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Based on the assumption that the heating floor radiation agrees with Lambert's cosine law and the outdoor human body could be equivalent to a "human cylinder", the mathematical model and formula to describe the thermal radiation from the floor to human body are established.

在基本假设和"人体柱"模型的基础上，建立采暖地板对室内人体热辐射的理论计算模型。利用该理论模型，对矩形等温地板的采暖辐射特性进行计算分析。

The discrete cosine transform is an important mathematical tool in digital image processing and many other fields.

摘 要：离散余弦变换是数字图像处理等许多领域的重要数学工具。

As a result, it shows thatthe static or dynamic subsystem optimum alone is not equal to the system optimum. Three initial value problems met in the optimal design of flying vehicle are studied andconclusions are derived that: orthogonal test method can be adopted to decide the initial valueof static optimization problem, some mathematical techniques can be used to deal with thecostate variables of Maximum Principle and decide the initial value of the costate variable,the indirect method can be used to get the analytical solution under ideal case to guide thechoice of the initial control curve in the direct method. With some numerical examples oftrajectory optimization, it shows that all these methods are useful not only in accelerating theconvergence but also in converging to the global optimum.

针对飞行器优化设计中的三种初始值问题进行了研究，以远程弹道导弹弹道的工程优化为例说明，对于静态优化问题，采用正交试验法选取初始值，不仅可以大大加快收敛的速度，而且更有可能收敛到全局最优解；以气动力辅助变轨问题为例说明，用共态变量的一阶泰勒级数展开可以解决极大值原理中共态变量初值难于确定的问题；以二级弹道导弹的主动段弹道优化为例说明，利用间接法在理想情况下得到的解析解来指导直接法初始控制曲线的选择，将大大有利于提高直接法的收敛速度。

The definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented. Some properties of the directional derivative and gradient are proved by using tangent and cotangent mapping. The minimization necessary condition of nonsmooth Lipschitz functions is given. Moreover, Fritz John necessary optimality condition in mathematical programming is provided on Riemannian manifold.

在黎曼流形上给出了Lipschitz函数的广义方向导数和广义梯度的概念，利用黎曼流形局部上与欧氏空间开集微分同胚的性质以及切映射和余切映射导出了广义梯度的性质和运算法则，证明了定义在黎曼流形上的函数取得极小值的必要条件是广义梯度包含零元素，并利用这些性质给出了黎曼流形上数学规划问题的Fritz John型最优性条件。

Based on detailed mathematical model of the heat and mass transfer processes in packed-type counterflow liquid desiccant systems, a set of linear ordinary differential equations describing the transfer processes is obtained by some appropriate simplications.

在建立逆流填料式液体除湿系统传热传质过程的数学模型基础上，通过合理的简化处理，导出了描述这一热质传递过程的常微分方程组，得到了相应的解析解；并与精确数学模型的数值解进行了对比，二者具有良好的吻合性；利用解析解分析了各参数对除湿性能的影响；所得解析解具有较好的理论及应用价

Based on detailed mathematical model of the heat and mass transfer processes in packed type counterflow liquid desiccant systems,a set of linear ordinary differential equations describing the tramsfer processes is obtained by some appropriate simplications.

通过对逆流填料式液体除湿系统传热传质过程数学模型的合理简化，推导出描述这一热质传递过程的常微分方程组的分析解，并与未简化数学模型的数值解作对比，二者具有良好的吻合性。

The ground stage mathematical model includs aerodynamics and the counterforce from the ground.

从飞行器的力和力矩角度对直升机进行建模，该模型包括地面阶段数学模型和离地阶段数学模型。

In this paper, under the guide of modern pedagogy, psychology and mathematical education theory, the cause for the problem and countermove were discussed and studied.

在数学学习中，她们存在的主要问题是课堂听课质量不高、数学阅读有障碍及综合解决问题的能力较差。

First, the mathematical model of thermal and mechanical coupling analysis is defined.

首先定义了用于热—机耦合分析的数学模型。

It is the story that a new ego knows next, in the process of study, his reappraise oneself mathematical endowment: The classmate is too crackajack, the talent is full of it is all round you.

接下来又是一个重新自我认识的故事，在学习的过程中，他重新评估了自己的数学天赋：同学太杰出，天才充斥在你周围。

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。