By Krassimir T Atanassov

A examine of Fibonacci sequences and the well known Fibonacci numbers. it's going to be of curiosity to analyze mathematicians wishing to enhance the guidelines themselves, and to leisure mathematicians, who may still benefit from the quite a few visible techniques 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 issues jointly, weaving round the unifying subject matters 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 used as a resource of enrichment fabric and undertaking paintings for college kids. 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**

I I JJ ((l),i l),i JJ ((2), 2 ) , ii II ii ii where H £+ marks the sum of i= l number of the neuron "i", N r JJ ((r r ) ) i i ii , T T JJ (|r],i r ],i ii ii index matrices (see App. 2), i is the is the number of the neurons which are i connected with neuron "i", JJ (k) / 1 i k i r 1 is the set of the numi i bers of the neurons which are connected with the neuron "i", for 1 4 JJ <, r , T is the synaptic strength of p-th connections, i J (JJ), i i ii JJ B **
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Tt *+ ( (n n --i i). | . Vt' I(lt ii i is <. 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.

A GH constructed in such a way represents the functioning of each SHQB and therefore it is a UGH for £ SHGH Therefore Theorem 1. 1. 3. 2 rem 1. 1, 3. 1 is also given. THEOREM i. 1. 3. e. is proved and another proof of Theo £ SHGH i s a conservative extension of £. Proof: From Theorem 1. 1. 3. 2, it follows that each SHGH sented by the UGH, which is an element of of £ can be represented £. by an element of can be repre Therefore every element £ and hence £ I- £ SHGH SHGH The other direction is obvious.