Search results for "C3"
showing 10 items of 1295 documents
Existence of common zeros for commuting vector fields on 3‐manifolds II. Solving global difficulties
2020
We address the following conjecture about the existence of common zeros for commuting vector fields in dimension three: if $X,Y$ are two $C^1$ commuting vector fields on a $3$-manifold $M$, and $U$ is a relatively compact open such that $X$ does not vanish on the boundary of $U$ and has a non vanishing Poincar\'e-Hopf index in $U$, then $X$ and $Y$ have a common zero inside $U$. We prove this conjecture when $X$ and $Y$ are of class $C^3$ and every periodic orbit of $Y$ along which $X$ and $Y$ are collinear is partially hyperbolic. We also prove the conjecture, still in the $C^3$ setting, assuming that the flow $Y$ leaves invariant a transverse plane field. These results shed new light on t…
Irreducible induction and nilpotent subgroups in finite groups
2019
Suppose that $G$ is a finite group and $H$ is a nilpotent subgroup of $G$. If a character of $H$ induces an irreducible character of $G$, then the generalized Fitting subgroup of $G$ is nilpotent.
Distributions Frames and bases
2018
In this paper we will consider, in the abstract setting of rigged Hilbert spaces, distribution valued functions and we will investigate, in particular, conditions for them to constitute a "continuous basis" for the smallest space $\mathcal D$ of a rigged Hilbert space. This analysis requires suitable extensions of familiar notions as those of frame, Riesz basis and orthonormal basis. A motivation for this study comes from the Gel'fand-Maurin theorem which states, under certain conditions, the existence of a family of generalized eigenvectors of an essentially self-adjoint operator on a domain $\mathcal D$ which acts like an orthonormal basis of the Hilbert space $\mathcal H$. The correspond…
The volume of geodesic balls and tubes about totally geodesic submanifolds in compact symmetric spaces
1997
AbstractLet M be a compact Riemannian symmetric space. We give an analytical expression for the area and volume functions of geodesic balls in M and for the area and volume functions of tubes around some totally geodesic submanifolds P of M. We plot the graphs of these functions for some compact irreducible Riemannian symmetric spaces of rank two.
Logarithmic bundles of deformed Weyl arrangements of type $A_2$
2016
We consider deformations of the Weyl arrangement of type $A_2$, which include the extended Shi and Catalan arrangements. These last ones are well-known to be free. We study their sheaves of logarithmic vector fields in all other cases, and show that they are Steiner bundles. Also, we determine explicitly their unstable lines. As a corollary, some counter-examples to the shift isomorphism problem are given.
On defects of characters and decomposition numbers
2017
We propose upper bounds for the number of modular constituents of the restriction modulo [math] of a complex irreducible character of a finite group, and for its decomposition numbers, in certain cases.
Hardy-Orlicz Spaces of conformal densities
2014
We define and prove characterizations of Hardy-Orlicz spaces of conformal densities.
Dermatopatología de la oclusión intraluminal vascular: parte I (trombos)
2021
Resumen: La patología vascular oclusiva es causante de diversas y variadas manifestaciones clínicas, algunas de las cuales son de catastróficas consecuencias para el paciente. Sin embargo, las causas de tal oclusión son muy variadas, extendiéndose desde trombos por acción descontrolada de los mecanismos de coagulación, hasta anomalías de los endotelios de los vasos u oclusión por materiales extrínsecos. En una serie de dos artículos hacemos una revisión de las principales causas de oclusión vascular, resumiendo sus manifestaciones clínicas principales y los hallazgos histopatológicos fundamentales. Esta primera parte corresponde a las oclusiones vasculares que cursan con trombos. Abstract: …
On-chip generation of high-dimensional entangled quantum states and their coherent control
2017
Optical quantum states based on entangled photons are essential for solving questions in fundamental physics and are at the heart of quantum information science1. Specifically, the realization of high-dimensional states (D-level quantum systems, that is, qudits, with D > 2) and their control are necessary for fundamental investigations of quantum mechanics2, for increasing the sensitivity of quantum imaging schemes3, for improving the robustness and key rate of quantum communication protocols4, for enabling a richer variety of quantum simulations5, and for achieving more efficient and error-tolerant quantum computation6. Integrated photonics has recently become a leading platform for the co…
Complex quantum state generation and coherent control based on integrated frequency combs
2019
The investigation of integrated frequency comb sources characterized by equidistant spectral modes was initially driven by considerations towards classical applications, seeking a more practical and miniaturized way to generate stable broadband sources of light. Recently, in the context of scaling the complexity of optical quantum circuits, these on-chip approaches have provided a new framework to address the challenges associated with non-classical state generation and manipulation. For example, multi-photon and high-dimensional states were to date either inaccessible, lacked scalability, or were difficult to manipulate, requiring elaborate approaches. The emerging field of quantum frequen…