本論文主要以擬似穩態馬赫反射流場參震波理論配合穏態馬赫反射流場之十階多項式多重解理論有系統地變化入射震波波角自最大可能的入射震波下游音速之波角至逆馬赫反射解域，對4個不同的弱與強擬似穏態馬赫反射流場之入射震波馬赫數，探討多原子分子理想氣體之擬似穏態馬赫反射流場高度非線性性質的多重解現象。吾人根據有系統地分析多重解現象行為之後，將其計算結果以 為入射震波馬赫數當橫座標、 為楔形斜平面角度當縱座標來建構出擬似穏態馬赫反射流場參震波理論在(Ms-Qw)平面之多重解域圖，來瞭解多原子分子理想氣體擬似穏態馬赫反射流場在 與 變化的情形下，其理論多重解型態的變化與具物理意義解個數(m)情形。我們依據此(Ms-Qw)平面之多重解域圖，主要發現多原子分子理想氣體在擬似穏態馬赫反射流場多重解有下列的結果：
1. a1=b2雙解曲線與Wuest I 三重根曲線相切於Ms=1.1985，因此在Ms<1.1985時，a1=b2雙解會發生在D2上方，Wuest I解具有(D2=a1)三重根性質，當Ms>1.1985時，a1=b2雙解會發生在 下方， Wuest I解則具有(D2=b2)三重根性質（D2 為反射震波極退化為馬赫波之重根解）。

2. a1=b2雙解曲線與Wuest II 三重根曲線相切於Ms=1.1890，因此在Ms<1.1890時，a1=b2雙解會發生在D2上方，Wuest II解具有(D2=a1)三重根性質，而Ms>1.1890時，a1=b2雙解會發生在D2下方， Wuest II解則具有(D2=b2)三重根性質。

3. a1=b2雙解曲線與前後分界曲線相穿過於Ms=1.4623，因此在Ms<1.4623時，擬似穏態馬赫反射參震波多重解隨著Qw由小到大，b1解尚未至後向解域時就發生了a1=b2雙解現象，在Ms>1.4623時，則b1解存在於後向解域之後才會發生a1=b2雙解。

4. Wuest I 三重根曲線與前後分界曲線在Ms=1到Ms=6區間分別在Ms=2.2263與Ms=4.950相穿過，在Ms<2.2263時，b1解尚未發生於後向解域時就存在著Wuest I(D2=b2)三重根解，在2.2263<Ms<4.950區間，b1解存在於後向解域之後才會發生Wuest I(D2=b2)三重根解，但是在Ms<4.950之後，b1解尚未至後向解域時就發生了Wuest I(D2=b2)三重根解。

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Ames Aeronautical Lab. Rep., ”AMES Equations, Tables and Charts for Compressible Flow,” NASA, No. 1135, (1953).
Ben-Dor, G. ”A reconsideration of the Three-Shock Theory of a Pseudo-Steady Mach Reflection.” J. Fluid Mech. Vol. 181, pp. 467-484, (1987).
Ben-Dor, G., ”Shock Wave Reflection Phenomena,” Springer-Verlag, New York, (1991).
Barbosa, F. and Skews, B. W., ”Experimental Confirmation of the von Neumann Theory of Shock Wave Reflection Transition,” J. Fluid Mech., Vol. 472, pp. 263-283, (2002).
Chpoun, A., Passerel, D., Li, H. and Ben-Dor, G., ”Reconsideration of Oblique Shock Wave Reflections in Steady Flows. Part 1. Experimental Investigation,” J. Fluid Mech., Vol. 301, pp. 19-35, (1995).
Henderson, L. F., ”On the Confluence of Three Shock Waves in a Perfect Gas, ” Aero. Quart., Vol. 15, pp. 181-197, (1964).
Henderson, L. F. and Lozzi, A., ”Further Experiments on Transition to Mach Reflection,” J. Fluid Mech., Vol. 94, pp. 541-560, (1979).
Henderson, L. F., ”Regions and Boundaries for Diffracting Shock Wave Systems,” Z. Angew, Vol 67, pp. 1-14, (1987).
Hunter, j., Brio. M., ”The von Neumann Paradox in Weak Shock Reflection,” J Fluid Mech., Vol. 422, pp. 193-205, (2000).
Kawamura, R. & Saito, H., ”Reflection of Shock Waves – 1. Pseudo-Stationary Case,” J. Phys. Soc. Japan, Vol. 11, pp. 584-592, (1956).

Liu, J.J., ”Sound Wave Structures Downstream of Pseudo-Steady Weak and Strong Mach Reflections,” J. Fluid Mech., Vol. 324, pp. 309-332, (1996).
Li, H., Chpoun, A. and Ben-Dor, G., ”Analytical and Experimental Investigations of the Reflection of Asymmetric Shock Waves in Steady Flows,” J. Fluid Mech., Vol. 399, pp. 25-43, (1999).
Liu, J.J., ”A one-dimensional stream-tube interpretation of Liu’s revised three-shock theory for pseudo-steady Mach reflections,” The 23 rd International symposium on shock Wave, Fort Worth, Texas. USA, (2001).
Liu, J.J., Chuang, C.C., Chuang, H.W., ”Multiple Solutions of Steady Mach Reflections in Monatomic Gases,” The 19th Nat’l Conference on Mechanical Engineering, Yun-Lin, No. A5-004, (2002).
Liu, J.J., “A Map of Multiplicity of Perfect-Gas Three-Shock Theoretical Solutions of Steady Mach Reflections in Diatomic Gases” The 5th International Workshop on Shock/Vortex Interactions, Kaohsiung, Taiwan, 120-127, (2003).
Liu, J.J. and Shih, M.C., “Preliminary Regimes of Multiplicity of Perfect-Gases Three-Shock Theoretical Solutions of Steady Mach Reflections,” The 27th Nat’l Conference on Theoretical and Applied Mechanics, 719-727, (2003).
Liu, J.J., Shih, M.C., Yang, Y.Q., Tseng K.Y., ”Preliminary Regimes of Multiplicity of Three-Shock Theoretical Solutions of Steady Mach Reflections in Perfect Triatomic Gases,” The 20th Nat’l Conference on Mechanical Engineering, pp. 427-434, (2003).
Liu, J.J., Tseng K.Y., ”Further Experimental and Theoretical Studies on Weak Pseudo-Steady Mach Reflections Over Wedges of Small Angles,” AASRC/CCAS Joint Conference, (2004).
Mach, E., ”Uber einige mechanische Wirkungen des electrischen Funkens, ” Akademie der Wissenschaften Wien, Vol. 77, No. II, pp. 819-838, (1878).
MATHEMATICA Pro. V5.1., Wolfram Research., 100 Trade Center Drive Champaign, IL 61820 USA., www. Wolfram. com
Neumann, J. von, ”Oblique Reflection of Shocks,” Explos. Res. Rep. 12, Navy Dept., Bureau of Ordinance, Washington, DC, (1943).
Wuest, W., ”Zur Theorie des gegabelten Verdichtungatosse,” Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 28, No. 3, pp. 73-80, (1948).
Zakharian AR, Brio M, Hunter JK, Webb GM ”The von Neumann paradox in weak shock reflection,” J. Fluid Mech., Vol. 422, pp. 193-205, (2000).