费马原理

When propagating light\|ray passes through two fixed points in the gradient index mediums and a cuspidal variable\|point （at this point the trace equation of propagating light\|ray is non\|differentiable） at the borderline of two different GRIN mediums, the mathematical relationship, which the trace equation of propagating light\|ray and borderline equation of two different GRIN mediums should satisfy, is derived by the Fermat's principle and calculus of variation.

当光线通过梯度折射率介质中两个固定点和两个GRIN介质界线上的可动尖点（光线轨迹方程的不可微点）时，由费马原理和变分法运算推得传输光线的轨迹方程与两种不同GRIN介质的界线方程应满足的微分关系式。

A method of velocity tomographic inversion based on Fermat principle is presented by using travel times of transmitted waves from one borehole to another.

利用井间透射波旅行时，给出了一种以费马原理为基础的井间地震弯曲射线速度层析成象方法，数值计算表明了该方法比直射线法反演成象精度高。

In this paper, the analytical formulations for every reflection point's Z coordinate are deduced by using Fermat's principle and law of reflection in the system of cylinder and cone.

以圆柱和圆锥二阶系统的反射寻迹为例，结合费马原理和反射定律，推导出各反射点Z坐标的解析表达式，从而减少了寻迹方程中未知数个数，使计算时间显著缩短，也提高了结果精度，文中给出了应用实例。

The main contents include the ray phenomenon and its generation conditions; the deduction and physical illumination of wave action conservation equation and wave number conservation equation; ray theory for sinusoidal waves; Fermat's principle; the variation of amplitude in the case of straight and parallel depth contours and circular depth contours; the amplitude near the caustics; wave trapping; deduction of mild-slope equation and the relevant numerical solution methods.

讲授折射现象及其发生的条件；波作用守恒方程和波数守恒方程的推导及物理解释；稳恒正弦波的控制方程及射线方程；费马原理；利用射线方程研究等深线是平行直线和圆周线时波振幅的变化，特别是焦散线附近波高的变化以及由此而产生的波的俘获；缓坡方程的推导及有关的数值求解方法。

Snell's law follows from Fermat's principle.

斯奈尔定律遵从费马原理。

Using geometrical method to calculate the gravitational deflection of light ray in the static spherically symmetric gravitational field;2. The reflection formulas of the ordinary and extraordinary light are given for determining their reflecting orientation of the wave normal and the light ray .

基于电磁波边界条件，从几何光学的角度，对单轴晶体内表面上光的反射规律进行了分析和讨论，给出了寻常光和非常光波法线和光线反射的公式同时指出了上述结果与由费马原理导出的结果是一致

The paper is to prove the refraction on two kinds of medium interfaces of electric displacement line using the boundary condition of the electric field and Fermat Principle.

利用电场边界条件和费马原理证明电位移线在两种介质界面上的折射。

The Fermat"s principle, Fresnel"s coefficients, Goos-Hanchen effect and Brewster angle at an interface between a PIM and a NIM were studied respectively. When the NIMs are introduced, the two traditional descriptions of Fermats principle are not consistent with each other and the least time principle do not hold true anymore.

随着负折射率介质的引入通过对费马原理的两种传统描述形式的研究可以发现，正—负折射率介质平界面处的最短时间原理已不成立，并进一步验证了使用光程表达的费马原理才是严格的正确的理论。

This paper presents the explicit expression of geodesic equation on a paraboloids of revolution using differential geometry which avoids the complexity of geodesic ray tracing by numerical approach.

本文根据微分几何原理，从广义费马原理出发，得到了旋转抛物面上短程线的解析式，避免了数值方法射线寻迹的复杂性。

The minimum travel-time tree algorithm is one of the main methods to trace rays, which is based on Huygens' and Fermat's principles and can be applied to complex geological model.

最小旅行时树法是目前主要射线追踪方法之一，该方法以惠更斯原理和费马原理为基础，具有适应复杂地质模型的优点，缺点是速度较慢。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。