Holomorphic Flows on Simply Connected Regions Have No Limit Cycles

The dynamical system or flow = f(z), where f is holomorphic on C, is considered. The behavior of the flow at critical points coincides with the behavior of the linearization when the critical points are non-degenerate: there is no center-focus dichotomy. Periodic orbits about a center have the same period and form an open subset. The flow has no limit cycles in simply connected regions. The advance mapping is holomorphic where the flow is complete. The structure of the separatrices bounding the orbits surrounding a center is determined. Some examples are given including the following: if a quartic polynomial system has four distinct centers, then they are collinear.     

Bogdanov‐Takens bifurcations of codimensions 2 and 3 in a Leslie‐Gower predator‐prey model with Michaelis‐Menten–type prey harvesting

The Bogdanov‐Takens bifurcations of a Leslie‐Gower predator‐prey model with Michaelis‐Menten–type prey harvesting were studied. In the paper “Diff. Equ. Dyn. Syst. 20(2012), 339‐366,” Gupta et al proved that the Leslie‐Gower predator‐prey model with Michaelis‐Menten–type prey harvesting has rich dynamics. Some equilibria of codimension 1 and their bifurcations were discussed. In this paper, we find that the model has an equilibrium of codimensions 2 and 3. We also prove analytically that the model undergoes Bogdanov‐Takens bifurcations (cusp cases) of codimensions 2 and 3. Hence, the model can have 2 limit cycles, coexistence of a stable homoclinic loop and an unstable limit cycle, supercritical and subcritical Hopf bifurcations, and homoclinic bifurcation of codimension 1 as the values of parameters vary. Moreover, several numerical simulations are conducted to illustrate the validity of our results.     

A note on global stability of three-dimensional Ricker models

In the recent paper [E. C. Balreira, S. Elaydi, and R. Luís, J. Differ. Equ. Appl. 23 (2017), pp. 2037–2071], Balreira, Elaydi and Luís established a good criterion for competitive mappings to have a globally asymptotically stable interior fixed point by a geometric approach. This criterion can be applied to three dimensional Kolmogorov competitive mappings on a monotone region with a carrying simplex whose planar fixed points are saddles but globally asymptotically stable on their positive coordinate planes. For three dimensional Ricker models, they found mild conditions on parameters such that the criterion can be applied to. Observing that Balreira, Elaydi and Luís' discussion is still valid for the monotone region with piecewise smooth boundary, we prove in this note that the interior fixed point of three dimensional Kolmogorov competitive mappings is globally asymptotically stable if they admit a carrying simplex and three planar fixed points which are saddles but globally asymptotically stable on their positive coordinate planes. This result is much easier to apply in the application.     

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems

Although planar quadratic differential systems and their applications have been studied in more than one thousand papers, we still have no complete understanding of these systems. In this paper we have two objectives.First we provide a brief bibliographical survey on the main results about quadratic systems. Here we do not consider the applications of these systems to many areas as in Physics, Chemist, Economics, Biology, …Second we characterize the new class of planar separable quadratic polynomial differential systems. For such class of systems we provide the normal forms which contain one parameter, and using the Poincaré compactification and the blow up technique, we prove that there exist 10 non-equivalent topological phase portraits in the Poincaré disc for the separable quadratic polynomial differential systems.     

大视角彩虹全息新设计

用光纤制成的光束变换元件代替大孔径透镜和狭缝拍摄彩虹全息图,大大提高了全息图的视角,而且方法简单.本文介绍了用光纤光束变换器的摄大视角彩虹全息图的原理、方法,并进行了实验验证,收到了较为满意的效果.     

Improvement of 1D off-axis computer-generated holograms

Creation of Fresnel off-axis computer-generated holograms and improvement of images reconstructed from the holograms are described. To improve the reconstructed images, we have created the holograms with high construct diffraction patterns by using a histogram method. From reconstruction experiments of the holograms, clear images have been obtained and 3D images have been seen directly with eyes.     

计算机产生全息图对补偿器检测的技术研究

用一种计算全息板代替补偿器零检验光路中理想的大型非球面,实现对补偿器的定量检验.用于检测补偿器旋转对称的二元反射式全息板根据非球面方程设计,并确定其光程差,再由激光直写(精度可达0.6μm)来制作完成,合成相当于理想非球面反射波前.其检测精度小于λ/10.补偿器的参量由抛物面和三级球差理论确定.     

紫外光致聚合物和制造镭射玻璃的技术

本文论述了制造镭射玻璃的技术和材料。技术包括：清洗玻璃板；将紫外光致聚合物材料涂到玻璃板上；将镭射玻璃母版粘贴到涂有光致聚合物的玻璃板上；紫外光曝光固化；丝网印刷；真空镀膜；涂保护层。紫外光致聚合物材料是由光引发剂、单体、预聚体和其它添加剂组成。实验结果表明：此种镭射玻璃具有很高的抗酸、碱、热和紫外照射的能力     

室外自然场景体视彩虹全息图的制作方法研究

本文介绍了一种用连续激光制作室外自然场景体视彩虹全息技术. 先用自制的透镜线阵照相机拍摄室外自然场景经透镜所成像的初级体视图，然后用连续激光照明初级体视图，原光路返回，透镜线阵此时不仅起到成像作用，而且起到了彩虹全息术中的狭缝作用. 这种技术也适用于室外动态物体. 本文制作了室外自然场景的体视彩虹全息图，并给出了实验结果.     

记录光强变化对光折变晶体多重存储衍射效率均匀性的影响

光折变晶体多重存储中,为获得均匀的衍射效率,要根据记录晶体的时间常数计算相继写入全息图的曝光时间,而晶体的时间常数是记录光强的幂函数.本文分析了光强变化对衍射效率的影响.结果表明,对曝光时间加以适当修正,可补偿光强变化对衍射效率均匀性的影响.