搜索结果：Comptes rendus biologies

In this paper we consider a punctured Riemann surface endowed with a Hermitian metric that equals the Poincaré metric near the punctures, and a holomorphic line bundle that polarizes the metric. We show that the quotient of the induced Fubini-Study forms by Kodaira maps of high tensor powers of the line bundle and the Poincaré form near the singularity grows polynomially uniformly on a neighborhood of the singularity as the tensor power tends to infinity, as an application of the method in [5].

We show that the algebraic K-theory of semi-valuation rings with stably coherent regular semi-fraction ring satisfies homotopy invariance. Moreover, we show that these rings are regular if their valuation is non-trivial. Thus they yield examples of regular rings which are not homotopy invariant for algebraic K-theory. On the other hand, they are not necessarily coherent, so that they provide a class of possibly non-coherent examples for homotopy invariance of algebraic K-theory. As an application, we show that Temkin's relative Riemann-Zariski spaces also satisfy homotopy invariance for K-theory under some finiteness assumption.

The braid group $B_4$ naturally acts on the rational projective plane $\mathbb{P}^2(\mathbb{Q})$, this action corresponds to the classical integral reduced Burau representation of $B_4$. The first result of this paper is a classification of the orbits of this action. The Burau representation then defines an action of $B_4$ on $\mathbb{P}^2(\mathbb{Z}(q))$, where $q$ is a formal parameter and $\mathbb{Z}(q)$ is the field of rational functions in $q$ with integer coefficients. We study orbits of the $B_4$-action on $\mathbb{P}^2(\mathbb{Z}(q))$, and show existence of embeddings of the $q$-deformed projective line $\mathbb{P}^1(\mathbb{Z}(q))$ that precisely correspond to the notion of $q$-rationals due to Morier-Genoud and Ovsienko.

Let $f$ be a holomorphic self-map of the unit disc. We show that if $\log (1-\lvert f(z) \rvert)$ is integrable on a sub-arc of the unit circle, $I$, then the set of points where the function f has finite Carathéodory angular derivative on I is a countable union of Beurling-Carleson sets of finite entropy. Conversely, given a countable union of Beurling-Carleson sets, $E$, we construct a holomorphic self-map of the unit disc, $f$, such that the set of points where the function has finite Carathéodory angular derivative is equal to $E$ and $\log(1-\lvert f(z) \rvert)$ is integrable on the unit circle. Our main technical tools are the Aleksandrov disintegration Theorem and a characterization of countable unions of Beurling-Carleson sets due to Makarov and Nikolski.

Understanding how giant and terrestrial planets form and evolve, what is their internal structure and that of their atmosphere, represents one of the major challenges of modern astronomy, which is directly connected to the ultimate search for life at the horizon 2040. However, several astrophysical, biological and technological obstacles must be overcome. From the astrophysical point of view, it is indeed crucial to understand the mechanisms of formation and evolution of giant planets, including planet and disk interactions, which will completely sculpt the planetary architectures and thus dominate the formation of terrestrial planets, especially in regions around the host star capable of supporting life. It is also important to develop dedicated instrumentation and techniques to study in their totality the population of giant and terrestrial planets, but also to reveal in the near future the first biological clues of life in the atmospheres of terrestrial planets. In that perspective, direct imaging from ground-based observatories or in space is playing a central role in concert with other observing techniques. This review introduces the genesis of this observing technique, the ma

In this short note, we construct an exotic example of a locally compact group $G$ with a Borel $2$-cocycle $ω$ such that the non-twisted group von Neumann algebra $L(G)$ is a factor, while the twisted group von Neumann algebra $L_ω(G)$ has a diffuse center.

(in english): Urbain-Jean-Joseph Le Verrier was born in Saint-Lô on March 11, 1811. He entered the Ecole Polytechnique in 1831, from which he was to emerge 8th two years later. After first devoting himself to chemistry, in 1836 he obtained a position as an astronomy assistant at the Ecole Polytechnique. This choice will decide his future career which culminates with the discovery of Neptune in 1846. Le Verrier wrote more than 200 contributions in the Comptes Rendus de l'Académie des Sciences. These contributions are very varied: some original articles but also reports on publications published elsewhere, sometimes even simple notes of a single page. The whole set gives a very vivid vision of the development of the science of the XIXth century. At that time, the Comptes Rendus are really a reflection of the debates of the sessions of the Academy. They are published very quickly, and leave a large freedom of speech to the authors. They are therefore a snapshot of the sometimes lively polemics which animated the sessions of the Academy of Sciences. In this limited essay, we will look to the first years of the career of Le Verrier until the discovery of Neptune. (in french) Le Verrier

We define the notion of reductive group schemes defined over the localization of a regular henselian ring A at a strict normal crossing divisor $D$. We provide a criterion for the existence for parabolic subgroups of a given type.

We have recently identified a protected topological semimetal in graphene which presents a zero-energy edge mode robust to disorder and interactions. Here, we address the characteristics of this semimetal and show that the $\mathbb{Z}$ topological invariant of the Hall conductivity associated to the lowest energy band can be equivalently measured from the resonant response to circularly polarized light resolved at the Dirac points. The (non-quantized) conductivity responses of the intermediate energy bands, including the Fermi surface, also give rise to a $\mathbb{Z}_2$ invariant. We emphasize on the bulk-edge correspondence as a protected topological half metal, i.e. one spin-population polarized in the plane is in the insulating phase related to the robust edge mode while the other is in the metallic regime. The quantized transport at the edges is equivalent to a $\frac{1}{2}-\frac{1}{2}$ conductance for spin polarizations along $z$ direction. We also build a parallel between the topological Hall response and a pair of half numbers (half Skyrmions) through the light response locally resolved in momentum space and on the sphere.

Exoplanetary science is a very active field of astronomy nowadays, with questions still opened such as how planetary systems form and evolve (occurrence, process), why such a diversity of exoplanets is observed (mass, radius, orbital parameters, temperature, composition), and what are the interactions between planets, circumstellar disk and their host star. Several complementary methods are used for the detection of exoplanets. Among these, imaging aims at the direct detection of the light reflected, scattered or emitted by exoplanets and circumstellar disks. This allows their spectral and polarimetric characterization. Such imaging remains challenging because of the large luminosity ratio (1e4-1e10$) and the small angular separation (fraction of an arcsecond) between the star and its environment. Over the past two decades, numerous techniques, including coronagraphy, have been developed to make exoplanet imaging a reality. This review gives a broad overview of the subsystems that make up a coronagraphic instrument for imaging exoplanetary systems. It is especially intended for non-specialists or newcomers in the field. We explain the principle of coronagraphy and propose a formali

We show that solutions to the Kashiwara-Vergne problem can be extended degree by degree. This can be used to simplify the computation of a class of Drinfel'd associators, which under the Alekseev-Torossian conjecture, may comprise all associators. We also give a proof that the associated graded Lie algebra of the Kashiwara-Vergne group is isomorphic to the graded Kashiwara-Vergne Lie algebra.

We prove that every finite dimensional unitary representation of $\mathrm{SL}_{4}(\mathbf{Z})$ contains a non-zero $\mathrm{SL}_{2}(\mathbf{Z})$-invariant vector. As a consequence, there is no sequence of finite-dimensional representations of $\mathrm{SL}_{4}(\mathbf{Z})$ that gives rise to an embedding of its reduced $C^*$-algebra into an ultraproduct of matrix algebras.

Envisioned by Richard Feynman in the early 1980s, quantum simulation has received dramatic impetus thanks to the development of a variety of plateforms able to emulate a wide class of quantum Hamiltonians. During the past decade, most of the quantum simulators have implemented rather well-known models, hence permitting a direct comparison with theoretical calculations and a precise benchmarking of their reliability. The field has now reached a maturity such that one can address difficult problems, which cannot be solved efficiently using classical algorithms. These advances provide unprecedented opportunities to explore previously unreachable fields, test theoretical predictions, and inspire novel approaches. This contribution is an introduction to quantum simulation. It is published as a forward to the special issue on Quantum Simulation of the Comptes-Rendus de Physique of the French Academy of Sciences.

Among the available quantum gravity proposals, string theory, loop quantum gravity, non-commutative geometry, group field theory, causal sets, asymptotic safety, causal dynamical triangulation, emergent gravity are among the best motivated models. As an introductory summary to this special issue of Comptes Rendus Physique, I explain how those different theories can be tested or constrained by cosmological observations.

Following the 2015 Planck release, we briefly comment on the status and some ongoing opportunities in the interface between inflationary cosmology, string theory, and CMB data. The constraints in the $r$-$n_s$ plane introduce a new parameter into inflationary cosmology relative to the simplest quadratic inflation model, in a direction which fits well with couplings to heavy fields as occurs in string theory. The precision of the data permits further searches for and constraints on additional model-dependent features, such as oscillatory $N$-spectra, a program requiring specific theoretically motivated shapes. Since the perturbations can easily be affected by additional sectors and couplings, null results can usefully bound such contributions. We also review the broader lessons string theory has contributed to our understanding of primordial inflation, and close with some approaches to a more complete framework. Published in a special volume of Comptes Rendus on Inflation: Theoretical and Observational Status.

This article gives a short description of pattern formation and coarsening phenomena and focuses on recent experimental and theoretical advances in these fields. It serves as an introduction to phase ordering kinetics and it will appear in the special issue `Coarsening dynamics', Comptes Rendus de Physique, edited by F. Corberi and P. Politi.

We review understanding of kinetics of fluid phase separation in various space dimensions. Morphological differences, percolating or disconnected, based on overall composition in a binary liquid or density in a vapor-liquid system, have been pointed out. Depending upon the morphology, various possible mechanisms and corresponding theoretical predictions for domain growth are discussed. On computational front, useful models and simulation methodologies have been presented. Theoretically predicted growth laws have been tested via molecular dynamics simulations of vapor-liquid transitions. In case of disconnected structure, the mechanism has been confirmed directly. This is a brief review on the topic for a special issue on coarsening dynamics, expected to appear in Comptes Rendus Physique.

Disorder in atomic positions can induce a topologically nontrivial phase - topological Anderson insulator (TAI) - for transverse electric optical quasimodes of a two-dimensional honeycomb lattice of immobile atoms. TAI requires both time-reversal and inversion symmetries to be broken to similar extents. It is characterized by a nonzero topological invariant, a reduced density of states and spatially localized quasimodes in the bulk, as well as propagating edge states. A transition from TAI to the topological insulator (TI) phase can take place at a constant value of the topological invariant, showing that TAI and TI represent the same topological phase.