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Full-Text Articles in Physical Sciences and Mathematics
Graphs Of Bounded Degree And The P-Harmonic Boundary, Michael J. Puls
Graphs Of Bounded Degree And The P-Harmonic Boundary, Michael J. Puls
Publications and Research
Let p be a real number greater than one and let G be a connected graph of bounded degree. We introduce the p-harmonic boundary of G and use it to characterize the graphs G for which the constant functions are the only p-harmonic functions on G. We show that any continuous function on the p-harmonic boundary of G can be extended to a function that is p-harmonic on G. We also give some properties of this boundary that are preserved under rough-isometries. Now let Gamma be a finitely generated group. As an application of our results, we characterize the vanishing …
Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, Nataniel Greene
Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, Nataniel Greene
Publications and Research
The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the discontinuities.In previous work [11,12] we described a numerical procedure for overcoming the Gibbs phenomenon called the Inverse Wavelet Reconstruction method (IWR). The method takes the Fourier coefficients of an oscillatory partial sum and uses them to construct the wavelet coefficients of a non-oscillatory wavelet series. However, we only described the method standard wavelet series and …
The Maximum Rectilinear Crossing Number Of The Petersen Graph, Elie Feder, Heiko Harborth, Steven Herzberg, Sheldon Klein
The Maximum Rectilinear Crossing Number Of The Petersen Graph, Elie Feder, Heiko Harborth, Steven Herzberg, Sheldon Klein
Publications and Research
We prove that the maximum rectilinear crossing number of the Petersen graph is 49. First, we illustrate a picture of the Petersen graph with 49 crossings to prove the lower bound. We then prove that this bound is sharp by carefully analyzing the ten Cs's which occur in the Petersen graph and their properties.