基于二维直方图和模糊熵准则的阈值化方法

图像分割是图像分析、识别和理解的基础。图像分割主要是指将图像分成各具特性的区域并提取出感兴趣目标的技术,其研究多年来一直受到人们的高度重视;阈值化法是图像分割的一种重要方法,在图像处理与识别中广为应用;针对图像分割中细节往往被忽略导致后续处理困难的问题,基于模糊关系和最大模糊熵原理提出了一种阈值化方法,对二维直方图进行模糊分割;为了获得图像分割中的细节,提出的方法根据最大熵原则自动确定模糊区域和门限,进而获得二维模糊熵和遗传算法最优解,最后获得图像细节;通过对不同灰度水平和颜色类型图像进行实验比较,实验结果表明提出的方法优于二维非模糊方法和一维模糊熵分割法,得到该方法在图像分割中获得细节的结论。     

An Alternative Method for Calculating Bound-State of Energy Eigenvalues of Klein-Gordon for Quasi-exactly Solvable Potentials

We obtain the bound-state energy of the Klein-Gordon equation for some examples of quasi-exactly solvable potentials within the framework of asymptotic iteration method （AIM）. The eigenvalues are calculated for type- 1 solutions. The whole quasi-exactly solvable potentials are generated from the defined relation between the vector and scalar potentials.     

Analytical solution of a multidimensional Langevin equation at high friction limits and probability passing over a two-dimensional saddle

The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.     

用三角级数和Maple软件求Burgers方程的精确解

用三角级数试探求解Burgers方程,得到关于待定系数的非线性代数方程组,利用Maple软件求解此非线性代数方程组,进而求得Burgers方程的精确解.     

Exact solutions of （3＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations

The symmetries and the exact solutions of the (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations, which describe atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the (3+1)-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the (3+1)-dimensional INHB system.     

Superposition solitons in two-component Bose-Einstein condensates

We develop the Hirota bilinear method and obtain the exact one and two superposition soliton solutions for two-component Bose-Einstein condensates. The conversion of three kinds of solitons including the superposition solitons, bright-bright solitons, and dark-bright solitons is discussed. With the energy analysis, we find that the superposition soliton state is an excitation state for this system. Moreover, the collision of two superposition solitons is found to be elastic.     

A Kind of Exact Inflationary Solution in the Chaotic Inflation Model to Non-minimally Coupled Scalar Field

We present a kind of exact inflationary solution in the chaotic inflation scenario to non-minimal coupled scalar field, taking the Hubble parameter directly as a function of the scalar field φ, H（φ） = αφ^n. Using the analysis of the WMAP3 data, we give the range of power index n.     

Singular Wave Solutions of Two Integrable Generalized KdV Equations

We present some singular wave solutions such as multi-peaked periodic waves, multi-peaked kink waves, multi-peaked peakons as well as kink-compactons, associated with singular curves of generalized KdV equation and modified KdV equation. When a trajectory intersects with the singular curve, it may be divided into segments. Different combinations of these segments may lead to different singular wave solutions, while at the intersection points, peaks on the waves can be observed.     

一个非线性方程的显示行波解

利用双曲函数法和吴元代数消元法,获得了Ｒ－Ｌ－Ｗ方程的多组行波解,其中包括新的行波解、有理函数形式的行波解。