By Krassimir T Atanassov

A research of Fibonacci sequences and the well known Fibonacci numbers. it may be of curiosity to analyze mathematicians wishing to boost the guidelines themselves, and to leisure mathematicians, who may still benefit from the quite a few visible ways and the issues inherent in them. there's a carrying on with emphasis on diagrams, either geometric and combinatorial, which is helping to tie disparate themes jointly, weaving round the unifying topics of the golden suggest and numerous generalizations of the Fibonacci recurrence relation. little or no earlier mathematical wisdom is thought, except the rudiments of algebra and geometry, so the textual content can be utilized as a resource of enrichment fabric and undertaking paintings for students. A bankruptcy on video games utilizing goldpoint tiles is incorporated on the finish, and it seeks to supply a lot fabric for exciting mathematical actions concerning geometric puzzles of a combinatoric nature

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**Sample text**

Z z The method of checking the functioning of a transition structed in such a way is similar to the one shown below and that con is why it will be emitted here. // R A06. Mark the first Ipr Z| 1 input places of Z with the corresponding place's identifiers of the input places of Z, and the other input K places of Z with other (different) are elements of the set (L' « - L'), Z identifiers - these places Go to A10. Z A07. Check the inequality (2) and if it is not valid, go to Aoa, else « mark the first Ipr Zi output places of Z 1 with the corresponding NEW RESULTS IN THE THEORY OF GENERALIZED NETS 35 place's identifiers of the output places of Z, and the other outK put places of Z with other (different) ces are elements of the set (L" * z identifiers - these pla - L").

Hie new GH will have transitions with S-fonns. It is conveni ent that this GH be a GH with a global memory (see § 3 in App. 1). Let this new component contain as parameters the lists of current capaci ties of the transition's arcs and of the numbers in the output places: for a transition 2 of the free location these lists are: H Z = [L', Z L", llm II], where m are the current capacities of the transition's Z i,j i, j arcs between places 1 and 1 ; and (<1, c(l)-c(l, TIME)>/l € L"], where i J Z c is a function giving the number of tokens in place 1 at the current time-moment TIME.

N n|,), 1 11 1 11 11 Z" i i ZZ t (n -- 11 + ii). i nn ). t = tt + (n ) . tt' ' (1 ). I l l 2 I l l A15. Determine all elements of the M-components of the transitions as "eo". A16. e. they will be activated when at least one token enters some of its places). A17. Define the characteristic function $ in the different places as follows $ gives as the current characteristic of the token the list of y i the output Z-places in which the token mist enter, $ , $ , $ are not defined, x' x" y" i,j i, J i $ 1" i coincides with § which is defined for the given GN.