Topological Conformal Dimension

We investigate a quasisymmetrically invariant counterpart of the topological Hausdorff dimension of a metric space. This invariant, called the topological conformal dimension, gives a lower bound on the topological Hausdorff dimension of quasisymmetric images of the space. We obtain results concerning the behavior of this quantity under products and unions, and compute it for some classical fractals. The range of possible values of the topological conformal dimension is also considered, and we show that this quantity can be fractional.Comment: 16 pages, revised after referee's reports. To appear in Conformal Geometry and Dynamic

The Virtues of Abstention: Separation of Powers in Al-Nashiri II

(Excerpt) Part I examines various scholarly approaches to judicial deference, then considers deference in the context of military commissions. In Part II, the history of military commissions in the United States is examined, paying particular attention to the extended dialogue among the coordinate federal branches that created the system currently in operation. The decision in Al-Nashiri II not to adjudicate a collateral attack on one of these commissions is the focus of Part III. That Part embraces the underlying jurisdictional challenge at stake in Al-Nashiri II, the development of abstention doctrine generally and as applied to the current commissions, as well as the role judicial deference played in the panel’s decision. Finally, in Part IV, this Note argues that the path of abstention had many virtues in this case and as a rule of law, because it furthered sound separation of powers principles by respecting the considered judgments of Congress and successive Presidents. Part IV first categorizes the type of deference the panel engaged in by abstaining. Next, it considers the effect the decision will have on future collateral attacks on commission proceedings, as federal courts will now review military commission final judgments, just as Congress and the President intended, rather than intervening indiscriminately. This Note argues that this effect will, in turn, preserve the commission system created by Congress—the branch best suited to weigh the intricate national security considerations involved in prosecuting and bringing to justice those who, in their attempt to thwart our military effort, violate the laws of war

Zygmund graphs are thin for doubling measures

The Zygmund functions form an intermediate class between Lipschitz and H\"older functions; their second order divided differences are uniformly bounded. It is well known that for $d \geq 1$ the graph of any Lipschitz function $f:\R^d \rightarrow \R$ is thin for doubling measures, and we extend this result to the Zygmund class

Weak decay processes in pre-supernova core evolution within the gross theory

The beta decay and electron capture rates are of fundamental importance in the evolution of massive stars in a pre-supernova core. The beta decay process gives its contribution by emitting electrons in the plasma of the stellar core, thereby increasing pressure, which in turn increases the temperature. From the other side, the electron capture removes free electrons from the plasma of the star core contributing to the reduction of pressure and temperature. In this work we calculate the beta decay and electron capture rates in stellar conditions for 63 nuclei of relevance in the pre-supernova stage, employing Gross Theory as the nuclear model. We use the abundances calculated with the Saha equations in the hypothesis of nuclear statistical equilibrium to evaluate the time derivative of the fraction of electrons. Our results are compared with other evaluations available in the literature. They have shown to be one order less or equal than the calculated within other models. Our results indicate that these differences may influence the evolution of the star in the later stages of pre-supernova. © 2014. The American Astronomical Society. All rights reserved..Fil: Ferreira, R. C.. Universidade Estadual Do Sudoeste Da Bahía; BrasilFil: Dimarco, A. J.. Universidade Estadual de Santa Cruz, Bahía, Brasil; BrasilFil: Samana, Arturo Rodolfo. Universidade Estadual de Santa Cruz, Bahía, Brasil; BrasilFil: Barbero, César Alberto. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin

Christian Legal Thought

(Excerpt) On January 26, 2018, the Journal of Catholic Legal Studies proudly hosted a conference on Christian Legal Thought: Materials and Cases a first-of-its-kind casebook authored by Patrick M. Brennan and William S. Brewbaker. Held in Manhattan at the New York Athletic Club, the conference brought together scholars from law schools across the country to discuss the casebook’s impact, as well as the role Christian legal thought might play in the contemporary law school curriculum

The effects of bedrest on crew performance during simulated shuttle reentry. Volume 2: Control task performance

A simplified space shuttle reentry simulation performed on the NASA Ames Research Center Centrifuge is described. Anticipating potentially deleterious effects of physiological deconditioning from orbital living (simulated here by 10 days of enforced bedrest) upon a shuttle pilot's ability to manually control his aircraft (should that be necessary in an emergency) a comprehensive battery of measurements was made roughly every 1/2 minute on eight military pilot subjects, over two 20-minute reentry Gz vs. time profiles, one peaking at 2 Gz and the other at 3 Gz. Alternate runs were made without and with g-suits to test the help or interference offered by such protective devices to manual control performance. A very demanding two-axis control task was employed, with a subcritical instability in the pitch axis to force a high attentional demand and a severe loss-of-control penalty. The results show that pilots experienced in high Gz flying can easily handle the shuttle manual control task during 2 Gz or 3 Gz reentry profiles, provided the degree of physiological deconditioning is no more than induced by these 10 days of enforced bedrest

Not all toxic butterflies are toxic: high intra- and interspecific variation in sequestration in subtropical swallowtails

Many herbivorous insects make use of plant secondary metabolites by consuming and storing these toxic compounds in their body tissue or integument, thereby obtaining chemical defense against their natural enemies. Swallowtail butterflies in the tribe Troidini (Papilionidae) sequester toxic alkaloids (aristolochic acids, AAs) from their host plants in the genus Aristolochia. Troidine butterflies have been a model group for development of theory on host plant chemical sequestration, but most studies on this group have been limited to a single species in North America. These studies have led, in part, to the paradigm that troidine butterflies are toxic, thereby explaining the numerous mimicry relationships that exist throughout most of their range. Herein, we present one of the first comparative studies in a single location of a community of troidine butterflies. We examined the AA content of five co-occurring troidine butterfly species and their two Aristolochia host plants. We found that one Aristolochia species, A. triangularis, was preferred in choice assays and did not possess quantifiable levels of AA. We also found that most troidine butterflies did not possess quantifiable levels of AAs, but larvae have the ability to sequester AAs when it is present in their diet. A larval preference experiment showed that host plant AA concentration did not influence larval feeding choice. A performance experiment showed that higher levels of AAs in the diet increased larval mortality, which might indicate a cost associated with sequestration of the chemical defense and also might shed some light on why so many troidine butterflies in this community have little or no AAs. We propose that automimicry might be operating in this system and many putative models of this paradigmatic system might not possess plant-derived defensive chemistry

The Moment Guided Monte Carlo method for the Boltzmann equation

In this work we propose a generalization of the Moment Guided Monte Carlo method developed in [11]. This approach permits to reduce the variance of the particle methods through a matching with a set of suitable macroscopic moment equations. In order to guarantee that the moment equations provide the correct solutions, they are coupled to the kinetic equation through a non equilibrium term. Here, at the contrary to the previous work in which we considered the simplified BGK operator, we deal with the full Boltzmann operator. Moreover, we introduce an hybrid setting which permits to entirely remove the resolution of the kinetic equation in the limit of infinite number of collisions and to consider only the solution of the compressible Euler equation. This modification additionally reduce the statistical error with respect to our previous work and permits to perform simulations of non equilibrium gases using only a few number of particles. We show at the end of the paper several numerical tests which prove the efficiency and the low level of numerical noise of the method.Comment: arXiv admin note: text overlap with arXiv:0908.026

Asymptotically complexity diminishing schemes (ACDS) for kinetic equations in the diffusive scaling

In this work, we develop a new class of numerical schemes for collisional kinetic equations in the diffusive regime. The first step consists in reformulating the problem by decomposing the solution in the time evolution of an equilibrium state plus a perturbation. Then, the scheme combines a Monte Carlo solver for the perturbation with an Eulerian method for the equilibrium part, and is designed in such a way to be uniformly stable with respect to the diffusive scaling and to be consistent with the asymptotic diffusion equation. Moreover, since particles are only used to describe the perturbation part of the solution, the scheme becomes computationally less expensive – and is thus an asymptotically complexity diminishing scheme (ACDS) – as the solution approaches the equilibrium state due to the fact that the number of particles diminishes accordingly. This contrasts with standard methods for kinetic equations where the computational cost increases (or at least does not decrease) with the number of interactions. At the same time, the statistical error due to the Monte Carlo part of the solution decreases as the system approaches the equilibrium state: the method automatically degenerates to a solution of the macroscopic diffusion equation in the limit of infinite number of interactions. After a detailed description of the method, we perform several numerical tests and compare this new approach with classical numerical methods on various problems up to the full three dimensional case