On the connectedness of planar self-affine sets

In this paper, we consider the connectedness of planar self-affine set $T(A,\mathcal{D})$ arising from an integral expanding matrix $A$ with characteristic polynomial $f(x)=x^2+bx+c$ and a digit set $\mathcal{D}=\{0,1,\dots, m\}v$. The necessary and sufficient conditions only depending on $b,c,m$ are given for the $T(A,\mathcal{D})$ to be connected. Moreover, we also consider the case that ${\mathcal D}$ is non-consecutively collinear.Comment: 18 pages; 18 figure

Polarization Decomposition Algorithm for Detection Efficiency Enhancement

In the paper, a new polarization decomposition of the optimal detection algorithm in the partially homogeneous environment is presented. Firstly, the detectors Matched Subspace Detector (MSD) and Adaptive Subspace Detector (ASD) are adopted to deal with detection problems in the partially homogeneous environment. Secondly, the fitness function with polarization parameters is equivalently decomposed to enhance time detection efficiency in the algorithm. It makes the multiplication number of the fitness function from square to a linear increase along with the increase in parameters. Simulation results indicate that the proposed decomposition is much more efficient than direct use of the fitness function