instability of standing wave, global existence and blowup for the klein-gordon-zakharov system with different-degree nonlinearities

This paper discusses the Klein–Gordon–Zakharov system with different-degree nonlinearities in two and three space dimensions. Firstly, we prove the existence of standing wave with ground state by applying an intricate variational argument. Next, by introducing an auxiliary functional and an equivalent minimization problem, we obtain two invariant manifolds under the solution flow generated by the Cauchy problem to the aforementioned Klein–Gordon–Zakharov system. Furthermore, by constructing a type of constrained variational problem, utilizing the above two invariant manifolds as well as applying potential well argument and concavity method, we derive a sharp threshold for global existence and blowup. Then, combining the above results, we obtain two conclusions of how small the initial data are for the solution to exist globally by using dilation transformation. Finally, we prove a modified instability of standing wave to the system under study.

A Video Quality Assessment Metric Based on Human Visual System

It is important for practical application to design an effective and efficient metric for video quality. The most reliable way is by subjective evaluation. Thus, to design an objective metric by simulating human visual system (HVS) is quite reasonable and available. In this paper, the video quality assessment metric based on visual perception is proposed. Three-dimensional wavelet is utilized to decompose video and then extract features to mimic the multichannel structure of HVS. Spatio-temporal contrast sensitivity function (S-T CSF) is employed to weight coefficient obtained by three-dimensional wavelet to simulate nonlinearity feature of the human eyes. Perceptual threshold is exploited to obtain visual sensitive coefficients after S-T CSF filtered. Visual sensitive coefficients are normalized representation and then visual sensitive errors are calculated between reference and distorted video. Finally, temporal perceptual mechanism is applied to count values of video quality for reducing computational cost. Experimental results prove the proposed method outperforms the most existing methods and is comparable to LHS and PVQM.

Global Translation Preferred Active Contour

具有全局平移优先属性的主动轮廓更适于目标跟踪。演化轮廓具有的全局平移优先性可以理解为沿轮廓的速度场具有相等的倾向。根据此思想,通过定义在曲线扰动集合上的新内积空间导出了一种简单,具有平移优先的梯度流。新的内积空间由于是通过向H0主动轮廓对应的內积空间引入曲线扰动的方差获得,所以此主动轮廓称为方差主动轮廓。方差主动轮廓是将H0主动轮廓与其对应的平均梯度流通过加权求和获得,而H1主动轮廓则是通过H0主动轮廓与特定类型的核函数进行卷积得到。因此方差主动轮廓实现时更简单和快速。最后给出了H0,H1和方差主动轮廓在频域与时域的分析。