Sentence examples for crossed system from inspiring English sources

In this case, the monoid A # α f B is called a crossed product of A and B associated to the crossed system ( A, B, α, f ) [5].

If ( A, B, α, f ) is a normalized crossed system, then we have f ( 1 B, b ) = f ( b, 1 B ) = 1 A and α 1 B ( a ) = a by [5].

for all b 1, b 2, b 3 ∈ B, a ∈ A. The crossed system ( A, B, α, f ) is called normalized if f ( 1 B, 1 B ) = 1 A. The map α : B → End ( A ) is called weak action and f : B × B → A is called an α-cocycle.

Definition 1 A crossed system of monoids is a quadruple ( A, B, α, f ), where A and B are two monoids, and f : B × B → A and α : B → End ( A ), where End ( A ) denotes the collection of endomorphism of A, are two maps such that the following conditions hold: (1).

for all b 1, b 2 ∈ B, a 1, a 2 ∈ A. Then ( A # α f B, ⋅ ) is a monoid with unit 1 A # α f B = ( 1 A, 1 B ) if and only if ( A, B, α, f ) is a normalized crossed system.

Cognitive work analysis was used to analyse rail level crossing systems using data derived from a range of activities.

This paper presents a systems analysis of current rail level crossing systems in Australia that was undertaken specifically to identify safety-related issues in rail level crossing environments.

Few available studies cross systems of care or permit direct comparisons of healthcare delivery strategies.

By the end of the 18th century, a "cross" system of canals connected the Thames, Humber, Mersey, and Severn estuaries.

MI5 had captured a number of German spies sent to Britain and was using them to feed fake intelligence to the Abwehr, German military intelligence, in an operation known as the Double Cross system.

"Twenty" derived from the Roman numeral XX, which itself was an allusion to the "Double-Cross System," run by the Committee, of turning enemy agents in place and fabricating intelligence deceptions to employ against the Axis powers.