Blow-up properties for a degenerate parabolic system with nonlinear localized sources

AbstractThis paper deals with blow-up properties for a degenerate parabolic system with nonlinear localized sources subject to the homogeneous Dirichlet boundary conditions. The main aim of this paper is to study the blow-up rate estimate and the uniform blow-up profile of the blow-up solution. Our conclusions extend the results of [L.L. Du, Blow-up for a degenerate reaction–diffusion system with nonlinear localized sources, J. Math. Anal. Appl. 324 (2006) 304–320]. At the end, the blow-up set and blow up rate with respect to the radial variable is considered when the domain Ω is a ball

Studies on Enlightenment of China: Haier Group’s Transnational Operations to Chinese Enterprise

After China joins World Trade Organization, enterprise carry on transnational operations is necessity; enterprise’s transnational operations are generally started from the export. Regarding the mature product, when after exporting develops certain stage, to follow the need of overseas market development, must carry on the comparison, by determined that which modes of business operation do serve the enterprise benefit. It must develop the transnational operations, the government should increase the support dynamics to the enterprise; The enterprise should raise own competitive advantage diligently; Speeds up the business management and the international trail connection step; Creates the new technology as circumstances permit; Pays special attention to the capital operation. Haier’s transnational operations have given Chinese Enterprise much enlightenment.Key words: Haier group; Transnational operations; Competitive; Internationa

Defending Black-box Classifiers by Bayesian Boundary Correction

Classifiers based on deep neural networks have been recently challenged by Adversarial Attack, where the widely existing vulnerability has invoked the research in defending them from potential threats. Given a vulnerable classifier, existing defense methods are mostly white-box and often require re-training the victim under modified loss functions/training regimes. While the model/data/training specifics of the victim are usually unavailable to the user, re-training is unappealing, if not impossible for reasons such as limited computational resources. To this end, we propose a new black-box defense framework. It can turn any pre-trained classifier into a resilient one with little knowledge of the model specifics. This is achieved by new joint Bayesian treatments on the clean data, the adversarial examples and the classifier, for maximizing their joint probability. It is further equipped with a new post-train strategy which keeps the victim intact. We name our framework Bayesian Boundary Correction (BBC). BBC is a general and flexible framework that can easily adapt to different data types. We instantiate BBC for image classification and skeleton-based human activity recognition, for both static and dynamic data. Exhaustive evaluation shows that BBC has superior robustness and can enhance robustness without severely hurting the clean accuracy, compared with existing defense methods.Comment: arXiv admin note: text overlap with arXiv:2203.0471

Diophantine estimates on shifts of trigonometric polynomials on Td\mathbb{T}^d

We establish Diophantine type estimates on shifts of trigonometric polynomials on the torus $\mathbb{T}^d$, as well as that of their square roots. These estimates arise from the spectral analysis of the quasi-periodic Schr\"odinger and the quasi-periodic wave operators. They have applications to the nonlinear quasi-periodic Schr\"odinger equations (NLS) and the nonlinear quasi-periodic wave equations (NLW). One could now, for example, extend the result of Bourgain (Geom. Funct. Anal. 17(3): 682-706, 2007) to the nonlinear setting.Comment: Comments welcom

Anderson localized states for the quasi-periodic nonlinear wave equation on Zd\mathbb Z^d

We establish large sets of Anderson localized states for the quasi-periodic nonlinear wave equation on $\mathbb Z^d$, thus extending nonlinear Anderson localization from the random \cite{BW08, LW22, GSW23} to a deterministic setting.Comment: 37 page