12,088 research outputs found
Auxiliary SDEs for homogenization of quasilinear PDEs with periodic coefficients
We study the homogenization property of systems of quasi-linear PDEs of
parabolic type with periodic coefficients, highly oscillating drift and highly
oscillating nonlinear term. To this end, we propose a probabilistic approach
based on the theory of forward-backward stochastic differential equations and
introduce the new concept of ``auxiliary SDEs.''Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Probability
(http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000014
Brief of Brian Wolfman, Aderson B. Francois, and Eric Schnapper as Amici Curiae in Support of Petitioner in Peterson v. Linear Controls Incorporated, No. 18-1401 (U.S. Supreme Court June 6, 2019)
In Title VII disparate-treatment, employment-discrimination cases, the term “adverse employment action” originally developed as judicial shorthand for the statute’s text, which broadly prohibits any discriminatory conduct by an employer against an employee based on the employee\u27s race, color, religion, sex, or national origin. See 42 U.S.C. 2000e-2(a)(1). But what started simply as shorthand has taken on a life of its own and now improperly limits the statute’s reach. The Fifth Circuit’s version of the adverse-employment-action rule stands out as especially improper: Only an “ultimate employment decision”—a refusal to hire, a firing, a demotion, or the like—constitutes impermissible discrimination.In this amicus brief, we urge the Supreme Court to grant review and overturn the Fifth Circuit\u27s standard. We argue, first, that the Fifth Circuit\u27s ultimate-employment-decision standard is inconsistent with Title VII’s text and the Supreme Court’s Title VII decisions. Next, we show that the Fifth Circuit’s rule excludes many discriminatory employment practices that are unlawful in its sister circuits. The stories of discrimination victims from these other jurisdictions demonstrate that the Fifth Circuit’s approach is wrong. These individuals suffered discrimination that Title VII prohibits, but the Fifth Circuit’s standard would enable their employers to discriminate without consequence. Finally, we propose a standard consistent with Title VII’s text and Supreme Court precedent: As long as the employer’s intentional, discriminatory conduct imposes meaningful harm on the employee, it is prohibited by, and may be remedied under, Title VII
Primitive geodesic lengths and (almost) arithmetic progressions
In this article, we investigate when the set of primitive geodesic lengths on
a Riemannian manifold have arbitrarily long arithmetic progressions. We prove
that in the space of negatively curved metrics, a metric having such arithmetic
progressions is quite rare. We introduce almost arithmetic progressions, a
coarsification of arithmetic progressions, and prove that every negatively
curved, closed Riemannian manifold has arbitrarily long almost arithmetic
progressions in its primitive length spectrum. Concerning genuine arithmetic
progressions, we prove that every non-compact, locally symmetric, arithmetic
manifold has arbitrarily long arithmetic progressions in its primitive length
spectrum. We end with a conjectural characterization of arithmeticity in terms
of arithmetic progressions in the primitive length spectrum. We also suggest an
approach to a well known spectral rigidity problem based on the scarcity of
manifolds with arithmetic progressions.Comment: v3: 23 pages. To appear in Publ. Ma
Effects of F, B2O3 and P2O5 on the solubility of water in haplogranite melts compared to natural silicate melts
The effects of F, B2O3 and P2O5 on the H2O solubility in a haplogranite liquid (36 wt. % SiO2, 39 wt. % NaAlSi3O8, 25 wt. % KAlSi3O8) have been determined at 0.5, 1, 2, and 3 kb and 800, 850, and 900°C. The H2O solubility increases with increasing F and B content of the melt. The H2O solubility increase in more important at high pressure (2 and 3 kb) than at low pressure (0.5 kb). At 2 kb and 800°C, the H2O solubility increases from 5.94 to 8.22 wt. % H2O with increasing F content in the melt from 0 to 4.55 wt. %, corresponding to a linear H2O solubility increase of 0.53 mol H2O/mol F. With addition of 4.35 wt. % B2O3, the H2O solubility increases up to 6.86 wt. % H2O at 2 kb and 800°C, corresponding to a linear increase of 1.05 mol H2O/mol B2O3. The results allow to define the individual effects of fluorine and boron on H2O solubility in haplogranitic melts with compositions close to that of H2O-saturated thermal minima (at 0.5–3 kb). Although P has a dramatic effect on the phase relations in the haplogranite system, its effect on the H2O solubility was found to be negligible in natural melt compositions. The concominant increase in H2O solubility and F can not be interpreted on the basis of the available spectroscopic data (existence of hydrated aluminofluoride complexes or not). In contrast, hydrated borates or more probably boroxol complexes have been demonstrated in B-bearing hydrous melts
The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance
For two decades, the Colless index has been the most frequently used
statistic for assessing the balance of phylogenetic trees. In this article,
this statistic is studied under the Yule and uniform model of phylogenetic
trees. The main tool of analysis is a coupling argument with another well-known
index called the Sackin statistic. Asymptotics for the mean, variance and
covariance of these two statistics are obtained, as well as their limiting
joint distribution for large phylogenies. Under the Yule model, the limiting
distribution arises as a solution of a functional fixed point equation. Under
the uniform model, the limiting distribution is the Airy distribution. The
cornerstone of this study is the fact that the probabilistic models for
phylogenetic trees are strongly related to the random permutation and the
Catalan models for binary search trees.Comment: Published at http://dx.doi.org/10.1214/105051606000000547 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Discrete rearranging disordered patterns, part I: Robust statistical tools in two or three dimensions
Discrete rearranging patterns include cellular patterns, for instance liquid
foams, biological tissues, grains in polycrystals; assemblies of particles such
as beads, granular materials, colloids, molecules, atoms; and interconnected
networks. Such a pattern can be described as a list of links between
neighbouring sites. Performing statistics on the links between neighbouring
sites yields average quantities (hereafter "tools") as the result of direct
measurements on images. These descriptive tools are flexible and suitable for
various problems where quantitative measurements are required, whether in two
or in three dimensions. Here, we present a coherent set of robust tools, in
three steps. First, we revisit the definitions of three existing tools based on
the texture matrix. Second, thanks to their more general definition, we embed
these three tools in a self-consistent formalism, which includes three
additional ones. Third, we show that the six tools together provide a direct
correspondence between a small scale, where they quantify the discrete
pattern's local distortion and rearrangements, and a large scale, where they
help describe a material as a continuous medium. This enables to formulate
elastic, plastic, fluid behaviours in a common, self-consistent modelling using
continuous mechanics. Experiments, simulations and models can be expressed in
the same language and directly compared. As an example, a companion paper
(Marmottant, Raufaste and Graner, joint paper) provides an application to foam
plasticity
Why not a di-NUT? or Gravitational duality and rotating solutions
We study how gravitational duality acts on rotating solutions, using the
Kerr-NUT black hole as an example. After properly reconsidering how to take
into account both electric (i.e. mass-like) and magnetic (i.e. NUT-like)
sources in the equations of general relativity, we propose a set of definitions
for the dual Lorentz charges. We then show that the Kerr-NUT solution has
non-trivial such charges. Further, we clarify in which respect Kerr's source
can be seen as a mass M with a dipole of NUT charges.Comment: 20 pages. v2: minor clarifications in section 4, version to appear in
PR
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