臺灣博碩士論文加值系統

放置三點電荷於空間中三點(1,0,0),(-1,0,0) 和 (u,v,0) ,並帶電荷量 s^3,k^3,1，此電荷產生靜電電位V. 通過變數變換,我們得到兩個具有兩個變量X,Y 和四個參數 S,K,u,v 的多項式方程組。
在這篇論文中，我們尋找多項式方程組的共同實根,對應到的就是V的臨界點.當中我們使用sturm定理對它進行研究並找到臨界點.
對於u=0 和 v= √3，獲得對於一般K 和 S 只有一個實零。並且觀察到,對於S>0 且 K>0 臨界點落於三點電荷所形成的三角形區域內。當S = 1 或 K = 1時，臨界點是落於對稱軸上的。

Let three point charges locate at (1,0,0),(-1,0,0) and (u,v,0) with charge value s^3,k^3,1 respectively, then they create an electrostatic potential V for three point charges. By changing variables, we get two polynomial equations with two variables X,Y and four parameters S,K,u,v.
In this thesis we intend to find the real zero from that equation and we prove our theorems it by Sturm theorem and find the critical point.
We consider u=0 and v= √3 and obtain that has only one real zero for general K and S. For >0 and K>0 , we observe that the critical point inside of the triangle regions. When S = 1 or K = 1 the critical point on the symmetric line.

Contents

1. Introduction 1
2. Point Charge Problem in General Potential 3
2.1. Three Point Charges in General Potential 3
2.2. Four Point Charges in General Potential 5
3. Simplest Equation of Three Point Charges in General Potential 8
4. Tools 10
4.1. Resultant 10
4.2. Subresultant Sequence 12
4.3. Sturm Theorem 14
5. Main Results 16
5.1. General Result 16
5.2. Bad Parameters 18
5.3. Good Parameters 22
5.4. Critical Point and Graph 25
5.4.1. Graph of Bad Parameters 25
5.4.2. Graph of Good Parameters 27
6. Summary and Future Work 29
References 30

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