三基色计算全息图

介绍了三基色计算全息图的设计与制作，用白光光源照明该全息图，可以演示光的叠加，再现彩色图像并给出了理论分析和相应的实验结果。     

Bifurcations of a parametrically excited oscillator with strong nonlinearity

A parametrically excited oscillator with strong nonlinearity, including van der Pol and Duffing types, is studied for static bifurcations. The applicable range of the modified Lindstedt－Poincaré method is extended to 1/2 subharmonic resonance systems. The bifurcation equation of a strongly nonlinear oscillator, which is transformed into a small parameter system, is determined by the multiple scales method. On the basis of the singularity theory, the transition set and the bifurcation diagram in various regions of the parameter plane are analysed.     

计算全息检测非球面干涉场的理论分析与实验结果

本文应用光学全息术及傅里叶光学的理论对计算全息图干涉检测非球面面形的光路及干涉场进行了理论分析,提出了其干涉场为不定域干涉的观点,并在实验中予以证实.     

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.     

Non-linear elliptic problems having natural growth and <Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript> data in Orlicz spaces

An existence result for a strongly non-linear elliptic equation with natural growth condition on the non-linearity and L¹-data is proved. Mathematics Subject Classification (2000) 35J25, 35J60     

Canonical maps to twisted rings

If A is a strongly noetherian graded algebra generated in degree one, then there is a canonically constructed graded ring homomorphism from A to a twisted homogeneous coordinate ring , which is surjective in large degree. This result is a key step in the study of projectively simple rings. The proof relies on some results concerning the growth of graded rings which are of independent interest. D. Rogalski was partially supported by NSF grant DMS-0202479. J. J. Zhang was partially supported by NSF grant DMS-0245420 and Leverhulme Research Interchange Grant F/00158/X (UK).     

Strongly regular locally <Emphasis Type="Italic">GQ</Emphasis>(4,<Emphasis Type="Italic">t</Emphasis>)-graphs

Amply regular with parameters (v, k, λ, μ) we call an undirected graph with v vertices in which the degrees of all vertices are equal to k, every edge belongs to λ triangles, and the intersection of the neighborhoods of every pair of vertices at distance 2 contains exactly μ vertices. An amply regular diameter 2 graph is called strongly regular. We prove the nonexistence of amply regular locally GQ(4,t)-graphs with (t,μ) = (4, 10) and (8, 30). This reduces the classification problem for strongly regular locally GQ(4,t)-graphs to studying locally GQ(4, 6)-graphs with parameters (726, 125, 28, 20).     

计算机制全息图的二值化噪声及取样影响

对用于超大规模集成电路光学互连的计算机制全息图(CGH)的量化噪声及取样影响进行了分析.CGH透过率函数的二值化将带来一些噪声,但仍可得到高的信噪比.在光学互连CGH的结构是菲涅耳波带片的条件下,对Nyquist和Whittaker-Shannon两种取样方法进行了分析和比较.结果表明,在小偏转角和高取样频率条件下,用Whittaker-Shannon取样方法得到的衍射效率比用Nyquist取样方法所得到的衍射效率大.     

基于层状模型的功能梯度板中兰姆波传播研究

功能梯度板中的兰姆波的传播在实际工程中有着非常广泛的应用。采用层状模型研究了兰姆波在材料特性沿厚度方向连续变化的功能梯度板中的传播特性。通过数值计算获得了层状板中兰姆波的色散关系,并与已有结果进行了比较,获得了材料属性沿厚度方向呈指数变化和多项式变化时功能梯度板中兰姆波的波速和位移解。当材料属性连续变化时,兰姆波各阶模态的波速与位移都将发生变化。相比于兰姆波的高阶模态,低阶模态的波速变化更加明显。本文的研究可为功能梯度板的设计提供参考。     

复Banach空间上推广的Roper-Suffridge算子

从定义出发证明复Banach空间特定域上推广的Roper-Suffridge算子保持α次强β型螺形性及ρ次抛物型β型螺形性,由此得到推广后的算子在复Banach空间特定域上保持α次强星形性、ρ次抛物星形性及抛物星形性,为由复平面C中单位圆盘D上的α次强β型螺形映照及ρ次抛物β型螺形映照来构造复Banach空间特定域上相应的映照提供了一种新的途径,充实了对Roper-Suffridge算子的研究.