Invariant sets which carry a one-form

On invariant sets topology

In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...

Fuzzy sets form A meta-system-theoretic point of view

Gorban : Invariant Sets ( A

Some sets in the space of compositions possessing an invariance property are considered for a closed system, where a complex chemical reaction of a known mechanism proceeds. If the vector of concentrations belongs to such a set at a certain moment of time, it will remain within it at any succeeding moment. Some possible applications are discussed. 3aKpbITOfl CHCTeMM, B KOTOpOl~ npoTeKaeT cHoXCd...

Interval or moments: which carry more information?

In many practical situations, we do not have enough observations to uniquely determine the corresponding probability distribution, we only have enough observations to estimate two parameters of this distribution. In such cases, the traditional statistical approach is to estimate the mean and the standard deviation. Alternatively, we can estimate the two bounds that form the range of the corresp...

Nets with Tokens Which Carry Data

We study data nets, a generalisation of Petri nets in which tokens carry data from linearlyordered infinite domains and in which whole-place operations such as resets and transfers are possible. Data nets subsume several known classes of infinite-state systems, including multiset rewriting systems and polymorphic systems with arrays. We show that coverability and termination are decidable for a...