Tanackov, Ilija J. and Tepić, Jovan and Kostelac, Milan (2011) Zlatni rez u vjerojatnosti i umjetnoj inteligenciji. = The golden ratio in probablistic and artificial intelligence. Tehnički vjesnik : znanstveno-stručni časopis tehničkih fakulteta Sveučilišta u Osijeku, 18 (4). pp. 641-647. ISSN 1330-3651. Vrsta rada: ["eprint_fieldopt_article_type_article" not defined]. Kvartili JCR: Q4 (2011). Točan broj autora: 3.
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Abstract (Croatian)
Problem linijskog odsječka utemeljenog na omjeru zlatnog reza φ = 1,618033 ima analogiju u vjerojatnosti. Rješenje elementarne eksponencijalne raspodjele, posebice ističe vrijednost 2lnφ. Ova vrijednost također ima ključnu ulogu u odnosu Rikatijevih hiperboličnih funkcija s Fibonačijevim i Lukasovim brojevima u kontinuiranom području. Time se uspostavlja bliska veza između konstanti e i φ. Izvedena su dva nova teorema o konvergenciji konstanti φ i e . Broj e je temelj Markovskih procesa, koji su našli primjenu u teoriji vjerojatnosni i umjetne inteligencije. Omjer konstanti e i φ, kao i mnogi drugi prirodni fenomeni na temelju zlatnog reza, ističu potrebu za proširenjem područja vjerojatnosni i umjetne inteligencije.
Abstract
The problem of the line section based on the golden ratio φ = 1,618033 has the analogy in probability. The solution of the elementary exponential distribution relies on the value 2ln φ in particular. This value also plays a key role to Riccati hyperbolic functions with Fibonacci and Lucas numbers in continuous domain. This establishes a close relationship between the constants e and φ Two new theorems on the convergence between the constants φ and e were derived. The number e is the foundation of Markov processes, which find applications in probabilistic and artificial intelligence theory. The ratio between the constants φ and e, as well as many other natural phenomena based on the golden ratio, highlight the need to expand the field of probabilistic and artificial intelligence.
| Item Type: | Article (["eprint_fieldopt_article_type_article" not defined]) |
|---|---|
| Keywords (Croatian): | Continuous domain; Exponential distributions; Golden ratio; Lucas numbers; Natural phenomena; Hyperbolic functions; Markov processes; Artificial intelligence |
| Subjects: | TECHNICAL SCIENCE |
| Divisions: | 400 Department of IC Engines and Mechanical Handling Equipment > 430 Chair of Track-guided Rail and Levitated Vehicles |
| Indexed in Web of Science: | Yes |
| Indexed in Current Contents: | No |
| Quartiles: | Q4 (2011) |
| Citations SCOPUS: | 2 (02.03.2017.) |
| Date Deposited: | 23 Apr 2015 12:43 |
| Last Modified: | 02 Mar 2017 13:09 |
| URI: | http://repozitorij.fsb.hr/id/eprint/3745 |
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