電容超音波膠體金粒子電位調控系統研發
費曼曾說：There is plenty of room at the bottom。喬治亞理工大學的Mostafa El-Sayed 教授發表的癌細胞辨識、與科學月刊報導『台大抗煞一號』引發我們對膠體金粒子的興趣。膠體的性質主要是由界達電位 (zeta potential)決定。參考台科大、成大、中山…等超音波應用研究，提出改良篩選物理法製造之膠體金粒子的儀器設計與製作。經沉降過濾可達平均粒徑 100 nm；而離心式篩選機與超音波管式篩選機可達平均粒徑30 nm。篩選後的膠體粒子以電容原理調控膠體金粒子之界達電位 (zeta potential)，成功地從-30 mV 提升至-59 mV，並發展成電容超音波界達電位控制儀(Capacitor Ultrasonic Zeta Potential Controller)。以膠體金粒子與蛋白質鍵結量來測試調控界達電位的效果，發現蛋白質鍵結量之增加曲線與界達電位的增加曲線的增加趨勢相似；此功能的發現對於生物科技方面的應用應會有很大的幫助。透過界達電位控制系統，本研究達到費曼先生所期望的「在原子或分子的尺度上來加工材料和製造設備」。“There is plenty room at the bottom.” The words of Mr. Feynman are the beginning of nano technology. Mostafa El-Sayed, a professor of Georgia Institute Technology, identified cancer cells through nano gold-antibody complex. So, our study focuses on the zeta potential of colloidal gold particles. At first, the filtering method and equipments were developed. The theories were based on the ultrasonic studies of universities such as National Taiwan University of Science and Technology. Then the colloidal gold’s sizes were filtered to100 nm through settling. At last, by using Continual-Filtering Centrifuge (CoCe.) and Tube Well Mass (TW-MS), the mean particles sizes can be filtered to 30 nm. The most important results are: Zeta potential of the gold colloid was controlled with Capacitor Ultrasonic Zeta Potential Controller. The zeta potential can be raised from -30 mV up to -59 mV, which is -20 mV higher than the conventional pH-changing way. The function of zeta potential to protein binding quantity was tested. The increasing curves of zeta potential and protein binding quantity were similar. This property would be a significance of biotechnology. Thourgh Capacitor Ultrasonic Zeta Potential Control system, the zeta potential’s limitation of gold colliod, which is produced by SANSS (Submerged Arc Nanoparticles Synthesis System), can be controled in a wilder range. The study which is focused on nano-scale, like the wish of Mr. Feynman – “To manufacture material and produce equipment in atom and molecular scale”.
移動棋子問題的致勝策略
We consider a game played with chips on a strip of squares. The squares are labeled, left to right, with 1, 2, 3, . . ., and there are k chips initially placed on distinct squares. Two players take turns to move one of these chips to the next empty square to its left. In this project, we study four different games according to the following \r rules: Game A: the player who places a chip on square 1 wins;Game B: the player who places a chip on square 1 loses;Game C: the player who finishes up with chips on 12 . . . k wins;Game D: the player who finishes up with chips on 12 . . . k loses. After studying the cases k = 3, 4,5 and 6 for Game A and the relation among these four games, we are led to discover the winning strategy of each game for any positive integer k. The strategies of Games A, B and C are closely related through a forward or backward shifting in position. We also found that such strategies are similar to the type of Nim game that awards the player taking the last chip. Game D is totally different from the rest. To solve this game, we investigate the Nim game that declares the player taking the last chips loser. Amazingly, the strategies of two Nim games can be concisely linked by two equations. Through these two Nim games, we not only find the winning strategy of Game D but also the precise relation between Game D and all others.\r 去年我研究一個遊戲：有一列n個的方格中，從左至右依序編號為1,2,3,....n。在X1個、第X2個、第X3個格子中各放置一個棋子。甲乙二個人按照下列規則輪流移動棋子：\r 一、甲乙兩個人每次只能動一個棋子(三個棋子中任選一個)。遊戲開始由甲先移動動棋子。二、甲乙兩個人每次移動某一個棋子時，只能將這個棋子移至左邊最近的空格(若前面連續有P個棋時可以跳過前面的P個棋子而且只能跳一次)，而且每個方格中最多只能放一個棋子。\r 研究這個遊戲問題時，我討論四種不同"輸贏結果"的規定：甲乙兩個人中，A誰先將三個棋子中任意一個棋子移到第一個方格，誰就是贏家。B誰先將三個棋子中任意一個棋子移到第一個方格，誰就是輸家。C誰先不能再移動任何棋子，誰就是輸家。D誰先不能再移動任何棋子，誰就是贏家。\r 當"輸贏結果"的規定採用ABCD時─我們稱為遊戲ABCD。今年我將把這個遊戲問題中棋子的個數由三個推廣到一般K個情形之後，再繼續研究遊戲的致勝策略，同時也將研究遊戲ABCD之間的關係。