Bán István: Csodabogarak - Anekdoták a matematikusokról & Light Biomathematics (2010)
6. Függelék (Selected Papers of István Bán)
Definition. From all of the specific features which were determined by means of the relations interpreted on the set of the given state characteristic values ajtm (j = 1,2,..., m = 1,2,...), the most advantageous one with respect to the global interest of nature is called the optimum of nature and it will be denoted by: ndt Optjirn<t,e<, — ^ • 6 o <C 6 By applying the foregoings, similarly to the theorem of the wanted optimum, there exists the theorem of the wanted optimum of nature, too, according to which the nat optjmt<ei> is a wanted element and it is the most advantageous wanted optimum among the existing wanted elements with respect to the global interest of nature. Its proof is analogous to the proof of the theorem of the optimum wanted entity. The optimum of nature is not additive. Definition. From two different local optima of a given natural phenomenon T, one is better than the other if one is more advantageous than the other from the point of view of global interest of nature. Consequence. From two unequal natural local optima of a natural phenomenon one is better than the other. Definition. The natural local optima of a given natural phenomenon are monotonously improving if they can be arranged into a sequence so that the arbitrary natural local optimum is better than that standing before it in the sequence. Consequence. The unequal natural local optima of a given natural phenomenon are monotonously improving. Definition. Two identical natural local optima of a given natural phenomenon can be substituted by the single natural local optimum being equal to them. Consequence. The identical natural local optima of a given natural phenomenon can be substituted by one single natural local optimum which is equal to them. Theorem of the existence of the local optima of nature Be the natural phenomenon T varying, and be its wanted entities CWl, c c WU>2 ) * * * > • _ Statement. In the natural phenomenon T there exist natural local optima denoted by nat 0\, nat 02, ..., nat on. This can be proved in the same way as done for the theorem of the existence of local optima by using the previous definitions and consequences. Consequence. It follows from the definition of the natural phenomenon T and from that of the natural absolute optimum that by taking into account the state characteristic values a;in Vi Vn, and all the possible relations