Peakon and cuspon solutions of a generalized Camassa-Holm-Novikov equation

The bounded traveling wave solutions of a generalized Camassa-Holm-Novikov equation with $p=2$ and $p=3$ are derived via the dynamical system approach. The singular wave solutions including peakons and cuspons are obtained by the bifurcation analysis of the corresponding singular dynamical system and the orbits intersecting with or approaching the singular lines. The results show that the generalized Camassa-Holm-Novikov equation with $p=2$ and $p=3$ both admit smooth solitary wave, smooth periodic wave solutions, solitary peakons, periodic peakons, solitary cuspons and periodic cuspons as well. It is worth pointing out that the Novikov equation has no bounded traveling wave solutions with negative wave speed, but has a family of new periodic cuspons which are distinguished with the normal periodic cuspons for their discontinuous first-order derivatives at both maximum and minimum.     

Dynamic analysis of a non-autonomous ratio-dependent predator-prey model with additional food

In this paper, a non-autonomous ratio-dependent three species predator-prey system with additional food to top predator was proposed. The permanence of the model is obtained. Based on the continuation theorem, the sufficient conditions for the existence of a periodic solution are obtained. By using the method of Lyapunov function, we prove that the system exists a unique positive almost periodic solution under some certain conditions.     

Fabrication of microlens arrays in photosensitive glass by femtosecond laser direct writing

This article reports the fabrication of high-fill-factor plano-convex cylindrical and spherical microlens arrays horizontally and vertically embedded in a photosensitive Foturan glass chip by femtosecond (fs) laser micromachining. The microlens arrays were fabricated by modifying the microstructure of Foturan glass using fs laser direct writing followed by thermal treatment, wet etching, and additional annealing. The focusing ability and image quality of the microlens arrays were examined, showing that the lens arrays not only can focus light well but also provide an imaging capability that holds great potential for lab-on-a-chip applications.     

七芯光子晶体光纤结构优化的数值分析

从耦合模方程出发,推导了描述七芯光子晶体光纤模场特性的本征方程,得到了这种结构光纤的本征值和本征矢.使用频域有限差分法数值模拟,通过改变传输波长、纤芯间距、包层孔大小分析了纤芯之间的强度分布与耦合系数的关系,分别实现了模式整形和高阶超模截止.掌握了具有强耦合特性的七芯光子晶体光纤设计规律,和这种结构光子晶体光纤的同相位超模的选取方法. 关键词： 光子晶体光纤 大模场面积光纤 多芯结构 频域有限差分法     

一种快速双目视觉立体匹配算法

针对目前双目视觉立体匹配算法计算量过大、实时性不强的问题,提出了一种平行配置系统的快速立体匹配算法.利用两幅视图的差异将视图分为特征点和非特征点,然后对特征点采用WTA(winner-take-all)方法进行匹配,而对非特征点只进行简单的验证,最后得出致密的视差图.该算法利用视差的分段连续性,大大减少了运算量.实验结果表明,该算法提取的特征点集中于视差不连续区,与目前其它基于区域的匹配算法相比,该算法得到的误匹配像素百分比与其它算法相当,而计算速度却提高了一个数量级,并且边缘特征较好,是一种有效可行的高实时性立体匹配算法.     

基于亚像素区域加权能量特征的多尺度图像融合算法

对矩形和圆形区域中各像素进行亚像素划分,确定各亚像素的权值,得到基于哑像素的综合加权区域能量.融合箅法首先对源图像进行金字塔分解,然后对金字塔的高频细节分量使用基于哑像素加权区域能量特征的融合规则取大,对低频粗糙分量取平均.得到融合图像的塔形分解,最后重构融合图像.仿真结果表明,新算法融合效果较常规的区域能量特征作为融合规则的多分辨率图像融合算法效果更好,从清晰度和熵的评价来看,提高了融合图像的品质.     

The transport properties in Nd0.75Sr1.25CoO4 film: Evidence for polaronic transport

The experiments of electrical resistivity and thermopower on Nd_0.75Sr_1.25CoO₄ film in the temperature range 90 K<T<310 K were carried out. The great difference in the activation energies estimated from thermopower and resistivity, a characteristic of small polarons, is observed, providing strong evidence for polaron-dominated transport mechanism in this material. Furthermore, the activation energy at intermediate-temperature region is larger than that at low-temperature region in resistivity, but it is not observed in thermopower, indicating that the energy for the creation of the carriers is slightly lower at low-temperature region than that at intermediate-temperature region. At the same time, the abrupt drop in the thermopower and the abnormal peak in the differential curve of resistivity indicate that a phase transition between a paramagnetic state and a ferromagnetic state occurs at temperature about 218 K. The positive thermopower in the whole temperature range measured suggests that the carriers are holes in this system.     

The mathematical model and optimistic algorithm of two protein structures alignment

Protein structure alignment is one of the most important computational problems in molecular biology. From the viewpoint of computational complexity, a pairwise structure alignment is a NP-hard problem. In this paper, based on the discrepancy of two proteins, we define the structure alignment as a mixed integer-programming (MIP) problem with the simpler form and prove the existence of optimal solution. The optimal alignment is achieved by incorporating improved complete information set method used to modify the score matrix into iterative double dynamic programming algorithm. Convergence of algorithm is proved. A number of benchmark examples are tested. The results show that our model and approach are general and improve computational efficiency as well as quality of the structure alignment.     

Role of absorption in grating erasure

In this paper, we have investigated the grating erasure of a reduced LiNbO₃:Fe crystal with different erasing wavelengths. The overall hologram evolution in the process of grating erasure is nonexponential due to strong absorption which is contrary to the mono-exponential law. The hologram in the rear part of the crystal can persist for a long time in the grating erasure due to weak erasing light intensity by strong absorption, which can enlarge the erasure time constant. From the erasure experiments, the global absorption d≈5 can be taken as the optimum absorption to acquire a good trade-off between the sensitivity and hologram strength in the crystal.     

Uniquely ergodic property of minimal probability measure in positive definite Lagrangian systems

Mane conjectured that every minimal measure in the generic Lagrangian systems is uniquely ergodic. In this paper, we will show that the answer to the Mane's conjecture is negative by analyzing the structure of the supports of minimal probability measures for some kinds of the Lagrangian systems.