Asymptotic behavior and uniqueness for an ultrahyperbolic equation with variable coefficients

AbstractThis paper describes the asymptotic behavior of solutions of a class of semilinear ultrahyperbolic equations with variable coefficients. One consequence of the general analysis is a uniqueness theorem for a mixed boundary-value problem. Another demonstrates unique continuation at infinity. These results extend previous work by M. H. Protter, [Asymptotic decay for ultrahyperbolic operators, in “Contributions to Analysis” (Lars Ahlfors et al., Eds.), Academic Press, New York, 1974], and A. C. Murray and M. M. Protter, [Indiana U. Math. J. 24 (1974), 115–130], on a more restricted class of equations

A Randomized Controlled Trial on Very Early Speech and Language Therapy in Acute Stroke Patients with Aphasia

Background: Aphasia affects one third of acute stroke patients. There is a considerable spontaneous recovery in aphasia, but impaired communication ability remains a great problem. Communication difficulties are an impediment to rehabilitation. Early treatment of the language deficits leading to increased communication ability would improve rehabilitation. The aim of this study is to elucidate the efficacy of very early speech and language therapy (SLT) in acute stroke patients with aphasia. Methods: A prospective, open, randomized, controlled trial was carried out with blinded endpoint evaluation of SLT, starting within 2 days of stroke onset and lasting for 21 days. 123 consecutive patients with acute, first-ever ischemic stroke and aphasia were randomized. The SLT treatment was Language Enrichment Therapy, and the aphasia tests used were the Norsk grunntest for afasi (NGA) and the Amsterdam-Nijmegen everyday language test (ANELT), both performed by speech pathologists, blinded for randomization. Results: The primary outcome, as measured by ANELT at day 21, was 1.3 in the actively treated patient group and 1.2 among controls. NGA led to similar results in both groups. Patients with a higher level of education (>12 years) improved more on ANELT by day 21 than those with Conclusions: Very early intensive SLT with the Language Enrichment Therapy program over 21 days had no effect on the degree of aphasia in unselected acute aphasic stroke patients. In aphasic patients with more fluency, SLT resulted in a significant improvement as compared to controls. A higher educational level of >12 years was beneficial

Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold

Ridge Formation and De-Spinning of Iapetus via an Impact-Generated Satellite

We present a scenario for building the equatorial ridge and de-spinning Iapetus through an impact-generated disk and satellite. This impact puts debris into orbit, forming a ring inside the Roche limit and a satellite outside. This satellite rapidly pushes the ring material down to the surface of Iapetus, and then itself tidally evolves outward, thereby helping to de-spin Iapetus. This scenario can de-spin Iapetus an order of magnitude faster than when tides due to Saturn act alone, almost independently of its interior geophysical evolution. Eventually, the satellite is stripped from its orbit by Saturn. The range of satellite and impactor masses required is compatible with the estimated impact history of Iapetus.Comment: 19 pages, 3 figures; Icarus, in pres

The SuperCOSMOS Sky Survey. Paper III: Astrometry

In this, the third in a series of three papers concerning the SuperCOSMOS Sky Survey, we describe the astrometric properties of the database. We describe the algorithms employed in the derivation of the astrometric parameters of the data, and demonstrate their accuracies by comparison with external datasets using the first release of data, the South Galactic Cap survey. We show that the celestial coordinates, which are tied to the International Celestial Reference Frame via the Tycho-2 reference catalogue, are accurate to better than +/- 0.2 arcsec at J,R=19,18 rising to +/- 0.3 arcsec at J,R=22,21 with positional dependent systematic effects from bright to faint magnitudes at the +/- 0.1 arcsec level. The proper motion measurements are shown to be accurate to typically +/- 10 mas/yr at J,R=19,18 rising to +/- 50 mas/yr at J,R=22,21 and are tied to zero using the extragalactic reference frame. We show that the zeropoint errors in the proper motions are 17 and are no larger than 10 mas/yr for R < 17 mas/yr.Comment: 15 pages, 12 figures; accepted for publication in MNRA

Frozen spatial chaos induced by boundaries

We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion equation in a two-dimensional undulated domain. Concepts from the theory of dynamical systems, and a transverse-single-mode approximation are used to describe the spatially chaotic structures.Comment: 9 pages, 6 figures, submitted for publication; for related work visit http://www.imedea.uib.es/~victo

Topological Defects, Orientational Order, and Depinning of the Electron Solid in a Random Potential

We report on the results of molecular dynamics simulation (MD) studies of the classical two-dimensional electron crystal in the presence disorder. Our study is motivated by recent experiments on this system in modulation doped semiconductor systems in very strong magnetic fields, where the magnetic length is much smaller than the average interelectron spacing $a_0$, as well as by recent studies of electrons on the surface of helium. We investigate the low temperature state of this system using a simulated annealing method. We find that the low temperature state of the system always has isolated dislocations, even at the weakest disorder levels investigated. We also find evidence for a transition from a hexatic glass to an isotropic glass as the disorder is increased. The former is characterized by quasi-long range orientational order, and the absence of disclination defects in the low temperature state, and the latter by short range orientational order and the presence of these defects. The threshold electric field is also studied as a function of the disorder strength, and is shown to have a characteristic signature of the transition. Finally, the qualitative behavior of the electron flow in the depinned state is shown to change continuously from an elastic flow to a channel-like, plastic flow as the disorder strength is increased.Comment: 31 pages, RevTex 3.0, 15 figures upon request, accepted for publication in Phys. Rev. B., HAF94MD