Showing 11 - 20 of 94 Items
On the sign representations for the complex reflection groups G(r, p, n)
Date: 2016-11-01
Creator: Aba Mbirika, Thomas Pietraho, William Silver
Access: Open access
- We present a formula for the values of the sign representations of a complex reflection group G(r, p, n) in terms of its image under a generalized Robinson–Schensted algorithm.
Dark breathers in granular crystals
Date: 2013-04-08
Creator: C. Chong, P. G. Kevrekidis, G. Theocharis, Chiara Daraio
Access: Open access
- We present a study of the existence, stability, and bifurcation structure of families of dark breathers in a one-dimensional uniform chain of spherical beads under static load. A defocusing nonlinear Schrödinger equation (NLS) is derived for frequencies that are close to the edge of the phonon band and is used to construct targeted initial conditions for numerical computations. Salient features of the system include the existence of large amplitude solutions that emerge from the small amplitude solutions described by the NLS equation, and the presence of a nonlinear instability that, to the best of the authors' knowledge, has not been observed in classical Fermi-Pasta-Ulam lattices. Finally, it is also demonstrated that these dark breathers can be detected in a physically realistic experimental settings by merely actuating the ends of an initially at rest chain of beads and inducing destructive interference between their signals. © 2013 American Physical Society.
Tree-based language complexity of Thompson's group F
Date: 2015-11-01
Creator: Jennifer Taback, Sharif Younes
Access: Open access
- The definition of graph automatic groups by Kharlampovich, Khoussainov and Miasnikov and its extension to C-graph automatic by Elder and the first author raise the question of whether Thompson's group F is graph automatic. We define a language of normal forms based on the combinatorial "caret types", which arise when elements of F are considered as pairs of finite rooted binary trees. The language is accepted by a finite state machine with two counters, and forms the basis of a 3-counter graph automatic structure for the group.
Dispersive Shock Waves in Granular Chains This record is embargoed.
- Embargo End Date: 2026-05-18
Date: 2023-01-01
Creator: Ari Geisler
Access: Embargoed
A Comprehensive Survey on Functional Approximation
Date: 2022-01-01
Creator: Yucheng Hua
Access: Open access
- The theory of functional approximation has numerous applications in sciences and industry. This thesis focuses on the possible approaches to approximate a continuous function on a compact subset of R2 using a variety of constructions. The results are presented from the following four general topics: polynomials, Fourier series, wavelets, and neural networks. Approximation with polynomials on subsets of R leads to the discussion of the Stone-Weierstrass theorem. Convergence of Fourier series is characterized on the unit circle. Wavelets are introduced following the Fourier transform, and their construction as well as ability to approximate functions in L2(R) is discussed. At the end, the universal approximation theorem for artificial neural networks is presented, and the function representation and approximation with single- and multilayer neural networks on R2 is constructed.
The Current Support Theorem in Context
Date: 2023-01-01
Creator: Ethan Winters
Access: Open access
- This work builds up the theory surrounding a recent result of Erlandsson, Leininger, and Sadanand: the Current Support Theorem. This theorem states precisely when a hyperbolic cone metric on a surface is determined by the support of its Liouville current. To provide background for this theorem, we will cover hyperbolic geometry and hyperbolic surfaces more generally, cone surfaces, covering spaces of surfaces, the notion of an orbifold, and geodesic currents. A corollary to this theorem found in the original paper is discussed which asserts that a surface with more than $32(g-1)$ cone points must be rigid. We extend this result to the case that there are more than $3(g-1)$ cone points. An infinite family of cone surfaces which are not rigid and which have precisely $3(g-1)$ cone points is also provided, hence demonstrating tightness.
The structure of singularities in Π-minimizing networks in R2
Date: 1991-01-01
Creator: M. Alfaro, M. Conger, K. Hodges, A. Levy, R., Kochar, L. Kuklinski
Access: Open access
Cells and constructible representations in type B
Date: 2008-10-13
Creator: Thomas Pietraho
Access: Open access
- We examine the partition of a finite Coxeter group of type B into cells determined by a weight function L. The main objective of these notes is to reconcile Lusztig's description of constructible representations in this setting with conjectured combinatorial descriptions of cells.
The large-scale geometry of some metabelian groups
Date: 2003-01-01
Creator: Jennifer Taback, Kevin Whyte
Access: Open access
Tame combing and almost convexity conditions
Date: 2011-12-01
Creator: Sean Cleary, Susan Hermiller, Melanie Stein, Jennifer Taback
Access: Open access
- We give the first examples of groups which admit a tame combing with linear radial tameness function with respect to any choice of finite presentation, but which are not minimally almost convex on a standard generating set. Namely, we explicitly construct such combings for Thompson's group F and the Baumslag-Solitar groups BS(1, p) with p ≥ 3. In order to make this construction for Thompson's group F, we significantly expand the understanding of the Cayley complex of this group with respect to the standard finite presentation. In particular we describe a quasigeodesic set of normal forms and combinatorially classify the arrangements of 2-cells adjacent to edges that do not lie on normal form paths. © 2010 Springer-Verlag.