Existence and uniqueness of viscosity solution for Hamilton-Jacobi equation with discontinuous coefficients dependent on time

The main result is a proof of the existence of a unique viscosity solution for Hamilton-Jacobi equation, where the hamiltonian is discontinuous with respect to variable, usually interpreted as the spatial one. Obtained generalized solution is continuous, but not necessarily differentiable.

On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable configurations are generated with positive probability Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.

On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable con gurations are generated with positive probability Lundh calls this percolation di usion. An integral condition for percolation di ffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.

Higher education as formation of the self and citizenship: an ethnography of the University Students from Amman, Jordan

My interest in higher education and citizenship in the Middle East at large and in Jordan in particular is fostered by some of the reflections Eickelman proposed (1992). Being a quite recent phenomenon, intimately linked with the more general topic of state formation it seemed to me more suitable to study it in a little country with a recent history (a field study left almost unexplored until now as far as Jordan is concerned, to the best of my knowledge, since Antoun 1994 focuses on the migration as a quest for higher education). The process of state formation in Jordan is quite studied. I thus intended to study the higher education policies as an attempt both to create a national citizenry and more recently as a way of controlling the more problematic part of the population (youth, which constitutes more than the double of the population. See UNDP and Ministry of Planning 2000). How do the young students enter the university system, and in which way does this system work? How is this system designed, in order to retain social control of the students (since they are usually perceived to be a factor of social and political instability, as in Iran or in Egypt)? Is there any significant difference between different faculties? And if so, why? My conclusions at this stage are that the university system is an integral part of the survival of the regime. The system works quite well, and Jordan has one of the best educational position in the region. Yet there are important distinctions to be made: the access to the better faculties is socially selective while the less valued faculties are left to the poorer and less wealthy youth. This results in a different treatment of the students and of the courses that I analysed. In the better faculties the teaching standards are quite high, and the relationship between professors and students is almost on a same-level base, while in the less privileged faculties the opposite is true. Thus we can observe a concrete politics of divide et impera intended to split the youth in two. For the more privileged there are some freedoms, both within and outside classes, designed I guess at forging them as autonomous individuals. On the opposite the less privileged are kept under tight control, even if also these students are a privileged category among youth at large.

Acute Damage to the Posterior Limb of the Internal Capsule on Diffusion Tensor Tractography as an Early Imaging Predictor of Motor Outcome after Stroke

Background and Purpose Early prediction of motor outcome is of interest in stroke management. We aimed to determine whether lesion location at DTT is predictive of motor outcome after acute stroke and whether this information improves the predictive accuracy of the clinical scores. Methods We evaluated 60 consecutive patients within 12 hours of MCA stroke onset. We used DTT to evaluate CST involvement in the MC and PMC, CS, CR, and PLIC and in combinations of these regions at admission, at day 3, and at day 30. Severity of limb weakness was assessed using the m-NIHSS (5a, 5b, 6a, 6b). We calculated volumes of infarct and FA values in the CST of the pons. Results Acute damage to the PLIC was the best predictor associated with poor motor outcome, axonal damage, and clinical severity at admission (P&.001). There was no significant correlation between acute infarct volume and motor outcome at day 90 (P=.176, r=0.485). The sensitivity, specificity, and positive and negative predictive values of acute CST involvement at the level of the PLIC for 4 motor outcome at day 90 were 73.7%, 100%, 100%, and 89.1%, respectively. In the acute stage, DTT predicted motor outcome at day 90 better than the clinical scores (R2=75.50, F=80.09, P&.001). Conclusions In the acute setting, DTT is promising for stroke mapping to predict motor outcome. Acute CST damage at the level of the PLIC is a significant predictor of unfavorable motor outcome.

On the analysis of travelling waves to a nonlinear flux limited reaction-diffusion equation

In this paper we study the existence and qualitative properties of travelling waves associated to a nonlinear flux limited partial differential equation coupled to a Fisher-Kolmogorov-Petrovskii-Piskunov type reaction term. We prove the existence and uniqueness of finite speed moving fronts of C2 classical regularity, but also the existence of discontinuous entropy travelling wave solutions.

Determinants of the educational use of digital learning materials: The mediating role of self-efficacy, perceived norm and attitude

Initiatives to stimulate the development and propagation of open educational resources (OER) need a sufficiently large community that can be mobilized to participate in this endeavour. Failure to achieve this could lead to underuse of OER. In the context of the Wikiwijs initiative a large scale survey was undertaken amongst primary and secondary school teachers to explore possible determinants of the educational use of digital learning materials (DLMs). Basing on the Integrative Model of Behaviour Prediction it was conjectured that self-efficacy, attitude and perceived norm would take a central role in explaining the intention to use DLMs. Several other predictors were added to the model as well whose effects were hypothesized to be mediated by the three central variables.All conjectured relationships were found using path analysis on survey data from 1484 teachers. Intention to DLMs was most strongly determined by self-efficacy, followed by attitude. ICT proficiency was in its turn the strongest predictor of self-efficacy. Perceived norm played only a limited role in the intention to use DLMs. Concluding, it seems paramount for the success of projects such as Wikiwijs to train teachers in the use of digital learning materials and ICT (e.g. the digital blackboard) and to impact on their attitude.