[Review of] Louis G. Mendoza. Conversations Across Our America: Talking about Immigration and the Latinoization of the United States

Louis G. Mendoza\u27s book, Conversations Across Our America: Talking about Immigration and the Latinoization of the United States, incorporates thirty-three conversations with forty-two Latinas/os of various nationalities in order to better understand the Latino influence in the United States. To collect this data, Mendoza rode a bicycle approximately 8,500 miles through thirty states from July to December 2007. He draws upon Ethnic Studies tradition as he was driven to conduct research that is relevant to his community. Mendoza draws upon the oral histories and lived experience of his participants to demonstrate the diverse nature of Latinas/os throughout the country. He presents what Pérez-Huber (2009) defines as testimonios - a verbal journey of a witness who speaks to reveal the racial, classed, gendered, and nativist injustices they have suffered as a means of healing, empowerment, and advocacy for a more humane present and future (p. 644)

Time reversal dualities for some random forests

We consider a random forest $\mathcal{F}^*$, defined as a sequence of i.i.d. birth-death (BD) trees, each started at time 0 from a single ancestor, stopped at the first tree having survived up to a fixed time $T$. We denote by $\left(\xi^*_t,\ 0\leq t\leq T\right)$ the population size process associated to this forest, and we prove that if the BD trees are supercritical, then the time-reversed process $\left(\xi^*_{T-t},\ 0\leq t\leq T\right)$, has the same distribution as $\left(\widetilde\xi^*_t,\ 0\leq t\leq T\right)$, the corresponding population size process of an equally defined forest $\widetilde{\mathcal{F}}^*$, but where the underlying BD trees are subcritical, obtained by swapping birth and death rates or equivalently, conditioning on ultimate extinction. We generalize this result to splitting trees (i.e. life durations of individuals are not necessarily exponential), provided that the i.i.d. lifetimes of the ancestors have a specific explicit distribution, different from that of their descendants. The results are based on an identity between the contour of these random forests truncated up to $T$ and the duality property of L\'evy processes. This identity allows us to also derive other useful properties such as the distribution of the population size process conditional on the reconstructed tree of individuals alive at $T$, which has potential applications in epidemiology.Comment: 28 pages, 3 figure

Regular solutions to a supercritical elliptic problem in exterior domains

We consider the supercritical elliptic problem -\Delta u = \lambda e^u, \lambda > 0, in an exterior domain $\Omega = \mathbb{R}^N \setminus D$ under zero Dirichlet condition, where D is smooth and bounded in \mathbb{R}^N, N greater or equal than 3. We prove that, for \lambda small, this problem admits infinitely many regular solutions

Exact computation of image disruption under reflection on a smooth surface and Ronchigrams

We use geometrical optics and the caustic-touching theorem to study, in an exact way, the change in the topology of the image of an object obtained by reflections on an arbitrary smooth surface. Since the procedure that we use to compute the image is exactly the same as that used to simulate the ideal patterns, referred to as Ronchigrams, in the Ronchi test used to test mirrors, we remark that the closed loop fringes commonly observed in the Ronchigrams when the grating, referred to as a Ronchi ruling, is located at the caustic place are due to a disruption of fringes, or, more correctly, as disruption of shadows corresponding to the ruling bands. To illustrate our results, we assume that the reflecting surface is a spherical mirror and we consider two kinds of objects: circles and line segments.Comment: 31 pages, 23 figure

C1,αC^{1,\alpha} regularity of solutions of degenerate fully non-linear elliptic equations

In the present paper, a class of fully non-linear elliptic equations are considered, which are degenerate as the gradient becomes small. H\"older estimates obtained by the first author (2011) are combined with new Lipschitz estimates obtained through the Ishii-Lions method in order to get $C^{1,\alpha}$ estimates for solutions of these equations.Comment: Submitte