思考公車車門開關時在地面上掃過的區域形狀與面積時，發現其中變動的直線為過定點與座標軸圍成三角形面積最小的直線，我們很好奇，這類圍成最小面積的直線更進一步的包絡現象，所以就動手去嘗試做研究。\r \r The research is done out of the curiosity we had when we pondered over the area and the shape a bus door sweeps on the floor when it opens or closes, and thus to discover the graph of the varying line which forms the smallest area so that we attempt to do research on such envelopment phenomena.

在這個科展中我們要研究兩個非常有趣的問題：\r 停車場問題 與 彈硬幣遊戲.\r 停車場問題是這樣的：在一條單行道上有n個車位，編號從1到n。現在有n個司機排成一排要進入停車。但是每個司機都有怪癖，各自有最想要停的位子。他們依序將車子開進單行道，如果想要停的位子是空的，當然停在這個位子。但是如果不巧那個位子已經被停了，不得已只好找下一個空位，姑且停之。但是如果往下找都沒有空位，由於是單行道，司機就只好開走不停了。\r 比如說，如果現在有五輛車，司機的喜好分別是(3,1,2,5,2)。則五輛車都可以順利停車。但是司機的喜好如果是(3,1,4,5,4)，有些車就無法停車了。\r 彈硬幣遊戲是這樣的：考慮圓內接正n+1邊形，任意兩點都連線。這正n+1邊形中有一個頂點P是特殊的，每個頂點上一開始都放有一些硬幣(各點硬幣數可以不同)。如果P以外的某個頂點上的硬幣數n個，我們可以對這個頂點進行操作：一次操作是指將這個頂點上的硬幣各分一個給每個其他頂點。點P只在其他點都無法操作時操作。我們不理會頂點P上的錢數，因此這個遊戲可以無限地玩下去。

Up to this time we have spent almost three years in studying condensation and water droplets. Little could we have done as compared with the almighty nature. However we are rewarded by the nature as we gradually found the secrets about electro-magneto field and water droplets: The size of water droplets turn smaller upon electro-magneto field and grow more uniformly especially upon electric field. This experiment presented here is actually the diary of the growth of water droplets in condensation, upon magnetic field and electric field. Through convection, it discusses the self assembly patterns of water droplets and peep into the uniformity both of the size and the distribution mode of water droplets. In former basic experiment, we focus on temperature and the speed of water moisture; generally speaking, higher temperature speeds up the coalescence procedure but does not affects the nucleation size of water droplets in simple plain surroundings; while speed of moisture does affects the nucleation size. As we went farther, deep into convection and found magneto-electric force did play an important role in the self assembly mechanism of water droplets. The topic is mostly concerned as we are surrounded by magneto-electric waves in today’s world. This experiment anchors the first step in discovering the uniformity of water droplets in different environment, and providing insights into the self assembly mechanism of water droplets upon electro-magneto field with nano sizes. 這是一系列關於水蒸氣冷凝為極細微小水珠的實驗。其中可以分為兩大部分； 第一部分是基礎實驗。將水蒸氣導入至潔淨的介面上(蓋玻片)，觀察冷凝水珠的結構。雖然看似簡單平常，但卻有令人驚奇的發現；不同溫度的水蒸氣，其冷凝最初始的細微顆粒之尺寸是相同的 ！爾後隨著溫度的升高，堆疊速率也跟著上升；以致於最後一起呈現出來的水珠大小不一，尺寸不一。 第二部分是將水蒸氣導到磁場及靜電場上，觀察其冷凝結構。這部分的實驗推翻了一般「水分子是電中性在電磁場中不受影響？」的刻板觀念 ！實驗所呈現出來的冷凝水珠，不但於附加磁場中尺寸縮小又不易長大，同時還有固定的自我組成模式( Slef-assembly pattern);而且也發現在磁場中的冷凝小水珠的尺寸比電場中的小，可是電場中的小水珠則表現出較大的均勻特質。

給定一平面E，A為平面上一點。取r>0，則我們知道到其距離為定值的點形成一圓，而A為此圓圓心。如果把A改成一平面圖形，則到其距離為定值的點形成的集合會是什麼樣子？類似地，給定平面上兩焦點F1及F2在平面上，則到其距離和為定值的點形成橢圓。同樣的，若把F1及F2改成平面圖形，其圖形會是什麼樣子？藉著GSP的輔助，到目前為止，我們得到了以下的結果： \r 1. 給定一平面E及此平面上的一個凸多邊形, 我們描繪出在此平面上到此凸多邊形之距離為定值的點所形成的圖形。\r 2. 設F1和F2分別為平面E上之點或線段或多邊形（未必是凸多邊形），我們利用包絡線描繪出所有滿足d(P,F1)+d(P,F2)=k（k夠大）的點所形成的圖形。 \r 3. 設C1,C2為平面E上之兩圓，我們討論所有滿足 d(P,C1)+d(P,C2)=k\r （k夠大）的點形成的圖形並討論其性質。 \r 4. 設L1和L2分別為平面E上之兩線段，我們討論所有滿足d(P,L1)+d(P,L2)=k（k夠大）的點形成的圖形並討論其性質。 \r 5. 設A為平面E上之一點，Γ為平面上一凸多邊形，我們討論所有滿足d(P,A)+D(P,Γ)=k（k夠大）的點形成的集合並討論其特性。 \r 6. 藉由和圓作比較，我們研究了變形圓的光學性質；而對變形橢圓也做類似的討論。\r Let E be a plane and A a fixed point on E. Given , it is known that all of the points on E with distance to 0r>rA form a circle and the point A is called the center of this circle. What is the corresponding graph if we replace the point A with a set (for example,a segament or a polygon) contained in FE? Similarly, what is the case when we modify the two focuses and in the definition of an ellcpse to sets and (or example,two segments or two polygons) contained in 1F2F1F2FE ? Taking advantages of GSP and analytic geomety, we research related situations and so far we have obtained the following results:\r 1. Let Γ?E be a segment, a convex polygon or a circle , etc. and r>0 be fixed. We sketch the graph of points on E with distance r to Γ and study properties of such graphs.\r 2. Let F1 and F2 be singletons, line segments , polygons(may not be convex), or circles,etc., on E Taking advantage of envelopes, we sketch the graph of those points P on E satisfying d(P,F1)=k(K>0 is large enough).\r 3. Let C1 and C2 be circles on 1C2CE. We sketch the graph of the points P on E that satisfiy d(P,C1)6d(P,C2)=k (k>0 is large enough) and study properties of this graph.\r 4. Let L1 and L2 be two line segments on E and be a large enough constant. We sketch the graph of points P on E that satisfy d(P,L1)+d(P,L2)=k(k >0is large enough) and research properties of this graph. 0k>\r 5. Let A?E and be a convex polygon on ΓE. We sketch the graph of points on E that satisfy d(P,L1)+d(P,L2)=k(k>0 is large enough) and research properties of this graph.\r 6.We compare the optical properties of metamorphic circles with circles and we deal with metamorphic ellipses similiarly.

本報告研究內容，是利用電化學氧化還原方法合成金、銀、銅三種奈米粒子，以及探討電流是否會影響電解合成奈米粒子，在前半部成功地利用控制電解的部份條件，如界面活性劑、以及電流值大小，而合成出金、銀、銅三種奈米粒子，利用UV-VIS的光譜分析，鑑定其三種奈米粒子不同的吸收波長，其光譜出現吸收的現象是因為金屬表面特殊的表面電漿共振吸收現象而產生的。但是在本實驗中發現在UV-VIS的光譜中，電壓值的大小對金奈米粒子吸收波長並沒有關係，這些奈米粒子在水溶液中藉由界面活性劑的包覆，而溶解的相當好。 The content of thesis focuses on using electrochemistry oxidation-reduction reaction to synthesis gold, silver, and copper nanoparticles. We confer whether current of the electrolysis is an influence for the synthesis of nanoparticles. We succeed in synthesizing nanoparticle by controlling some terms of the electrolysis, like the micelle concentration, and current value. Using UV-VIS spectrum to analyse wavelength of three kinds of nanoparticles. The special phenomenon of absorption spectra is appeared because the surface plasma resonance on the surface of metal. From the UV-Vis spectra, we didn’t find the exact relationship between the potential value and the absorption spectra of gold nanoparticles. Finally, we also obtained good results in spectra observation, which meant that these nanoparticles encapsulated with surfactants were well solved in the solution.

流行病學資料顯示，近年來口腔癌發生率明顯增加。本研究之目的是探討口腔黏膜細胞微核發生頻率及彗星分析法之基因傷害指標是否與菸、酒、檳榔暴露有關，以及是否可以看到菸、酒、檳榔之交互作用。 研究對象為桃園地區山地鄉之民眾，利用問卷收集個人之菸、酒、檳榔及干擾因子之暴露資料，再採集樣本之口腔黏膜細胞及血液樣本，進行基因傷害評估。 結果顯示，口腔黏膜之微核發生率與檳榔之暴露相關性最大，可以解釋12.6％；然而，彗星尾部動量和尾部長度則以香菸暴露解釋力最大；同時，檳榔與香菸的基因傷害交互作用似乎存在。因此我們認為，口腔黏膜細胞之微核發生頻率對於檳榔暴露者應是不錯的基因傷害指標，而香菸暴露則以彗星分析法之指標較為敏感。 ;Epidemiological studies showed that the incidence of oral cancer increased significantly in recent years. The purpose of this study is to evaluate the genotoxicity of cigarette smoke, alcohol and betel quid use as well as the. interaction effect between these three risk factors. The study subjects were selected from residents lived in a mountain area of Tao-Yuan county. We used questionnaire as a tool of exposure measurement. The exfoliated oral buccal cells and blood samples were collected for the assay of micronucleus frequency (MNF) and comet assay. We find that there are higher MNF in smokers, alcohol drinkers, and betel quid users compared with nonusers. However, a significant difference can not be found because of small sample size. The relationship between MNF and three risk factors was strongest in betel quid use, however, for smokers the parameters in comet assay were more sensitive than MNF. There is a tendency of additive effect between cigarette, alcohol and betel quid although without statistical significance. Advanced statistical analysis is suggested to find stronger evidence in the genotoxicity biomarker.

隨著工商業發展，環境污染日益嚴重，對多數生長在這塊土地上的人，無疑造成了非常嚴重的影響。但若想要監控目前環境中的空氣品質，則必須具備專業的訓練，及昂貴的實驗設備，對一般民眾而言，根本就做不到。\r 藉由指標植物對所生長環境的高度敏感性，可以發展出一套純天然且免費的環境污染偵測器，不但方便、免攜帶、無須高級儀器協助、更不需要專業的分析技術。為此，我們以對二氧化硫等空氣污染物極為敏感的地衣作為指標植物，對其進行生態與環境污染關係的一系列觀察，並設計相關的實驗，找出環境污染物對地衣的實際影響，使其能夠實際的應用於日常生活，並可加以推廣，讓人人都可以利用地衣來了解自己所處的環境是否遭受污染，為自己家園的環境優劣把關。\r \r 文摘要 :\r With the development of industry and business , environmental pollutions become more and more serious . Undoubtedly , those pollutions have a great effect on us.\r However , by the means of the indicator plant which is highly sensitive to its environment , we can develop a set of natural and free environmental pollution detectors . In this project , we use lichenes,which are very sensitive to air pollution , to do a series of observations and to find out the influence the pollutants have on lichenes . If we can apply this to our regular lives , everyone can use lichenes to see if their environment is polluted or not .

聖嬰現象為全球的共同話題之一，由於其發生會影響全球性氣候的改變，使原本乾旱處下起傾盆大雨，原本潮濕氣候的地區成了乾旱地區，導致生命、財產嚴重性損失，這也是引發本研究想站在不同科學領域角度來探就聖嬰現象的發生的原因。目前科學家大都以大氣觀點來說明聖嬰的成因：太平洋上因風向改變引起海水流向或動能變化，導致太平洋赤道地區及南美洲西側海面溫度的改變，而觸發聖嬰的發生。由於海水的熱容量比空氣大，因此我們想以海洋觀點來說明另一種可能觸動聖嬰發生的動力，在生活經驗裡，我們發現水流通過障礙物會在後方形成渦流，因此，當南極繞極環流通過德瑞克通道受到南美洲南端阻礙時，有可能在南美洲形成週期性渦流生成及脫離的現象。「這樣的渦流是否存在？」、「渦流脫離後在南美洲左右岸海面溫度、高度是否發生變化？」、「此動力是否進而觸發聖嬰現象？」，是本研究期待以新思惟解釋引發這個全球現象的另一可能動力。

The definition of "Fermat Point" is that a dot, which lies in a triangle, has the minimum distance to the three apexes. In other words, "Fermat Point" has the minimum distance to three dots which are not on the same line. In the broad sense, then, in a N polygon, a dot which has the minimum distance to the N apexes could be named "Fermat Point." But what if we link up the N apexes and find out that they cannot make a convex polygon? The above is what we wish to fully discuss. Our inspiration comes from a paper on"Fermat Point." It just describes N convex polygon, so we think of putting the case to naturally polygon. The case may be that it is a concave polygon or part of the apexes which lies on the same line. We would not base our study on the conventional methods. Moreover, strictly defined, the repeated line segment will not be taken into account. That is, if the "Fermat Point" drops on the line with more than two dots on it, we just count the\r line segments except for the shorter line segments which were originally included in other studies. According to the theorem, our conclusions are as follows: 1. If N points lie on the same line segment, then the "Fermat Point"can be any point on the line segment. 2. If (N-1) points are on the same line segment, then the "Fermat Point" is on the point which two lines join together. One is that the line segment, and the other is the one which passes the remaining point and\r perpendicular to the first line segment. 3. Now there are (M+N) points. Among them, M points will make a M jog-polygon. The others all drop in the polygon. As the diagram shown beneath, we know that the "Fermat Point" drops on the point which two lines join together. The two lines must pass as many points as possible. 所謂的「費馬點」是指三角形內到三頂點距離和最小的點。換言之，「費馬點」就是到平面上不共線三點距離和最小的點。因此，我們可定義，廣義的「費馬點」即是n 多邊形內到各頂點距離和最小的點，亦即到平面上不共線n 點距離和最小的點，但若平面上n 點不能恰為n 多邊形的頂點呢？這就是我們所要討論的。由於我們的靈感來自一份關於「費馬點」的科展作品，所以我們想到，當平面上n 點不能恰為n 凸多邊形的頂點，甚或其中有一部分的點共線時，將不能以n邊形的方法來探討，但我們可以將之化為m 邊形內（n-m）個點來討論。而更重要的是，我\r 們增加了另一個限制，重複的線段將不被我們列入計算。亦即當所求點落在某一多點共線的線段上時，我們只計算該線段的總長，而不計其中重複的較短線段。根據這個原則，我們試行證明平面上三點、四點、五點及六點的可能情況，期望能從中找出足以推廣至平面上n 點的一般性。結果雖不完美，但我們總算差強人意的歸納出了下列結論：1.若n 點共線段，所求點可為所共線段上任一點。2.若（n-1）點共線段，則由該不共線點引一線與共線段垂直，其交點即為所求。3.若（n+m）個點中有m 個點為一m 多邊形的頂點，另外n 個點落在該m 多邊形內，則由兩個外頂點引直線盡可能通過最多點，該兩直線的交點即為所求。

利用陰極電弧蒸鍍各種薄膜，如：類鑽膜（DLC）、氮化鈦膜（TiN）、氮化鉻膜（CrN）、氮化鋁鈦膜（TiAlN）以及先披覆上一層氮化鋁鈦膜（TiAlN）再加上類鑽膜（DLC）的合成膜等。這些薄膜現在已經被廣泛的應用於各種刀具、模具的表面處理之中。本研究主要在探討高速鋼鍍上氮化鉻膜（CrN）之後，對於硬度、磨耗性質的改變，以及觀察氮化鉻膜（CrN）表面結構之組織。 在研究中我們運用陰極電弧蒸鍍系統蒸鍍氮化鉻薄膜，分析上運用SEM來觀察薄膜表面結構組織，以及運用洛氏微硬度機來觀察試片的硬度，另外還有使用磨耗試驗機來進行磨耗測試。以上這些測試總括來說都是在得知性質有無實際上的改變，而這些實際上的改變對於蒸鍍之後的模具或刀具都能夠大幅的提高使用的壽命。 We evaporated different kinds of thin films by using the anode of the electronic arc, such as DLC (Diamond-Like Carbon), TiN (Titanium Nitride), CrN (Chromium Nitride), TiAlN (Titanium Aluminum Nitride), and synthetic films of covering TiAlN and DLC. These thin films have been used widely in processing the surface of a variety of cutters and moulds. The purposes of this research were to investigate changes of hardness and abrasion and to observe the organization of the surface structure of CrN after High-speed steel evaporates CrN. In this study, we use the system of the anode of electronic arc to evaporate CrN. Besides, SEM is used to observe the organization of the surface structure of the thin films and Rockwell Micro-hardness Test Machine is used to investigate hardness of testing samples. Moreover, we use Abrasion Tester to test abrasion. These tests are taken to lead to a better understanding whether the quality really changed. These changes of evaporated moulds or cutters would extend their frequency of using.