Isometric approximation property in euclidean spaces

2002 ◽  
Vol 128 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Jussi Väisälä
Keyword(s):  
Approximation Property ◽  
Euclidean Spaces ◽  
Isometric Approximation

scholarly journals Hyers-Ulam stability of isometries on bounded domains

2021 ◽  
Vol 19 (1) ◽  
pp. 675-689
Author(s):  
Soon-Mo Jung
Keyword(s):  
Approximation Property ◽  
Bounded Domains ◽  
Ulam Stability ◽  
Euclidean Spaces ◽  
Efficient Approach ◽  
Isometric Approximation

Abstract More than 20 years after Fickett attempted to prove the Hyers-Ulam stability of isometries defined on bounded subsets of R n {{\mathbb{R}}}^{n} in 1981, Alestalo et al. [Isometric approximation, Israel J. Math. 125 (2001), 61–82] and Väisälä [Isometric approximation property in Euclidean spaces, Israel J. Math. 128 (2002), 127] improved Fickett’s theorem significantly. In this paper, we will improve Fickett’s theorem by proving the Hyers-Ulam stability of isometries defined on bounded subsets of R n {{\mathbb{R}}}^{n} using a more intuitive and more efficient approach that differs greatly from the methods used by Alestalo et al. and Väisälä.

scholarly journals Isometric approximation property of unbounded sets

2003 ◽  
Vol 43 (3-4) ◽  
pp. 359-372 ◽  
Author(s):  
Jussi Väisälä
Keyword(s):  
Approximation Property ◽  
Isometric Approximation

ON INTRINSIC ISOMETRIES AND RIGID SUBSETS OF EUCLIDEAN SPACES

1989 ◽  
Vol 22 (4) ◽  
Author(s):  
Irmina Herburt
Keyword(s):  
Euclidean Spaces

scholarly journals Ancient solutions for Andrews’ hypersurface flow

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Peng Lu ◽  
Jiuru Zhou
Keyword(s):  
Ricci Flow ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Euclidean Spaces ◽  
Round Cylinder ◽  
Ancient Solutions ◽  
Singular Time

AbstractWe construct the ancient solutions of the hypersurface flows in Euclidean spaces studied by B. Andrews in 1994.As time {t\rightarrow 0^{-}} the solutions collapse to a round point where 0 is the singular time. But as {t\rightarrow-\infty} the solutions become more and more oval. Near the center the appropriately-rescaled pointed Cheeger–Gromov limits are round cylinder solutions {S^{J}\times\mathbb{R}^{n-J}}, {1\leq J\leq n-1}. These results are the analog of the corresponding results in Ricci flow ({J=n-1}) and mean curvature flow.

scholarly journals Equiangular lines in Euclidean spaces

2016 ◽  
Vol 138 ◽  
pp. 208-235 ◽  
Author(s):  
Gary Greaves ◽  
Jacobus H. Koolen ◽  
Akihiro Munemasa ◽  
Ferenc Szöllősi
Keyword(s):  
Euclidean Spaces ◽  
Equiangular Lines

scholarly journals Comment on “Packing hyperspheres in high-dimensional Euclidean spaces”

2007 ◽  
Vol 75 (4) ◽  
Author(s):  
Francesco Zamponi
Keyword(s):  
High Dimensional ◽  
Euclidean Spaces

NORMAL FORMS FOR FUZZY LOGIC — AN APPLICATION OF KOLMOGOROV’S THEOREM

1996 ◽  
Vol 04 (04) ◽  
pp. 331-349 ◽  
Author(s):  
VLADIK KREINOVICH ◽  
HUNG T. NGUYEN ◽  
DAVID A. SPRECHER
Keyword(s):  
Neural Networks ◽  
Fuzzy Logic ◽  
Normal Form ◽  
Normal Forms ◽  
Approximation Property ◽  
Universal Approximation ◽  
Approximation Result ◽  
Logical Operations ◽  
Kolmogorov's Theorem

This paper addresses mathematical aspects of fuzzy logic. The main results obtained in this paper are: 1. the introduction of a concept of normal form in fuzzy logic using hedges; 2. using Kolmogorov’s theorem, we prove that all logical operations in fuzzy logic have normal forms; 3. for min-max operators, we obtain an approximation result similar to the universal approximation property of neural networks.

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