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Displaying similar documents to “A closure condition which is equivalent to the Thomsen condition in quasigroups.”

Kurepa's functional equation on semigroups.

Bruce R. Ebanks (1982)

Stochastica

Similarity:

The functional equation to which the title refers is: F(x,y) + F(xy,z) = F(x,yz) + F(y,z), where x, y and z are in a commutative semigroup S and F: S x S --> X with (X,+) a divisible abelian group (Divisibility means that for any y belonging to X and natural number n there exists a (unique) solution x belonging to X to nx = y).

Representation of continuous associative functions.

Barbara Baccheli (1986)

Stochastica

Similarity:

Strengthened forms of Ling's representation theorem concerning a class of continuous associative functions are given: Firstly the monotonicity condition is removed. Then the associativity condition is replaced by the power associativity.

On symmetries and parallelogram spaces.

Mirko Polonijo (1985)

Stochastica

Similarity:

The notion of a TST-space is introduced and its connection with a parallelogram space is given. The existence of a TST-space is equivalent to the existence of a parallelogram space, which is a new characterization of a parallelogram space. The structure of a TST-space is described in terms of an abelian group.

A theorem on implication functions defined from triangular norms.

Didier Dubois, Henri Prade (1984)

Stochastica

Similarity:

Several transformation which enable implication functions in multivalued logics to be generated from conjunctions have been proposed in the literature. It is proved that for a rather general class of conjunctions modeled by triangular norms, the generation process is closed, thus shedding some light on the relationships between seemingly independent classes of implication functions.

New metrics for weak convergence of distribution functions.

Michael D. Taylor (1985)

Stochastica

Similarity:

Sibley and Sempi have constructed metrics on the space of probability distribution functions with the property that weak convergence of a sequence is equivalent to metric convergence. Sibley's work is a modification of Levy's metric, but Sempi's construction is of a different sort. Here we construct a family of metrics having the same convergence properties as Sibley's and Sempi's but which does not appear to be related to theirs in any simple way. Some instances are brought out in which...