本論文探討比熱值 ( )介於1.093與1.4之理想氣體三震波匯流場理論多重解及其所對應之壓力─轉折角震波極圖解，建構出 =1.1115、1.179、1.244、1.344理想氣體三震波匯流場於 ( )平面上之理論雙解 ( 、 )曲線、Wuest limit I曲線、Wuest limit II曲線及入射震波下游馬赫數為1.0條件之曲線解所構成的解域。在這些比熱值範圍內應用理想氣體三震波匯流場十階多項式理論計算 ( )平面上有下列的結果：
1. 穩態三震波匯流場理論多重解於 ( , )平面上 曲線與 曲線在 之後會相切於正與負 的平面，此切點是 曲線 不連續現象發生的上端點，也就是定義為Fall點 ( 三重根)，簡稱為F點，Fall的發生同時造成了在正 平面的一個向左開口的 迴路曲線，在負 平面的一個向左開口的 迴路曲線，並且 迴路分為上曲線與下曲線。 的F點發生在 ， =1.3847的解域，負 平面上的Fall點發生在 =1.0的極限位置， >1.3847負 平面不存在Fall點。正 平面的Fall點於 >1.1115都存在。其中 為入射震波上游流場馬赫數， 為入射震波下游流場轉折角。
2. 對 穩態三震波匯流場理論多重解於 ( , )平面都存在I、C、D點，他們的定義為：I點是Wuest limit I與 上曲線相切的點、C點是Wuest limit I與 曲線相切的點、D點是Wuest limit II上曲線與 下曲線相切的點。 增加到 之 ( , )平面上，I點與F點逐漸靠近，當 增加到1.179時，I點、F點與B點三者相重合，並且隨 持續增加，I點消失，同時，B點起始於 =1.179，B點的定義是Wuest limit I與 曲線相切的點，B點隨著 增加會逐漸移動至Fall下游的Fall< <C點之間，並且B、C兩點隨著 增加相互靠近，直到 時解域上的B、C兩點重合後消失。D點隨著 增加而朝 較小的區域移動直到 ，此點發生在Wuest limit II與 下曲線相切於Fall之下端點 (E點)，當 ，此D點繼續隨著 增加，此D點銳變為A點，因為此時與Wuest limit II曲線相切的雙解曲線已由 轉變為 。
3. 對1.093< <1.4之穩態三震波匯流場理論 重根發生時相對於 的位置，於 ( , )平面上，依 由小到大，可藉第1、2點所定義的F、A、B、C點來描述：
<1.179： 發生都在 之上方，通過C點之後 ( 比C點之 為大)， 發生在 下方。1.179< <1.244：在正 區域的F點上游， 發生在 上方，經過F點， 發生在 下方，通過B點， 發生在 上方，然後通過C點， 發生在 下方。 1.244< <1.344：正 區域的F點上游， 發生在 上方，經過F點， 發生在 下方。 >1.344： A點存在於Fall上游，通過A點， 發生在 上方，通過A點， 發生在 下方，其下游之F點不影響 發生時相對於 的位置，Fall下游的 仍發生在 的下方。上述沒有說明正與負 區域代表正與負 區域都適用。
4. 對1.093< <1.4之穩態三震波匯流場理論 重根發生時相對於 的位置，於 ( , )平面上，依 由小到大，負 平面上的 重根發生都在 上方，正 平面上的 重根可藉第2點所定義的D點、I點來描述：
<1.179： 上曲線發生在 上方，通過I點， 發生在 下方， 發生在 上方，經過D點， 發生在 下方。1.179< <1.344： 上曲線都發生在 下方。 下曲線發生在 上方，經過D點， 發生在 下方。 >1.344： 正 平面 上曲線與下曲線，都已無 曲線與Wuest limit I & II曲線之切點存在， 都發生在 下方。

Multiply possible three shock theoretical solutions and corresponding pressure-deflection shock polar solutions of perfect gas three-shock confluences with the specific heat ratio ( ) varying between 1.093 and 1.4 are investigated in this work. The preliminary maps of the multiplicity of three-shock theoretical solutions of the confluences of =1.1115, 1.179, 1.244 and 1.344 are constructed on the ( , ) plane, is the incident shock Mach number, is flow reflection behind the incident shock, using , theoretical double-root lines, Wuest limit I line, Wuest limit II line, and ( , Mach number downstream of the incident shock) line. The tenth degree polynomial equation of the three-shock confluences (Liu 2003) is applied theoretical for analyses, and the following results are obtained expressed on the ( , ) plane, as from 1.093 to 1.4.
1. There are four point of tangency which determine the locations of double roots relative to point. They are: point A defined by the point of tangency between and Wuest limit II curve; point B defined by that between curve and Wuest limit I curve; point C defined the same as point B, but occurring at larges ; point F defined by that between curve and curve. For <1.179, the location of the occurrence of roots vary from above to below it, as increases from unity to pass point C. For 1.179< <1.244, the location of the roots vary from above to below it, as the passes point F. The roots then move above , as point B is past, and they then move below , as point C is past. For 1.244< 1.344, the roots move from above point to below it, as increases to pass point A. The downstream F point does not affect the relative location of roots relative to point for this range of .
2. There are two points of tangency which determine the locations of double roots relative to point. They are: point I defined by the point of tangency between (upper lone) curve and Wuest limit I curve; point D defined by that between (lower line) curve are Wuest limit II curve. For the upper curve, the location of roots vary from above point to below it, as increases from unity to pass point I for 1.093< . These roots then remain below point for >1.179. For the lower curve, the location of roots move from above point to below it, as the passes point D for 1.093< . These roots then remain below point for >1.344.
The significance of the location of or double roots relative to point is the dependence of the classification of the physical possibility ( ) or impossibility (< ) of these three-shock theoretical double roots on point.

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