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Using Cartesian Product for Animation
The Journal of Visualization and Computer Animation, 2000AbstractIn the field of geometric modelling for animation, 4D modelling (time being the fourth dimension) seems to be a natural extension of 3D modelling. But time dimension is not easy to apprehend and 4D objects are difficult to interpret and to control in general.
Xavier Skapin, Pascal Lienhardt
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Connectivity of Cartesian Product of Hypergraphs
Bulletin of the Iranian Mathematical Society, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Na, Meng, Jixiang, Tian, Yingzhi
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American Journal of Mathematics, 1969
0. Introduction. Let as be an arc in the interior In of the n-cell In and let X be the quotient space I"/ac obtained by shrinking a to a point. According to Kwun and Raymond [4], X X 12 is an (n + 2)-cell. The crucial tool in their proof is the result of Andrews-Curtis that, under the above conditions, In/a X R1 is homeomorphic to In XR1.
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0. Introduction. Let as be an arc in the interior In of the n-cell In and let X be the quotient space I"/ac obtained by shrinking a to a point. According to Kwun and Raymond [4], X X 12 is an (n + 2)-cell. The crucial tool in their proof is the result of Andrews-Curtis that, under the above conditions, In/a X R1 is homeomorphic to In XR1.
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Cartesian product-based hierarchical scheme for multi-agent systems
Automatica, 2018 In this paper, we solve the average-consensus problem using a hierarchical scheme based on Cartesian product of strongly connected balanced graphs — an algebraic approach to design complex networks.
John-Josef Leth +2 more
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On the Discrepancy for Cartesian Products
Journal of the London Mathematical Society, 2000We prove that the discrepancy for the family of Cartesian products \(B_1\times B_2\subseteq \mathbb{R}^4\), where \(B_1\) and \(B_2\) are circular discs in the plane, is \(O(n^{1/4+\varepsilon})\) for an arbitrarily small constant \(\varepsilon>0\), i.e. essentially the same as that for discs in the plane.
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Behzad-Vizing conjecture and Cartesian-product graphs [PDF]
Applied Mathematics Letters, 2002 We prove the following theorem: if the Behzad-Vizing conjecture is true for graphs G and H, then is it true for the Cartesian product G ...
Ẑerovnik, J., Zmazek, B.
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Radicals commuting with cartesian products
Archiv der Mathematik, 1998Given an Abelian group \(G\), the group radical is defined by \(R_G(X)=\bigcap\{\text{Ker }\phi\mid\phi\colon X\to G\}\), for Abelian groups \(X\). This radical does not always commute with infinite direct products (for instance, when \(G=\mathbb{Q}\), it turns into the torsion radical).
Corner, A. L. S., Göbel, Rüdiger
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1970
When we say in analytic geometry that a point has co-ordinates (x, y), the order in which x and y occur, in the symbol (x, y), is important: (1, 2) ≠ (2, 1). For this reason we call (x, y) an ordered pair. Moreover, x and y come from sets; in this case x, y ∈ R. This idea can be generalizedf as follows. Let 𝒰 be a universe.
H. B. Griffiths, P. J. Hilton
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When we say in analytic geometry that a point has co-ordinates (x, y), the order in which x and y occur, in the symbol (x, y), is important: (1, 2) ≠ (2, 1). For this reason we call (x, y) an ordered pair. Moreover, x and y come from sets; in this case x, y ∈ R. This idea can be generalizedf as follows. Let 𝒰 be a universe.
H. B. Griffiths, P. J. Hilton
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Homogeneous Cartesian products
Australas. J Comb., 2002Summary: A graph \(G\) is 1-homogeneous if certain isomorphisms between similarly embedded induced subgraphs of \(G\) extend to automorphisms of \(G\). We show that the only connected composite 1-homogeneous graphs are the cube, and \(K_n\times K_2\) and \(K_n\times K_n\) with \(n\geq 2\).
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