Expanding translates of shrinking submanifolds in homogeneous spaces and Diophantine approximation

On the space $\mathcal{L}_{n+1}$ of unimodular lattices in $\mathbb{R}^{n+1}$, we consider the action of $a(t)={\rm diag}(t^n,t^{-1},\ldots,t^{-1})\in {\rm SL}(n+1,\mathbb{R})$ for $t>1$. Let $M$ be a nondegenerate $C^{n+1}$-submanifold of an expanding horospherical leaf in $\mathcal{L}_{n+1}$. We prove that for almost every $x\in M$, the shrinking balls in $M$ of radii $t^{-1}$ around $x$ get asymptotically equidistributed in $\mathcal{L}_{n+1}$ under the action of $a(t)$ as $t\to\infty$. This result implies non-improvability of Dirichlet's Diophantine approximation theorem for almost every point on a nondegenerate $C^{n+1}$-submanifold of $\mathbb{R}^n$, answering a question of Davenport and Schmidt (1969).Comment: 16 page

An upper bound of the Hausdorff dimension of singular vectors on affine subspaces

In Diophantine approximation, the notion of singular vectors was introduced by Khintchine in the 1920's. We study the set of singular vectors on an affine subspace of $\mathbb{R}^n$. We give an upper bound of its Hausdorff dimension in terms of the Diophantine exponent of the parameter of the affine subspace.Comment: 18 page

Activity-based Chemical Proteomics Profiling of Natural Products and Drug-like Small Molecules

Ph.DDOCTOR OF PHILOSOPH

Investigation of the Geomechanical Behavior of Mine Backfill and its Interaction with Rock Walls and Barricades

RÉSUMÉ Les rejets solides produits par les mines comprennent les rejets de concentrateur (résidus miniers) et les roches stériles. Ces rejets sont usuellement entreposés en surface, ce qui peut engendrer divers risques environnementaux et géotechniques. Une autre option consiste à remblayer les chantiers miniers avec des stériles ou des résidus miniers. Cette pratique permet de réduire les quantités de rejets entreposés en surface, et aussi d'améliorer la stabilité du terrain, de diminuer la dilution et d’augmenter la récupération de minerai. Le remblayage est utilisé avec diverses méthodes d'exploitation souterraine, pour différentes fonctions. Les préoccupations majeures associées à cette pratique sont la stabilité des structures de support (barricades) peu après le versement du remblai dans le chantier et la stabilité du remblai cimenté exposé après un certain temps après le remblayage. L'état des contraintes dans les chantiers remblayés a été largement étudié au cours des dernières années. Cependant, plusieurs incertitudes existent encore en lien avec des préoccupations majeures, notamment sur le peu de solutions disponibles afin d’évaluer l'évolution des contraintes dans les chantiers, pour concevoir les barricades et le remblai cimenté exposé, ainsi que sur pour estimer la valeur du coefficient de pression des terres K (= ζ’h/ζ’v). L'objectif principal de ce projet est d'évaluer l'état des contraintes dans le remblai confiné et ses interactions avec les barricades peu après sa mise en place et avec les trois parois latérales pour le remblai exposé à plus long terme. De nouvelles solutions analytiques sont proposées pour évaluer l’évolution du niveau d’eau dans un chantier remblayé d’un remblai hydraulique. Ces solutions sont vérifiées à l'aide de simulations numériques réalisées avec le logiciel d'éléments finis SEEP/W. Ces analyses indiquent que l’eau accumulée sur le remblai hydraulique peut induire des pressions interstitielles plus élevées et ainsi compromettre la sécurité des barricades----------ABSTRACT Solid wastes produced by mines include tailings and waste rock. These wastes are usually stored on the surface, which may raise various environmental and geotechnical risks. Another option is to backfill underground mine stopes with waste rock or tailings. This practice can reduce the surface disposal, and also improve ground stability and ore recovery in mining operations. Backfill is widely applied in different underground mining methods for various purposes. The associated major concerns are the stability of the support structure (barricades) at very early time and that of the exposed cemented fill at longer time. In recent years, the stress state in backfilled stopes has been extensively investigated. However, there are uncertainties regarding the major concerns including limited solutions for stress evolution in stopes and for design of barricades and exposed backfill, as well as the actual value of earth pressure coefficient K (= ζ’h/ζ’v) in confined fills. The main objective of this project is to evaluate the stress state within confined backfill and its interactions with barricades at very early time (shortly after the filling) and remaining three sidewalls upon exposure at longer time (typically a few weeks after the filling). New analytical solutions for evaluating the transient seepage are proposed for stopes filled with hydraulic fill. These solutions are verified using simulations conducted with the finite element code SEEP/W. These analyses indicate that ponding, generated on the top of the settled hydraulic fill, can induce higher pore water pressures and jeopardize the barricade safety

Does Residence in an Ethnic Community Help Immigrants in a Recession?

Research on how the residential segregation of immigrant populations has impacted their labor market outcomes presents many challenges because of the fact that immigrants often choose to locate near co-ethnics to share resources and cultural amenities. Because not all immigrants choose to live in these ethnic communities, identification of a causal effect on living in an ethnic community is problematic. The estimation of the effect of living in these ethnic communities is also difficult because it is ambiguous whether such residence will help or harm the labor market outcomes of immigrants. This study implements a number of approaches to help identify a causal effect, including using sample of adults whose residential location is plausibly exogenous with respect to their labor market outcomes and using the current recession as a source of exogenous variation. Results suggest that residence in an ethnic community after the recession increases the likelihood of working, albeit with longer commutes