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.     

Compact, reliable asymmetric optical configuration for cost-effective fabrication of multiplex dot matrix hologram in anti-counterfeiting applications

This study presents a compact optical configuration that can generate a multiplex dot-matrix hologram with complex interlaced images for anti-counterfeiting applications on valuable paper. Varying the orientation of the interference plane can enable the multiplex hologram to be recorded without changing the interference angle of two laser beams. With its simple asymmetric optical setup, a multiplex hologram with many interlaced images can be efficiently fabricated, increasing the cost of imitation. Experimental details of the asymmetric optical setup are also described.     

彩色全息图的计算机产生和数字再现

提出了一种基于色彩合成以及菲涅尔衍射原理,用计算机产生全息图并用数字方法再现彩色全息图的方法。该方法的第一步是将物体的彩色RGB图像分离为三基色强度图,再利用博奇编码的方法制成修正离轴参考光分色计算机全息图;第二步是分别对分色全息图在频域进行调制以实现用原参考光真实再现原始物光波。通过滤波消除零级衍射及共轭像的影响,获得了所需要的实像并提高了像质。提供的实验是选用一幅RGB图像作为原始物体,给出了用博奇编码法制成的全息图以及最后经色彩合成获得的再现像。结果表明,该方法能使各分色全息图的再现像准确重合,解决了在色彩合成时容易出现的色串扰问题。     

全息彩虹字的实用化研究

全息彩虹字要能达到实用化，必须满足大视角、大面积，制作方便、再现容易的要求。通过研究，本文报导一种简单有效的制作方法，用满足一定要求的两个双光束干涉光路来拍摄，对实心字和空心字分别进行两次曝光，并用线光源在一定条件下进行再现。     

Double Hopf bifurcation for van der Pol-Duffing oscillator with parametric delay feedback control

The stability and bifurcation of a van der Pol-Duffing oscillator with the delay feedback are investigated, in which the strength of feedback control is a nonlinear function of delay. A geometrical method in conjunction with an analytical method is developed to identify the critical values for stability switches and Hopf bifurcations. The Hopf bifurcation curves and multi-stable regions are obtained as two parameters vary. Some weak resonant and non-resonant double Hopf bifurcation phenomena are observed due to the vanishing of the real parts of two pairs of characteristic roots on the margins of the “death island” regions simultaneously. By applying the center manifold theory, the normal forms near the double Hopf bifurcation points, as well as classifications of local dynamics are analyzed. Furthermore, some quasi-periodic and chaotic motions are verified in both theoretical and numerical ways.     

CLASSIFICATION OF THE PHASE PORTRAIT FOR PLANAR Z_8-EQUIVARIANT HAMILTONIAN SYSTEM OF DEGREE 7

The Hilbert's sixteenth problem, that is the problem on the rlurnber anddistribution of limit cycles of planar polynomial system, has not solved fOr acentury. Since the original problem is so difficuIt, in 1977, V.I.Arnold posed"weakened Hilbert's sixteenth problem"-- the possibility of the number anddistribution of limit cycles fOr polynomial HamiItonian system of degrees n -- lunder perturbation of the polynomial of degrees m 1. From l983, Prof.Li Jibin etc. began to study cubic vecto…     

Existence and nonexistence of curved front solution of a biological equation

This paper deals with the existence of curved front solution of a partial differential equation coming from a mathematical model of stroke. The equation is of reaction-diffusion type in a cylinder of radius R and of diffusion and absorption type outside of the cylinder. We prove the nonexistence of a travelling front when R is small enough and the existence if R is large enough using a recent energy method. We construct the travelling front as the limit in time of a solution with a well-chosen initial condition, in a travelling referential.     

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.