Trapping dust particles in the outer regions of protoplanetary disks

Aims. We attempt to explain grain growth to mm sized particles and their retention in the outer regions of protoplanetary disks, as observed at sub-mm and mm wavelengths, by investigating whether strong inhomogeneities in the gas density profiles can decelerate excessive radial drift and help the dust particles to grow. Methods. We use coagulation/fragmentation and disk-structure models, to simulate the evolution of dust in a bumpy surface density profile, which we mimic with a sinusoidal disturbance. For different values of the amplitude and length scale of the bumps, we investigate the ability of this model to produce and retain large particles on million-year timescales. In addition, we compare the pressure inhomogeneities considered in this work with the pressure profiles that come from magnetorotational instability. Using the Common Astronomy Software Applications ALMA simulator, we study whether there are observational signatures of these pressure inhomogeneities that can be seen with ALMA. Results. We present the conditions required to trap dust particles and the corresponding calculations predicting the spectral slope in the mm-wavelength range, to compare with current observations. Finally, we present simulated images using different antenna configurations of ALMA at different frequencies, to show that the ring structures will be detectable at the distances of either the Taurus Auriga or Ophiucus star-forming regions

Entrando en cintura: implicaciones de política económica sobre la sostenibilidad de la deuda pública en la zona euro.

En este artículo se muestra el marco teórico implícito en la restricción presupuestaria intertemporal del gobierno. A partir de este, se realizan una serie de simulaciones sobre el problema de sostenibilidad de la deuda pública, y los sacrificios fiscales necesarios para juzgar el actual nivel de endeudamiento sostenible en algunos países de la zona Euro. En particular, Grecia, Portugal, Italia y España deben generar un superávit primario de 44.1%, 10.5%, 6.8% y 4.5% del PIB, respectivamente para mantener sus actuales niveles de endeudamiento. La situación de Reino unido, Alemania y Francia es diferente, puesto que pueden presentar déficits debido a la relación entre crecimiento esperado y tasa de interés

Weighted norm inequalities for the geometric maximal operator

We consider two closely related but distinct operators,This extends the work of X. Shi; H. Wei, S. Xianliang and S. Qiyu; X. Yin and B. Muckenhoupt; and C. Sbordone and I. Wik. F I W e give sufficient conditions for the two operators to be equal and show that these conditions are sharp. We also prove two-weight, weighted norm inequalities for both operators using our earlier results about weighted norm inequalities for the minimal operator: \ text{\mgran{m}} f(x) = \inf_{I \ni x} \frac{1}{ \ align M_0f(x)&= \sup_{I\ni x}\exp\left(\frac{1}{\ ,dy\right) \quad\text{and}\\M_0^*f(x) &= \lim_{r\rightarrow0} \sup_{I\ni x}\left(\frac{1}{ \ ,dy. ^ r\,dy\right)^{1/r}.\endalign } \int_I\log } \int_

Boundedness of Pseudodifferential Operators on Banach Function Spaces

We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$, then a pseudodifferential operator $\operatorname{Op}(a)$ is bounded on $X(\mathbb{R}^n)$ whenever the symbol $a$ belongs to the H\"ormander class $S_{\rho,\delta}^{n(\rho-1)}$ with $0<\rho\le 1$, $0\le\delta<1$ or to the the Miyachi class $S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)$ with $0\le\delta\le\rho\le 1$, $0\le\delta0$. This result is applied to the case of variable Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^n)$.Comment: To appear in a special volume of Operator Theory: Advances and Applications dedicated to Ant\'onio Ferreira dos Santo

A note on the off-diagonal Muckenhoupt-Wheeden conjecture

We obtain the off-diagonal Muckenhoupt-Wheeden conjecture for Calderón-Zygmund operators. Namely, given $1 < p < q < \infty$ and a pair of weights $(u; v)$, if the Hardy-Littlewood maximal function satisfies the following two weight inequalities: M:L^p(v) \to L^q(u) \quad \mbox{and} \quad M: L^{q'} (u^{1-q'}) \to (v^{1-p'} ); then any Calderón-Zygmund operator $T$ and its associated truncated maximal operator $T_{*}$ are bounded from $M:L^p(v)$ to $L^q(u)$. Additionally, assuming only the second estimate for $M$ then $T$ and $T_{*}$ map continuously $M:L^p(v)$ to $L^{q,\infty}(u)$ We also consider the case of generalized Haar shift operators and show that their off-diagonal two weight estimates are governed by the corresponding estimates for the dyadic Hardy-Littlewood maximal function