公式

By academic analyzing, it is concluded that two order discrete paraxial approximation formula of the paper, multiple transmitting formula and polynomial extrapolation formula are the different forms of continuous paraxial approximation formula, so they are with nearly equivalent precision and stability and with equivalent applicability and limitation.

据此文献[3]将傍轴近似公式归结为一类从特定的无限域模型导出的人工边界条件，并且提出了新的从一般无限域模型导出的具有普适性的、称为"多次透射公式"的局部人工边界条件。那么，是否也可以从一般无限域模型导出具有普适性的傍轴近似公式呢？

In this paper,the methods of distance geometry are used to explore the angles of a simplex ,and the second cosine law of a simplex in another form is obtained.

运用距离几何的研究方法，研究了和单形相关的角，给出了单形第二余弦定理的另一种形式，以此为基础得出了BartO¨s体积公式一种简洁的证法；探讨了单形的几个体积公式之间的联系，并推广了单形的一个体积公式。

Based on these ideas, we suggest a generalized critical angle equation including mass effects.

依据上述观点，我们提出了一个包含经典公式与质量效应公式的广义沟道临界角公式。

On the basis of the hydraulic and kinematics calculations about revolving water decanter ,dynamics calculations were made in this paper.

在对旋转式滗水器进行了水力学和运动学计算的基础上，对旋转式滗水器进行了动力学计算，给出了其动力学计算公式，与水力学和运动学计算公式一起，共同给出了旋转式滗水器完整的设计计算公式。

The assessment formula for shear capacity was established as well, and in which various impact factors of shear strength was considered comprehensively.3. Directed against the main forms of transverse connection in concrete beam bridges, model test and finite element analysis were carried out to find the impact laws of damage on concrete T-beam bridges, in which the three ways of hinged joint, flange rigid connection and cross slab rigid connection were considered. Transverse distribution and degenerate state of transverse connection were studied under various damage conditions. Based on the analysis of test and simulation results, the rule of live load adjustment coefficient of T-beam bridge was put forward, as well as the calculation formula.4. In view of the influence of the damaged transverse connections to load effect, the load effect model was amended by live load adjustment coefficient.

依据损伤出现频率与重要性等级，提出典型损伤混凝土梁式桥按体系损伤、构件损伤和材料损伤三个层次进行评定的原则。2、基于构件和材料层次损伤评估研究成果，对比分析损伤机理和适用条件，提出了《公路钢筋混凝土及预应力混凝土桥涵设计规范》(JTG D62-2004)抗弯承载力修正计算公式、抗剪承载力修正计算公式以及综合考虑抗剪强度影响因素的抗剪承载力评定公式。3、针对混凝土梁式桥主要横向连接形式，分别按铰结、翼缘刚接和横隔梁刚性连接损伤对T桥梁桥承载能力的影响进行了模型试验和有限元分析，研究了不同损伤工况对T梁桥荷载横向分配的影响及横向连接状态退化情况。

Then the finite element software ANSYS is used to simulate the orthotropic flattened Brazilian disc specimen subjected to diametrical compression, the accuracy of the approximate formula of compression displacement is checked. The formula is further modified with a semi-empirical and semi-analytical approach, and it is shown to have better accuracy than the original formula covering the whole range of orthotropic anisotropic index of rock, the error is less than 6%.

用有限元分析软件ANSYS模拟正交异性岩石的巴西圆盘试样的对径压缩实验；利用有限元分析结果对正交异性平台位移压缩公式进行精度检验，并用半经验半解析的方法，对该公式进行局部的修改，修改后的公式在岩石材料的正交异性指数的整个范围的总体评价上，误差小于6%，具有更好的计算精度。

ChinaWang Yonghuidirected by Zhang ~Venpeng The main purpose of thesis is using the mean value theorem of the Dirichlet Lunctions to study the asymptotic property of the Dedekind sums and Hardy sums, and give two sharper asymptotic formulas.

关于Dedekind和的推广型均值公式及Hardy和的推广型均值公式本论文利用Dirichlet L-函数的均值定理研究了Dedekind和及Hardy和的一类均值估计问题，并给出了较为精确的渐近公式。

The emphases of the article are the formula region search, the sign of formula division, the positional information of sign record, the sign of formula recognition and so on.

本文重点研究了汉字文章中公式区域的查找、公式中字符的分割以及其位置信息的记录、公式中字符的识别等。

Lagrange interpolation focus on the application of the formula .The comparison between the method of Transform and that of Lagrange's interpolation formula in square matrix form is made. Also the form of Lagrange's interpolation formula is generalized to include the double root case.The application of the generalized lagrange's interpolation formula in square matrix to solving state equations is found to be effective.

重点介绍了Lagrange插值公式在状态方程求解中的应用，用对角矩阵及相似矩阵的性质证明了，当状态转移矩阵中方阵的特征根相异时，拉格朗日插值公式与Laplace变换法对表达具有一致性，并用极限方法对方阵含二重根时拉格朗日插值公式的应用进行了推导。

After that, by making use of dual basis, the general reconstruction formula about frame is discussed, and the computation formula for the dual frame is presented, in which no operators are contained.

然后，利用对偶基概念讨论了一般框架下信号的重构公式，并给出了对偶框架的具体计算公式，该公式不包含任何算符，可以明显看出基矢的相关性与框架类型之间的关系。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。