最小作用原理

Today, his formula for entropy S is famous: S = klnΩ K is the Boltzmann constant andΩ is the number of possible microscopic states which give the same thermodynamical state that a system may be in.

在论文中，他利用原子运动轨道闭合的假设，将熵的表示与力学的最小作用原理直接联系起来，试图从纯力学的角度证明热力学第二定律。

In the ***, all types and fundamental principles of Radon transform are summarized systematacially. This *** starts from the general linear Radon transform, and then researches how to use the damped least square method to find the solution of the forward transform. However, the least squares smoothing effect will lead to a certain degree of trails in the data of Radon domain, which led to the application\'s limitations. After that the implementation in Radon domain and relative merits of linear Radon transform, parabolic Radon transform and polynomial Radon transform which have time invariance are introduced, the conjugate gradient method that can solve numerical solution is also given. And then the high resolution Randon transform is discussed, it introduces the regularization theory and Bayes principle into inversion, which successfully remove the negative affect caused by discrete Radon transform. Finally, we introduce the optimal weighting similar coefficient Radon transform, which adapt to the time variant quality of hyperbolic Radon transform.

本文系统总结了Radon变换的各种类型及其基本原理，从τ- p变换(即一般线性Radon变换)出发，研究利用阻尼最小二乘平方法求解其正变换，但是最小平方法的平滑作用会导致Radon域数据存在一定程度的拖尾效应，给这种方法的应用带来了很大的局限性；然后先容了具有时不变性的线性、抛物和多项式Radon变换在频率域的实现及其优缺点，给出了求解其数值解的共轭梯度算法；接着讨论了高分辨率Radon变换，它把正则化思想和贝叶斯原理引进到了反演中，很好的克服了离散Radon变换产生的截断效应对结果的不利影响；最后先容了适应双曲Radon变换时变性质的高分辨率最优相似系数加权Radon变换。

The development of Wave Mechanics goes back to ancient times. The principle of least action is the source of Wave Mechanics, so it is the mother of several principles.

波动力学的发展源远流长，最早发端于最小作用原理，该原理可以说是"众理之母"。

The calculus of variations; Euler's equation; the principle of least action;δ-method; the multiplier rule

基础科学，数学，古典数学变分法；欧拉方程；最小作用原理；δ-方法；乘子法则

The argument exploits the variational structure of the problem, and is bas...

该证明利用了问题本身具有的变分结构，是以在给定的道路类上的"拉格朗日作用的最小化原理"为根据的。

The hooping mechanism of the CFST member was analyzed by using energy principle and minimum potatial energy principle .

利用修正弹性模量的方法来计入内填式钢管混凝土轴压构件承载力的提高，并用能量法和最小势能原理从中导出了在轴向压力作用下内填式钢管混凝土构件受箍机理。

The paper presents work principium of hydropneumatic elevating-equilibrium mechanism , and the mathematical model for balance of elevating-equilibrium mechanism was proposed, the design model was solved by using Maximum-minimize Method in MATLAB optimization toolbox and optimum procedure was presented.

对液体气压式高平机的工作原理进行了介绍，建立了高平机的平衡作用数学模型，应用MATLAB优化工具箱中的最大最小化方法对设计模型进行了优化求解，给出了高平机的结构优化程序，计算结果表明该方法是正确和有效的，并且适用于火炮平衡机等类似结构的优化设计中。

According to the dynamics analysis of the cotton sliver coiling process,by considering the minimum friction of cotton sliver caused by screwy pipes as objective function the design of screwy pipes of can coiler is explained based on the theory of the variational direct-method.

对棉条圈条过程定量地进行了动力学分析，以棉条所受曲线斜管摩擦力最小为目标函数，基于变分问题直接法原理设计出圈条盘螺旋形曲线斜管。这种螺旋形曲线斜管充分利用圈条盘的转动对棉条产生的离心力甩摆作用，使棉条所受曲线斜管摩擦力较小，从而使出条更顺畅；在一定程度上降低了圈条盘螺旋形曲线斜管堵眼频率与条筒乱条几率，使其更适应现代并条机生产高速化的要求

Firstly, aiming at the problems existed in former models, with isotropic elastic damage exampled, based on strain equivalent principle, a novel failure process model is developed and formula for calculating rock failure critical value is also presented.

首先，针对前人模型存在的题目，以岩石的各向同性弹性损伤为例，根据最小耗能原理在应变等效原理条件下提出了一种新的损伤演变模型，克服以上模型存在的题目，同时也给出了岩石损伤临界值的计算公式，并对三向应力作用下做了简单的探讨。

By careful study to the deflection response of a hinged-fixed circular plate u nder concentrated impulse loading,the saturated impulse phenomenon in the proces s of response is discussed.

利用有限变形弹塑性连续体的最小加速度原理，建立了分析圆板动力响应问题的数值方法，并通过对均匀分布的脉冲载荷作用下铰支圆板位移响应的细致分析，探讨了响应过程中的饱和冲量现象，指出对于高载范围内的脉冲载荷，相应于最大变形的饱和冲量确实是存在的。

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。