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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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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.
Skapin, X., Lienhardt, P.
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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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1989
The Cartesian product of two sets is the set of all pairs of elements such that the first element of the pair is in one input set and the second element is in the other input set. We discuss derivations of algorithms to find Cartesian set products from Manna and Waldinger [42] and from Smith [53].
D. M. Steier, A. P. Anderson
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The Cartesian product of two sets is the set of all pairs of elements such that the first element of the pair is in one input set and the second element is in the other input set. We discuss derivations of algorithms to find Cartesian set products from Manna and Waldinger [42] and from Smith [53].
D. M. Steier, A. P. Anderson
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Semi-cartesian product of graphs
Journal of Mathematical Chemistry, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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1989
In this section we introduce on X, the set of alternatives, the main structure of interest in this monograph. We shall assume throughout the sequel that X is a Cartesian product \({\prod _{{\text{i}} \in {\text{I}}}}{\Gamma _{\text{i}}}\), with I an index set. We shall nearly always, with Chapter V excepted, assume that I is a finite set (1,...,n), for
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In this section we introduce on X, the set of alternatives, the main structure of interest in this monograph. We shall assume throughout the sequel that X is a Cartesian product \({\prod _{{\text{i}} \in {\text{I}}}}{\Gamma _{\text{i}}}\), with I an index set. We shall nearly always, with Chapter V excepted, assume that I is a finite set (1,...,n), for
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Mathematical Notes of the Academy of Sciences of the USSR, 1984
In the present paper the author introduces the concept of almost slender modules, which is very useful for studying the Cartesian products of modules over a Dedekind domain. The ring R is called slender [see \textit{E. L. Lady}, Pac. J. Math. 49, 397-406 (1973; Zbl 0274.16015)] if for every homomorphism \(f: \prod^{\infty}_{i=1}A_ i\to R\), where ...
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In the present paper the author introduces the concept of almost slender modules, which is very useful for studying the Cartesian products of modules over a Dedekind domain. The ring R is called slender [see \textit{E. L. Lady}, Pac. J. Math. 49, 397-406 (1973; Zbl 0274.16015)] if for every homomorphism \(f: \prod^{\infty}_{i=1}A_ i\to R\), where ...
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Physics-Inspired Structural Representations for Molecules and Materials
Chemical Reviews, 2021Félix Musil +2 more
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