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Exponentially Small Soundness for the Direct Product Z-test
Electron. Colloquium Comput. Complex., 2017Given a function 5 : [#]: → ["]: , the Z-test is a three-query test for checking if the function 5 is a direct product, i. e., if there are functions ,1 , . . . , ,: : [#] → ["] such that 5 (G1 , . . . , G:) = (,1(G1), . . . , ,:(G:)) for every input G ∈
Irit Dinur, I. Navon
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On extending and optimising the direct product decomposition
Molecular Physics, 2018The concept of the direct product decomposition (DPD) is extended to arbitrary tensors while maintaining the same theoretical reduction in storage and computation.
D. Matthews
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Archiv der Mathematik, 2002
Let \(R\) be a ring. All modules considered are right modules. A module \(M\) is said to be (finitely) product-rigid if any (finitely presented) direct summand of a product of copies of \(M\) having a local endomorphism ring is isomorphic to some indecomposable direct summand of \(M\) itself.
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Let \(R\) be a ring. All modules considered are right modules. A module \(M\) is said to be (finitely) product-rigid if any (finitely presented) direct summand of a product of copies of \(M\) having a local endomorphism ring is isomorphic to some indecomposable direct summand of \(M\) itself.
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Resolvability and Strong Resolvability in the Direct Product of Graphs
, 2015Given a connected graph G, a vertex $${w \in V(G)}$$w∈V(G) distinguishes two different vertices u, v of G if the distances between w and u, and between w and v are different.
D. Kuziak, Iztok Peterin, I. G. Yero
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Direct Product Decompositions of Twisted Wreath Products
Canadian Mathematical Bulletin, 1975The twisted wreath product of two groups was first defined by B. H. Neumann ([1]) who used this construction to present a group-theoretic proof of a theorem due to Auslander and Lyndon. In this paper we present a complete characterization of the direct product decompositions of a restricted twisted wreath product of two groups A and B provided this ...
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CONSTRUCTION PRODUCTS DIRECTIVE
Facilities, 1989The Construction Products Directive of 21 December 1988 — on the approximation of laws, regulations and administrative provisions of the member states relating to construction products — provides for free trade in construction products throughout the European Economic Community. Implementation must be achieved by 27 June 1991.
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2017
In this chapter we introduce semi-direct products such as the Poincare group, the Galilei group and the Bargmann group. We describe their irreducible unitary representations, which are induced from representations of their translation subgroup combined with a so-called little group.
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In this chapter we introduce semi-direct products such as the Poincare group, the Galilei group and the Bargmann group. We describe their irreducible unitary representations, which are induced from representations of their translation subgroup combined with a so-called little group.
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Direct Sums and Direct Products
2015The concept of direct sum is of utmost importance for the theory. This is mostly due to two facts: first, if we succeed in decomposing a group into a direct sum, then it can be studied by investigating the summands separately, which are, in numerous cases, simpler to deal with.
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