By M. Hazewinkel (auth.), M. Hazewinkel (eds.)
This is the 1st Supplementary quantity to Kluwer's hugely acclaimed Encyclopaedia of Mathematics. this extra quantity comprises approximately six hundred new entries written via specialists and covers advancements and issues now not integrated within the already released 10-volume set. those entries were prepared alphabetically all through. a close index is incorporated within the e-book.
This Supplementary quantity complements the present 10-volume set. jointly, those 11 volumes signify the main authoritative, accomplished updated Encyclopaedia of Mathematics available.
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Extra resources for Encyclopaedia of Mathematics: Supplement Volume I
On the other hand, ;;::io also has a basic role in treating quasi-senses connected with any other synonymy notion. Moreover, the definitions of ;;::io and ;;::il can be extended to a certain theory 7* endowed with the definition system D of 7, provided that D is of a suitable kind. Finally, in  a general rigorous definition of synonymy is introduced. For any synonymy notion ;;::i one has ;;::io~;;::i. A formal theory of senses. e. a model (in logic) for D. In the semantics adopted by , every expression of a theory T has both an intension and a sense, depending on the notion of synonymy chosen.
Rinkinys 17 (1977), 75-86. : Random processes with independent increments, Kluwer Acad. , 1991. ) B. Grigelionis MSC 1991: 60J30 ADEQUACY THEOREM for senses - A theorem from the theories of sense and synonymy. This theory provides a solution for the treatment of hyperintensional predications. The statement of the theorem is as follows. Assume that: i) b. and Il> are well-formed expressions of an interpreted theory (T,D,I), where T is a theory based on the modal calculus (cf. , the primitive constants and free variables) of b.
A semimartingale X is an additive process if and only if the triplet of predictable characteristics of X is non-random (see ). The method of characteristic functions (cf. Characteristic function) and the factorization identities are main tools for the investigation of properties of additive stochastic processes (see ). The theory of additive stochastic processes can be extended to stochastic processes with values in a topological group. A general reference for this area is . : Boundary problems for processes with independent increments, Naukova Dumka, 1990.