公式的

Inthe paper, we study the relation of pairs of lines and pairs of needles, and two results ofintegral formulas are gained. Thus, the geometric probability problem is solved. Also.we give a solution to the problem: pick two points randomly in a convex body K anddraw two lines passing through two points.

文章考虑了线偶与针偶的依附关系，得到了两个积分公式的结果，从而解决了这一问题，并得到了随机地在凸体K内任取两点，通过这两点任意投掷两直线，两直线的交点落入凸体K内的概率及其它的一些结果和推论。

Two normal forms, best-simple normal form and literal normal form, are presented at first in order to eliminate the complexity of formulas decision. Based on the two normal forms, a deduction proof of decidability theorem in L and a decision algorithm P based on deduction for proportional formulas are given and a decision machine found on P, DMBD, is also designed.

首先提出了消解复杂性的两种范式：最简范式和文字范式，在此基础上给出了L的可判性定理的演绎证明及命题公式的演绎判定算法P，并基于ML语言设计了基于P的演绎判定机DMBD。

In Chapter 2, we mainly study the exact inversion and approximate inversion of the exponential Radon transform, and obtain the Sobolev analytic results; for convenience of practical calculation, we establish the another form of reconstruction formula through harmonic decomposition.

第二章我们主要讨论平面上的指数型Radon变换的精确反演和近似反演，得到了它们的有关Sobolev分析结果；为了实际计算的方便，我们用调和分解法作了进一步讨论，得到了重构公式的另一种表达形式。

The results were validated in terms of the analytic solution in frequency domain. The effect of laneway is existent which would be further studied in 3D model space.

用频率域的解析解验证了该公式的正确性，并对比了巷道有无时场的变化情况，说明了巷道的影响是客观存在的，应在3D模型空间中进一步研究。

The mold for modern equations of female creativity with psychological abnormality -- the Emily Dickinson or Sylvia Plath stereotype -- is Ovid's portrayal of Sappho as a desolate melancholiac.

罗马诗人奥维德把萨福描绘成一个孤独的忧郁症患者，这是把女性的创造力等同于心理反常的现代公式的原型－－例如针对爱蜜丽·狄更森（译注：十九世纪美国著名诗人）或希尔维亚·普拉斯（译注：1932-1963，美国著名女诗人）的老套评论。

A new form of Arbitrary-Lagrangian-Eulerian formulas are developed based on the basic law of Newtonian mechanics and hypothesis of Newtonian fluid, in which the conception of domain mapping is introduced so these formulas can be used to describe the fluid flow in an arbitrary deforming domain.

从最基本的牛顿运动定律和流体粘性的牛顿假设出发，基于区域映射的概念推导了ALE(Arbitrary-Lagrangian-Eulerian)公式的一种表达方式，能够在二维任意变形区域内描述牛顿型流体的运动。

According to the experience gained in traditional penetrating tests, this thesis has produced a high-pressure clay permeameter and discussed the instruments testing principle, measuring method and derivation of the calculation formula in details. Meanwhile, plenty of testing research has been done by taking an example for the permeability coefficient measuring of plastic concrete and the influencing factors of tests to the permeability coefficient of plastic concrete measured by this instrument have been analyzed.

3本文根据常规渗透试验中积累的经验，自行研制了一种高压土工渗透仪，对该仪器试验原理、测定方法以及计算公式的推导进行了详细的探讨，并以塑性混凝土渗透系数的测定为例进行了试验研究，对使用该仪器测定塑性混凝土渗透系数时影响渗透系数的试验因素进行了分析。

During the iterations the trial step is truncated when necessary in order to keep the strict feasibility of the iteration points. It is shown that the LMTI approach and the STI approach have global convergence properties under some reasonable assumptions and will achieve local quadratic convergence rate under some even stronger conditions.

LMTI方法主要利用由有限内存BFGS公式的紧致形式获取的目标函数海色阵的近似矩阵构造信赖域问题模型并对其进行求解；而STI方法在构造的低维子空间上求信赖域子问题的解。

At the same time it provides open design interface for different designers, which not only to realize self-definition of the formula, but also to define different function-models.

同时它为不同的设计者提供了开放的设计模式，不仅能实现设计公式的的自定义，更能实现功能的自定义。

According to the lateral deflection equation of the wall frame-structure ,an exact flexibility matrix is developed first and, then, the natural period and vibration mode of the wall-frame structure is defermined in this paper. According to actual earthquake action, the structural response is calculated with statical analysis.

本文在框架-剪力墙侧移公式的基础上建立结构的柔度矩阵，确定结构的自振周期和振型，采用静力方法按实际的地震作用分布计算结构的作用效应，然后采用振型分解反应谱法对结构进行抗震分析。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！