自由基VS抗氧化物
自由基會產生在神經系統、免疫系統、血液循環系統等等，進而影響到人體各器官的運作,甚至於近年來許多醫生學者提出自由基病理:自由基是百病之源。本次實驗筆者挑選葡萄子、維生素C、綠茶來抑制清氧自由基(OH.)所採用的方法是將10%雙氧水製入注射筒並加亞鐵離子催化,,使其與抗氧化物反應,由於雙氧水分解會產生氫氣自由基與氧氣,因此筆者用倍率放大器(OPA)放大生成氧氣造成的電壓,並用Data Studio測量記錄,最後可由氧氣體積對電壓的趨勢圖看出抑制氫氣自由基的效果;Free radicals will be produced in our nerves system blood circulation immunization system etc. and they able to influene the operaion for our organs many medical scholars have even come up with "free radical pathology"-free radicals are sourse of all he diseases in recent years.In this study, I chose rape stone vitaminC and green tea to restrain hydroxide radicals(OH.) Here is summary of the experimental process. First,I put 10%hydrogen peroxide into an injector and then added ferrous ion to hydrogen peroxide to catalyze it. Second I let it reaact with the sample. Because hydrogen peroxide can produce hydroxide radicals and oxygen, I used the mutiplier(OPA) to amplify the pressure caused with the prducion of oxygen, measuring and recording resuls by the software"Data Studio"Finally, we can tell which antioxidant is more effective in restraining hydrode radicals from volume-voltage gragh.
Double Pedal Curve
設Γ為一平面曲線而 P 為一定點 , 自P 向Γ所有的切線作對稱點，則所有對稱點所成的圖形Γ1 稱為曲線Γ對定點P 的double pedal curve , Γ1 對定點P 的double pedal curve Γ2 稱為曲線Γ對定點P 的2-th double pedal curve , Γ2 對定點P 的double pedal curve Γ3 稱為曲線 Γ對定點P 的3-th double pedal curve ,…… 。以下是本文主要的結果：結論A：當Γ為一圓形而P 為圓上一點時 , 計算其n−th double pedal curve 的方程式。結論B：當Γ為任意平滑的參數曲線而P 為任意一點時 , Γ的 double pedal curve 的切線性質。結論C：當Γ為任意平滑的參數曲線而P 為(0,0)時, 計算其n−th double pedal curve 的方程式。
Given a plane curve Γand a fixed point P ,the locus of the reflection of P about the tangent to the curveΓis called the double pedal curve of Γwith respect to P.We denote Γ1 as the double pedal curve of Γwith respect to P, Γ2 as the double pedal curve of Γ1 with respect to P , Γ3 as the double pedal curve of Γ2 with respect to P ,and so on , we call Γn the n-th double pedal curve of Γwith respect to P. If Γ is a circle, and P is a point on the circle, we got the parametric equation of the n−th double pedal curve of Γ with respect to P. And, for any parametric plane curve Γ; we got the method to draw the tangent of the double pedal curve of Γ.
奈米溶膠製成蓮花效應及應用
Lotus effect（蓮花效應）是蓮葉表面化學組成（wax）與物理組成（微纖維結構）兩者所造成。本研究是以模擬Lotus effect，採用Sol-Gel 製成，將氟化矽聚合為奈米膠體。實驗結果發現，以異丙醇為溶劑，再依序加入氟化矽、硝酸以製成的Sol-Gel，將其塗覆於玻璃表面，可得到最高的接觸角（114.71°），且少量的氟化矽可製成大量的成品，已具有實用價值又兼顧成本的優點，最重要的是，本研究克服了目前Sol-Gel 製程與應用的四大難題（機械強度、與基材接著問題、透明度、溶膠凝固問題），可說是一大創舉。利用所研發出來的奈米溶膠，我們能成功地將Sol-Gel 附著於布料、玻璃、釉表面、粉體，也能成功地研發出具有自潔透氣的布料、救生衣、雪衣、棉被及自潔功能的玻璃、磁磚與市面上尚未研發出的防水粉體（接觸角＞140°），因此我們研發出的Sol-Gel 應用甚廣，有無限的發展潛力。Chemical composition (wax) and physical characteristics (microstructure) of lotus leaves are both responsible of the so call Lotus Effect. In this study we intend to demonstrate louts effect by applying Sol-Gel method to polymerize fluorosilane into nano-scale colloid. Our experimental results shown that the sol-gel made based on isopropanol solvent with fluorosilane and nitric acid added in order, when coated on glass plate, can achieve highest (liquid-surface) contact angle of 114.7 degrees. In addition, only small quantity of fluorosilane is sufficient to produce large amount of product, making this method feasible and cost-effective. More importantly, this procedure overcome the four major difficulty of sol-gel processing and application, namely mechanical toughness, adhesion with substrate, transparency, and consolidation. Using the nano-sol-gel developed in this study, we have successfully coated the sol-gel onto fabric, glass, ceramic grazing surface, and powder, which allow one to make self-cleaning breathable clothes, life jacket, snow cloth, futon and self-cleaning glass and tiles, as well as water-proof powder (contact angle > 140 degrees) which is brand new on market. We therefore believe that there is a great potential for the application of sol-gel developed in this study.
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。