Exact Ground States of Frustrated Spin-1 Ising-Heisenberg and Heisenberg Ladders in a Magnetic Field

Ground states of the frustrated spin-1 Ising-Heisenberg two-leg ladder with Heisenberg intra-rung coupling and only Ising interaction along legs and diagonals are rigorously found by taking advantage of local conservation of the total spin on each rung. The constructed ground-state phase diagram of the frustrated spin-1 Ising-Heisenberg ladder is then compared with the analogous phase diagram of the fully quantum spin-1 Heisenberg two-leg ladder obtained by density matrix renormalization group (DMRG) calculations. It is demonstrated that both investigated spin models exhibit quite similar magnetization scenarios, which involve intermediate plateaux at one-quarter, one-half and three-quarters of the saturation magnetization.Comment: 3 pages, 1 figure, contribution to proceedings of CSMAG'13 conferenc

Intermediate magnetization plateaus in the spin-1/2 Ising-Heisenberg and Heisenberg models on two-dimensional triangulated lattices

The ground state and zero-temperature magnetization process of the spin-1/2 Ising-Heisenberg model on two-dimensional triangles-in-triangles lattices is exactly calculated using eigenstates of the smallest commuting spin clusters. Our ground-state analysis of the investigated classical--quantum spin model reveals three unconventional dimerized or trimerized quantum ground states besides two classical ground states. It is demonstrated that the spin frustration is responsible for a variety of magnetization scenarios with up to three or four intermediate magnetization plateaus of either quantum or classical nature. The exact analytical results for the Ising-Heisenberg model are confronted with the corresponding results for the purely quantum Heisenberg model, which were obtained by numerical exact diagonalizations based on the Lanczos algorithm for finite-size spin clusters of 24 and 21 sites, respectively. It is shown that the zero-temperature magnetization process of both models is quite reminiscent and hence, one may obtain some insight into the ground states of the quantum Heisenberg model from the rigorous results for the Ising-Heisenberg model even though exact ground states for the Ising-Heisenberg model do not represent true ground states for the pure quantum Heisenberg model.Comment: 10 pages, 7 figure

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

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

David Patterson, Anti-Semitism and Its Metaphysical Origins (Cambridge: Cambridge University Press, 2015)

This is a critical review of David Patterson's book Anti-Semitism and Its Metaphysical Origins (2015). In this review, I present the author's new explanation of the roots of anti-Semitism, which he finds in the anti-Semite's desire to become like God himself. Patterson's explanation makes an anti-Semite of all those who partake in the "Western rationalist project," especially philosophers (including Jewish philosophers such as Spinoza, Hermann Cohen, and Marx), but also Islamists and anti-Zionist Jews. I criticize Patterson on two fronts: First, his "metaphysical" explanation relies on a petitio principii. Second, he should have argued his stance against that of Zeev Sternhell's thesis, according to which Western anti-Semitism is rooted, not in Western rationalism, but rather in the Western anti-rationalist (anti-Enlightenment) movement

A Compactness Theorem for The Dual Gromov-Hausdorff Propinquity

We prove a compactness theorem for the dual Gromov-Hausdorff propinquity as a noncommutative analogue of the Gromov compactness theorem for the Gromov-Hausdorff distance. Our theorem is valid for subclasses of quasi-Leibniz compact quantum metric spaces of the closure of finite dimensional quasi-Leibniz compact quantum metric spaces for the dual propinquity. While finding characterizations of this class proves delicate, we show that all nuclear, quasi-diagonal quasi-Leibniz compact quantum metric spaces are limits of finite dimensional quasi-Leibniz compact quantum metric spaces. This result involves a mild extension of the definition of the dual propinquity to quasi-Leibniz compact quantum metric spaces, which is presented in the first part of this paper.Comment: 40 Pages. Version 4 includes several minor corrections and is accepted in the Indiana University Mathematics Journa