The Institute for Global Studies (IGS) at Claremont High School in Victoria, Canada is a distinctive local example of “transformative education” that features a transdisciplinary, problem-based and globally oriented program within the public secondary school system. Launched in 2012, and arising from earlier pioneering courses in global studies, the IGS has now graduated two cohorts, and has led the founding educators to raise questions about which aspects of the students’ experience were thought to be most important after graduation and what graduates did with the skills they acquired. Part 1 is an extensive description of the background experience of the main founding educator that led to the creation of the original global studies course, and eventually the IGS itself. Part 2, the study itself, includes a review of relevant literature. It draws upon a range of writings about transformative education, including reviews of “whole school approaches to sustainability”. Relatively few systematic evaluations of these programs were found. A recent study from Bangladesh evaluated the effect of a climate change curriculum using a randomized cluster design. It demonstrated significant increases in relevant knowledge gain by students using the government recommended curriculum. The research question in this study was: “What impact has Global Studies/Global Solutions had on students who have taken it and what will they do with the skills they have acquired? Semi-structured interviews were conducted with eight (8) program graduates, using a set of standard questions as a guide. Study participants were selected from a pool of graduates by an independent researcher, to ensure a range of views, taking into account gender diversity, ethnic diversity, experience with both programs (Global studies and IGS), and post-program experiences. Research findings about program impact included both expected and unexpected results. Expected impacts included the transformative nature of the learning, the positive (hopeful) experience itself, and the effectiveness of the interdisciplinary, problem-solving approach. Unexpected impacts included the power of collaborative learning, and the value of guest speakers from various backgrounds who served as powerful role models. Regarding how graduates used what they learned, this included the further application of interdisciplinary learning and problem solving at a university level, and increased confidence that they could “make a difference”. The experience also guided career directions--for example, in the choice of university study programs. One graduate is volunteering with a non-government organization at a rural school in a low-income setting. Another graduate, while not going on to tertiary education, is using the experience to guide his work vocation. In summary, the global studies/IGS program has had important impacts on graduates, both expected and unexpected. Graduates use distinctive learning skills in subsequent university studies. For some the experience influenced specific career directions. / Graduate

In this paper, a global existence result of smooth solutions to the multidimen- sional nonisentropic hydrodynamic model for semiconductors is proved, under the assumption that the initial data is a perturbation of the stationary solutions for the thermal equilibrium state. The resulting evolutionary solutions converge to the stationary solutions in time asymptotically exponentially fast.

We study stochastic heat equations of the forms $[\partial_t u-\sL u]\d t\d x=\lambda\int_\R\sigma(u,h)\tilde{N}(\d t,\d x,\d h),$ and $[\partial_t u-\sL u]\d t\d x=\lambda\int_{\R^d}\sigma(u,h)N(\d t,\d x,\d h)$. Here, $u(0,x)=u_0(x)$ is a non-random initial function, $N$ a Poisson random measure with its intensity $\d t\d x\nu(\d h)$ and $\nu(\d h)$ a L\'vy measure; $\tilde$ is the compensated Poisson random measure and $\sL$ a generator of a L\'{e}vy process. The function $\sigma:\R\rightarrow\R$ is Lipschitz continuous and $\lambda>0$ the noise level. The above discontinuous noise driven equations are not always easy to handle. They are discontinuous analogues of the equation introduced in \cite{Foondun} and also more general than those considered in \cite{Saint}. We do not only compare the growth moments of the two equations with each other but also compare them with growth moments of the class of equations studied in \cite{Foondun}. Some of our results are significant generalisations of those given in \cite{Saint} while the rest are completely new. Second and first growth moments properties and estimates were obtained under some linear growth conditions on $\sigma$. We also consider $\sL:=-(-\Delta)^{\alpha/2}$, the generator of $\alpha$-stable processes and use some explicit bounds on its corresponding fractional heat kernel to obtain more precise results. We also show that when the solutions satisfy some non-linear growth conditions on $\sigma$, the solutions cease to exist for both compensated and non-compensated noise terms for different conditions on the initial function $u_0(x)$. We consider also fractional heat equations of the form $ \partial_t u(t,x)=-(-\Delta)^{\alpha/2}u(t,x)+\lambda\sigma(u(t,x)\dot{F}(t,x),\,\, \text{for}\,\, x\in\R^d,\,t>0,\,\alpha\in(1,2),$ where $\dot{F}$ denotes the Gaussian coloured noise. Under suitable assumptions, we show that the second moment $\E|u(t,x)|^2$ of the solution grows exponentially with time. In particular we give an affirmative answer to the open problem posed in \cite{Conus3}: given $u_0$ a positive function on a set of positive measure, does $\sup_{x\in\R^d}\E|u(t,x)|^2$ grow exponentially with time? Consequently we give the precise growth rate with respect to the parameter $\lambda$.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-07-22T13:22:56Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese-Ricardo-Castillo.pdf: 814247 bytes, checksum: 0f3a9a10694a3324cae6464d5e29a2f6 (MD5) / Made available in DSpace on 2016-07-22T13:22:56Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese-Ricardo-Castillo.pdf: 814247 bytes, checksum: 0f3a9a10694a3324cae6464d5e29a2f6 (MD5) Previous issue date: 2016-02-17 / Estudamos condições de existência e não existência de soluções globais para um sistema acoplado de equações parabólicas não lineares e para um problema parabólico com expoente variável. Em ambos os casos, consideramos um domínio arbitrário de RN com fronteira regular e com condições de Dirichlet na fronteira. Como consequência destes resultados é possível determinar o coe ciente de Fujita destes problemas. / We study conditions for existence and non existence of global solutions for a nonlinear coupled parabolic systems and for parabolic problem with variable exponent. In both cases, we consider an arbitrary domain of RN with smooth boundary and Dirichlet condition on the boundary. As consequence of these results is possible to determinate the Fujita's exponent of ones.

Dans cette thèse, on construit un grand nombre de solutions globales pour de nombreuses équations de Schrödinger sur-critiques. Le principe consiste à rendre la donnée initiale aléatoire, selon les mêmes méthodes que Nicolas Burq, Nikolay Tzvetkov et Laurent Thomann afin de gagner de la dérivabilité.On considère d'abord l'équation de Schrödinger cubique en dimension 3. En partant de variables aléatoires gaussiennes et de la base de L^2(R^3) formée des fonctions d'Hermite tensorielles, on construit des ensembles de solutions globales pour des données initiales qui sont moralement dans L^2(R^3). Les points clefs de la démonstration sont l'existence d'une estimée bilinéaire de type Bourgain pour l'oscillateur harmonique et la transformation de lentille qui permet de se ramener à prouver l'existence locale de solutions à l'équation de Schrödinger avec potentiel harmonique.On étudie ensuite l'effet régularisant pour prouver un théorème analogue où le gain de dérivée vaut 1/2-2/(p-1) où p correspond à la non linéarité de l'équation. Le gain est donc plus faible que précédemment mais la base de fonctions propres quelconques. De plus, la méthode s'appuyant sur des estimées linéaires, on établit le résultat pour des variables aléatoires dont la queue de distribution est à décroissance exponentielle.Enfin, on démontre des estimées multilinéaires en dimension 2 pour une base de fonctions propres quelconques ainsi que des inégalités de types chaos de Wiener pour une classe générale de variables aléatoires. Cela nous permet d'établir le théorème pour l'équation de Schrödinger quintique, avec un gain de dérivée égal à 1/3, dans le même cadre que la partie précédente. / In this thesis, we build a large number of global solutions for many supercritical Schrödinger equations. The method is to make the random initial data, using the same methods that Nicolas Burq, Nikolay Tzvetkov and Laurent Thomann in order to obtain differentiability. First, we consider the cubic Schrödinger equation in three dimensional. Using Gaussian random variables and the basis of L^2(R^3) consists of tensorial Hermite functions, we construct sets of solutions for initial data that are morally in L^2(R^3). The main ingredients of the proof are the existence of Bourgain type bilinear estimates for the harmonic oscillator and the lens transform which can be reduced to prove a local existence of solutions for the Schrödinger equation with harmonic potential. Next, we study the smoothing effect to prove an analogous theorem which the gain of differentiability is equalto 1/2-2/(p-1) which p is the nonlinearity of the equation. This gain is lower than previously but the basis of eigenfunctions are general. As the method uses only linear estimates, we establish the result for a general class of random variables.Finally, we prove multilinear estimates in two dimensional for a basis of ordinaries eigenfunctions and Wienerchaos type inequalities for classical random variables. This allows us to establish the theorem for the quinticSchrödinger equation, with a gain of differentiability equals to 1/3, in the same context as the previous chapter.

Orientador: Lucas Catão de Freitas Ferreira / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T19:31:34Z (GMT). No. of bitstreams: 1 Moitinho_ValterVictorCerqueira_M.pdf: 1171427 bytes, checksum: 9207703fa3477244cb0e004220ae2827 (MD5) Previous issue date: 2015 / Resumo: Nesta dissertação, estudamos o problema de existência de soluções globais suaves para a equação quase-geostrófica em R2 (2DQG) com condições periódicas e no caso de valor crítico para a viscosidade fracionária. Esta equação aparece em estudos de alguns fluidos geofísicos que apresentam altas velocidades de rotação. De um ponto de vista dimensional, a equação é considerada um análogo em 2D das equações de Navier-Stokes em 3D. Primeiramente, estudamos a teoria de soluções fracas com dados iniciais em L2 via o método de Galerkin. Depois mostramos um princípio do máximo em espaços Lp e investigamos a regularidade de soluções para tempos pequenos e dados iniciais nos espaços de Sobolev Hs com s > 1. Finalmente, mostramos que a solução suave localmente no tempo de fato existe globalmente e é suave para todo tempo. Esta dissertação é baseada na Tese de Doutorado de Resnick [36] e no recente trabalho de Kiselev, Narazov e Volberg [33] / Abstract: In this dissertation, we study existence of smooth global solutions for the quasi-geostrophic equation in R2 (2DQG) with periodic conditions and critical value for the fractional viscosity. This equation appears in studies of some geophysical fluids that present high rotational speed. Dimensionally speaking, the equation is the analogue in 2D of the Navier-Stokes equations in 3D. First, we study the theory of weak solutions with initial data in L2 via the Galerkin method. After we show a maximum principle in Lp spaces and investigate regularity of solutions for small times and initial data in Sobolev spaces Hs with s > 1. Finally, we show that local-in-time smooth solutions are indeed global ones. This dissertation is based on the PhD thesis of Resnick [36] and recent work of Kiselev, Narazov e Volberg [33] / Mestrado / Matematica / Mestre em Matemática