Abstract We obtain a nontrivial upper bound for the multiplicative energy of any sufficiently large subset subvariety finite algebraic group. also find some applications our results to growth conjugates classes, estimates exponential sums, and restriction phenomenon.

For a convergent sequence {xi} generated by xi+l = ~(x~, xt_ l , . . . , Xi_d+l) , define the multiplicative efficiency measure E to be (log~p)/M, where p is the order of convergence and M is the number of multiplications or divisions needed to compute rp. Then, if 9 is any multivariate rational function, E < 1. Since E = 1 for the sequence {xi} generated by x~+l = x~ ~ + xi -~ with the limit -...

Semilinear stochastic evolution equations with multiplicative L'evy noise are considered‎. ‎The drift term is assumed to be monotone nonlinear and with linear growth‎. ‎Unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎As corollaries of ...

A novel super-twisting adaptive sliding mode control law is derived using Lyapunov function technique. The both drift uncertain term and multiplicative perturbation are assumed to be bounded with unknown boundaries. The proposed approach consists in using dynamically adapted control gains that ensure the establishment, in a finite time, of a real second order sliding mode. The efficacy of the p...

We consider the problem of detecting an anomaly in the form of a path of correlations hidden in white noise. We provide a minimax lower bound and a test that, under mild assumptions, is able to achieve the lower bound up to a multiplicative constant.

The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical aimulations show two distinct parameter regimes, corresponding to freerunning near-deterministic particles, and particles which are trapped in local minima of the...

We prove finite time extinction for stochastic sign fast diffusion equations driven by linear multiplicative space-time noise, corresponding to the Bak-Tang-Wiesenfeld model for self-organized criticality. This solves a problem posed and left open in several works: [Bar13, RW13, BDPR12, BR12, BDPR09b, BDPR09a]. The highly singular-degenerate nature of the drift in interplay with the stochastic ...