We consider classical Tsirelson-type norms of T [An, θ] and their modified versions on lp spaces. We show that for any 1 < p < ∞ there is a constant λp such that considered Tsirelson-type norms do not λp-distort any of subspaces of lp.

We consider homogeneous solutions of the Vlasov—Fokker—Planck equation in plasma theory proving that they reach the equilibrium with a time exponential rate in various norms. By Csiszar—Kullback inequality, strong ̧1-convergence is a consequence of the ‘sharp’ exponential decay of relative entropy and relative Fisher information. To prove exponential strong decay in Sobolev spaces Hk, k*0, we ta...

We consider the large time behavior of solutions to defocusing nonlinear Schrödinger equation in the presence of a time dependent external potential. The main assumption on the potential is that it grows at most quadratically in space, uniformly with respect to the time variable. We show a general exponential control of first order derivatives and momenta, which yields a double exponential boun...

In this paper we study the local and global regularity properties of the Zakharov system on the half line with rough initial data. These properties include local and global wellposedness results, local and global smoothing results and the behavior of higher order Sobolev norms of the solutions. Smoothing means that the nonlinear part of the solution on the half line is smoother than the initial...

We consider the large time behavior of solutions to defocusing nonlinear Schrödinger equation in the presence of a time dependent external potential. The main assumption on the potential is that it grows at most quadratically in space, uniformly with respect to the time variable. We show a general exponential control of first order derivatives and momenta, which yields a double exponential boun...

In this paper, we present a novel method for editing stylistic human motions. We represent styles as differences between stylistic motions and introduced neutral motions, including timing differences and spatial differences. Timing differences are defined as time alignment curves, while spatial differences are found by a machine learning technique: Independent Feature Subspaces Analysis, which ...

For a regression model Yt = gO(x t) + e t , the unknown function gO is estimated consistently using varying degree polynomial regression. Consistency is with respect to a class of norms similar to weighted Sobolev norms, and the method of proof involves metric entropy calculations that enable the development of rates of convergence in these norms. The estimator is viewed as the solution to some...