Displaying similar documents to “Triangle functions and composition of probability distribution functions.”

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...

A theorem on implication functions defined from triangular norms.

Didier Dubois, Henri Prade (1984)

Stochastica

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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.

Integral equations and time varying linear systems.

Lucas Jódar (1986)

Stochastica

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In this paper we study the resolution problem of an integral equation with operator valued kernel. We prove the equivalence between this equation and certain time varying linear operator system. Sufficient conditions for solving the problem and explicit expressions of the solutions are given.

Generalized normal distributions.

Robert M. Tardiff (1980)

Stochastica

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It is well known (see [2], p. 158) that if X and Y are independent random variables with a continuous joint probability density function (pdf) which is spherically symmetric about the origin, then both X and Y are normally distributed. In this note we examine the condition that the joint pdf be spherically symmetric about the origin and show that the normal distribution is strongly dependent on the choice of metric for R.

On a generalization of sum form functional equation (I).

Palaniappan Kannappan (1983)

Stochastica

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The Shannon entropy has the sum form ∑f(p) with f(x) = -x logx (x belonging to [0,1]). This together with the property of additivity leads to the 'sum' functional equation...

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.

On the extension of Rosenbrock's theory in algebraic design on multivariable controllers.

Manuel de la Sen (1986)

Stochastica

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System similarity and system strict equivalence concepts from Rosenbrock's theory on linear systems are used to establish algebraic conditions of model matching as well as an algebraic method for design of centralized compensators. The ideas seem to be extensible without difficulty to a class of decentralized control.