Displaying similar documents to “On a functional equation connected to sum form nonadditive information measures on an open domain (III).”

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...

Some remarks on a problem of C. Alsina.

J. Matkowski, M. Sablik (1986)

Stochastica

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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: ...

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.

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.

Weighted shift operators on l spaces.

Lucas Jódar (1986)

Stochastica

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The analytic-spectral structure of the commutant of a weighted shift operator defined on a l space (1 ≤ p < ∞) is studied. The cases unilateral, bilateral and quasinilpotent are treated. We apply the results to study certain questions related to unicellularity, strictly cyclicity and the existence of hyperinvariant subspaces.

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.