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It provided a correct and reasonable mathematical model for the analysis of the ultimate bearing capacity and crankle stability of the thin-walled structure.

论文在比较了两种运动描述方法（完全拉格朗日法和更新拉格朗日法）异同点并分析了非线性几何关系及大变形下的弹性物理关系的基础上，基于增量虚功原理推导了几何非线性空间梁元单元切线刚度矩阵，采取分模块形式，分别表示了轴力、弯矩、双力矩对几何矩阵的贡献；通过球面显式荷载增量迭代式弧长法求解方法编制程序，很好地实现了几何非线性增量荷载的自动步长选择及全过程跟踪，为薄壁杆系结构的极限承载力分析和弯扭失稳分析，提供了较为精确合理的分析力学模型。

He also includes as Strange Loops the famous paradox about Cretan liars who say they never lie, and Gdel's proof of unprovable mathematical axioms.

他把著名的说自己从不骗人的克里特岛骗子的悖论，以及哥德尔无法证明的数学公理的证明也算在"怪圈"里。

In order to solve the double parameters enveloped in the gear tooth flank generating,the complicated double parameter envelope is simplified to the generating process between work-piece and imaginary crown generating gear by means of mathematical transformation.

摘 要：为了解决直接求解展成法加工中存在的复杂双参数包络问题时的困难，提出通过数学变换，将此包络问题转化为假想平面产形轮与工件之间的展成问题来进行研究。

In order to solve the double parameters enveloped in the geartooth flank generating,the complicated double parameter envelope is simplified to the generating process between work-piece and imaginary crown generating gear by means of mathematical transformation.

为了解决直接求解展成法加工中存在的复杂双参数包络问题时的困难，提出通过数学变换，将此包络问题转化为假想平面产形轮与工件之间的展成问题来进行研究。

Taking the minimization of the tooth crown of a worm wheel and the maximization of transmission efficiency and the distance from the center as objectives,we establish the mathematical model for the multi-objective optimal design of worm transmission on the condition that the worm wheel and the worm transmission meet the requirements for load,strength and others.

以蜗轮齿冠体积最小、传动效率最高和中心距最小为目标，在保证蜗轮和蜗杆满足承载、强度及其它要求的前提下建立蜗杆传动多目标优化设计的数学模型。

A mathematical model of stress distribution in vacuum glass was established by using crunode method.

用结点法建立真空玻璃应力分布数学模型。

The mathematical model of brace stress-strain in the vacuum glazing was established based upon the crunode method of elastic mechanics.

用弹性力学的结点法建立真空玻璃支撑应力-应变数学模型，求出真空玻璃的支撑应力-应变场，分析了其应力-应变分布规律，同时用电测方法进行试验验证。

Reliable cryptograph is set up in math and formal computer science. According to the computational theory, the paper expounds mathematical background for public-key cryptosystem including: the complexity of algorithm and problem, relationship between the length of key and security of cryptogram.

可靠的密码学是建立在数学和形式化的计算机科学产生的结论之上的，本文从计算理论的角度阐述了构建对称密码体制所需的数学背景：算法复杂性与问题复杂性的关系；NP问题与密码学的关系；密钥长度与密码安全的关系。

With this course, the students will learn the mathematical background of cryptography.

通过本课程的学习，使学生掌握密码学的数学基础。

First, the mathematical model of the HT oxide crystal growth is set, and then the dimensionless equations are given out. Finally, the boundary conditions are determined and the equations are solved by FDM. The simulation program is given by the above method.

首先建立了高温氧化物晶体生长的数学模型，然后给出了无量纲方程，最后确定了边界条件，使用有限差分方法求解了方程，并在此基础上编制了仿真程序。

I can still vividly recall the impressive scenes you gave. You were among my friends and relatives who accompanied me from my house to the seaport and when the porters were slow to show up, you obligingly carried my suitcase for me.

你对我的种种感人情意，使我记忆犹新，那天你随着我的亲友从家里送我上轮船，搬运工迟迟不来，你毅然替我提着皮箱上船。

St. Nicholas became the patron saint of Russia, where he was famous for his red cape, flowing white beard, and bishop's mitre.

圣尼古拉成了俄罗斯人的守护神，在那里，他以身披红斗篷，留着飘逸的白胡须，戴着主教法冠而闻名。