In many applied areas, such as tomography and crystallography, one is confronted by an unknown subset 5 of a measure space (X, X) such as R" , or an unknown function 0 < (j> < 1 on X , having known moments (integrals) relative to a specified class F of functions f:X—*R. Usually, these F-moments do not fully determine the object S or function . We will say that 5 is a set of uniqueness if no ...

We study Sturm-Liouville operators on closed sets of a special structure, which are sometimes referred as time scales and often appear in modelling various real processes. Depending the set such unify both differential difference operators. obtain properties their spectral characteristics inverse problems with respect to them. prove that uniquely determine operator.

A notion of Paley-Wiener spaces on combinatorial graphs is introduced. It is shown that functions from some of these spaces are uniquely determined by their values on some sets of vertices which are called the uniqueness sets. Such uniqueness sets are described in terms of Poincare-Wirtingertype inequalities. A reconstruction algorithm of Paley-Wiener functions from uniqueness sets which uses t...

Fuzzy Sets and Systems 161 (2010) 412-432 Elsevier www.elsevier.com/locate/fss A Categorical Semantics for Fuzzy Predicate Logic

does not satisfy (EP), because for x = 0.3, y = 0.5 and z = 0.5 we get I (x, I (y, z)) = 0.7 = 0.5 = I (y, I (x, z)). The corrected last two rows are provided in Table 1 here. In both of these cases the natural negation NI is the classical negation NC(x) = 1 − x. One can easily check that the first function satisfies (I1) and it does not satisfy (EP), because for x = 0.3, y = 1 and z = 0, we ge...

In this work we solve an open problem of U.Höhle [Problem 11, Fuzzy Sets and Systems 145 (2004) 471-479]. We show that the solution gives a characterization of all conditionally cancellative t-subnorms. Further, we give an equivalence condition for a conditionally cancellativite t-subnorm to be a t-norm and hence show that conditionally cancellativite t-subnorms whose natural negations are stro...