_{ab}, represent the locally free curvature - i.e. they are
not pointwise determined by the matter fields. By performing a complete
covariant decomposition of the derivatives of E_{ab} and H_{ab}, we show that
the parts of the derivative of the curvature which are locally free (i.e. not
pointwise determined by the matter via the Bianchi identities) are exactly the
symmetrised trace-free spatial derivatives of E_{ab} and H_{ab} together with
their spatial curls. These parts of the derivatives are shown to be crucial for
the existence of gravitational waves.Comment: New results on gravitational waves included; new references added;
revised version (IOP style) to appear Class. Quantum Gra
Dynamical systems approach to G2 cosmology
In this paper we present a new approach for studying the dynamics of
spatially inhomogeneous cosmological models with one spatial degree of freedom.
By introducing suitable scale-invariant dependent variables we write the
evolution equations of the Einstein field equations as a system of autonomous
partial differential equations in first-order symmetric hyperbolic format,
whose explicit form depends on the choice of gauge. As a first application, we
show that the asymptotic behaviour near the cosmological initial singularity
can be given a simple geometrical description in terms of the local past
attractor on the boundary of the scale-invariant dynamical state space. The
analysis suggests the name ``asymptotic silence'' to describe the evolution of
the gravitational field near the cosmological initial singularity.Comment: 28 pages, 3 tables, 1 *.eps figure, LaTeX2e (10pt), matches version
accepted for publication by Classical and Quantum Gravit
A dynamical system approach to higher order gravity
The dynamical system approach has recently acquired great importance in the
investigation on higher order theories of gravity. In this talk I review the
main results and I give brief comments on the perspectives for further
developments.Comment: 6 pages, 1 figure, 2 tables, talk given at IRGAC 2006, July 200
On the propagation of jump discontinuities in relativistic cosmology
A recent dynamical formulation at derivative level \ptl^{3}g for fluid
spacetime geometries , that employs the concept
of evolution systems in first-order symmetric hyperbolic format, implies the
existence in the Weyl curvature branch of a set of timelike characteristic
3-surfaces associated with propagation speed |v| = \sfrac{1}{2} relative to
fluid-comoving observers. We show it is the physical role of the constraint
equations to prevent realisation of jump discontinuities in the derivatives of
the related initial data so that Weyl curvature modes propagating along these
3-surfaces cannot be activated. In addition we introduce a new, illustrative
first-order symmetric hyperbolic evolution system at derivative level
\ptl^{2}g for baryotropic perfect fluid cosmological models that are
invariant under the transformations of an Abelian isometry group.Comment: 19 pages, 1 table, REVTeX v3.1 (10pt), submitted for publication to
Physical Review D; added Report-No, corrected typo
Isotropic singularity in inhomogeneous brane cosmological models
We discuss the asymptotic dynamical evolution of spatially inhomogeneous
brane-world cosmological models close to the initial singularity. By
introducing suitable scale-invariant dependent variables and a suitable gauge,
we write the evolution equations of the spatially inhomogeneous brane
cosmological models with one spatial degree of freedom as a system of
autonomous first-order partial differential equations. We study the system
numerically, and we find that there always exists an initial singularity, which
is characterized by the fact that spatial derivatives are dynamically
negligible. More importantly, from the numerical analysis we conclude that
there is an initial isotropic singularity in all of these spatially
inhomogeneous brane cosmologies for a range of parameter values which include
the physically important cases of radiation and a scalar field source. The
numerical results are supported by a qualitative dynamical analysis and a
calculation of the past asymptotic decay rates. Although the analysis is local
in nature, the numerics indicates that the singularity is isotropic for all
relevant initial conditions. Therefore this analysis, and a preliminary
investigation of general inhomogeneous () models, indicates that it is
plausible that the initial singularity is isotropic in spatially inhomogeneous
brane-world cosmological models and consequently that brane cosmology naturally
gives rise to a set of initial data that provide the conditions for inflation
to subsequently take place.Comment: 32 pages with 8 pictures. submitted to Class. Quant. Gra
Causal propagation of geometrical fields in relativistic cosmology
We employ the extended 1+3 orthonormal frame formalism for fluid spacetime
geometries , which contains the Bianchi field
equations for the Weyl curvature, to derive a 44-D evolution system of
first-order symmetric hyperbolic form for a set of geometrically defined
dynamical field variables. Describing the matter source fields
phenomenologically in terms of a barotropic perfect fluid, the propagation
velocities (with respect to matter-comoving observers that Fermi-propagate
their spatial reference frames) of disturbances in the matter and the
gravitational field, represented as wavefronts by the characteristic 3-surfaces
of the system, are obtained. In particular, the Weyl curvature is found to
account for two (non-Lorentz-invariant) Coulomb-like characteristic eigenfields
propagating with and four transverse characteristic eigenfields
propagating with , which are well known, and four
(non-Lorentz-invariant) longitudinal characteristic eigenfields propagating
with |v| = \sfrac{1}{2}. The implications of this result are discussed in
some detail and a parallel is drawn to the propagation of irregularities in the
matter distribution. In a worked example, we specialise the equations to
cosmological models in locally rotationally symmetric class II and include the
constraints into the set of causally propagating dynamical variables.Comment: 25 pages, RevTeX (10pt), accepted for publication by Physical Review
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