未得獎作品

我們研究的主題是曲率，且以高中所學的函數為主。雖然大學已有曲率公式，但我們將其表示成高中生較易了解的型式，並且以f(x) 的方式呈現。我們在函數曲線上取不共線三點，構成一個三角形，並求出此三角形的外接圓半徑。再將所取三點逼近，所求之半徑即為特定點的密切圓，也就是曲率半徑。而此曲率半徑的倒數，就是所求的曲率，同時我們將公式帶入高中各常見函數，以導出函數上各點曲率。;Our study is about curvature, especially about the fuctions we learn in senior high school. In university, there is a certain formula for curvature, but we hope to change it into a form that can be easily accepted by senior high school students, and express the formula with f(x), the symbol of functions. We pick three incollinear points from the curve of a function, making the three points into a triangle, and figure out the circumradius of this triangle. Then, we approximate the three points to one of them, and the circumradius will also be the radius of the osculating circle of the point. We define the radius as radius of curvature. The reciprocal of the radius of curvature will be the curvature. Then, we use the formula to figure out the curvature of the functions we learn in senior high school.

無意間在某大學的科學討論版中，發現有人提問了一個關於旗子的問題，但遲遲無人回應。 \r 經過仔細思考這個問題後，想起許多旗幟在空中隨風飄揚的景象，那些旗子似乎有著一定的律動，而這個律動中，風扮演著一個十分重要的角色，不禁使我感到好奇：「風與旗子的擺動究竟有什麼關係？」，恰好有研究的機會，於是就以『旗海飄揚------旗面波之探討』為題目，展開了一系列的研究。

在一次意外的發現中，我觀察到以鱷魚夾夾住的鎂帶在海水中竟然不斷的冒出氣泡，引起了我一探究竟的興趣。經由一系列的探索和實驗，我驗證了此種奇特電化學行為的反應機制，並且藉著此種機制，我嘗試尋找可以產生最大電流、電壓的伏打電池組合，以便製出一個又產電、又生氫的新式伏打電池，一方面可作為直流電的電源，另一方面產生的氫氣又可作為燃料電池的燃料來源。 In one accidental discovery, I’ve observed that there were continuously bubbles coming out when a magnesium stripe was attached by the metal clip in the sea water. This incident aroused my curiosity to find out the reason. Through a series of searching and experiments, I have proved the mechanic reaction of this spectacular electronic chemical behavior. Then I tried to search for a combination which can produce the greatest electronic current and voltage in order to produce a new type of voltage battery that can produce electricity and hydrogen. In one way, it can be the source of producing the direct-current. On the other way, the hydrogen it produced can also be the source of a fuel battery.

由於奈米科技之進步發展神速，許多難以偵測的奈米污染物可能對生物體造成不可預知的負面影響，然而傳統之感測方法主要針對氣體分子，可能不適用於感測粒狀奈米污染物質。因此，本研究之主要目的是探討(也建立一套)奈米污染物簡易感測方法之可行性。利用二至三個塑膠瓶、塑膠管組裝簡易感測實驗，並且使用非常少量(約0.05 mL)之綠色溶劑(離子熔液)，實驗結果顯示奈米ZnO 及螢光粉塵灰(2 或奈米CuO 反而使電阻增加；未通過過濾材料之螢光粉塵灰(2 and phosphor particulates was conducted in a home-made nanopollutant sensing system. Experimentally, abstraction of nano ZnO into the IL caused a reduction of the IL resistance. Similarly, decreasing of the IL resistance was also observed in the abstraction of phosphor particles with particles sizes of 2 particles was found. Abstraction of nano CuO in the IL also led to a slight increase of the IL resistance. The determined characteristic resistances of the IL for abstraction of select nano particles such as nano ZnO, nano CuO, nano TiO2 and phosphor particulates may be used in the development of novel nanopollutants sensors.

快門，捕捉最原始的感動；科技，創造最完美的呈現。當攝影遇上科學，成就了本研究的主題──高階電腦數位影像之研發。在我的研究過程中困難重重，從外景攝影、後製研究、影像創作到本研究撰寫完工，一切由我個人獨力進行，經歷了多次失敗，仍堅持的完成這重大的研究突破。 相信多數人會使用相機，但是對數位攝影這領域卻不甚了解，更別談藝術與科學的結合。因此希望本科展研究將會成為未來科技數位電腦的主軸，強調科技、即時、便利、環保、生活及教育的科學推廣，以實用並超越新世紀的數位領域，讓所有電腦愛好者，都可以輕鬆的應用此高階的數位暗房後製。讓電腦科技不只是零與一的組合，而是心靈與世界的互動！ ;Camera shutter captures the most original affection; technology creates the most perfect display. High-level digital image—when photography meets technology—is the theme of this research. However, in the process of the research, I have encountered many problems—from outdoor scene shot, production research, image creation to report writing—I did them individually and had undergone many failures, but I still insisted on finishing this big research breakthrough. I believe that many people can use the camera, but didn’t understand anything about the field of digital photography, let alone the combination of art and technology. I hope this technology development research would become the main perch of digital technology in the future—emphasizing technology ,instantaneous,convenience,environmentalprotection, livelihood, and popularize technology education—to use and go beyond the new age of digital field and to make computer lovers apply high-level darkroom production easily. Making computer technology not just combinations of zeros and ones, but the interaction between life and the world.

靈光乍現：弦的震盪由直到彎，從單懸到雙懸迴盪不已，共振駐波顯現半波長的微妙變化。故佈疑陣：曲弦振盪、共振頻率、弦上張力、半駐波長，玄機重重。 高潮迭起：推翻同一弦上所受張力相同，得知曲弦曲度不同所受張力亦不等的真相。 明天過後：重現曲弦程度，知彈性係數迴旋，將曲弦駐波性質變化摸透透。 ;Inspirations: Vibrating the string of thing bar from longittudinal to transverse; from both arm to single arm; from the waves of the string to the mystery ofλ/4. Battle: Resonance frequency, string tension force, half stationary wave, questions flying everywhere. Revolution: Overturn the theory that the tension force on the same string equalizes everywhere by measuring the length of eachλ/2 ; proof that the tension force enlarges from the top of the string to the end because of the gravity of the string ; Calculate the constant of the difference between the length of the incomplete wave on the end andλ/4 / the last completeλ/2. Proof that the constant is decided by the thickness of the string rather than the length of the string ; Finding the fact that the number of completeλ/2 on the same string equals no matter where the vibrating spot is.

This study of health diagnosis based on using computer signal analysis technology. In order to make health management more perfect. The main points of this study are wrist pulse and body temperature information, remit to the database of the computer, analyze with the computer. With the internet network , transmit it to the medical center in order to carry and control, seek medical advice, prevent infective disease from spreading, defending healthy purposes of people, this research system includes the following six functions:（1） Automation measured: Can prevent popular disease from spreading , and ensure the medical personnel to avoid being infected.（2） The heart and lungs function warning system:When the pulse beats too fast or slowly, computer will send out warning signal immediately .（3） The body temperature is unusually warning system: When the body temperature is too high or too low, will send out warning signal immediately.（4） Pathology analyzed: Will pick and fetch the pulse wave form, which use the computer procedure to carry on frequency spectrum in order to analyze, then compared with database, with the purpose of analyze pathology. （5） The health managed: Remit the physiological information that quantity examines to the database of computer, offer pathology analysis, carry on the prevention of the disease. （6） Analysis results of the human exercise: With the operation of the database, we can analyze and obtain the effect that all previous sports accumulate .本研究係運用電腦訊號分析科技、資料庫軟體，使健康管理更為完善。研究重點為擷取人體手腕脈象、體溫生理訊息，匯入電腦資料庫，以電腦進行分析。藉由網際網路，傳輸至醫療單位，達到遠端監控、緊急就醫、防止傳染性疾病蔓延，守護國民健康之目的，本研究系統包含下列六大功能：（1） 自動化檢測：可防止流行疾病蔓延，並保障醫護人員避免遭受感染。（2） 心肺功能異常警示：脈搏跳動過快或過慢，立即發出警示。（3） 體溫異常警示：當體溫過高或過低，會發出警示。（4） 病理分析：將擷取脈搏波形，運用電腦程式進行頻譜分析，與資料庫比對，藉以分析病理。（5） 健康管理：將量測之生理訊息匯入電腦資料庫，提供病理分析，進行疾病之預防。（6） 運動成效分析：藉由資料庫之運作，可解析獲得歷次運動累積之成效。

在此文中我們研究： 一個 n×4 的長方形網格中，所有從(1, 1)或(1, 4)出發，在不重複且經過每個格子點的情況下，走到(n, 1)結束的所有路徑總數分別為 Tn 、Un。 In our research, we study a n× 4 rectangular network lattice, of which all the routes are starting from (1, 1) (resp.(1, 4)), and ending at (n, 1) (situations are considered only on the conditions of passing every spot and not being repeated ). And we set the sum of all the different routes as Tn (resp. Un).

由於工商科技的發展帶給環境負面的影響日漸嚴重，其中尤以重金屬對台灣環境的影響較為顯著，故探討能移除排放廢水中的重金屬之有效天然資材有其重要性。以台灣天然存在之大地資源土壤中的奈米粒子來進行對汞、鎘的吸附，試驗結果得知，台灣三種代表性土類土壤中的奈米粒子確實能有效地吸附汞離子和鎘離子，且其中以對汞的吸附要大於對鎘的吸附。屬於砂頁岩沖積土的奈米粒子對汞、鎘的吸附最大，其次是黏板岩沖積土的奈米粒子，而最小的則是屬於台灣紅壤的奈米粒子。以上結果經由電化學方波伏安法的測定、電導度計法的測定與發芽率試驗結果都有相同的趨勢，顯示土壤奈米粒子可用來當作移除汞、鎘等重金屬的天然資材。 ;Effects of heavy metals are significant in Taiwanese environment due to serious impact of environment was made by development of industry and commerce. Therefore, study of removing heavy metals from waste water by natural materials is important. We need nanoparticles of natural soils to study the adsorption of mercury and cadmium ions. The experimental results indicated nanoparticles of three represent soil groups in Taiwan could adsorb effectively mercury and cadmium ions, and the adsorption of mercury ion was more than that of cadmium ion. The nanoparticles of sandstone-shale alluvial soil had largest adsorption for mercury and cadmium ions, and next for that of slate alluvial soil. The nanoparticles of red soil had smallest adsorption. All results were proved by voltammetry of electrochemistry, conductivity method and germinant percentage of vegetable seed. That obviously revealed soil nanoparticles could remove effectively mercury and cadmium ions.

由於塑膠不能在自然情況下順利分解，所以我們在塑膠中添加其他成分使塑膠可以較易分解。我們選定常見的塑膠—熱塑性的耐綸-66。在聚合物的製作過程中添加葡萄糖、澱粉、洋菜粉末以及甲基纖維素，並觀察加入添加物的塑膠在結構上是否有變化？其塑膠在線型時之張力是否有增強？耐酸鹼性是否有變化？由實驗結果我們可以得知含有甲基纖維素之耐綸-66 所能承受之張力強度最高，且其彈性係數也比無添加物之耐綸-66 高出近2 倍；而含可溶性澱粉之耐綸-66 所能承受之張力最小，且彈性係數也最低。此外，進行生物分解的實驗可發現，含洋菜粉末的耐綸-66 分解的速率最快。使用400 倍的光學顯微鏡可發現含有洋菜粉末的耐綸-66 表面與其他耐綸-66 複合材料差異較大，值得進一步研究。;Because plastic cannot be decomposed naturally by itself, therefore, additives needed to be added to facile the decomposing process. Let us choose one common material: thermoformed Nylon 66. During the formation process, add the following additives: glucose powder, methyl cellulose, soluble starch and agar powder. Observe whether adding additives would allow changes to occur structurally, or would the elasticity be improved when exist in a linear state, or even it would form a better pH resistance property. Most importantly, observe whether the decomposing rate has increased or not. According to the experiments, when Nylon 66 contains methyl cellulose, it can sustain the highest tension. Its coefficient of elasticity is 2 times as large as the original one. In terms of the data, we can also observe that when Nylon 66 contains soluble starch, it has the lowest ability to sustain tension. Besides, it has the lowest coefficient of elasticity. And when Nylon 66 contains glucose, it has the highest rate in the process of decomposing. As we look at the surface of polymers under 400 diameters, we can observe that the Nylon 66 with agar powder has some filiferous substance. But we have not confirmed what the matter is. As to decomposing rate, we found that when Nylon 66 contains additives, it could accelerate its decomposing rate. And the one with agar powder has the highest rate of decomposing.