One of the most attractive problems in 1740s was a motion of a rotating tube around a fixed point and that of a small body included in it. Representative mechanicians in those days, such as Daniel Bernoulli, Alexis-Claude Clairaut, Leonhard Euler and Jean le Rond d’Alembert, tried to solve this problem. This problem was later applied to astronomical mechanics. It was posed by Euler for Johann B...

This paper is a synthesis of previously published material on the topic. We show that an adequate mathematical model for the physical (i.e., perceptible and therefore past) reality must be finite. A finite approach to past proper time is given. Proper time turns out to be proportional to the sum of the return probabilities of a Bernoulli random walk. 1. Introduction. Every physical measurement ...

We prove that the one-dimensional random fields with finite first moment are isomorphic to Bernoulli schemes. §

We provide a derivation of the Poisson multiBernoulli mixture (PMBM) filter for multi-target tracking with the standard point target measurements without using probability generating functionals or functional derivatives. We also establish the connection with the δ-generalised labelled multiBernoulli (δ-GLMB) filter, showing that a δ-GLMB density represents a multi-Bernoulli mixture with labell...

The complete 3D nonlinear dynamic problem of extensible, flexible risers conveying fluid is considered. For describing the dynamics of the system, the Newtonian derivation procedure is followed. The velocity field inside the pipe formulated using hydrostatic and Bernoulli equations. The hydrodynamic effects of external fluids are taken into consideration through the nonlinear drag forces in var...

the static pull-in instability of beam-type micro-electromechanical systems is theoretically investigated. two engineering cases including cantilever and double cantilever micro-beam are considered. considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent euler-bernoulli beam model is used based on a modified couple stress theory, c...

In this paper, the buckling and vibration behaviour of functionally graded flexoelectric nanobeam is examined. The vibration and buckling formulations of functionally graded nanobeam are developed by using a new theory that’s presented exclusively for flexoelecteric nano-materials. So by considering Von-Karman strain and forming enthalpy equation based on displacement, polarization and electric...