未得獎作品

我們的題目是”座標平面上任意三點與x軸的最短距離和”。我們一開始直接由尺規作圖著手，把距離和最小時的那點設為p，但始終無法找到一個方法精確畫到p點。後來變轉入公式的研究，我們設第一象限中A B 和C三點，固定A B C的y座標為d，並討論不同d時的情況，求出B點的範圍。另外我們也從橢圓方面著手，但此部份目前還待努力。;A B and C are three points in the plane, and L is a line in the same plane. Our target is to find a point P in L make the sum of PA+PB+PC minimum. At first we undertake by drawing pictures but we can’t find the solution we want in any case. We make L to be X-axis make A B C’s Y-coordinate to be d, and then we discuss various situations of d, and figure out the range of B. We also analyze the situation in oval, but still have no conclusion.

COP8 is the second unit of COP9 signalsome. In the comparison of BLAST ,we found that\r LLPC14 cDNA and the protein sequence are quit similar to the COP8 of Arabidopsis thaliana\r Therefore, we are interested in the role that COP8 plays in the photomorphogenesis and try to find\r the length of the sequence. So far, no result is obtained about the 3’-RACE, but we’re surprised to\r find that the sequence found in 5’-RACE is shorter than what we’re know, which suggests the RNA\r length of the cDNA used in the RACE combination has decreased.\r Although the final results of the COP8 5’and 3’-RACE haven’t been achieved, it is sure the\r COP8 is highly-conserved in many species. Since the similarity between LLPC14 and the COP8 of\r Arabidopsis thaliana is as high as 90 percent, we used the COP8 of Arabidopsis thaliana to detect the\r COP8 protein in pollen.在過去種綠豆芽的經驗中，不難發現它本身因為環境的不同，而有不同型態白化\r 的現象，例如：黑暗下萌發的豆苗。但尚未深入去理解白化的原因；而在後來的種植\r 經驗上，也發現有許多令自己覺得困惑的相同處。\r 在高二的生命科學第四章中，有提到光照與黑暗生長的植株，在構造比較上有明\r 顯的不同；其中，提及植物的活性組織存在「光敏素」（phytochrome），此色素蛋白的\r 存在於光照後，會引發一連串反應，至此，也稍微了解植物的萌發反應的差別。\r 故藉由個人在中研院植物所的資優生培訓過程，便以此為前題,進一步探究植物基\r 因組COP 8 與白化現象的相關性

常常看到一些防污染系統的不實際及曠廢時日以致造\r 成污染面的擴大；最常見的為油輪漏油污染海面，而我們能\r 做的僅是利用攔油繩鏈(oil disaster)將污染海面的油污圈圍\r 起來防止其擴大範圍。從文獻資料得知最新的觸媒材料TiO2\r 可以在紫外光照射下發揮分解油污及廢液的功能。因此想以\r TiO2 為主題對類似油污污染及廢液污染的濾淨作一番探\r 討，進而研究出一套快速的除汙設計來嘗試解決層出不窮的\r 污染事件。\r TiO2廉價、無毒、穩定性高，為一種良好的光催化觸媒，\r 其實它早已被用來加入化妝品及口香糖中，以期促成人體內\r 外部(含口腔)的淨化功能。所以我們進一步配合空心玻璃球\r 粒的應用及TiO2 薄膜的鍍製來設計出具有分解液態污染源\r 的攔油繩及快速分解液態污染源的簡易濾淨系統。

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.

In any , we prove that there exist cycles which have any length between 3 and 3n and paths which have any length between their smallest distance and longest Hamiltonian paths in any two different nodes; for any two nodes, there exist varied Hamiltonian cycles, making the two nodes locate on any possible counterpart position(only limited by the distance between the two nodes). In , there are 2n internally-disjoint spanning cycles, and 2n-1 internally-disjoint spanning paths. Besides, we also prove has no more than 2n disjoint spanning paths, and calculate its wide diameter. 本報告證明在環狀網路 中，存在有長度3到 3n 的所有迴圈；任何相異兩點都有各種不同的長度的路徑:從最短的距離到最長的漢米頓路徑；取定任意兩點，存在有各種不同的漢米爾頓迴圈，使得兩點位於所有可能的相對位置上(僅被兩點之間的距離限制)。在 中，也具有2n 個彼此不相交、經過所有點的迴圈，以及2n-1 個彼此不相交、經過所有點的路徑。除此之外，也證明了，在兩相異點間，具有個數不超過2n 且互斥的路徑，且這些路徑經過所有點。我們也估算了它的寬直徑。

桂枝?樟科植物肉桂之嫩枝，依古籍記載具解熱、鎮痙、抗菌及對消化液分泌有抗拮作用，藥理作用廣泛。近年來，國內外學者對其進行了大量的研究，且達到了較高的水平，查閱國內大量文獻，發現研究者對桂枝的成分、藥理等方面進行了深入的研究，其中較大比例的研究是對桂枝中有效成分桂皮醛(Cinnamic aldehyde)的討論，而我們希望能用新技術、新方法探討其藥理作用機制。

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.

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.

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.

Positive –A Study on a Nanoscale Revision Method and Sensitivity Evaluation This paper took a pyramid and a fixed point as the reference level. It was the intention of our team to establish and prove a new hardness value revising method that is to be used in the deflection of indentation of nano indentor. Such new method was named Material Surface Nanoscale Hardness Revision Method with which we re-measured various materials and error sensitivity of hardness values. We obtained the following conclusions:(1). This paper revision modification method have a highly precision. (2). When the round tip or plane tip was closed to ideal indentor tip, the contact areas during indentation process were close, not demonstrating significant difference. (3). The indentation triangle created when loading effort P was similar with the one left on the sample material when unloading the effort; thus, even though the sink-in and pile up effects due to the mechanical properties of sample material caused the differentiation of side lengths and two indentation areas, the angles of two indentation areas was the same. (4). When the effort was loaded by the tip onto the sample material, if the tip had a certain deflection ψ or rotation ω, the indentation triangle left on the sample material was still significant. (5). In the observation of the indentation triangle left on the sample material, when the triangle cannot become a regular triangle, it meant that there is a deflection or rotation happening to the tip and a further revision of the deflected angle ψ or rotated angle ω is required. (6). The hardness value revision method under indentation deflection situation had the best effect on the projected area revision; the second was on the indentation volume revision and than on the indentation contact area revision. (7). The hardness error sensitivity of hardness value revision method under indentation deflection situation had the best effect on the projected area; the second was on the contact area and than on the indentation volume revision. (8). The method proposed by this study was proved by the silica and aluminum single crystal indentation results and is thus able to be applied to the engineering in the nanoscale measurement of metal materials to obtain more precise data.不偏不倚-奈米級修準方法與敏感度評估之研究在這篇研究報告中，以一個三角錐和一個定點為基準，本團隊建立並證明一個新的在奈米硬度測試儀壓痕偏斜情況下，硬度值的修正方法，取名材料表面奈米硬度修正方法。在新的材料表面奈米硬度修正方法下，重新檢測各種材料及硬度誤差敏感度，得到許多好的結論：（1）本研究之修準方法具有高度精確性。（2）利用圓球尖端或平面尖端的方法近似理想壓頭時其壓痕過程中之接 觸面積相近，並無明顯差異。（3）作用力P 施加(Loading)時之壓痕三角形與卸載時(unloading)殘留於測試材料上之壓痕三角形係屬於相似形；因此，即使各該三角形之邊長因為該測試材料本身的機械性質所產生的滲入(sink-in)與堆放(pile-up)的效應而造成作用力施加與卸載時，壓痕面積上的差異。不過，該兩壓痕面積的角度卻是一致的。（4）當該作用力隨著該壓頭施加於測試材料時，若該壓頭產生某一程度的偏斜ψ 或旋轉ω 時，該殘留於測試材料上之壓痕三角形仍然具有代表性。（5）藉由觀察該殘留於測試材料上之壓痕三角形，當該三角形無法成為一正三角形時，其係表示壓頭已產生偏斜或旋轉的之情況，需要進一步對該偏斜角度ψ 或旋轉角度ω 進行修正。（6）在壓痕偏斜情況下硬度值的修正方法以投影面積修正為最佳，其次是壓痕體積再其次是壓痕接觸面積方法作修正。（7）在壓痕偏斜情況下硬度值修正方法的硬度誤差敏感度則以投影面積為最佳，其次是接觸面積再其次是壓痕體積修正方法。（8）本研究提出之修正方法經由矽、鋁單晶壓痕結果驗證，足以說明適用於工程學上金屬材料進行奈米壓痕硬度檢測時更精確的數據獲得。