1,720,962 research outputs found
A dynamical approach to the Sard problem in Carnot groups
Full text linkWe introduce a dynamical-systems approach for the study of the Sard problem in sub-Riemannian Carnot groups. We show that singular curves can be obtained by concatenating trajectories of suitable dynamical systems. As an application, we positively answer the Sard problem in some classes of Carnot groups
On the Set of Points of Smoothness for the Value Function of Affine Optimal Control Problems
Full text linkWe study the regularity properties of the value function associated with an affine optimal control problem with quadratic cost plus a potential, for a fixed final time and initial point. Without assuming any condition on singular minimizers, we prove that the value function is continuous on an open and dense subset of the interior of the attain able set. As a byproduct we obtain that it is actually smooth on a possibly smaller set, still open a nd dense
Higher Order Goh Conditions for Singular Extremals of Corank 1
Full text linkWe prove Goh conditions of order n >= 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} for strictly singular length-minimizing curves of corank 1, under the assumption that the domain of the nth instrinsic differential is of finite codimension. This result relies upon the proof of an open mapping theorem for maps with a regular nth differential
Normal forms for the endpoint map near nice singular curves for rank-two distributions
No full textGiven a rank-two sub-Riemannian structure (M, Δ) and a point x0 ∈ M, a singular curve is a critical point of the endpoint map F : γ ↦ γ (1) defined on the space of horizontal curves starting at x0. The typical least degenerate singular curves of these structures are called regular singular curves; they are nice if their endpoint is not conjugate along γ. The main goal of this paper is to show that locally around a nice singular curve γ, once we choose a suitable topology on the control space we can find a normal form for the endpoint map, in which F writes essentially as a sum of a linear map and a quadratic form. This is a preparation for a forthcoming generalization of the Morse theory to rank-two sub-Riemannian structures
The Sard problem in step 2 and in filiform Carnot groups
Full text linkWe study the Sard problem for the endpoint map in some well-known classes of Carnot groups. Our first main result deals with step 2 Carnot groups, where we provide lower bounds (depending only on the algebra of the group) on the codimension of the abnormal set; it turns out that our bound is always at least 3, which improves the result proved in Le Donne et al. [Ann. Inst. H. Poincare Anal. Non Lineaire 33 (2016) 1639-1666] and settles a question emerged in Ottazzi and Vittone [ESAIM: COCV 25 (2019) 18]. In our second main result we characterize the abnormal set in filiform groups and show that it is either a horizontal line, or a 3-dimensional algebraic variety
When does the evoluted set have negligible boundary?
Full text linkThe evoluted set at time T is the union of all images of an initial set A via the flow at times t ∈ (0, T). Its regularity is for interest for control, being the attainable set in several relevant examples.We first show that it is not sufficient for A to have negligible boundary (i.e. zero Lebesgue measure) to ensure that the evoluted set has negligible boundary too. Instead, we prove that such property holds when A is a C1,1 domain
Third order open mapping theorems and applications to the end-point map
Full text linkThis paper is devoted to a third order study of the end-point map in
sub-Riemannian geometry. We first prove third order open mapping results for
maps from a Banach space into a finite dimensional manifold. In a second step,
we compute the third order term in the Taylor expansion of the end-point map
and we specialize the abstract theory to the study of length-minimality of
sub-Riemannian strictly singular curves. We conclude with the third order
analysis of a specific strictly singular extremal that is not
length-minimizing
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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