A zero-sqrt(5)/ 2 law for cosine families

Let $a \in \R,$ and let $k(a)$ be the largest constant such that sup\vert cos(na)-cos(nb)\vert \textless{} k(a) for $b\in \R$ implies that $b \in \pm a+2\pi\Z.$ We show that if a cosine sequence $(C(n))\_{n\in \Z}$ with values in a Banach algebra $A$ satisfies sup\_{n\ge 1}\Vert C(n) -cos(na).1\_A\Vert \textless{} k(a), then $C(n)=cos(na)$ for $n\in \Z.$ Since ${\sqrt 5\over 2} \le k(a) \le {8\over 3\sqrt 3}$ for every $a \in \R,$ this shows that if some cosine family $(C(g))\_{g\in G}$ over an abelian group $G$ in a Banach algebra satisfies sup\_{g\in G}\Vert C(g)-c(g)\Vert \textless{} {\sqrt 5\over 2} for some scalar cosine family $(c(g))\_{g\in G},$ then $C(g)=c(g)$ for $g\in G,$ and the constant ${\sqrt 5\over 2}$ is optimal. We also describe the set of all real numbers $a \in [0,\pi]$ satisfying $k(a)\le {3\over 2}.

From Specifications to Behavior: Maneuver Verification in a Semantic State Space

To realize a market entry of autonomous vehicles in the foreseeable future, the behavior planning system will need to abide by the same rules that humans follow. Product liability cannot be enforced without a proper solution to the approval trap. In this paper, we define a semantic abstraction of the continuous space and formalize traffic rules in linear temporal logic (LTL). Sequences in the semantic state space represent maneuvers a high-level planner could choose to execute. We check these maneuvers against the formalized traffic rules using runtime verification. By using the standard model checker NuSMV, we demonstrate the effectiveness of our approach and provide runtime properties for the maneuver verification. We show that high-level behavior can be verified in a semantic state space to fulfill a set of formalized rules, which could serve as a step towards safety of the intended functionality.Comment: Published at IEEE Intelligent Vehicles Symposium (IV), 201

Prevencion y tratamiento del absentismo y de la desescolarizacion en Francia: experiencias y nuevas formas de actuar

A partir de la síntesis de dos investigaciones cualitativas en Roubaix, (Norte de Francia, particularmente afectada por el paro y el consiguiente desarrollo de la pobreza y precariedad), entre 2001 y 2004, y de varias investigaciones sobre el tema, se presentarán los procesos de desescolarizacion antes de los 16 años. Se analizará el contexto de aparición del tema y se distinguirán las etapas, las lógicas de los actores y las interacciones entre ellos (alumnos, instituciones, familias, medio ambiente, grupos de jóvenes), estudiando las consecuencias para los jóvenes mismos. Se presentará un análisis crítico de los dispositivos de prevención y tratamiento del absentismo y de la desescolarización. Estos dispositivos permiten desarrollar experiencias de recorridos individualizados para unos jóvenes desviantes en el sistema escolar clásico, pero a la vez no modifican fundalmentalmente los mecanismos de selección et de exclusión, que siguen vigentes en el sistema escola

Lower estimates near the origin for functional calculus on operator semigroups

This paper provides sharp lower estimates near the origin for the functional calculus F(-uA) of a generator A of an operator semi- group defined on the (strictly) positive real line; here F is given as the Laplace transform of a measure or distribution. The results are linked to the existence of an identity element or an exhaustive sequence of idempotents in the Banach algebra generated by the semigroup. Both the quasinilpotent and non-quasinilpotent cases are considered, and sharp results are proved extending many in the literature

Closed ideals in some algebras of analytic functions

We obtain a complete description of closed ideals of the algebra \mathcal{D}\cap \mathrm{lip}_\alpha}, $0<\alpha\leq{1/2},$ where $\mathcal{D}$ is the Dirichlet space and \mathrm{lip}_\alpha} is the algebra of analytic functions satisfying the Lipschitz condition of order $\alpha.$Comment: 19 page

Horizontal stress anisotropy and effective stress as regulator of coal seam gas zonation in the Sydney Basin, Australia

Coal seam gas zonation in the Sydney Basin, NSW, Australia is related to basin hydrodynamics and hydrochemical facies evolution along the flow path from the subcrop to the basin center. Biogenic methane corresponds with meteoric water under hydrostatic pressure and persists down to the top of the geopressured zone (~800 to 1000m). Thermogenic gases, including wet hydrocarbons, can reach up to relatively shallow horizons of less than 500-600m depth. In the transition zone between the top of the geopressured and base of the hydrostatic zone, a mixed water and gas regime prevails, comprising brackish waters, and gases of mixed biogenic, thermogenic and inorganic origins, including CO. Mechanisms for and the role of stress in the development of this layered hydrogeological and gas environment are investigated in this paper.The inverse relationship between effective horizontal stress and permeability in coals through regulation of cleat volumes is well documented, and there is evidence of regionally compartmentalized stress regimes with depth within the Sydney and other eastern Australian coal basins. This regional stress regime can be overprinted by the effect of localized geological features. It is hypothesized that the in situ stress regime plays an important role in the regulation of groundwater flow regimes and extents, resulting in the development of the reported gas content and compositional zonation.Analysis of regional gas and stress data obtained from public and private databases, as well as literature, supports this hypothesis. Changes in gas concentration and composition with depth correspond with discernable variations in horizontal stress anisotropy. Gas contents generally increase with depth down to a 'peak gas' horizon, below which concentrations decrease. This 'peak gas' zone is coincident with a horizontal stress anisotropy change from moderately high to low levels, associated with reverse to strike-slip faulting conditions, respectively. The stress release zone also marks the top of the thermogenic gas zone, identified by the first appearance of ethane in the vertical profile. This zone also hosts gases of mixed origins: biogenic, thermogenic and inorganic (CO) and represents a mixed (transitional) groundwater flow environment. The base of the mixed gas zone is the top of the 'geopressured-only' flow associated with thermogenic gases and is signaled by the return to high stress reverse faulting conditions below 850-900m depth in the Sydney Basin

Sur quelques extensions au cadre Banachique de la notion d'op\'erateur de Hilbert-Schmidt

In this work we discuss several ways to extend to the context of Banach spaces the notion of Hilbert-Schmidt operators: $p$-summing operators, $\gamma$-summing or $\gamma$-radonifying operators, weakly $*1$-nuclear operators and classes of operators defined via factorization properties. We introduce the class $PS_2(E; F)$ of pre-Hilbert-Schmidt operators as the class of all operators $u:E\to F$ such that $w\circ u \circ v$ is Hilbert-Schmidt for every bounded operator $v: H_1\to E$ and every bounded operator $w:F\to H_2$, where $H_1$ et $H_2$ are Hilbert spaces. Besides the trivial case where one of the spaces $E$ or $F$ is a "Hilbert-Schmidt space", this space seems to have been described only in the easy situation where one of the spaces $E$ or $F$ is a Hilbert space.Comment: 18 pages, in Frenc

Variety of idempotents in nonassociative algebras

In this paper, we study the variety of all nonassociative (NA) algebras from the idempotent point of view. We are interested, in particular, in the spectral properties of idempotents when algebra is generic, i.e. idempotents are in general position. Our main result states that in this case, there exist at least $n-1$ nontrivial obstructions (syzygies) on the Peirce spectrum of a generic NA algebra of dimension $n$. We also discuss the exceptionality of the eigenvalue $\lambda=\frac12$ which appears in the spectrum of idempotents in many classical examples of NA algebras and characterize its extremal properties in metrised algebras.Comment: 27 pages, 1 figure, submitte