Bán István: Csodabogarak - Anekdoták a matematikusokról & Light Biomathematics (2010)
6. Függelék (Selected Papers of István Bán)
ALGORITHMIZATION OF THE WANTED ELEMENT AND ITS APPLICATION IN LOCAL OPTIMA One of the most important features of the biological process, state, state characteristics, and state characteristic value is their ability of interpreting the so-called continuous temporal states or events in nature (Bán 1988) and of determining and investigating the projections. Each member of the nature requires to perceive natural phenomena occurring as the entity of natural processes on the basis of the possibilities ensured by the observation system. The entity of all possible state characteristic values of the states occurring in the nature, of all projections possible among them, and of all properties of state characteristics and projections should be accepted as the biomathematical definition of the natural phenomenon. The set of states perceivable by the possibilities of the living and non-living observation system, of interpretable projections and of deducible features is called the wanted entity and its elements are called the wanted elements. The notions are defined as follows: Be all the possible state characteristic values of the states occurring in the nature (ai,„, 02,n, 0*3,m ■ ■ ■, ai,n)> where i — 1,2,... is the index of the state characteristic, n — 1,2,... is the indicating index of the observed value. Definition. Out of all the possible state characteristic values the state characteristic values observed within the possibilities given by the observation system should be: (ßl,77M ®2,mi ^3,mi • • • i where j ^ i. Til ^ 71. Definition. Relation means the arbitrary adequacy between the state characteristic values. The following types of relations between state characteristics must be distinguished: relations which correspond theoretically to all combinatorial possibilities among the state characteristics above, relations existing in reality, and relations perceivable within the possibilities of the observing system. Definition. Be br = Rr(ai,n) (r = 1,2,...) the relations corresponding to all theoretically possible combinations of the former state characteristics a;)Tl. Definition. Be bs = i?s(a,;in) (s = 1,2,... N < r) the really existing relations among the former state characteristics ai>n. Definition. Be bt = Rt{aitm) (t = 1,2,... < s) the relations perceivable on the basis of the possibilities of the observing system among the state characteristics aiiTn. Definition. The peculiarities of the state characteristic values and relations detectable by mathematical methods are called specific features.