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It is shown that the modified Schrodinger equation proposed by Janossy cannot describe the behavior of the electron correctly. However, it is further shown that the equation can be regarded as a model of a possible phenomenalogical theory of nuclei or as a model of a possible theory of elementary particles. The quantization of the equation is discussed. 本文指出杨诺赛波动方程作为电子的个体理论的困难;指出这一类型波动方程可以作为原子核系综理论的数学形式,也可以作为元粒子系综理论的数学形式。本文并讨论了这一类型波动方程的第二级量子化问题。 In this paper Wang's generalization of Bethe's theory of superlattices is applied to the case of a binary alloy AB in a body-centred cubic lattice. Only neighbour interaction is taken into consideration. All the calculations are carried out to the second approximation. 本文把王氏理论应用到体心立方晶AB型二元合金超点阵问题;讨论它的平衡态性质,如秩序度与温度的关系,比热的性质,临界温度等;采取近邻作用假设及二级近似。计算结果较布拉格-威廉近似为佳,而与倍脱一级近似结果则相差不多。至于与有关β-黄铜实验结果的比较,定量的符合还较差;特别是在临界温度附近(T This paper is to discuss the properties of high order aberrations taking advantage of as much as possible of using the methods of approximation. The number of independent terms of secondary aberrations is first accessed and its geometrical significance ascertained. By a coordinate transformation the effects of the change of stop position on aberration coefficients are determined. The relations between the position of the object and its aberration coefficients are found on the basis of Fermat principle, by regarding... This paper is to discuss the properties of high order aberrations taking advantage of as much as possible of using the methods of approximation. The number of independent terms of secondary aberrations is first accessed and its geometrical significance ascertained. By a coordinate transformation the effects of the change of stop position on aberration coefficients are determined. The relations between the position of the object and its aberration coefficients are found on the basis of Fermat principle, by regarding each ray as emitting from different object points lying along this ray. 本文的主要目的在以近似方法讨论高级象差特性。首先由对称性讨论了二级象差的独立象差数,近似讨论了象差的几何意义,再由坐标变换的观点导出了光栏移动时象差变化的规律。由Fermat原理和同一光线可看作是各不同点发出的观点导出了物体移动时象差变化的规律。由于运用Fermat原理,所得的结果实际上是略去初级象差影响后的近似结果,因此表示式相当简单。 然后我们把象差产生的原因分为二类。其一称作是本徵的,是入射光束无象差时必然产生的象差,用象差看作球差的观点导出了它们的表示式,结果表明,高级球差和本徵轴外球差是象差产生的原因,并导出了各种象差同时产生的状况。象差的另一类称作是衍生的,它们是由入射光线原有象差引起的初级象差差异,由初级象差理论即可得出它们的表示式。这一些高级象差的规律和近似表示可作为评断象差产生原因的半定量依据。 最后,用Fermat原理讨论了高级色差问题,并说明Fermat原理之所以可在高级象差理论中应用的理由及不致误差过大的应用范围。
二级
second order
Second order CARS of benzene 苯的二级相干反斯托克斯喇曼散射(CARS) 短句来源 The Ion Optical Properties and the Second Order Ion Trajectories of the E×B Crossed Field and its Aberrations E×B交叉场的离子光学性质和二级近似离子轨迹及其象差 短句来源 DIRECTIONS OF SECOND ORDER STRUCTURE PHASE TRANSITION AT T POINT OF O_h~3-P_(m3n) GROUP O_h~3-P_m3n群Γ点二级结构相变的方向 短句来源 ANALYSIS OF GROUP THEORY OF THE SECOND ORDER PHASE TRANSITIONS AT M POINT OF SPACE GROUP O_h~3 O_h~3空间群M点二级结构相变方向的群论分析 短句来源 Study on Second Order Phase Transition by Laser Raman Spectrum 以激光喇曼谱研究二级相变 短句来源 更多 “二级”译为未确定词的双语例句
Dye laser amplification system pumped by Xecl excimer laser XeCl准分子激光泵浦的二级放大染料激光特性 短句来源 THE SCOND ORDER PERTURBATION FORMULA WHEN DEGENERACY IS NOT REMOVED COMPLETELY 简并完全未消除情形下的二级微扰公式 短句来源 Numerical Calculation for the Second-order Stark Effect of the n=2 Level of Hydrogen Atom 氢原子n=2 能级的二级斯塔克效应的数值计算 短句来源 Study on FrequencyTuning By 2th Order Diffraction of Grating for Axial Flow CO Laser CO激光器光栅二级衍射调谐实验研究 短句来源 A new kind of nonlinear optical phenomena ——Cascaded second-order nonlinear optical effect 一种新的非线性光学现象——Cascaded二级非线性光学效应 短句来源 更多 
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Behavior near the boundary of positive solutions of second order parabolic equations
We state a localization principle for expansions in eigenfunctions of a self-adjoint second order elliptic operator and we prove an equiconvergence result between eigenfunction expansions and trigonometric expansions.
We also obtain a way of constructing an arbitrary number of non-Gaussian continuous time processes whose second order properties are the same as those of fractional Brownian motion.
The line search functions used are Han's nondifferentiable penalty functions with a second order penalty term.
Finally, we prove the global convergence and the local second order convergence of the algorithm.
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