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Displaying similar documents to “Kurepa's functional equation on semigroups.”

Representation of continuous associative functions.

Barbara Baccheli (1986)

Stochastica

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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.

Some remarks on a problem of C. Alsina.

J. Matkowski, M. Sablik (1986)

Stochastica

Similarity:

Equation [1] f(x+y) + f (f(x)+f(y)) = f (f(x+f(y)) + f(f(x)+y)) has been proposed by C. Alsina in the class of continuous and decreasing involutions of (0,+∞). General solution of [1] is not known yet. Nevertheless we give solutions of the following equations which may be derived from [1]: [2] f(x+1) + f (f(x)+1) = 1, [3] f(2x) + f(2f(x)) = f(2f(x + f(x))). Equation [3] leads to a Cauchy functional equation: ...

New metrics for weak convergence of distribution functions.

Michael D. Taylor (1985)

Stochastica

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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...

Metric similarities in the logic of approximation.

Michael Katz (1982)

Stochastica

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We describe restricted and extended versions of the logic of approximation which is meant to handle formally the problems of measurement error and of deduction under conditions of uncertainty. We apply the logic to the foundations of social and behavioral inquiry, axiomatizing in it an inexact similarity predicate which behaves like a metric approximation to identity. In the restricted version of the logic we formulate conditions for the imbeddability of similarity models in the real...

On measures of concordance.

Marco Scarsini (1984)

Stochastica

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We give a general definition of concordance and a set of axioms for measures of concordance. We then consider a family of measures satisfying these axioms. We compare our results with known results, in the discrete case.

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.