scholarly journals Two cartesian products which are euclidean spaces

1960 ◽  
Vol 79 ◽  
pp. 131-135 ◽  
Author(s):  
James Glimm
Keyword(s):  
Euclidean Spaces ◽  
Cartesian Products

scholarly journals Fractal Intersections and Products via Algorithmic Dimension

2021 ◽  
Vol 13 (3) ◽  
pp. 1-15
Author(s):  
Neil Lutz
Keyword(s):  
Kolmogorov Complexity ◽  
Fractal Dimensions ◽  
Euclidean Spaces ◽  
Cartesian Products ◽  
Information Density ◽  
Algorithmic Dimension ◽  
Packing Dimensions ◽  
Algorithmic Information ◽  
Analytic Sets

Algorithmic fractal dimensions quantify the algorithmic information density of individual points and may be defined in terms of Kolmogorov complexity. This work uses these dimensions to bound the classical Hausdorff and packing dimensions of intersections and Cartesian products of fractals in Euclidean spaces. This approach shows that two prominent, fundamental results about the dimension of Borel or analytic sets also hold for arbitrary sets.

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 Peg Solitaire on Cartesian Products of Graphs

2021 ◽  
Vol 37 (3) ◽  
pp. 907-917
Author(s):  
Martin Kreh ◽  
Jan-Hendrik de Wiljes
Keyword(s):  
Cartesian Product ◽  
Cartesian Products ◽  
Connected Graphs ◽  
Grid Graphs ◽  
Cartesian Products Of Graphs

AbstractIn 2011, Beeler and Hoilman generalized the game of peg solitaire to arbitrary connected graphs. In the same article, the authors proved some results on the solvability of Cartesian products, given solvable or distance 2-solvable graphs. We extend these results to Cartesian products of certain unsolvable graphs. In particular, we prove that ladders and grid graphs are solvable and, further, even the Cartesian product of two stars, which in a sense are the “most” unsolvable graphs.

scholarly journals On embedding of graphs into euclidean spaces of small dimension

1992 ◽  
Vol 56 (1) ◽  
pp. 1-8 ◽  
Author(s):  
J Reiterman ◽  
V Rödl ◽  
E S̆in̆ajová
Keyword(s):  
Small Dimension ◽  
Euclidean Spaces
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