scholarly journals New Non-existence Proofs for Ovoids of Hermitian Polar Spaces and Hyperbolic Quadrics

2017 ◽  
Vol 21 (1) ◽  
pp. 25-42
Author(s):  
John Bamberg ◽  
Jan De Beule ◽  
Ferdinand Ihringer
Keyword(s):  
Polar Spaces ◽  
Existence Proofs

The Explanatory Role of Existence Proofs

Ethics ◽  
1986 ◽  
Vol 97 (1) ◽  
pp. 177-186
Author(s):  
Alexander Rosenberg
Keyword(s):  
Explanatory Role ◽  
Existence Proofs

A simple proof of existence of weak and statistical solutions of Navier–Stokes equations

1992 ◽  
Vol 436 (1896) ◽  
pp. 1-11 ◽  
Keyword(s):  
Weak Solution ◽  
Initial Data ◽  
Natural Number ◽  
Simple Proof ◽  
Stokes Equations ◽  
Galerkin Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Existence Proofs ◽  
Statistical Solutions

The Galerkin approximation to the Navier–Stokes equations in dimension N , where N is an infinite non-standard natural number, is shown to have standard part that is a weak solution. This construction is uniform with respect to non-standard representation of the initial data, and provides easy existence proofs for statistical solutions.

On the embeddability of polar spaces

1992 ◽  
Vol 44 (3) ◽  
Author(s):  
Hans Cuypers ◽  
Peter Johnson ◽  
Antonio Pasini
Keyword(s):  
Polar Spaces

scholarly journals Minimal scattered sets and polarized embeddings of dual polar spaces

2007 ◽  
Vol 28 (7) ◽  
pp. 1890-1909 ◽  
Author(s):  
Bart De Bruyn ◽  
Antonio Pasini
Keyword(s):  
Polar Spaces ◽  
Dual Polar Spaces

scholarly journals Opposite Relation on Dual Polar Spaces and Half-Spin Grassmann Spaces

2009 ◽  
Vol 54 (3-4) ◽  
pp. 301-308 ◽  
Author(s):  
Mariusz Kwiatkowski ◽  
Mark Pankov
Keyword(s):  
Polar Spaces ◽  
Dual Polar Spaces

scholarly journals Non-Classical Hyperplanes of Finite Thick Dual Polar Spaces

10.37236/7348 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Bart De Bruyn
Keyword(s):  
Complete Classification ◽  
Polar Spaces ◽  
Dual Polar Spaces

We obtain a classification of the nonclassical hyperplanes of all finite thick dual polar spaces of rank at least 3 under the assumption that there are no ovoidal and semi-singular hex intersections. In view of the absence of known examples of ovoids and semi-singular hyperplanes in finite thick dual polar spaces of rank 3, the condition on the nonexistence of these hex intersections can be regarded as not very restrictive. As a corollary, we also obtain a classification of the nonclassical hyperplanes of $DW(2n-1,q)$, $q$ even. In particular, we obtain a complete classification of all nonclassical hyperplanes of $DW(2n-1,q)$ if $q \in \{ 8,32 \}$.

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