Faculty Research Publications (Mathematics)
http://hdl.handle.net/1957/13818
2014-07-23T22:25:01ZCommensurable continued fractions
http://hdl.handle.net/1957/50460
Commensurable continued fractions
Arnoux, Pierre; Schmidt, Thomas A.
We compare two families of continued fractions algorithms, the
symmetrized Rosen algorithm and the Veech algorithm. Each of these algorithms
expands real numbers in terms of certain algebraic integers. We give
explicit models of the natural extension of the maps associated with these algorithms;
prove that these natural extensions are in fact conjugate to the first
return map of the geodesic flow on a related surface; and, deduce that, up
to a conjugacy, almost every real number has an infinite number of common
approximants for both algorithms.
This is the publisher’s final pdf. The published article is copyrighted by the American Institute of Mathematical Sciences and can be found at: http://aimsciences.org/journals/home.jsp?journalID=1.
2014-11-01T00:00:00ZSparse Recovery by means of Nonnegative Least Squares
http://hdl.handle.net/1957/50336
Sparse Recovery by means of Nonnegative Least Squares
Foucart, Simon; Koslicki, David
This short note demonstrates that sparse
recovery can be achieved by an l₁-minimization ersatz
easily implemented using a conventional nonnegative
least squares algorithm. A connection with orthogonal
matching pursuit is also highlighted. The preliminary
results call for more investigations on the potential
of the method and on its relations to classical sparse
recovery algorithms.
(c) 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article can be found at: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=97.
2014-04-01T00:00:00ZNonlinear Plates Interacting with A Subsonic, Inviscid Flow via Kutta-Joukowski Interface Conditions
http://hdl.handle.net/1957/49987
Nonlinear Plates Interacting with A Subsonic, Inviscid Flow via Kutta-Joukowski Interface Conditions
Lasiecka, Irena; Webster, Justin T.
We analyze the well-posedness of a flow-plate interaction considered in [22, 24]. Specifically, we consider the
Kutta-Joukowski boundary conditions for the flow [20, 28, 26], which
ultimately give rise to a hyperbolic equation in the half-space (for the flow) with mixed
boundary conditions. This boundary condition has been considered previously in the lower-dimensional interactions [1, 2], and dramatically changes the properties of the flow-plate
interaction and requisite analytical techniques.
We present results on well-posedness of the fluid-structure interaction with the Kutta-Joukowski
flow conditions in force. The semigroup approach to the proof utilizes an abstract setup related to that in [16] but requires (1) the use of a Neumann-flow map to address a Zaremba type elliptic problem and (2) a trace regularity assumption on the acceleration potential of the flow. This assumption is linked to invertibility of singular integral
operators which are analogous to the finite Hilbert transform in two dimensions. (We show
the validity of this assumption when the model is reduced to a two dimensional flow interacting with a one dimensional structure; this requires microlocal techniques.) Our results link the analysis in [16] to that in [1, 2].
This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier and can be found at: http://www.journals.elsevier.com/nonlinear-analysis-real-world-applications/.
2014-06-01T00:00:00ZSimply connected open 3-manifolds with rigid genus one ends
http://hdl.handle.net/1957/49868
Simply connected open 3-manifolds with rigid genus one ends
Garity, Dennis; Repovš, Dušan; Wright, David
We construct uncountably many simply connected open
3-manifolds with genus one ends homeomorphic to the Cantor set.
Each constructed manifold has the property that any self homeomorphism of the manifold (which necessarily extends to a homeomorphism of the ends) fixes the ends pointwise. These manifolds
are complements of rigid generalized Bing-Whitehead (BW) Cantor sets. Previous examples of rigid Cantor sets with simply connected complement in R³ had infinite genus and it was an open
question as to whether finite genus examples existed. The examples
here exhibit the minimum possible genus, genus one. These rigid
generalized BW Cantor sets are constructed using variable numbers of Bing and Whitehead links. Our previous result with Željko
determining when BW Cantor sets are equivalently embedded in
R³ extends to the generalized construction. This characterization
is used to prove rigidity and to distinguish the uncountably many
examples.
This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer and can be found at: http://link.springer.com/journal/13163.
2014-01-01T00:00:00Z