Iterated Brownian motion in an open set

Suppose a solid has a crack filled with a gas. If the crack reaches the surrounding medium, how long does it take the gas to diffuse out of the crack? Iterated Brownian motion serves as a model for diffusion in a crack. If \tau is the first exit time of iterated Brownian motion from the solid, then P(\tau>t) can be viewed as a measurement of the amount of contaminant left in the crack at time t. We determine the large time asymptotics of P(\tau>t) for both bounded and unbounded sets. We also discuss a strange connection between iterated Brownian motion and the parabolic operator {1/8}\Delta^2-\frac{\partial}{\partial t}

Poverty, inequality, and welfare in a rapid-growth economy: The Chilean experience

Poverty reduction, Hunger, Inequality, Poverty, Equal opportunity, Education,

Revisiting B→DℓνB\to D \ell \nu

We re-examine the determination of $|V_{cb}|$ from $B\to D \ell \nu$ in view of recent experimental and theoretical progress, discussing the parameterization of the form factors and studying the role played by the unitarity constraints. Our fit to experimental and lattice results for $B\to D \ell \nu$ gives $|V_{cb}|=40.49(97)\ 10^{-3}$ and to $R(D)= 0.299(3)$.Comment: 19 pages, 2 figures; v2: BCL fits, various clarifications and refs adde

Rational Landen transformations on the real line

The rational Landen transformation is a map on the space of coefficients of a rational integrand that preserves the value of the integral. We provide a family of these transformations that apply to rational integrands on the whole line. Given an integer m, these transformations produce a numerical scheme to evaluate the integral that is of order m.Comment: 22 page