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Full-Text Articles in Mathematics
Dynamics Of Quasiconformal Fields, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
Dynamics Of Quasiconformal Fields, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
Mathematics - All Scholarship
A uniqueness theorem is established for autonomous systems of ODEs, x= f(x), where f is a Sobolev vector field with additional geometric structure, such as delta-monoticity or reduced quasiconformality. Specifically, through every non-critical point of f there passes a unique integral curve.
On Injectivity Of Quasiregular Mappings, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
On Injectivity Of Quasiregular Mappings, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
Mathematics - All Scholarship
We give sufficient conditions for a planar quasiregular mapping to be injective in terms of the range of the differential matrix.
On The Colored Jones Polynomial, Sutured Floer Homology, And Knot Floer Homology, J. Elisenda Grigsby, Stephan Wehrli
On The Colored Jones Polynomial, Sutured Floer Homology, And Knot Floer Homology, J. Elisenda Grigsby, Stephan Wehrli
Mathematics - All Scholarship
Let K in S3 be a knot, and let K denote the preimage of K inside its double branched cover, Sigma(S3, K). We prove, for each integer n > 1, the existence of a spectral sequence from Khovanov's categorification of the reduced n-colored Jones polynomial of K (mirror of K) and whose Einfinity term is the knot Floer homology of (Sigma(S3,K),K) (when n odd) and to (S3, K # K) (when n even). A corollary of our result is that Khovanov's categorification of the reduced n-colored Jones polynomial detects the unknot whenever n …
Contributions To Khovanov Homology, Stephan M. Wehrli
Contributions To Khovanov Homology, Stephan M. Wehrli
Mathematics - All Scholarship
Khovanov homology ist a new link invariant, discovered by M. Khovanov, and used by J. Rasmussen to give a combinatorial proof of the Milnor conjecture. In this thesis, we give examples of mutant links with different Khovanov homology. We prove that Khovanov's chain complex retracts to a subcomplex, whose generators are related to spanning trees of the Tait graph, and we exploit this result to investigate the structure of Khovanov homology for alternating knots. Further, we extend Rasmussen's invariant to links. Finally, we generalize Khovanov's categorifications of the colored Jones polynomial, and study conditions under which our categorifications are functorial …
On Gradient Ricci Solitons With Symmetry, Peter Petersen, William Wylie
On Gradient Ricci Solitons With Symmetry, Peter Petersen, William Wylie
Mathematics - All Scholarship
We study gradient Ricci solitons with maximal symmetry. First we show that there are no non-trivial homogeneous gradient Ricci solitons. Thus the most symmetry one can expect is an isometric cohomogeneity one group action. Many examples of cohomogeneity one gradient solitons have been constructed. However, we apply the main result in our paper "Rigidity of gradient Ricci solitons" to show that there are no noncompact cohomogeneity one shrinking gradient solitons with nonnegative curvature.
On The Classification Of Gradient Ricci Solitons, Peter Petersen, William Wylie
On The Classification Of Gradient Ricci Solitons, Peter Petersen, William Wylie
Mathematics - All Scholarship
We show that the only complete shrinking gradient Ricci solitons with vanishing Weyl tensor are quotients of the standard ones. This gives a new proof of the Hamilton-Ivey-Perel'man classification of 3-dimensional shrinking gradient solitons. We also prove a classification for expanding gradient Ricci solitons with constant scalar curvature and suitably decaying Weyl tensor.
The Mixed Problem For Harmonic Functions In Polyhedra, Moises Venouziou, Gregory C. Verchota
The Mixed Problem For Harmonic Functions In Polyhedra, Moises Venouziou, Gregory C. Verchota
Mathematics - All Scholarship
R. M. Brown's theorem on mixed Dirichlet and Neumann boundary conditions is extended in two ways for the special case of polyhedral domains. A (1) more general partition of the boundary into Dirichlet and Neumann sets is used on (2) manifold boundaries that are not locally given as the graphs of functions. Examples are constructed to illustrate necessity and other implications of the geometric hypotheses.
Elliptic Complexes And Generalized Poincaré Inequalities, Derek Gustafson
Elliptic Complexes And Generalized Poincaré Inequalities, Derek Gustafson
Mathematics - All Scholarship
We study first order differential operators with constant coefficients. The main question is under what conditions a generalized Poincar\'e inequality holds. We show that the constant rank condition is sufficient. The concept of the Moore-Penrose generalized inverse of a matrix comes into play.
Fixed-Effect Estimation Of Highly-Mobile Production Technologies, William Clinton Horrace, Kurt E. Schnier
Fixed-Effect Estimation Of Highly-Mobile Production Technologies, William Clinton Horrace, Kurt E. Schnier
Center for Policy Research
Revised from November 2006 and July 2007. We consider fixed-effect estimation of a production function where inputs and outputs vary over time, space, and cross-sectional unit. Variability in the spatial dimension allows for time-varying individual effects, without parametric assumptions on the effects. Asymptotics along the spatial dimension provide consistency and normality of the marginal products. A finite-sample example is provided: a production function for bottom-trawler fishing vessels in the flatfish fisheries of the Bering Sea. We find significant spatial variability of output (catch) which we exploit in estimation of a harvesting function.
Semiparametric Deconvolution With Unknown Error Variance, William C. Horrace, Christopher F. Parmeter
Semiparametric Deconvolution With Unknown Error Variance, William C. Horrace, Christopher F. Parmeter
Center for Policy Research
Deconvolution is a useful statistical technique for recovering an unknown density in the presence of measurement error. Typically, the method hinges on stringent assumptions about the nature of the measurement error, more specifically, that the distribution is *entirely* known. We relax this assumption in the context of a regression error component model and develop an estimator for the unknown density. We show semi-uniform consistency of the estimator and provide Monte Carlo evidence that demonstrates the merits of the method.