以下为句子列表：
英文: Abstract: It is observed that the Sommerfeld's formula for a progressive spherical wave is not covariant with respectro the rotation of the coordinate system.It contains complex partial waves that are not physical.The standing wave representation of the s
中文: 文摘:说明了球面行波的索末菲公式在坐标转动下不协变.证明了球面波的驻波表示是协变的，因而是一个物理的关系式，故适用于圆柱坐标中各类波动方程的定解问题.作为一个例，应用于光纤光学，导出了受导简正模和辐射模的表达式，以及各模式的强度分布.
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英文: It is observed that considerable liquation microcracks and some other microffissures called solid-state microcrack initiate in the regions nearby the fusion line and propagate across the grain boundary.
中文: 研究发现，熔合线附近的热影响区产生大量液化裂纹和沿晶扩展的固相裂纹。
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英文: It is observed that many animals do not breed when in captivity.
中文: 人们注意到许多动物一被关入笼中就不生育了。
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