Rothberger gaps in fragmented ideals

The~\emph{Rothberger number} $\mathfrak{b} (\mathcal{I})$ of a definable ideal $\mathcal{I}$ on $\omega$ is the least cardinal $\kappa$ such that there exists a Rothberger gap of type $(\omega,\kappa)$ in the quotient algebra $\mathcal{P} (\omega) / \mathcal{I}$. We investigate $\mathfrak{b} (\mathcal{I})$ for a subclass of the $F_\sigma$ ideals, the fragmented ideals, and prove that for some of these ideals, like the linear growth ideal, the Rothberger number is $\aleph_1$ while for others, like the polynomial growth ideal, it is above the additivity of measure. We also show that it is consistent that there are infinitely many (even continuum many) different Rothberger numbers associated with fragmented ideals.Comment: 28 page

Mobility of solitons in one-dimensional lattices with the cubic-quintic nonlinearity

We investigate mobility regimes for localized modes in the discrete nonlinear Schr\"{o}dinger (DNLS) equation with the cubic-quintic onsite terms. Using the variational approximation (VA), the largest soliton's total power admitting progressive motion of kicked discrete solitons is predicted, by comparing the effective kinetic energy with the respective Peierls-Nabarro (PN) potential barrier. The prediction is novel for the DNLS model with the cubic-only nonlinearity too, demonstrating a reasonable agreement with numerical findings. Small self-focusing quintic term quickly suppresses the mobility. In the case of the competition between the cubic self-focusing and quintic self-defocusing terms, we identify parameter regions where odd and even fundamental modes exchange their stability, involving intermediate asymmetric modes. In this case, stable solitons can be set in motion by kicking, so as to let them pass the PN barrier. Unstable solitons spontaneously start oscillatory or progressive motion, if they are located, respectively, below or above a mobility threshold. Collisions between moving discrete solitons, at the competing nonlinearities frame, are studied too.Comment: 12 pages, 15 figure

On the Empirics of Sudden Stops: The Relevance of Balance-Sheet Effects

Using a sample of 32 developed and developing countries we analyze the empirical characteristics of Sudden Stops in capital flows and the relevance of balance-sheet effects in the likelihood of their occurrence. We find that large real exchange rate (RER) fluctuations accompanied by Sudden Stops are basically an emerging market (EM) phenomenon. Sudden Stops seem to come in bunches, grouping together countries that are different in many respects. However, countries are similar in that they remain vulnerable to large RER fluctuations. This may be the case because countries are forced to make large adjustments in the absorption of tradable goods, and/or because the size of dollar liabilities in the banking system (i. e. , domestic liability dollarization, or DLD) is large. Openness, understood as a large supply of tradable goods that reduces leverage over the current account deficit, in combination with DLD, is a key determinant of the probability of Sudden Stops. The relationship between Openness and DLD in the determination of the probability of Sudden Stops is highly non-linear, implying that the interaction of high current account leverage and high dollarization may be a dangerous cocktail.