基于偏振测量的雾天图像场景分割

现有场景分割方法主要依赖于图像亮度、颜色和纹理等特征,然而在雾天图像中提取这些特征将变得困难且不稳定.基于此本文提出了适用于雾天图像场景分割的特征矢量,以及相应的特征提取算法.特征矢量由目标偏振度、深度和颜色三部分组成.特征提取算法分别为:用去相关的方法从图像偏振度分离出大气偏振度和目标偏振度;根据雾天退化模型和雾天图像偏振表示形式推导出场景深度信息;利用两幅偏振图像求出非偏振彩色图像,从而得到场景的颜色信息.将这些特征构成的特征矢量用于基于图的分割算法中,并从两个方面比较了仅使用颜色特征和使用本文特征矢量的分割结果.最后得出结论:对于雾天图像而言,这些特征比通常的颜色特征更加有效和鲁棒.     

Hausdorf Dimension of Quadratic Rational Julia Sets

Suppose a quadratic rational map has a Siegel disk and a parabolic fxed point.If the rotation number of the Siegel disk is an irrational of bounded type,then the Julia set of the map is shallow.This implies that its Hausdorf dimension is strictly less than two.     

Non-wandering Expanding Maps on Branched 1-Manifolds and Smale–Williams Solenoids

In this paper, we give a criterion of whether there are non-wandering expanding maps on a given branched 1-manifold. As an application, we give an example of a dynamic on a 3-manifold having non-zero first Betti number, the non-wander sets of which are two Smale–Williams solenoids.     

Uniqueness of Fq-quadratic perfect nonlinear maps from Fq3 to Fq2

Let q be a power of an odd prime. We prove that all ${\mathbb{F}}_q$-quadratic perfect nonlinear maps from ${\mathbb{F}}_{q^3}$ to ${\mathbb{F}}_q^2$ are equivalent. We also give a geometric method to find the corresponding equivalence explicitly.     

The Compression Property for Affine Variational Inequalities

In 1965, Gale and Nikaidô showed that for any n × n P-matrix A, the only nonnegative vector that A sends into a nonpositive vector is the origin. They applied that result to derive various results including univalence properties of certain nonlinear functions. In this article, we show that an extension of their result holds with the nonnegative orthant replaced by any nonempty polyhedral convex cone. In place of the P-matrix condition, we require a determinantal condition that we call the compression property. When the polyhedral convex cone is the nonnegative orthant, the compression property reduces to the property of being a P-matrix and we recover the Gale-Nikaidô result. We apply the extended theorem to derive tools useful in the analysis of affine variational inequalities over polyhedral convex cones.     

Bifurcations and chaos of a discrete mathematical model for respiratory process in bacterial culture

The discrete mathematical model for the respiratory process in bacterial culture obtained by Euler method is investigated. The conditions of existence for flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, condition of existence of chaos in the sense of Marotto＇s definition of chaos is proved. The bifurcation diagrams, Lyapunov exponents and phase portraits are given for different parameters of the model, and the fractal dimension of chaotic attractor was also calculated. The numerical simulation results confirm the theoretical analysis and also display the new and complex dynamical behaviors compared with the continuous model. In particular~ we found that the new chaotic attractor, and new types of two or four coexisting chaotic attractors, and two coexisting invariant torus.     

On a piecewise-smooth map arising in ecology

In this paper, we study a two-dimensional piecewise smooth map arising in ecology. Such map, containing two parameters d and β, is derived from a model describing how masting of a mature forest happens and synchronizes. Here d is the energy depletion quantity and β   is the coupling strength. Our main results are the following. First, we obtain a “weak” Sharkovskii ordering for the map on its nondiagonal invariant region for a certain set of parameters. In particular, we show that its Sharkovskii ordering is the natural number (resp., the positive even number) for β>1$\beta >1$ (resp., 0<β<1$0<\beta <1$). Second, we obtain a region of parameter space for which its corresponding global dynamics can be completely characterized.