高阶半线性抛物型方程组的生命跨度

其中m,P,q>1．利用试验函数方法,首先推导一些积分不等式,然后对方程组爆破解的生命跨度 [0,T)给出估计．     

一类不可微规划的高阶对称对偶性

本文我们利用一个可微函数给出了一对高阶对称规划问题 ,其中目标函数包含了Rn 中一紧凸集的支撑函数 .在引入高阶F 凸性 (F 伪凸性 ,F 拟凸性 )后 ,证明了高阶弱、高阶强及高阶逆对称对偶性质 .     

Higher-order radiative perturbation theory

As a computationally effective tool, the first-order term of the radiative perturbation theory has been computed successfully, and has been applied in a number of areas. In this article, we develop the computational expressions for the higher-order terms of the perturbation expansion in a plane parallel atmosphere. These expressions are then implemented, and numerical results for some typical cases are presented. These results indicate that the computation is successful and that the higher-order terms are essential in cases where the first-order term alone cannot predict the perturbation with sufficient accuracy.     

Higher-order necessary conditions for infinite and semi-infinite optimization

In this paper, we present a unified theory of first-order and higher-order necessary optimality conditions for abstract vector optimization problems in normed linear spaces. We prove general multiplier rules, from which nearly all known first-order, second-order, and higher-order necessary conditions can be derived. In the last section, we prove higher-order necessary conditions for semi-infinite programming problems.This work was developed within the Forschungsschwerpunkt Dynamische Systeme, Universität Bremen, Bremen, West Germany.The author wishes to thank Prof. Dr. D. Hinrichsen for his helpful remarks and discussions during the preparation of this work.     

Resolution enhancement at a large convergence angle by a delta corrector with a CFEG in a low-accelerating-voltage STEM

Resolution reduction by a diffraction limit becomes severe with an increase in the wavelength of an electron at a relatively low accelerating voltage. For maintaining atomic resolution at a low accelerating voltage, a larger convergence angle with aberration correction is required. The developed aberration corrector, which compensates for higher-order aberration, can expand the uniform phase angle. Sub-angstrom imaging of a Ge [1 1 2] specimen with a narrow energy spread obtained by a cold field emission gun at 60 kV was performed using the aberration corrector. We achieved a resolution of 82 pm for a Ge–Ge dumbbell structure image by high angle annular dark-field imaging.     

Higher-order Dirac solitons in binary waveguide arrays

We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range.     

Multi-way dual Cheeger constants and spectral bounds of graphs

We introduce a set of multi-way dual Cheeger constants and prove universal higher-order dual Cheeger inequalities for eigenvalues of normalized Laplace operators on weighted finite graphs. Our proof proposes a new spectral clustering phenomenon deduced from metrics on real projective spaces. We further extend those results to a general reversible Markov operator and find applications in characterizing its essential spectrum.     

New representation and factorizations of the higher-order ultraspherical-type differential equations

The paper deals with the class of linear differential equations of any even order 2α+4$2\alpha +4$, α∈_N0$\alpha \in {\mathbb{N}}_0$, which are associated with the so-called ultraspherical-type polynomials. These polynomials form an orthogonal system on the interval [−1,1]$[-1,1]$ with respect to the ultraspherical weight function (1−x²)^α${(1-x^2)}^{\alpha }$ and additional point masses of equal size at the two endpoints. The differential equations of “ultraspherical-type” were developed by R. Koekoek in 1994 by utilizing special function methods. In the present paper, a new and completely elementary representation of these higher-order differential equations is presented. This result is used to deduce the orthogonality relation of the ultraspherical-type polynomials directly from the differential equation property. Moreover, we introduce two types of factorizations of the corresponding differential operators of order 2α+4$2\alpha +4$ into a product of α+2$\alpha +2$ linear second-order operators.     

利用液晶空间光调制器产生高阶拉盖尔高斯光束

本文采用反射式纯相位液晶空间光调制器产生了实验需要的高阶拉盖尔高斯光束。理论上详细计算了生成高阶拉盖尔高斯(Laguerre-Gaussian)光束的最优参数选择,用MATLAB编写程序,制作产生高阶LG光束的相息图。通过CCD采集图像数据,观测了以平面波入射生成拉盖尔高斯光束的强度分布,并利用干涉法验证了产生高阶拉盖尔高斯光束的螺旋相位分布。在此基础上,对实验测得一维强度轮廓进行拟合分析并估算了实验产生LG光束的纯度。