Local in time results for local and non-local capillary Navier-Stokes systems with large data

In this article we study three capillary compressible models (the classical local Navier-Stokes-Korteweg system and two non-local models) for large initial data, bounded away from zero, and with a reference pressure state $\bar{\rho}$ which is not necessarily stable ($P'(\bar{\rho})$ can be non-positive). We prove that these systems have a unique local in time solution and we study the convergence rate of the solutions of the non-local models towards the local Korteweg model. The results are given for constant viscous coefficients and we explain how to extend them for density dependant coefficients.Comment: 39 page

Dollarization of Liabilities in Non-tradable Goods Sector

This paper questions the motivation of dollar indebtedness by firms of the non-tradable good sectors in a period of exchange rate pressure. Given the structure of banks' indebtedness and protection of banks' foreign lenders, a dollar denominated loan may allow firms to insure (partially) against the risk of an early liquidation of their projects if they turn out to be poor. Then it is shown that under dollarization of liabilities the government may be urged to soften monetary policy to induce a real appreciation that supports the domestic banking system. Therefore, it might be constrained in its ability to enforce an efficient regulatory policy.http://deepblue.lib.umich.edu/bitstream/2027.42/39764/3/wp380.pd

A Comparison of the American Model and French (-Inspired) Appellate Model

Both the American and the French legal system have a three-tiered structure. However, the respective roles and functions of the courts on each step of the ladder is vastly different in both. Whereas the general system in the U.S. is to have one trial court and two ‘higher’ courts (a court of appeals and a supreme court), the French / European continental system consists of two ‘factual’ courts (the basic level and the court of appeals), and one ‘legal’ (the supreme court) with limited or even inexistent possibilities to look at the facts. The purpose of this thesis is to look at these two models of division of labor between the three tiers through the lens of (i) the procedural leeway each of the courts has and (ii) their focus on fact or law, in function of what questions can be raised in appeal and have to be answered by the courts. We will add Germany to the comparison, as (i) the structure of its court system was inspired by the French, but (ii) has evolved over the years and has been recently (2002) overhauled specifically as to appeals, both to the second level of courts and to the supreme court. We will do so by examining the avenues open for the parties in filing an appeal as well as for the courts in adjudicating those. It will be clear that the distinct philosophies regarding the appellate systems have influence on the entire organization of the different court systems. We conclude that the present-day German system offers the best differentiation of roles between the three tiers while balancing access to the appellate and supreme court level

Special Varieties and classification Theory

A new class of compact K\"ahler manifolds, called special, is defined, which are the ones having no surjective meromorphic map to an orbifold of general type. The special manifolds are in many respect higher-dimensional generalisations of rational and elliptic curves. For example, we show that being rationally connected or having vanishing Kodaira dimension implies being special. Moreover, for any compact K\"ahler $X$ we define a fibration $c_X:X\to C(X)$, which we call its core, such that the general fibres of $c_X$ are special, and every special subvariety of $X$ containing a general point of $X$ is contained in the corresponding fibre of $c_X$. We then conjecture and prove in low dimensions and some cases that: 1) Special manifolds have an almost abelian fundamental group. 2) Special manifolds are exactly the ones having a vanishing Kobayashi pseudometric. 3) The core is a fibration of general type, which means that so is its base $C(X)$,when equipped with its orbifold structure coming from the multiple fibres of $c_X$. 4) The Kobayashi pseudometric of $X$ is obtained as the pull-back of the orbifold Kobayashi pseudo-metric on $C(X)$, which is a metric outside some proper algebraic subset. 5) If $X$ is projective,defined over some finitely generated (over $\Bbb Q$) subfield $K$ of the complex number field, the set of $K$-rational points of $X$ is mapped by the core into a proper algebraic subset of $C(X)$. These two last conjectures are the natural generalisations to arbitrary $X$ of Lang's conjectures formulated when $X$ is of general type.Comment: 72 pages, latex fil

Convergence of Fuzzy Tori and Quantum Tori for the quantum Gromov-Hausdorff Propinquity: an explicit approach

Quantum tori are limits of finite dimensional C*-algebras for the quantum Gromov-Hausdorff propinquity, a metric defined by the author as a strengthening of Rieffel's quantum Gromov-Hausdorff designed to retain the C*-algebraic structure. In this paper, we propose a proof of the continuity of the family of quantum and fuzzy tori which relies on explicit representations of the C*-algebras rather than on more abstract arguments, in a manner which takes full advantage of the notion of bridge defining the quantum propinquity.Comment: 41 Pages. This paper is the second half of ArXiv:1302.4058v2. The latter paper has been divided in two halves for publications purposes, with the first half now the current version of 1302.4058, which has been accepted in Trans. Amer. Math. Soc. This second half is now a stand-alone paper, with a brief summary of 1302.4058 and a new introductio

Ladders in a magnetic field: a strong coupling approach

We show that non-frustrated and frustrated ladders in a magnetic field can be systematically mapped onto an XXZ Heisenberg model in a longitudinal magnetic field in the limit where the rung coupling is the dominant one. This mapping is valid in the critical region where the magnetization goes from zero to saturation. It allows one to relate the properties of the critical phase ($H_c^1$, $H_c^2$, the critical exponents) to the exchange integrals and provide quantitative estimates of the frustration needed to create a plateau at half the saturation value for different models of frustration.Comment: One mistake corrected, one reference adde

Control of Nonholonomic Systems and Sub-Riemannian Geometry

Lectures given at the CIMPA School "Geometrie sous-riemannienne", Beirut, Lebanon, 201