1,720,979 research outputs found
Non-dense orbits on homogeneous spaces and applications to geometry and number theory
No full textAbstract Let G be a Lie group, let be a discrete subgroup, let =G/\Gamma with f -trajectories avoiding Z is hyperplane absolute winning (a property which implies full Hausdorff dimension and is stable under countable intersections). A similar result is proved for one-parameter actions on X . This has applications in constructing exceptional geodesics on locally symmetric spaces and in non-density of the set of values of certain functions at integer points
Badly Approximable Systems of Affine Forms
No full textAbstractWe prove an inhomogeneous analogue of W. M. Schmidt's theorem on the Hausdorff dimension of the set of badly approximable systems of linear forms. The proof is based on ideas and methods from the theory of dynamical systems, in particular, on abundance of bounded orbits of mixing flows on homogeneous spaces of Lie group
Recommended from our members
Homogeneous Dynamics and Number Theory
Get PDFThe theory of flows on homogeneous spaces of Lie groups has emerged as a distinct, rapidly advancing subject over the last few decades incorporating ergodic theory, geometry and number theory. The workshop showcased the latest advances in the subject as well as a wide range of applications
Khintchine-type theorems via estimates for Siegel transform
No full textRecently there has been a surge of activity in quantifying the density of values of generic quadratic forms at integer points. I will present some new and quite general results in this direction obtained via the so-called Siegel-Rogers method, which has recently been utilized by Athreya and Margulis, and later by Kelmer and Yu. This work is joint with Mishel Skenderi.Non UBCUnreviewedAuthor affiliation: Brandeis UniversityFacult
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
Inhomogeneous Diophantine approximation for generic homogeneous functions
No full textThe present paper is a sequel to [Monatsh.~Math.\ {\bf 194} (2021), 523--554]
in which results of that paper are generalized so that they hold in the setting
of inhomogeneous Diophantine approximation. Given any integers and
, any , and any homogeneous function \linebreak that satisfies a certain
nonsingularity assumption, we obtain a biconditional criterion on the
approximating function for a generic
element in the -orbit of to be
(respectively, not to be) -approximable at : that is, for there to exist infinitely many
(respectively, only finitely many) such that
for each . In this setting, we also obtain a sufficient condition for
uniform approximation. We also consider some examples of that do not
satisfy our nonsingularity assumptions and prove similar results for these
examples. Moreover, one can replace above by
any closed subgroup of that satisfies
certain integrability axioms (being of Siegel and Rogers type) introduced by
the authors in the aforementioned previous paper.Comment: 19 pages; exposition reworded, more examples adde
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
- …
