In this paper, we prove the global regularity of smooth solutions to 2D surface quasi-geostrophic (SQG) equations with supercritical dissipation for a class large initial data, where velocity and temperature can be arbitrarily in spaces L ? ( ? 2 ) H 3 ). This result seen as an improvement work Liu et al (2019) it's without any smallness hypothesis norm data.

In this paper we prove the persistence of space periodic multi-solitons arbitrary size under any quasi-linear Hamiltonian perturbation, which is smooth and sufficiently small. This answers positively a longstanding question whether KAM techniques can be further developed to existence quasi-periodic solutions strongly nonlinear perturbations integrable PDEs.

We present a general motion planning algorithm for robotic systems with a “stratified” configuration space. Such systems include quasi-static legged robots and kinematic models of object manipulation by finger repositioning. Our method extends a nonlinear motion planning algorithm for smooth systems to the stratified case, where the relevant dynamics are not smooth. The method does not depend u...

Abstract We construct explicitly a finite cover of the moduli stack compact Riemann surfaces with given group symmetries by smooth quasi-projective variety.

As a severe threat in anonymized data publication, proximity breach is gaining increasing attention. Such breach occurs when an attacker learns with high confidence that the sensitive value of a targeted victim belongs to a set of semantically proximate values, even though not sure about the exact value. Focusing on tackling proximity breach under specific data models (e.g., categorical or nume...

Piecewise linear convex functions arise as integrands in stochastic programs. They are Lipschitz continuous on their domain, but do not belong to tensor product Sobolev spaces. Motivated by applying Quasi-Monte Carlo methods we show that all terms of their ANOVA decomposition, except the one of highest order, are smooth if the underlying densities are smooth and a certain geometric condition is...