Bán István: Csodabogarak - Anekdoták a matematikusokról & Light Biomathematics (2010)
6. Függelék (Selected Papers of István Bán)
Statement. In the natural phenomenon T, there exist the local optima cq, C>2? • • • j On. Proof. Fromjhe conditions and from the definition of the varying natural phenomenon T it follows that the wanted entities CWl, CW2, ..., CWn in the condition are also varying. In this case, however, these wanted entities have unequal wanted elements due to the definition of the varying wanted entities Ci.i, C2,i, ..• ) ^n,Z> Due to consequence 2, and to the definition of the optimum following it, as well as to the definitions of the partial state and of the local optimum, and by applying the theorem of the wanted optima to the foregoing wanted elements, Cwj has an optimum which is equal with the local optimum oi, CWi2 has an optimum which is equal with the local optimum 02, Cw<n has an optimum which is equal with the local optimum on. Consequently the local optima oi, 02, ..., on exist. Consequence. It follows from the definitions of the varying natural phenomenon and from the absolute optimum that by taking into account the state characteristic values a1<n Vi Vn, all the possible relations Rr(aitTl) Vr, and all the specific features Fc[a^n : i?r(ai,n)] Vc, the occurrence of the natural phenomenon, the most advantageous for mankind is '•Po ^aio,no U [I^r0 (*Ao,no)] kJ Pco[^io,no * 7Co(&io,no)j ^ > and this is the absolute optimum. Definition. From the possible occurring set of the natural phenomena, that one which is the most advantageous not only with respect to the interest of mankind, but also with respect to the interest of the global nature is the global absolute optimum. Definition. Out of all existed, existing or future natural phenomena, the occurrence of the most advantageous natural phenomenon with respect to the global interest of nature is the absolute imaginary optimum. Definition. When all local optima of the natural phenomenon T are arranged into a monotonously improving sequence, including the absolute optimum, too, then the^ocal optimum next to the absolute optimum of the natural phenomenon T can be accepted as the local optimum best approximating the absolute optimum. Consequence. A local optimum may not be better than the absolute optimum, the global absolute optimum, or the imaginary absolute optimum. Ci,i, C2,1, .. Cn>1 Cl,2, C2,2) • •• ) Cn%2