Zobrazeno 1 - 10
of 149
pro vyhledávání: '"Falk, Richard S."'
Autor:
Falk, Richard S., Winther, Ragnar
The bubble transform is a procedure to decompose differential forms, which are piecewise smooth with respect to a given triangulation of the domain, into a sum of local bubbles. In this paper, an improved version of a construction in the setting of t
Externí odkaz:
http://arxiv.org/abs/2312.13161
Autor:
Falk, Richard S., Winther, Ragnar
A classical technique to construct polynomial preserving extensions of scalar functions defined on the boundary of an $n$ simplex to the interior is to use so-called rational blending functions. The purpose of this paper is to generalize the construc
Externí odkaz:
http://arxiv.org/abs/2202.02811
Autor:
Falk, Richard S., Winther, Ragnar
The purpose of this paper is to discuss a generalization of the bubble transform to differential forms. The bubble transform was discussed in a previous paper by the authors for scalar valued functions, or zero-forms, and represents a new tool for th
Externí odkaz:
http://arxiv.org/abs/2111.08123
Autor:
Falk, Richard S., Nussbaum, Roger D.
In [14], the authors developed a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In this paper, we extend this approach to incorporate high order approximation methods. We again r
Externí odkaz:
http://arxiv.org/abs/2008.11150
Autor:
Falk, Richard S.1 (AUTHOR) falk@math.rutgers.edu, Winther, Ragnar2 (AUTHOR)
Publikováno v:
Foundations of Computational Mathematics. Feb2024, Vol. 24 Issue 1, p99-147. 49p.
Autor:
Falk, Richard S., Nussbaum, Roger D.
We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case that we consider here, our methods require only $C^3$ regularity of the maps in the IFS. T
Externí odkaz:
http://arxiv.org/abs/1612.00870
Autor:
Falk, Richard S., Nussbaum, Roger D.
In a previous paper, dealing with "Applications in $\mathbb{R}^1$," the authors developed a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS and studied some applications in one dim
Externí odkaz:
http://arxiv.org/abs/1612.00869
Autor:
Falk, Richard S., Nussbaum, Roger D.
We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case, our methods require only C^3 regularity of the maps in the IFS. The key idea, which has b
Externí odkaz:
http://arxiv.org/abs/1601.06737
Autor:
Falk, Richard S., Winther, Ragnar
The purpose of this paper is to discuss the construction of a linear operator, referred to as the bubble transform, which maps scalar functions defined on a bounded domain $\Omega$ in $\mathbb{R}^n$ into a collection of functions with local support.
Externí odkaz:
http://arxiv.org/abs/1312.1524
Publikováno v:
Trans. Amer. Math. Soc. 366 (2014) 5487-5502
In 1976, Dodziuk and Patodi employed Whitney forms to define a combinatorial codifferential operator on cochains, and they raised the question whether it is consistent in the sense that for a smooth enough differential form the combinatorial codiffer
Externí odkaz:
http://arxiv.org/abs/1212.4472