Keywords:Brownian motion Neutral stochastic functional differential equation Razumikhin-type theorems pth moment exponential stability Almost sure exponential stability The paper discusses both pth moment and almost sure exponential stability of solutions to neutral stochastic functional differential equations and neutral stochastic differential delay equations, by using the Razumikhin-type technique. The main goal is to find sufficient stability conditions that could be verified more easily then by using the usual method with Lyapunov functionals. The analysis is based on paper [X. Mao, Razumikhin-type theorems on exponential stability of neutral stochastic functional differential equations, SIAM J. Math. Anal. 28 (2) (1997) 389-401], referring to mean square and almost sure exponential stability.

No abstract

No abstract

No abstract

No abstract

Original scientific paper The paper presents the issues with the dynamic analysis of mine elevators used with underground exploitation of raw materials. Dynamic occurrences are particularly emphasized with those elevators due to the fact that they are facilities with extreme heights (up to 2000 m) and lifting speeds (up to 20 m/s) using the steel ropes. It shows the forming path of a competent dynamic model for the analysis of such elevators. Basic parameters (stiffness and damping) are of variable magnitude during the lifting, so their values are defined through a combination of theoretical analysis and performed experiments at RTB mine elevators at the town of Bor (Serbia). Keywords: damping; dynamic model; experimental analysis; mine elevators; stiffness Teorijsko-eksperimentalna analiza dinamičkih karakteristika rudničkih liftovaIzvorni znanstveni članak U radu je prezentirana problematika dinamičke analize rudničkih liftova koji se koriste pri podzemnoj eksploataciji sirovina. Kod ovih postrojenja posebno su izražene dinamičke pojave, jer se radi o postrojenjima s ekstremnim visinama (do 2000 m) i brzinama dizanja (do 20 m/s) pomoću čeličnih užadi. Prikazan je postupak formiranja mjerodavnog dinamičkog modela za analizu ovakvih postrojenja. Osnovni parametri (krutost i prigušenje) su, u toku dizanja, promjenjive veličine i njihove vrijednosti su određene kombiniranjem teorijske analize i realiziranih eksperimenata na rudničkom liftu u RTB u Boru (Srbija).

Since neutral stochastic functional differential equations are essentially complex, it is not easy to study stability problems of their solutions by applying usual procedures based on Lyapunov functionals. In this paper we present criteria on the bases of which it is relatively easy to verify the p-th moment exponential stability.

No abstract