This paper is devoted to the study of the existence of solutions to a general elliptic problemAu+g(x,u,∇u)=f-div⁡F, withf∈L1(Ω)andF∈∏i=1NLp'(Ω,ωi*), whereAis a Leray-Lions operator from a weighted Sobolev space into its dual andg(x,s,ξ)is a nonlinear term satisfyinggx,s,ξsgn⁡(s)≥ρ∑i=1Nωi|ξi|p,|s|≥h>0, and a growth condition with respect toξ. Here,ωi,ωi*are weight functions that will be defined in the Preliminaries.

In embedded video surveillance system, many moving target detection methods are used. But for some complex environmental, they have some problems in detection accuracy and speed of moving target detection. In this paper, a target detection method based on improved adaptive threshold hybrid difference is proposed, then for wiping off the noise, the method of morphological filtering is adopted to gain exact moving objects. Finally, according to the requirement, the area method is used to choose the final images to avoid false alarms. Experimental results show that the proposed method not only gets moving objects completely, but also adapts to the complex environmental change, at the same time, the method is rapid, efficient, and is applied to embedded system well.

The aim of this paper is to study bounds for lifespan of solutions to the following equation: u tt-u + t 0 g(t-τ) u(τ) dτ + |u t | m(x,t)-2 u t = |u| p(x,t)-2 u under homogeneous Dirichlet boundary conditions. It is worth pointing out that it is not a trivial generalization for constant-exponent problems because we have to face some essential difficulties in studying such problems. The first difficulty is that the monotonicity of the energy functional fails. Another one is that there exists a gap between the norm and the modular to the generalized function space, which leads to the failure of the Poincaré inequality for modular form. To overcome such difficulties, the authors construct control function and apply new energy estimates to establish the quantitative relationship between the source Ω |u| p(x,t) dx and the initial energy, and then obtain the finite-time blow-up of solutions for a positive initial energy, especially, the authors only assume that p t (x, t) is integrable rather than uniformly bounded. Such weak conditions are seldom seen for the variable exponent case. At last, an estimate of lower bound for lifespan is established by applying differential inequality argument and energy inequalities.

A motion information analysis system based on the acceleration data is proposed in this paper, consisting of filtering, feature extraction and classification. The Kalman filter is adopted to eliminate the noise. With the time-domain and frequency-domain analysis, acceleration features like the amplitude, the period and the acceleration region values are obtained. Furthermore, the accuracy of the motion classification is improved by using the k -nearest neighbor (KNN) algorithm.