Appendix: On Set Coverings in Cartesian Product Spaces

2006 ◽  
pp. 926-937 ◽  
Author(s):  
R. Ahlswede
Keyword(s):  
Cartesian Product ◽  
Product Spaces

Haar polynomials on Cartesian product spaces

1969 ◽  
Vol 36 (1) ◽  
pp. 193-205 ◽  
Author(s):  
M. S. Grosof ◽  
D. J. Newman
Keyword(s):  
Cartesian Product ◽  
Product Spaces

scholarly journals On Extremal Set Partitions in Cartesian Product Spaces

1993 ◽  
Vol 2 (3) ◽  
pp. 211-220 ◽  
Author(s):  
Rudolf Ahlswede ◽  
Ning Cai
Keyword(s):  
Cartesian Product ◽  
Product Spaces ◽  
Minimal Size ◽  
Set Partitions ◽  
Partition Number ◽  
Vertex Set ◽  
Extremal Set

The partition number of a product hypergraph is introduced as the minimal size of a partition of its vertex set into sets that are edges. This number is shown to be multiplicative if all factors are graphs with all loops included.

scholarly journals Inequalities for Hypo-q-Norms on a Cartesian Product of Inner Product Spaces

2017 ◽  
Author(s):  
Silvestru Dragomir
Keyword(s):  
Cartesian Product ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Inner Products ◽  
Reverse Inequalities

In this paper we introduce the hypo-q-norms on a Cartesian product of inner product spaces. A representation of these norms in terms of inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar Shisha-Mond, Birnacki et al., Grüss type inequalities, Boas-Bellman and Bombieri type inequalities are also given.

On the Homology of the n-Special Reduced Product Space of a Euclidean Space

1972 ◽  
Vol 15 (3) ◽  
pp. 427-431
Author(s):  
M. Wakae ◽  
O. Hamara
Keyword(s):  
Euclidean Space ◽  
Topological Space ◽  
Product Space ◽  
Cartesian Product ◽  
Product Spaces

In [2] and [3] the homology of reduced product spaces of certain type of polyhedra was studied. Let Xn=X×X×…×X be the Cartesian product of n copies of a topological space X.

scholarly journals Componentwise localization of critical points for functionals defined on product spaces

2021 ◽  
pp. 1-27
Author(s):  
Radu Precup
Keyword(s):  
Critical Points ◽  
Cartesian Product ◽  
Mountain Pass ◽  
Product Spaces ◽  
Minimax Points

A new notion of linking is introduced to treat minima as minimax points in a unitary way. Critical points are located in conical annuli making possible to obtain multiplicity. For functionals defined on a Cartesian product, the localization of critical points is given on components and the variational properties of the components can differ, part of them being of minimum type, others of mountain pass type.

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