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Maxwell’s Problem on Point Charges in the PlaneKillian, Kenneth 19 June 2008 (has links)
This paper deals with approximating an upper bound for the number of equilibrium points of a potential field produced by point charges in the plane. This is a simplified form of a problem posed by Maxwell [4], who considered spatial configurations of the point charges. Using algebraic techniques, we will give an upper bound for planar charges that is sharper than the bound given in [6] for most general configurations of charges. Then we will study an example of a configuration of charges that has exactly the number of equilibrium points that Maxwell's conjecture predicts, and we will look into the nature of the extremal points in this case. We will conclude with a solution to the twin problem for the logarithmic potential, followed by a discussion of the conditions necessary for a degenerate case in the plane.
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The Moduli Space of Polynomial Maps and Their Fixed-Point Multipliers / 多項式写像のモジュライ空間とその固定点における微分係数Sugiyama, Toshi 23 July 2018 (has links)
京都大学 / 0048 / 新制・論文博士 / 博士(理学) / 乙第13201号 / 論理博第1560号 / 新制||理||1635(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 宍倉 光広, 教授 泉 正己, 教授 國府 寛司 / 学位規則第4条第2項該当 / Doctor of Science / Kyoto University / DFAM
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