加法公式

We derive the addition formulas for sine and cosine from the arithmetic of complex numbers.

用复数算术推导了正弦，余弦的加法公式。

We derive the addition formulas for sine and co sine from the arithmetic of complex numbers.

用复数算术推导了正弦，余弦的加法公式。

For this purpose, two expressions for the Graf′s addition theorem are deeply clarified and an auxiliary function method for mixed boundary-value problems is presented in the paper.

为此，文中深入阐明了Graf加法公式的两种表达形式并提出了处理混合边值问题的辅助函数法。

The problem of the error of calculation formula calculating the variance of grouping data within distances in statistics was put forward,and the concrete forms of correcting formula were given by the theorem of addition and the variance of even distribution.

提出统计学中的组距分组资料方差和标准差计算公式误差问题，由方差的加法定理和均匀分布方差给出分组资料方差计算和标准差计算的修正公式具体形式，并就均匀分布数列和正态分布数列组内方差平均数进行了讨论

Using the exterior expression for the Graf′s addition theorem, the closed form solution for scattering of plane SH waves by circular inclusion in half-space is given in the paper. The effect of the inclusion on the surface ground motion is ellustrated and the effect region of the scattering field from the inclusion is analyzed.

文中利用Graf加法公式的内域型表达给出了半空间内含圆形夹塞区出平面散射的封闭级数解答，讨论了夹塞区散射场对附近地表运动的作用，并特别分析了这一作用在地面上的影响范围。

Basing on the Graf′s addition theorem, two expessions, interior and exterior expression, are deduced and the suitable problems for them are discussed. It has been found that the interior expression is the main point for sovling the scattering problem of circular inclusion in half-space. It also has been found that the exterior expression is the key for the scattering problem of circular arc canyon and circular arc alluvial valley, and is one of the main points for scattering problem of circular arc hill as well.

从Graf原有加法公式出发，本文给出了其内域型和外域型两种表达形式并讨论了这两种表达的适用范围，同时指出：内域型表达是求解半空间内含夹塞区出平面散射问题的要点，而外域型表达是解决任意圆弧型凹陷地形和任意圆弧型沉积盆地出平面散射问题中求解难点的关键，同时也是克服任意圆弧型凸起地形出平面散射问题求解困难的要点之一。

Also using the exterior expression for the Graf′s addition theorem, the exact solution for scattering of plane SH waves by circular arc alluvial valley is presented in the paper. From the numerical results the complex effect of the depth-to-width ratio of the alluvial valley on the surface ground motion is found.

利用Graf加法公式的外域型表达，本文还给出了任意圆弧型沉积盆地出平面散射的精确级数解答，提供了大量数值结果并指出了盆地深宽比对地面运动的复杂影响作用。

Then we use the diagram of Venn to analyse and predigest the theorem proof. And it is also used in probability addition and multiply、conditional probability、total probability formula、 Bayes formula to simplify the calculation of probability. So it is easy to understand and master.

进而利用Venn图分析、简化概率性质的证明以及Venn图在概率的加法与乘法、条件概率、全概率公式和贝叶斯公式中的应用，简化概率的计算，便于学习者理解和掌握。

By analyzing the differences of three rank parameter curve from zero rank to three ranks, the interpolation successive formula is deduced.

通过对三次参数曲线 0 3阶差分的分析，导出了其插补递推公式，其中只包含加法运算，可以得到很高的插补速度。

For the partial products generation, the novel method of Booth encoding combined with partial products generating is put up, which can directly map the multiplicand and multiplicator to partition products without generating the BOOTH encoding results. For the optimization of Wallace tree adding, the series formulas of full-adder and 4-2 Compressor realization are introduced to guidance the selection. For the non-bias round, forwarding round disposal in Wallace tree method is brought forward to avoid the final multi-bit adder. Also, the idea of delay-oriented partition of the MAC frame is put up to achieve the perfect match with multi-pipeline DSP architecture.

提出了一种构建多模式算法最小并集的MAC通用结构思想与一种划分MAC通用结构以适应多流水级DSP处理器设计的通用MAC设计方法；对于BOOTH编码和部分积产生，提出了直接建立被乘数与部分积的多路选择映射关系的BOOTH编码和部分积联合产生方法；对于最优Wallace树型加法实现，提出了全加器和4-2 compressor电路实现Wallace树加法所需的关键加法路径级数公式以指导实现选择；对于无偏舍入处理，提出了在Wallace树处理舍入问题的舍入运算前置方法；提出了以时延为导向的MAC各部分单元组合与流水线匹配具体方法。

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。