12 research outputs found
The golden ratio in probablistic and artificial intelligence
Problem linijskog odsjeÄka utemeljenog na omjeru zlatnog reza Ļ = 1,618033 ima analogiju u vjerojatnosti. RjeÅ”enje elementarne eksponencijalne raspodjele, posebice istiÄe vrijednost 2lnĻ. Ova vrijednost takoÄer ima kljuÄnu ulogu u odnosu Rikatijevih hiperboliÄnih funkcija s FibonaÄijevim i Lukasovim brojevima u kontinuiranom podruÄju. Time se uspostavlja bliska veza izmeÄu konstanti e i Ļ. Izvedena su dva nova teorema o konvergenciji konstanti Ļ i e . Broj e je temelj Markovskih procesa, koji su naÅ”li primjenu u teoriji vjerojatnosni i umjetne inteligencije. Omjer konstanti e i Ļ, kao i mnogi drugi prirodni fenomeni na temelju zlatnog reza, istiÄu potrebu za proÅ”irenjem podruÄja vjerojatnosni i umjetne inteligencije.The problem of the line section based on the golden ratio Ļ = 1,618033 has the analogy in probability. The solution of the elementary exponential distribution relies on the value 2lnĻ 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 Ļ. Two new theorems on the convergence between the constants Ļ 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 Ļ 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
Mathematical identification of influential parameters on the elastic buckling of variable geometry plate
The problem of elastic stability of plates with square, rectangular, and circular holes as well as slotted holes was discussed. The existence of the hole reduces the deformation energy of the plate and it affects the redistribution of stress flow in comparison to a uniform plate which causes a change of the external operation of compressive forces. The distribution of compressive force is defined as the approximate model of plane state of stress. The significant parameters of elastic stability compared to the uniform plate, including the dominant role of the shape, size, and orientation of the hole were identified. Comparative analysis of the shape of the hole was carried out on the data from the literature, which are based on different approaches and methods. Qualitative and quantitative accordance of the results has been found out and it verifies exposed methodology as applicable in the study of the phenomenon of elastic stability. Sensitivity factor is defined that is proportional to the reciprocal value of the buckling coefficient and it is a measure of sensitivity of plate to the existence of the hole. Mechanism of loss of stability is interpreted through the absorption of the external operation, induced by the shape of the hole
Metodologija izraÄuna otpora u zavoju vlaka u ovisnosti od mase i brzine
A methodology for determining curving resistances of track vehicles is
proposed. The methodology is aimed to gain insight into influence of the
arrangement of masses along the train and the train speed on the curving
resistance based on test results conducted by using a scaled down train. The
utilized scaled down train is a HO scale line freight train in ratio of 1:87
consisting of a EMD SD 35 locomotive and FALNS 121 freight wagons.
The considered variants of the train arrangements are as follows: empty
train (PPPPPP), one loaded wagon in the front/in the end (TPPPPP and
PPPPPT) and two loaded wagons in the front/in the end (TTPPPP and
PPPPTT). The total train curving resistance WR is determined based on
the decrease of the train steady-state curving speed vR when compared to
the train steady-state speed on the straight track vā under same operating
conditions. The curving resistance of a train of arbitrary arrangement is
calculated as the difference between the train driving force when driving
on a straight, horizontal track FV (constant resistance WS) and the total
resistance when curving WU (driving force FV in curve). The constant
resistances of the locomotive and empty and loaded wagons are determined
by application of the gravitational method.Metodologija izraÄuna otpora u zavoju traÄniÄkih vozila osmiÅ”ljena je
za izvoÄenje eksperimenta na umanjenom modelu teretnog vlaka u HO
standardu 1:87, lokomotiva EMD SD 35 i vagoni FALNS 121. Formirani
model služi za istraživanje utjecaja vrijednosti i rasporeda mase tereta
unutar sastava voza, te brzine gibanja na vrijednost otpora u zavoju.
Gravitacijskom metodom se odreÄuju stalni otpori (otpori u ravnini)
lokomotive, praznog i natovarenog vagona. Razmatrane kombinacije
sastava vlaka su: prazan vlak (PPPPPP), jedan natovaren vagon napred
nazad (TPPPPP i PPPPPT) i dva natovarena vagona napred nazad
(TTPPPP i PPPPTT). Otpor u zavoju cijelog vlaka WR dobije se na osnovu
smanjenja brzine gibanja vlaka u zavoju vR prema brzini gibanja vlaka na
pravcu vā pri istim referentnim uvjetima. Otpor u zavoju WR izraÄunava
se kao razlika vuÄne sile vlaka na pravcu FV (stalnog otpora WS) i ukupnog
otpora cijelog vlaka WU (vuÄna sila FV u zavoju) pri gibanju u zavoju za
svaku odabranu kombinaciju sastava vlaka
Ancient logistics ā historical timeline and etymology
Fenomen logistike ima iznimnu genezu. Po nalazima koji su prikazani u radu, logistika datira iz razdoblja kasnog bronÄanog doba, iz antiÄkog doba. Uvjet za razvoj logistike bio je evolucija metriÄkih sustava, prije svega numeriÄkog sustava. Osnove mezopotamijskog i egipatskog numeriÄkog sustava FeniÄani su prilagodili u trgovaÄke svrhe. TadaÅ”nji fenomen broja nije imao odgovarajuÄi simbol, nego je predstavljen kao slika. Primarno znaÄenje rijeÄi logos je raÄunati. Etimologija rijeÄi logistike je izvedena iz sinteze raÄunanja i slike, "vjeÅ”tina raÄunanja pomoÄu slika". Detaljna analiza najstarije olupine broda ā Uluburun, dokazuje intenzivne proizvodne i trgovaÄke aktivnosti kasnog bronÄanog doba na Mediteranu. Takve aktivnosti su mogle biti realizirane samo uz podrÅ”ku intenzivnih logistiÄkih aktivnosti. Prikazana analiza pomiÄe definiciju logistike daleko u razdoblje p.n.e. Äuveni Pitagora je bio prvi imenovani logistiÄar.The phenomenon of logistics has an exceptional genesis. According to the findings presented in this paper, logistics dates back to Late Bronze Age (LBA), to ancient times. The bases for logistics development were an evolution of metrics systems, first of all numerical systems. The grounds of Mesopotamian and Egyptian numerical systems were used for commercial purposes by the Phoenicians. In that time the numbers were not displayed as symbols but as pictures. Primary meaning of the word logos was to count. The etymology of the word logistic was drawn from two words, the counting and the picture or the knowing of "numeracy skills through images". The detailed analysis of the oldest known shipwreck ā Uluburun, proved intensive production and commercial activities in the LBA period in the Mediterranean. These activities could be realized only with the support of intensive logistic activities. The analysis of the logistics change, given below, shows that the definition of logistics starts far in the period of BC. The famous Pythagoras was the first logistician to be appointed
Zlatni rez u vjerojatnosti i umjetnoj inteligenciji
Problem linijskog odsjeÄka utemeljenog na omjeru zlatnog reza Ļ = 1,618033 ima analogiju u vjerojatnosti. RjeÅ”enje elementarne eksponencijalne raspodjele, posebice istiÄe vrijednost 2lnĻ. Ova vrijednost takoÄer ima kljuÄnu ulogu u odnosu Rikatijevih hiperboliÄnih funkcija s FibonaÄijevim i Lukasovim brojevima u kontinuiranom podruÄju. Time se uspostavlja bliska veza izmeÄu konstanti e i Ļ. Izvedena su dva nova teorema o konvergenciji konstanti Ļ i e . Broj e je temelj Markovskih procesa, koji su naÅ”li primjenu u teoriji vjerojatnosni i umjetne inteligencije. Omjer konstanti e i Ļ, kao i mnogi drugi prirodni fenomeni na temelju zlatnog reza, istiÄu potrebu za proÅ”irenjem podruÄja vjerojatnosni i umjetne inteligencije