Bán István: Biomathematics - PMSB Methods in Forestry (2002)
2. The environment - 2.2. Algorithmization of a wanted phenomenon and its application in local optima
2.2. Algorithmization of a wanted phenomenon Definition: Be all the theoretically possible features of the state characteristics a; „ and of the relations 6r = Rr(ai n): Fc[ai,n< ^r(a.,n)] C = 1, 2, ... . Definition: Be the features existing on the basis of the state characteristics „ and the relations 6r = fr(ai n): Fdiai,n’ RÁai,n)] d = 1,2,.... Definition: Be the features interpretable on the basis of the state characteristics Oj m, and the relations = Rt(p,jm) interpretable within the possibilities of the observing system: FÄaj,m’ Äi(a7,m)] e=l,2,.„. Definition: By using these the natural phenomenon T, i.e. the entity of the state characteristic values a, n Vt and Vn, of all the possible relations Rfa^f) Vr and all of the features Fc[ai n-, Rr(ai n)] Vc, will be: T = {ai n Miffri) [Rr(ai n); Vr] kj [Fc[ain; Rr(ai n)]; Vc). Definition. Out of it the entity of the states conceivable by the living and nonliving observing systems, of the interpretable relations and of the deducible features, i.e. the entity Cw of the wanted phenomena is: 0w = (aj,m Ji'- m) \Rf aj'), Vt] \F(,Rt(ajir;i)], Vc}. One element of the entity Cw of the phenomena looked for is the phenomenon C looked for, i.e. Cjym,t,e = ^aj,rri’ Ft^aj,m)^'< Fe^aj,m< Ft^aj,m^ for a given arbitrary, fixed index j, m, t, e. It follows from the definitions of the state characteristic values yielded by the observing system and of the conceivable relations among them, as well as from the definition of the interpretable features that Cj>m t e is an indexdependent mathematical construction, i.e. a locally dependent notion. On the basis of foregoing the theorem of the wanted local phenomena can be formulated: Theorem: Two wanted phenomena are then and only then equal, if their corresponding state characteristic values, their relations and features are also equal. Be: C Cj2,m2,t2,e2 - taj2,mf m2)l ’ Fe2iaj2,mf Ftfaj2,mf]