The Elliptic Case: Two Complex Characteristics

2020 ◽  
pp. 85-109
Author(s):  
Otto D. L. Strack
Keyword(s):  
Elliptic Case

scholarly journals Random Walks with Invariant Loop Probabilities: Stereographic Random Walks

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 729
Author(s):  
Miquel Montero
Keyword(s):  
Random Walks ◽  
Stereographic Projection ◽  
Transition Probabilities ◽  
Simple Random Walk ◽  
General Introduction ◽  
Elliptic Case ◽  
One Step ◽  
Underlying Geometry ◽  
Step Transition ◽  
Wide Family

Random walks with invariant loop probabilities comprise a wide family of Markov processes with site-dependent, one-step transition probabilities. The whole family, which includes the simple random walk, emerges from geometric considerations related to the stereographic projection of an underlying geometry into a line. After a general introduction, we focus our attention on the elliptic case: random walks on a circle with built-in reflexing boundaries.

Adaptive Wavelet Methods II—Beyond the Elliptic Case

2002 ◽  
Vol 2 (3) ◽  
pp. 203-202 ◽  
Author(s):  
A. Cohen ◽  
W. Dahmen ◽  
R. DeVore
Keyword(s):  
Adaptive Wavelet ◽  
Elliptic Case ◽  
Wavelet Methods

Arithmetic Applications:- The Elliptic Case

1992 ◽  
pp. 202-208
Author(s):  
Klaus W. Roggenkamp ◽  
Martin J. Taylor
Keyword(s):  
Elliptic Case

scholarly journals Lipschitz Bounds and Nonautonomous Integrals

2021 ◽  
Author(s):  
Cristiana De Filippis ◽  
Giuseppe Mingione
Keyword(s):  
Variational Problems ◽  
Growth Conditions ◽  
Regularity Criteria ◽  
Regularity Of Solutions ◽  
Optimal Regularity ◽  
Lipschitz Regularity ◽  
Elliptic Case ◽  
Different Types ◽  
Vector Valued

AbstractWe provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range from those with unbalanced polynomial growth conditions to those with fast, exponential type growth. The results obtained are sharp with respect to all the data considered and also yield new, optimal regularity criteria in the classical uniformly elliptic case. We give a classification of different types of nonuniform ellipticity, accordingly identifying suitable conditions to get regularity theorems.

scholarly journals Curvilinear vector finite difference approach to the computation of waveguide modes

2012 ◽  
Vol 1 (1) ◽  
pp. 29 ◽  
Author(s):  
A. Fanti ◽  
G. Mazzarella ◽  
G. Montisci
Keyword(s):  
Finite Difference ◽  
Decomposition Method ◽  
Taylor Expansion ◽  
Waveguide Section ◽  
Elliptic Case ◽  
Waveguide Modes ◽  
Mode Function ◽  
Vector Mode ◽  
Spurious Modes ◽  
Finite Difference Approach

We describe here a Vector Finite Difference approach to the evaluation of waveguide eigenvalues and modes for rectangular, circular and elliptical waveguides. The FD is applied using a 2D cartesian, polar and elliptical grid in the waveguide section. A suitable Taylor expansion of the vector mode function allows to take exactly into account the boundary condition. To prevent the raising of spurious modes, our FD approximation results in a constrained eigenvalue problem, that we solve using a decomposition method. This approach has been evaluated comparing our results to the analytical modes of rectangular and circula rwaveguide, and to known data for the elliptic case.

scholarly journals A strongly degenerate quasilinear equation: the elliptic case

2009 ◽  
pp. 555-587
Author(s):  
Fuentasanta Andreu ◽  
Vincent Caselles ◽  
José M. Mazón
Keyword(s):  
Quasilinear Equation ◽  
Elliptic Case ◽  
Strongly Degenerate

scholarly journals Parabolic fixed points, invariant curves and action-angle variables

1990 ◽  
Vol 10 (2) ◽  
pp. 231-245 ◽  
Author(s):  
Dov Aharonov ◽  
Uri Elias
Keyword(s):  
Fixed Point ◽  
Hamiltonian System ◽  
Fixed Points ◽  
Phase Flow ◽  
Invariant Curves ◽  
Elliptic Case ◽  
System A ◽  
Twist Mapping ◽  
Area Preserving ◽  
Parabolic Fixed Point

AbstractA fixed point of an area-preserving mapping of the plane is called elliptic if the eigenvalues of its linearization are of unit modulus but not ±1; it is parabolic if both eigenvalues are 1 or −1. The elliptic case is well understood by Moser's theory. Here we study when is a parabolic fixed point surrounded by closed invariant curves. We approximate our mapping T by the phase flow of an Hamiltonian system. A pair of variables, closely related to the action-angle variables, is used to reduce T into a twist mapping. The conditions for T to have closed invariant curves are stated in terms of the Hamiltonian.

scholarly journals Remarks on the Elliptic Case of the Mapping Theorem for Simply-Connected Riemann Surfaces

1955 ◽  
Vol 9 ◽  
pp. 17-20 ◽  
Author(s):  
Maurice Heins
Keyword(s):  
Riemann Surface ◽  
Meromorphic Function ◽  
Riemann Surfaces ◽  
Simple Pole ◽  
Conformal Map ◽  
Elliptic Case ◽  
Extended Plane ◽  
Simply Connected ◽  
Conformal Equivalence

It is well-known that the conformal equivalence of a compact simply-connected Riemann surface to the extended plane is readily established once it is shown that given a local uniformizer t(p) which carries a given point p0 of the surface into 0, there exists a function u harmonic on the surface save at p0 which admits near p0 a representation of the form(α complex 0; h harmonic at p0). For the monodromy theorem then implies the existence of a meromorphic function on the surface whose real part is u. Such a meromorphic function has a simple pole at p0 and elsewhere is analytic. It defines a univalent conformal map of the surface onto the extended plane.

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