2,513 research outputs found
Arc Operads and Arc Algebras
Several topological and homological operads based on families of projectively
weighted arcs in bounded surfaces are introduced and studied. The spaces
underlying the basic operad are identified with open subsets of a
compactification due to Penner of a space closely related to Riemann's moduli
space. Algebras over these operads are shown to be Batalin-Vilkovisky algebras,
where the entire BV structure is realized simplicially. Furthermore, our basic
operad contains the cacti operad up to homotopy, and it similarly acts on the
loop space of any topological space. New operad structures on the circle are
classified and combined with the basic operad to produce geometrically natural
extensions of the algebraic structure of BV algebras, which are also computed.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol7/paper15.abs.htm
AC impedance analysis of polypyrrole thin films
The AC impedance spectra of thin polypyrrole films were obtained at open circuit potentials from -0.4 to 0.4 V vs SCE. Two limiting cases are discussed for which simplified equivalent circuits are applicable. At very positive potentials, the predominantly nonfaradaic AC impedance of polypyrrole is very similar to that observed previously for finite porous metallic films. Modeling of the data with the appropriate equivalent circuit permits effective pore diameter and pore number densities of the oxidized film to be estimated. At potentials from -0.4 to -0.3 V, the polypyrrole film is essentially nonelectronically conductive and diffusion of polymer oxidized sites with their associated counterions can be assumed to be linear from the film/substrate electrode interface. The equivalent circuit for the polypyrrole film at these potentials is that previously described for metal oxide, lithium intercalation thin films. Using this model, counterion diffusion coefficients are determined for both semi-infinite and finite diffusion domains. In addition, the limiting low frequency resistance and capacitance of the polypyrrole thin fims was determined and compared to that obtained previously for thicker films of the polymer. The origin of the observed potential dependence of these low frequency circuit components is discussed
Filtered screens and augmented Teichm\"uller space
We study a new bordification of the decorated Teichm\"uller space for a
multiply punctured surface F by a space of filtered screens on the surface that
arises from a natural elaboration of earlier work of McShane-Penner. We
identify necessary and sufficient conditions for paths in this space of
filtered screens to yield short curves having vanishing length in the
underlying surface F. As a result, an appropriate quotient of this space of
filtered screens on F yields a decorated augmented Teichm\"uller space which is
shown to admit a CW decomposition that naturally projects to the augmented
Teichm\"uller space by forgetting decorations and whose strata are indexed by a
new object termed partially oriented stratum graphs.Comment: Final version to appear in Geometriae Dedicat
Determination of diffusion coefficients in polypyrrole thin films using a current pulse relaxation method
The current pulse E sub oc relaxation method and its application to the determination of diffusion coefficients in electrochemically synthesized polypyrrole thin films is described. Diffusion coefficients for such films in Et4NBF4 and MeCN are determined for a series of submicron film thicknesses. Measurement of the double-layer capacitance, C sub dl, and the resistance, R sub u, of polypyrrole thin films as a function of potential obtained with the galvanostatic pulse method is reported. Measurements of the electrolyte concentration in reduced polypyrrole films are also presented to aid in the interpretation of the data
Interrogating race: color, racial categories, and class across the Americas
We address long-standing debates on the utility of racial categories and color scales for understanding inequality in the United States and Latin America, using novel data that enable comparisons of these measures across both broad regions. In particular, we attend to the degree to which color and racial category inequality operate independently of parental socioeconomic status. We find a variety of patterns of racial category and color inequality, but that in most countries accounting for maternal education changes our coefficients by 5% or less. Overall, we argue that several posited divergences in ethnoracial stratification processes in the United States, compared with Latin America, might be overstated. We conclude that the comparison of the effects of multiple ethnoracial markers, such as color and racial categories, for the analysis of social stratification holds substantial promise for untangling the complexities of âraceâ across the Americas
Topological Entropy of Braids on the Torus
A fast method is presented for computing the topological entropy of braids on
the torus. This work is motivated by the need to analyze large braids when
studying two-dimensional flows via the braiding of a large number of particle
trajectories. Our approach is a generalization of Moussafir's technique for
braids on the sphere. Previous methods for computing topological entropies
include the Bestvina--Handel train-track algorithm and matrix representations
of the braid group. However, the Bestvina--Handel algorithm quickly becomes
computationally intractable for large braid words, and matrix methods give only
lower bounds, which are often poor for large braids. Our method is
computationally fast and appears to give exponential convergence towards the
exact entropy. As an illustration we apply our approach to the braiding of both
periodic and aperiodic trajectories in the sine flow. The efficiency of the
method allows us to explore how much extra information about flow entropy is
encoded in the braid as the number of trajectories becomes large.Comment: 19 pages, 44 figures. SIAM journal styl
Lectures on the Asymptotic Expansion of a Hermitian Matrix Integral
In these lectures three different methods of computing the asymptotic
expansion of a Hermitian matrix integral is presented. The first one is a
combinatorial method using Feynman diagrams. This leads us to the generating
function of the reciprocal of the order of the automorphism group of a tiling
of a Riemann surface. The second method is based on the classical analysis of
orthogonal polynomials. A rigorous asymptotic method is established, and a
special case of the matrix integral is computed in terms of the Riemann
-function. The third method is derived from a formula for the
-function solution to the KP equations. This method leads us to a new
class of solutions of the KP equations that are
\emph{transcendental}, in the sense that they cannot be obtained by the
celebrated Krichever construction and its generalizations based on algebraic
geometry of vector bundles on Riemann surfaces. In each case a mathematically
rigorous way of dealing with asymptotic series in an infinite number of
variables is established
A super-analogue of Kontsevich's theorem on graph homology
In this paper we will prove a super-analogue of a well-known result by
Kontsevich which states that the homology of a certain complex which is
generated by isomorphism classes of oriented graphs can be calculated as the
Lie algebra homology of an infinite-dimensional Lie algebra of symplectic
vector fields.Comment: 15 page
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