臺灣

本研究從理想城鎮(Ideal City)街道開始，討論平面上相異n 點到某一點的最短距離和。經研究後發現：當n 為偶數時，則到相異n 點的最短距離和所形成的區域可能是一個點、一個線段或是一個矩形；當n 為奇數時，則相異n 點的最短距離和所形成的區域將會退化成一個點。此外，本研究將理想城鎮的街道換成正三角形的街道幾何平面，同樣是討論平面上相異n 點到某一點的最短距離和。經研究後發現：當n 為偶數時，則相異n 點的最短距離和所形成的區域可能為一個點、一個線段、一個四邊形、一個五邊形及一個六邊形；當n 為奇數時，相異n 點的最短距離和所形成的區域則可能為點、三角形的情況。假使考量各點重要性的比重，分別加權後再求最小點。研究發現無論在理想城鎮或正三角形幾何平面上，皆可將各點視為多個權數相同之點重疊於此點上，便可利用先前的方式求得最小點區域。透過這次的研究，可以利用n 個相異點到某一點的最短距離和實際應用在貨物運送的問題或是消防設施配置等問題。The present study was intended to start with the Ideal City and proceed to discuss the sum of the shortest distance between a point and n different points on a plane. After the discussion, it was found that if n is even, the formed region could be a point, a line segment, or a rectangle. If n is odd, then the formed region must be a mere point. Further, the current study transformed the Ideal City into the geometric plane of an equilateral triangle. Similar to the previous discussion, if n is even, the formed region could be a point, a line segment, a quadrangle, a pentagon, or a hexagon. On the other hand, if n is odd, then the formed region could be a point, or a triangle. The result of this study, which investigated the sum of the shortest distance of a certain point to n different points can be applied to the real life situation, such as transporting goods or distributing fire control facilities.

牛樟芝(Antrodia cinnamomea)是台灣特有的原生藥用真菌，長期被民間認為具有治療癌症、腹瀉、高血壓或保肝的效果。本研究的目的是探討牛樟芝子實體乙醇萃取物對人類乳癌細胞的抑制效用，乳癌是全世界女性最常見的癌症之一，我們透過比較不同培養時期三個月(AC-3)、六個月(AC-6)及九個月(AC-9)子實體之化學指紋圖譜，並測試它們抑乳癌細胞活性之差異。結果顯示，培養三個月的牛樟芝子實體AC-3抽出成份對乳癌細胞的生長抑制作用最佳；而利用西方墨點法探討牛樟芝對細胞週期或凋亡相關蛋白質的變化，推測AC-3可影響乳癌細胞的細胞週期調控，並誘發細胞凋亡。未來我們將進一步深入研究牛樟芝子實體AC-3之抗癌作用機制，並研究對乳癌細胞轉移作用的影響，找出牛樟芝子實體中主要的抗乳癌活性成分。

三軸向六自由度動感平台（六軸平台）或稱史都華平台，最常見的用途是做為訓練用途的飛行模擬器或是娛樂用途的動感電影院。然而較鮮為人知的也被用於模擬地震來作為防震研究。六軸平台利用六支線性致動器的伸縮來控制平台姿態與加速度以製造出地震模擬波動來模擬地震。地震研究和人類生活最直接關係的就是房子的耐震研究。耐震取決於建築結構形狀及所使用之材料；結構決定了整個房子吸收或消除震盪能量的方式。本專題即是利用平台模擬集集地震和阪神地震來測試各種材料相同但結構不同之建築結構拓樸，以控制變因法來分析討論各種結構拓樸的耐震能力，把結構所能承受的最大相對振幅為數據做分析。本專題之部份研究亦參與2004年國家地震研究中心所舉辦之抗震盃競賽。 Three Axis Six Degree Of Freedom Motion Platforms, also named the Stewart Platform, are usually used for flight simulator in training purpose or for motion- theater in entertainment. Yet, the use of motion platform in earthquake simulation is rarely known in public. The motion platform uses 6 linear actuators to control position and acceleration to simulate earthquake. The direct connection between human life and earthquake research is to study quake-resistance of buildings. The quake-resistance depends on the structure and the material of the buildings. The structure decides how the building absorbs and/or eliminates the shaking energy. This project studies how different structure topologies stand in the simulated earthquake generated by a motion platform. Controlling factors method is utilized to discuss the quake-resistance of different structures. Data of the maximal resisted acceleration are also analyzed. A part of this research also participates in “IDEERS” contest held by the National Center for Research on Earthquake Engineering (NCREE).

In this research, we investigated the interactions between goldfish’ (Carassius auratus) sensory experiences (electric shock, high osmotic pressure and colors). We separated the sensory experiences into two parts. One of them, we used different kinds of environmental color-models to analyze goldfish’s environmental preference behavior and different kinds of stress experience(electric shock and high osmotic pressure) to build the animal model of environmental preference behavior. We found that goldfish prefer brown-colored environment (compared with white) and different stress has different effects on fish’s environmental preference behavior. It proves that fish has the ability to learn and memorize the stress experience and shows that there are complicated interactions among environmental stimulus, memories of stress and behaviors caused by different kinds of stress. Also, we investigated the interactions between spatial memory and color distinction. We measured the duration of goldfish getting through the color-marked barriers driven by regular electric shock. We found that goldfish spend less time to get through color-marked barriers than those unmarked. It shows that there are some interactions between spatial memory and color distinction. In conclusion, the research proves that different sensory experiences can affect goldfish’s behaviors.本實驗利用感官經驗(電擊、高滲透壓、色彩)，探討與朱文錦(Carassius auratus)行為調控的交互作用。我們將感官經驗分成兩模式：利用環境色彩特徵的差異，探討不同逆境刺激經驗(施予電擊或高滲透壓環境)，與魚類環境偏好行為的交互作用，建立朱文錦環境偏好行為之動物模式。我們發現朱文錦偏好土色環境(相對於白色環境)，而不同性質的逆境經驗，對魚類的環境偏好行為具有不同的影響，顯示魚類具有記憶逆境環境的學習能力，且證明「環境刺激—經驗(記憶)—行為表現」三者之間具複雜的交互作用。另外，我們亦探討空間記憶與色彩辨識的交互作用，利用規律的電擊刺激使朱文錦通過有色彩標示的關卡，以研究色彩差異與空間變化對朱文錦通過關卡能力的影響。我們發現色彩的標示可降低通過關卡的時間，且不同的色彩具不同程度的效果，顯示空間記憶與色彩辨識具交互作用。本實驗證明了不同的感官經驗或刺激，對朱文錦的行為調控具質與量的差異。

此研究的目的是要設計出一套完整編輯顯現數學式、加以計算，並求出解的一套方法與成品。而這項工作的執行者，在此稱之Equatetor 。一般的數學式子，若要計算的話，普通的計算機是不足夠的。原因是它們沒有辦法表現出數學式的「原貌」，例如分號、指數、函數、根號等數學符號混在一起時的情況。於是，我便擬定了一個研究，希望設計出一套更方便且實用的方法。換句話說，我要設計出一個功能強大的工程計算機程式。其中，自然牽扯到數學式子的顯現方式（以MathML 實現），以及計算機科學的演算法及資料結構。我主要的目的有四：(1) 顯示數學式(2) 方便編輯數學式(3) 計算數學式(4) 處理可以以不同形式輸出解答的計算（如輸出分數、根號、函數解等）。研究結果中，成功地運用XML 中的MathML 與二分逼近分數等演算法及若干資料結構，達到了以下實用的幾點：(1) 結構化的數學式編輯(2) 完整地顯示數學式(3) 正確運算並輸出運算式的答案(4) 提供一般數學形式之解（非小數之解）;The object of this study is to design a method and processor which is able to edit, display a mathematical expression representing a number, calculate and output the answer. The executor of this task is called Equatetor. Normal calculators are not adequate for this kind of task. The main reason is that they can’t reveal the original expression, such as fractions, radicals, exponents or mathematic functions. Therefore, a simple and convenient method is needed. To perform the possible way of handling those tasks, a computer program has been written. Several techniques were used, such as MathML, computing algorithms, data structures, and so on. Following are main purposes: (1) Displaying mathematical expressions. (2) Editing mathematical expressions simply. (3) Calculating mathematical expressions. (4) Outputting the answers(in different expressions). And the achievements:(1) Structured methods of editing of mathematical expressions. (2) Displaying mathematical expressions completely. (3) Calculating mathematical expressions precisely. (4) Offering answers in different expressions.

線蟲為植物發生病蟲害感染的病源之一，而台灣的松樹，目前正面臨著松材線蟲入侵的危機。從文獻的探討中，發現線蟲有其自然界的天敵 － 線蟲捕捉菌。本實驗著重在探討線蟲捕捉菌特殊的捕捉機制。當線蟲捕捉菌附近出現線蟲時，會展生誘引線蟲的物質，並設計了一步步的實驗，去探討此誘引物質的捕蟲效能及其成分。現在，已經發現此誘引物質為一揮發性氣體。往後將會設法增加其誘引氣體的產量，並使用氣相層析儀分析之。最後希望可以將此物質應用到微生物防治上，期望能解決台灣松樹被線蟲感染的問題。 In Taiwan, all of the pine trees have one common problem - nematodes, which causes diseases in plants. And this experiment focuses on the nematodes’ natural enemy - nematophagous fungi and its “peculiarly caused mechanism.” When nematodes appear near nematophagous fungi, the latter will produce some substance to tempt the former. To investigate this alluring substance, a series of experiments are done and systematic steps are taken. The first finding is that this substance is a volatility gas. Later in this research, measures will be taken to make “rematophagous fungi” produce more of this gas. And “gas chromatograph” will be used to analyze this gas in the future. Finally, the possibility of applying this substance to the defensive measure of microbiology will be discussed.

掃描式穿隧顯微鏡(Scanning Tunneling Microscope)，是在奈米尺度下觀察物體表面的一大利器。但一台精密的STM，造價動輒數百萬元新台幣，本研究嘗試利用簡單、便宜的材料，製作一台簡易的掃描式穿隧顯微鏡。眾所皆知：掃描式穿隧顯微鏡的關鍵，就是量子力學中的穿隧效應原理，及壓電材料的應用，所以這些主題都是本實驗涉及的內容。除此之外，我們也運用簡單的物理原理，取代價格高昂的儀器，例如：利用彈簧代替昂貴的避震系統等。此研究利用穿隧效應的原理，並進而利用電腦得知樣品表面的結構，以達顯微鏡觀察分析物體之功用。 ;The major purpose of our project is to assemble a simple scanning tunneling microscopy with cheap and available materials for ordinary senior high school students. For example, we use springs for damping instead of electromotive force device. Weweld all the electronic circuit boards for ourselves in order to not only lower the cost but also inspect the inner structure more clearly and precisely. After the microscopy is assembled, we will use it as an appliance to observe the samples of nano-particles. We must repeat this procedure several times so as to make sure that the images we’ve gained is true, not just some disturbances produced by the environment. Finally, the microscopy can be applied to research fields as well as academic courses.

We report an investigation on the synthesis, characterization, and application of photonic crystal. In the study of the synthesis of SiO? nanoparticles for the building blocks of photonic crystal, it is found that by changing the concentration of NH3 solution, we are able to control the size of SiO? nanoparticles. After trying several different methods, we discover that the vertical substrate method is the best way to arrange nanoparticles into a periodic structure. From scanning electron microscope, we confirm that SiO? nanoparticles can form a three dimensional hexagonal photonic crystal. From transmission experiment, we find that the wavelength of the minimum transmission is proportional to the size of nanoparticles. This result implies that using photonic crystals we can control the behavior of electromagnetic wave. Finally, we fabricate CdS nanoparticles on the top of photonic crystals with different diameter of SiO? nanoparticles. Using photoluminescence measurements, we show that by controlling the lattice constant of a photonic crystal the luminescent efficiency of CdS nanoparticles can be substantially enhanced. Out results, therefore demonstrate that photonic crystals are very important for the application of light emitting devices. 本研究主要是著重於探討光子晶體合成、特性分析及其應用。在有關合成光子晶體之奈米二氧化矽顆粒方面， 發現在合成過程中利用氨水的溶量可以控制顆粒的大小。在將奈米顆粒排列成光子晶體的研究中， 嘗試了多種方法後， 發現垂直基座法為最快速有效的方法。從掃瞄電子顯微鏡的觀測， 證實奈米顆粒是以六角對稱排列成整齊的光子晶體。在光子晶體的特性分析中， 利用光穿透實驗， 發現電磁波穿透率最小的波長與奈米顆粒成正比關係， 這顯示出可以利用光子晶體來控制光的行為。最後，本研究將光子晶體與硫化鎘奈米顆粒結合，經由光激螢光譜， 證明光子晶體確實可以增進物體之發光效率,這對發光元件的應用， 將有很大的幫助， 可以節省大量的能源

本研究主要是探討液晶面板在不同的電壓下，對紅外光區及可見光區之穿透光譜。藉由控制外加液晶面板兩側的電壓，改變內部的電場強度，驅使液晶分子長軸方向改變(偏轉)，以達到控制穿透率之目的。施加於液晶面板兩側的電壓V大於起始電壓V0時，液晶分子長軸受電場作用與電場方向平行，減弱引導偏振光扭轉之能力，讓部分光通過偏振片。令及分別代表穿透率達到最大穿透率之10%及90%時的外加電壓，則定義「光-電開關斜率」γ為：γ =(V90-V10)/V10。透射光強度與外加電壓關係曲線則稱為「光-電開關特性曲線」。穿透率除與液晶分子之旋光程度有關，我們也做了在不同電壓下，液晶分子之穿透光譜，並討論其特性。The main idea of the project is to discuss the transmittance spectra of liquid-crystal device in the range of infrared and visual light (400~900 nm) with different electric field by changing voltage. Different biases are applied to the liquid-crystal cell, causing the axis of liquid-crystal to rotate, and the transmittances are measured. If the application of bias is greater than the threshold voltage (V0), the axis of liquid-crystal will be parallel to the electric field, and make the beam pass through polaroid. Electro-optical switching slope γ is defined as γ =(V90-V10)/V10 , where V10 and V90 are the applied voltages enabling output light signal reaches up to 10% and 90% of its maximum intensity, respectively. It is understood that transmittance depends on the optical activity of liquid-crystal cells. Besides, we will discuss the relation between wavelength and transmittance of liquid-crystal cells.

In this study, we mainly explore the geometric construction in 3D. By conducting some problems about constructing circles, we define the PLC construction in 2D as constructing a circle, either passing through a given point (P), tangent to a given line (L) or tangent to a given circle (C). Besides, we aim to discuss the properties of the PLC construction and the relations between each other. We discover if we find a plane satisfying certain conditions in space, the properties in the PLC construction can apply to such a plane. Furthermore, we extend the properties in PLC to the PES construction in 3D, defined as constructing a sphere, either passing through a given point (P), tangent to a given plane (E) or tangent to a given sphere (S). Also we discuss the relations among them.這個研究主要在探討3D 的尺規實作。藉由歸納某些有關作圓的題目，我們定義2D 中的PLC作圖─作圓，過已知點（P）、切已知線（L）、切已知圓（C）。並探討PLC 作圖的性質及彼此的關聯性。而我們發現：在空間中只要找到滿足特定條件的平面，則2D 幾何作圖性質在該平面仍能沿用。此外，運用PLC 作圖性質，我們進一步推廣到空間中的PES 作圖─作球，過已知點（P）、切已知面（E）、切已知球（S），並探討各個類型間的關聯性。