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Content available Predicate Data Model in the Form of a Linear Space
The restriction of the input set in the form of a positive cone of the space is not always correct. For instance, while studying the organ of vision, people are limited not only to positive, but also to radiation with not very high energies, because excessively intense can disturb the visual organ. In this particular case, a convex body of a linear space is a fairly acceptable model of the set of input signals. Therefore, we consider linear predicates with this domain of definition.
Content available remote Bounded solutions of a generalized Gołąb-Schinzel equation
Let X be a linear space over the field K of real or complex numbers. We characterize solutions f : X - > K and M : K - > K of the equation f(x+M)(f)y)=f(x)f(y) in the case where the set {x is an element of X : f (x) = 0} has an algebraically interior point. As a consequence we give solutions of the equation such that f is bounded on this set.
Content available remote One-to-one solutions of generalized Gołąb-Schinzel equation
Let K be the field of real or complex numbers and let X be a nontrivial linear space over K. Assume that [...]. We give a necessary and sufficient condition for functions f and M to satisfy the equation The functional equation f(x+M(f(x))y)=f(x)f(y) is a generalization of the well-known Gołąb-Schinzel functional equation f(x+f(x)y)=f(x)f(y).
The theory of right invertible operators was started with works of D. Przeworska-Rolewicz and then it has been developed by M. Tasche, H. von Trotha, Z. Binderman and many other mathematicians (see [10]). Nguyen Dinh Quyet (in [5, 7]), has considered the controllability of linear system described by right invertible operators where the resolving operator is invertible. These results were generalized by A. Pogorzelec in the case of one-sized invertible resolving operator (see [9]) and by Nguyen Van Mau for the system described by generalized invertible operator (see [3]). However, for the degenerate systems, the problem has not been investigated. In this paper, we deal with the initial value problem for degenerate system of the form (2.7)-(2.8) and the controllability of this system.
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