1,720,969 research outputs found
On feedback classification of generic control-affine systems with one and two-dimensional inputs
No full textThe paper is devoted to the local classification of generic control-affine systems on an
n-dimensional manifold with scalar input for any n > 3 or with two inputs for n = 4
and n = 5, up to state-feedback transformations, preserving the affine structure (in C^1
category for n = 4 and C^\omega category for n > 4). First using the Poincare series of moduli
numbers we introduce the intrinsic numbers of functional moduli of each prescribed number
of variables on which a classification problem depends. In order to classify affine systems
with scalar input we associate with such a system the canonical frame by normalizing some
structural functions in a commutative relation of the vector fields, which define our control
system. Then, using this canonical frame, we introduce the canonical coordinates and find
a complete system of state-feedback invariants of the system. It also gives automatically
the micro-local (i.e. local in state-input space) classification of the generic non-affine n-dimensional
control system with scalar input for n >2 (in C^1 category for n = 3 and in
C^\omega category for n > 3). Further we show how the problem of feedback-equivalence of affine
systems with two-dimensional input in state space of dimensions 4 and 5 can be reduced to
the same problem for affine systems with scalar input. In order to make this reduction we
distinguish the subsystem of our control system, consisting of the directions of all extremals
in dimension 4 and all abnormal extremals in dimension 5 of the time optimal problem,
defined by the original control system. In each classification problem under consideration
we find the intrinsic numbers of functional moduli of each prescribed number of variables
according to its Poincare series
Nurowski's conformal structures for (2,5)-distributions via dynamics of abnormal extremals
No full textOn curvatures and focal points of dynamical Lagrange distributions and their reductions by first integrals
No full textPairs (Hamiltonian system, Lagrangian distribution) called dynamical Lagrangian distributions, appear naturally in differential geometry, calculus of variations, and rational mechanics. The basic differential invariants of a dynamical Lagrangian distribution with respect to the action of the group of symplectomorphisms of the ambient symplectic manifold are the curvature operator and curvature form. These invariants can be considered as generalizations of the classical curvature tensor in Riemannian geometry. In particular, in terms of these invariants one can localize the focal points along extremals of the corresponding variational problems. In the present paper we study the behavior of the curvature operator, the curvature form, and the focal points of a dynamical Lagrangian distribution after its reduction by arbitrary first integrals in involution. An interesting phenomenon is that the curvature form of so-called monotone increasing Lagrangian dynamical distributions, which appear naturally in mechanical systems, does not decrease after reduction. It also turns out that the set of focal points to the given point with respect to the monotone increasing dynamical Lagrangian distribution and the corresponding set of focal points with respect to its reduction by one integral are alternating sets on the corresponding integral curve of the Hamiltonian system of the considered dynamical distributions. Moreover, the first focal point corresponding to the reduced Lagrangian distribution comes before any focal point related to the original dynamical distribution. We illustrate our results on the classical N-body problem
A canonical connection on sub-Riemannian contact manifolds
Get PDFsummary:We construct a canonically defined affine connection in sub-Riemannian contact geometry. Our method mimics that of the Levi-Civita connection in Riemannian geometry. We compare it with the Tanaka-Webster connection in the three-dimensional case
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Get PDF“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
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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