平面上三點集中度判別法之探討
關於平面上若干點的集中度之定義，一直很少有人予以仔細的探討，因為判別的方法有很多種。本研究是以平面上三點所構成的三角形之三頂點作討論，分別以三角形的面積、周長，內心、外心和重心至三頂點距離，三點的標準差及平均差的概念，作為不同的判別方式，並以動態幾何化版ＧＳＰ模擬不同的判斷方法做為研究，在利用統計學上的方法，找出哪一種定義方式最為適合、誤差最少的判斷方法。There are many ways to determine the centralness of three dots on a plane; however, no definition study has been applied. In this study, we focus our interests on the entralness of three vertices of a triangle formed from three dots on a plane. Various methods such as the relationship of area, and the distance of the triangle to the centralness of three dots, the distance from the interior point, exterior point, the barycenter to the vertices of triangle, and the standard error and differences average obtained from three dots were determined with a dynamic geometry software GSP, and a statistic method was used to find a least error way to determine the centralness of three dots on a plane.
遞迥數列及渾沌現象
給定一個P∈(0,1),令k0=0, p0=p，定義k1為能使 的最小正整數k，而 ; 相同的，對於給定的kn-1, kn 為能使的最小正整數k, 。若存在kn 使得，則稱p∈ In; 若對於所有n 與kn ，，則稱p∈ I∞。如此區間(0,1)可分解成集合I1,I2,…,I∞。
聚苯胺導電高分子在鐵系金屬防蝕上的應用與研究
聚苯胺導電高分子的發展蓬勃迅速，其應用也愈趨廣泛，金屬防蝕為其可能應用之一。台灣四面環海，工業發達，造成金屬腐蝕損害嚴重。本文為探討聚苯胺導電高分子在鐵系金屬防蝕上之應用，針對以下各點進行研究： ( 1）探討導電高分子聚苯胺性質與合成方法（2）探討聚苯胺導電原理（3）測試不同腐蝕條件下聚苯胺的防蝕效果（4）探討聚苯胺防蝕原理（5）各種氧化還原態聚苯胺防蝕效果之比較。實驗結果顯示塗布聚苯胺與未塗布聚苯胺之鐵系金屬（生鐵、不鏽鋼、鍍鋅鐵）在 3 ％氯化鈉、 0 . 5M 鹽酸、1M 鹽酸溶液中之腐蝕狀況，以鹼式中問氧化態聚苯胺（ Emeraldine base 。）最具防蝕效果。聚苯胺防蝕機構包含阻隔防護、腐蝕抑制劑、陽極保護、惰性化、形成保護性氧化物薄膜、阻礙離子擴散速率、電化學介面遷移等機構 ·The development and application of the conducting polymer polyaniline is getting prosperous and popular. One of the applications is corrosion protection. Because Taiwan is surrounded by sea and the pollution of industry is more and more serious than before the damage of corrosion is greater and should be properly controlled. In this paper, the authors attempted to study the effect of the corrosion protection of polyaniline in ferrous metal. This study could be divided into four parts: (1) the study of the property and synthesis methods for the conducting polymer polyaniline, (2) the conduction theory of the polymer polyaniline, (3) The corrosion protection effects of the polymer polyaniline under different corrosion situations, (4) the corrosion protection theory of the polymer polyaniline, and (5) the comparison of the corrosion protection effects of various polymer polyanilines. According to the experimental results the Erneraldine-based polyaniline gets the best corrosion protection effect. The mechanism of corrosion protection may be the result of the following ones: barrier protection, corrosion inhibitor, anode protection, innobeling, chemical active layer. inhibition of diffusion rate, and the shift of electrochemical interface.
聚苯胺導電高分子二次電池之研製及性能研究
塑膠一向被認為絕緣體。但Heeger，MacDiarmid，以及Shirakawa證實，塑膠可以被改製成電的良導體。這須在高分子合成的過程中，使碳鏈呈現單、雙鍵交錯排列情形。此外，高分子也須加以摻雜(doped)，換言之，電子必須在氧化過程中被移除或在還原過程中被加進聚合物。電子移除所留下的電洞，或新加進的電子則可自由在分子鏈上移動，形成導電性。我們所要製備的導電高分子二次電池就是由這個原理完成的。所謂的二次電池(Secondary Cell)簡單的定義就是「可反覆充電、放電，循環使用的電池」，我們將會將其與市售電池比較，並改良出合適商品化的高分子二次電池。我們將以聚苯胺做為我們電池的正極，並用鋅片(原本我們要用鋰金屬的，但其再空氣中即易氧化，因此改採鋅)做為負極，製成一聚苯胺二次電池。The plastics is thought to be a insulator, but Heeger, MacDiarmid, and Shirakawa had proved that conductivity of plastics can be improved by doping other media. The conjugated polymers such as polyacetylene、polyaniline have the interlaced single-double bonds that electrons can move from one side to another side caused the production of electric currents. The purpose of this study is try to study the application of the conjugated polymer polyaniline to make a secondary battery. First, we use the chemical and electrochemical method to compose the polyaniline. Then we test the conductivity of the produced polyaniline and test the current and electrical potential of the polymer battery. The battery that we made from our laboratory has the electric potential about 0.5 volts and the electric current is greater than 50 microamperes. Finally, we also try to use the lithium as cathode to improve the performance of the polyaniline battery.
溫度與光週期對淡黃蝶的影響
為了了解淡黃蝶Catopsilia pomona無紋型crocale-like及銀紋型pomona-like中間受到環境因子的差異。先比對兩型的粒線體ＤＮＡ，之後模擬夏季和冬季自然環境進行實驗。得知兩型為同種。另一方面進行溫度和光週期的實驗，顯示淡黃蝶幼蟲和成蟲雌雄個體各部位會受到此兩環境因子的影響。In order to realize if Catopsilia Pomona and Catosilia crocale are the same species, we analyzed and compared the DNA sequences of Mitochondria, and the result revealed they are indeed the same species. Then we observed the developmental process of the butterfly, and inspected the effects of different factors: photoperiod and temperature were shown to affect the phenotype of the butterfly; lower temperature and shorter day resulted in phenotypic shift from crocale-like to pomona-like, and vice versa. Also, the conflicting factors produced intermediated form. (e.g. lower temperature with longer day) Not only changed the phenotypes of adult with photoperiod and temperature, those of larvae also did. However, the mechanism how photoperiod and temperature affect the phenotype of the butterfly is unknown.
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。
網路監控與家庭自動化系統之研究
The paper presents a new technique for the Internet monition and control system. The user not only can “watch” the current operation of remote home appliances from the client computer, but also directly control the behavior of remote home appliances through the Internet network. In the mean while, concerning the interface between users and appliances, the virtual reality is combined into the system so that users operate the system easily. First, virtual reality, CGI , HEML . I/O control code, 8255 I/O card and CCD are applied in the server computer to control and “watch” home appliances. Next, the client computer is connected to the sever computer through the Internet WWW(World Wide Web) network. Then, the user can control remote home appliances directly through the homepage. Finally, the experiment results are presented and discussed.本研究提出一種高效率且易維護的網路監控技術，從遠端確實“看”到監控系統現場動作，並下達控制指令。同時顧慮到使用者操作介面，結合虛擬實境，讓使用者可更輕鬆操作。首先，伺服端結合VR(虛擬實境)、CGI技術、基本的HTML、I/O控制指令、8255 I/O介面卡及CCD(網路攝影機)，應用於家用電氣，接著用戶端透過WWW全球資訊網連上伺服端首頁，然後依首頁之畫面，來達到遠端監控與家庭自動化之目的。
關於渦旋
A professor once told me that scientists have already known a lot about vortices, but less about how to tackle with them in here and there cases. As to my mind, this means knowing by halves. As a matter of fact, I gradually found that human may not know more than a dragonfly! A dragonfly flying in a figure of eight pattern does know about Vortices Recycling. The highlight of the experiment is the hovering ability upon a fixed point in the air. Who can stay longer will be the king of Vortices. Sometimes I am not so optimistic about mimicking a fly or a bat, but I am really very interesting in discovering which flying mechanism is more effective,『Fling Mechanism』 or 『In a figure of eight pattern』, if with the same weight and energy? How to implement their mechanism in our flying machine? It is always the best policy to do naturally with vortices. The conservation of vortices is found here and there. Vortex itself is energetic. To gain means to keep. The one who is able to keep vortices will be rewarded. As in life generation and the ability of hovering, the rule follows. Typhoons and tornados still threat us like the beasts. And what’s more, a jumbo-airplane was crashed as beaten by tip vortices of the former airplane. As the dragonflies, the beautiful acrobats of vortices , infuse in tip vortices. Not the strong contradistinction did we realize that it is time for vortices!研究渦旋已經四年。四年之中，涉獵了許多關於渦旋的實驗。當我越了解渦旋，就越佩服那些卓越的昆蟲朋友們，他們可說是調配利用渦旋的大師。從候鳥遷徙的V字型隊伍、海豚的渦旋氣球、到蜻蜓八字型的飛行機制，我很想知道：在一個固定的流場中，到底哪一種運動機制，能最有效率的提供上升的力量？而如何將昆蟲朋友們的高超技術，運用到人類飛行載具上？將是我有興趣的另一項課題。『關於渦旋』是一系列渦旋實驗，目的就是自基礎開始深入了解在地球這樣環境下渦旋的性質。（一）探討基礎的渦旋本質（二）產生相對運動下物體的的渦旋架構（三）物體取得升力和失去升力的要件（四）昆蟲飛行機制探密（五）未來展望與渦旋的運用經過長時間的觀察可以了解到：1、渦旋遵守動量守恆。是以渦旋出現時是成對的2、渦旋是具有能量的。在上升力取得方面，當攻角過大時，渦旋剝離，造成能量的損失；以至於飛行載具失速。而蜻蜓是保有渦旋並加以利用的高手，自然事半功倍。順勢而為，渦旋增強。