For a one-dimensional motion, a constant of motion for non autonomous an linear system (position and velocity) is given from the constant of motion associated to its autonomous system. This approach is used in the study of the harmonic oscillator with an additional time depending force.

We give results on the probability of absorption at zero of the diffusion process Xt with X0 = K > 0 and non-Lipschitz diffusion coefficient σx , γ ∈ [ 1 2 , 1): dXt = μXtdt + σX γ t dBt relative to Brownian motion Bt. Our results give information on the time to ruin τ0 = inf{t : Xt = 0}. We show that P (τ0 ≤ T ) > 0 for all T , give the probability of ultimate ruin, and establish asymptotics i...

background: in order to improve the evaluation of possible rectal toxicity based on the rectal normal tissue complication probability (ntcp), we consider the fractional dependence of the ntcp on the wall thickness (tw) and rectal displacement (rm). materials and methods: the two-dimensional ntcp model (ntcp2d) was developed using radiotherapy plans of ten randomly selected patients with prostat...

Coherent motion is found to emerge out of fluctuations in a vibrated asymmetric particle. Depending on the parameters, amplitude, and frequency of the box, the motion of the particle is classified into several phases. The transition between fluctuating motion and unidirectional motion occurs with constant acceleration in the low-frequency regime and constant amplitude in the high-frequency regi...

For a relativistic particle under a constant force and a linear velocity dissi-pation force, a constant of motion is found. Problems are shown for getting the Hamiltonian of this system. Thus, the quantization of this system is carried out through the constant of motion and using the quantization on the velocity variable. The dissipative relativistic quantum bouncer is outlined within this quan...

In certain applications, for instance biomechanics, turbulence, finance, or Internet traffic, it seems suitable to model the data by a generalization of a fractional Brownian motion for which the Hurst parameter H is depending on the frequency as a piece-wise constant function. These processes are called multiscale fractional Brownian motions. In this contribution, we provide a statistical stud...

This paper addresses how to determine a sufficient frame (sampling) rate for an optical motion tracking system using passive reflective markers. When using passive markers for the optical motion tracking, avoiding identity confusion between the markers becomes a problem as the speed of motion increases, necessitating a higher frame rate to avoid a failure of the motion tracking caused by marker...

Let t (dx) denote a three dimensional super-Brownian motion with deterministic initial state 0 (dx) = dx, the Lebesgue measure. Let V : R 3 7 ! R be HH older continuous with compact support, not identically zero and such that Z R 3 V (x)dx = 0. We show that log P Z t 0 Z R 3 V (x) s (dx)ds > bt 3=4 is of order t 1=2 as t ! 1, for b > 0. This should be compared with the known result for the case...