270 research outputs found
Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization
In this article, we study an analog of the Bj\"orling problem for isothermic
surfaces (that are more general than minimal surfaces): given a real analytic
curve in , and two analytic non-vanishing orthogonal
vector fields and along , find an isothermic surface that is
tangent to and that has and as principal directions of
curvature. We prove that solutions to that problem can be obtained by
constructing a family of discrete isothermic surfaces (in the sense of Bobenko
and Pinkall) from data that is sampled along , and passing to the limit
of vanishing mesh size. The proof relies on a rephrasing of the
Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its
discretization which is induced from the geometry of discrete isothermic
surfaces. The discrete-to-continuous limit is carried out for the Christoffel
and the Darboux transformations as well.Comment: 29 pages, some figure
Piecewise Linear Models for the Quasiperiodic Transition to Chaos
We formulate and study analytically and computationally two families of
piecewise linear degree one circle maps. These families offer the rare
advantage of being non-trivial but essentially solvable models for the
phenomenon of mode-locking and the quasi-periodic transition to chaos. For
instance, for these families, we obtain complete solutions to several questions
still largely unanswered for families of smooth circle maps. Our main results
describe (1) the sets of maps in these families having some prescribed rotation
interval; (2) the boundaries between zero and positive topological entropy and
between zero length and non-zero length rotation interval; and (3) the
structure and bifurcations of the attractors in one of these families. We
discuss the interpretation of these maps as low-order spline approximations to
the classic ``sine-circle'' map and examine more generally the implications of
our results for the case of smooth circle maps. We also mention a possible
connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request
A Population‐Based Twin Study on Sleep Duration and Body Composition
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/93648/1/oby.2011.274.pd
The impact of Stieltjes' work on continued fractions and orthogonal polynomials
Stieltjes' work on continued fractions and the orthogonal polynomials related
to continued fraction expansions is summarized and an attempt is made to
describe the influence of Stieltjes' ideas and work in research done after his
death, with an emphasis on the theory of orthogonal polynomials
A Global Assessment of the Degree of Price Stickiness - Results from the NBB Business Survey
The Macroeconomic Effects of the Euro Area's Fiscal Consolidation 2011-2013: A Simulation-Based Approach
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