1,720,959 research outputs found
Symmetric bases for finite element exterior calculus spaces
Full text linkIn 2006, Arnold, Falk, and Winther developed finite element exterior calculus, using the language of differential forms to generalize the Lagrange, Raviart--Thomas, Brezzi--Douglas--Marini, and Nédélec finite element spaces for simplicial triangulations. In a recent paper, Licht asks whether, on a single simplex, one can construct bases for these spaces that are invariant with respect to permuting the vertices of the simplex. For scalar fields, standard bases all have this symmetry property, but for vector fields, this question is more complicated: such invariant bases may or may not exist, depending on the polynomial degree of the element.
In dimensions two and three, Licht constructs such invariant bases for certain values of the polynomial degree , and he conjectures that his list is complete, that is, that no such basis exists for other values of . In this paper, we show that Licht\u27s conjecture is true in dimension two. However, in dimension three, we show that Licht\u27s ideas can be extended to give invariant bases for many more values of ; we then show that this new larger list is complete. Along the way, we develop a more general framework for the geometric decomposition ideas of Arnold, Falk, and Winther.31 page
Uncovering the Lagrangian from Observations of Trajectories
Full text linkWe approach the problem of automatically modeling a mechanical system from data about its dynamics, using a method motivated by variational integrators. We write the discrete Lagrangian as a quadratic polynomial with varying coefficients, and then use the discrete Euler-Lagrange equations to numerically solve for the values of these coefficients near the data points. This method correctly modeled the Lagrangian of a simple harmonic oscillator and a simple pendulum, even with significant measurement noise added to the trajectories
Minimum product sets sizes in nonabelian groups
No full textAbstractGiven a group G and integers r and s, let μG(r,s) be the minimum cardinality of the product set AB, where A and B are subsets of G of cardinality r and s, respectively. We compute μG for all nonabelian groups of order pq, where p and q are distinct odd primes, thus proving a conjecture of Deckelbaum. In addition, we apply a theorem of Eliahou and Kervaire to compute μG for all finite nilpotent groups
Yang-Mills replacement
No full textThesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged from PDF version of thesis.Includes bibliographical references (pages 87-88).We develop an analog of the harmonic replacement technique of Colding and Minicozzi in the gauge theory context. The idea behind harmonic replacement dates back to Schwarz and Perron, and the technique involves taking a function v: ... defined on a surface ... and replacing its values on a small ball B2 ... with a harmonic function u that has the same values as v on the boundary &B2 . The resulting function on ... has lower energy, and repeating this process on balls covering ..., one can obtain a global harmonic map in the limit. We develop the analogous procedure in the gauge theory context. We take a connection B on a bundle over a four-manifold X, and replace it on a small ball ... with a Yang-Mills connection A that has the same restriction to the boundary [alpha]B4 as B, and we obtain bounds on the difference ... in terms of the drop in energy. Throughout, we work with connections of the lowest possible regularity ... (X), the natural choice for this context, and so our gauge transformations are in ... (X) and therefore almost but not quite continuous, leading to more delicate arguments than are available in higher regularity.by Yakov Berchenko-Kogan.Ph. D
Finite element approximation of the Levi-Civita connection and its curvature in two dimensions
Full text linkWe construct finite element approximations of the Levi-Civita connection and
its curvature on triangulations of oriented two-dimensional manifolds. Our
construction relies on the Regge finite elements, which are piecewise
polynomial symmetric (0,2)-tensor fields possessing single-valued
tangential-tangential components along element interfaces. When used to
discretize the Riemannian metric tensor, these piecewise polynomial tensor
fields do not possess enough regularity to define connections and curvature in
the classical sense, but we show how to make sense of these quantities in a
distributional sense. We then show that these distributional quantities
converge in certain dual Sobolev norms to their smooth counterparts under
refinement of the triangulation. We also discuss projections of the
distributional curvature and distributional connection onto piecewise
polynomial finite element spaces. We show that the relevant projection
operators commute with certain linearized differential operators, yielding a
commutative diagram of differential complexes.Comment: v2: Several revisions throughout, including major revisions to
Section 2.4, Section 5, and the beginning of Section
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
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe 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
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