臺灣

本研究利用偏振片、量角器為刻度盤、雷射光為光源，及照度計為偵測器，組裝一個簡易且可靠的旋光度計。我們利用單位時間旋光度的變化量當作反應速率，來測量蔗糖的水解速率，同時求出蔗糖水解反應的反應級數、速率常數(k)。利用糖類的旋光度具有加成性之特性，找出不同混合比例時的旋光度，追蹤實際蔗糖水解的每個狀態，找出最後平衡狀態，同時將蔗糖水解平衡結果顯示，旋光度與濃度有線性關係，而蔗糖水解反應對蔗糖而言為一級反應。接著，我們在蔗糖水溶液中加入不同種類的酸，探討催化劑的種類與蔗糖水解反應速率的關係。 In this research, in order to measure the optical rotation accurately without expensive equipments or complex process, we assembled a polarimeter by ourselves. With simple materials which can be found in ordinary senior high school laboratories, including a calibrated scale, a simple Luxmeter, a laser as the photo source, and other side devices. The Polarimeter ended up operating fluently and accurately. We put the laser under a tube, which has two pieces of polar screens on the top of it and on the bottom of it, ,and put a luxmeter just above the tube. When we slowly rotate the polar screen on the top, the figure shown on the luxmeter changes. By numerical analysis, we can get information about the hydrolysis of polarized substance. Secondary, we measured the optical rotation of glucose, fructose, malt sugar, galactose, and sucrose to get their specific rotation. Then we measured the optical rotation of sucrose every five minutes. By doing this, we could keep track of the hydrolysis rate of sucrose, figure out the order of reaction, and the rate constant (k) and the equilibrium constant (K). Thirdly, we used different kinds of acids into sucrose solution as the catalyst, and observed the effect. The result showed that hydrochloric acid is a better catalyst to this reaction than sulfuric acid and nitric acid. The polarimeter of this research can be used in science education of junior and senior high school. By teaching students to assemble and operate the self-made polarimeter, students can know better about optical rotation and polarized substance. Also, the interest in this experiement will add to students’ motivation to do science research.

本文藉由模糊數學理論所提的分類方式，來設計一套對於DNA序列的分類方法，並利用了40筆人工已分完的樣本，分別作為測試及學習樣本。\r 發現可以順利的將每筆DNA序列中的鹼基每3個一組轉成胺基酸序列，再利用模糊分類方式將所有胺基酸序列進行分類，最後並利用原先滾動方式的環狀排列方式，來對同一筆鹼基的3組胺基酸資料進行檢核，發現可以有效提高分類的正確性。\r 之後我們再利用182筆自然樣本進行檢檢，也發現模糊分類方式亦可正確完成此次分類結果。

可聽聲有向四周擴散繞射特性，而超聲波具有指向性，改以超聲波載送可聽音訊號後，其載波與旁頻帶均在超聲波範圍，實驗中人耳卻可聽到高度指向性聲音，且調幅解調後的可聽聲衰減率比純超聲波來的低。那為什麼超聲波會解調可聽音？我們以非線性的數學轉換概念，成功以數學推導解釋實驗中所聽到的可聽聲，是由旁頻經由非線性轉換而來的。為了證實空氣中的超聲波有非線性現象，以發射40KHz單頻訊號，除了接收到40KHz訊號外還可接收80KHz訊號，而80KHz訊號振幅，會隨著發射強度而遞增，也會隨著傳輸距離增加至穩定狀態，這所我們從文獻中的非線性理論所吻合。接下來進行調幅超聲波實驗，我們經理論計算旁頻帶強度為頻率響應與調變率乘積的一半，而解調可聽聲的強度為調變率、頻率響應與非線性係數三者乘積，我們也由實驗數據證實理論計算結果，在實驗中，換能器在40KHz有最佳的頻率響應，其非線性係數與所載送可聽聲頻率高低約略成正相關，並且與換能器距離遞增而越遠而增加。此外在提高高指向可聽音輸出功率方面，除製作專屬的放大器、運用方波取代正弦波來載波、配合陣列換能器輸出；在改善音質方面，利用等化器調整訊源頻譜分佈，降低低頻振幅，增強高頻振幅，讓各頻率的原始訊號都能有適當的調變，達到最佳音質。The audible sound has the characteristics of spreading and diffracting. And ultrasonic is directive. We modulate sound into ultrasonic signal. The carrier and sideband are ultrasonic frequency bands. But in the experiment, human can hear highly directive sound. In terms of attenuation rate, AM demodulation sound is lower than pure ultrasonic wave. Why can human hear the directive sound? By using the nonlinear mathematical transform, we managed to explain the audible sound which is transformed from sideband with nonlinear effect in the experiment. In order to confirm that nonlinear phenomena in the air ultrasonic, we launch 40KHz single tone ultrasonic signal. Besides the 40KHz signal, we also received 80KHz signal. The amplitude of 80KHz signal will increase with the emission intensity, and also with the transmission distance to increase its stability. These are consistent with nonlinear theory in the literature. Next we began AM ultrasonic experiment. We calculated the sideband intensity that is the product of frequency response and modulation index. The demodulation sound intensity is the product of modulation index, frequency response, and nonlinear coefficient. We also proved the calculated consequence through the experiment. In the experiment, the ultrasonic transducer has a best frequency response in 40KHz. The nonlinear coefficient has positive correlation with the modulation frequency, and increases transmission distance. To boost the power of directive audible sound, we made an amplifier, using square wave to replace sine wave of carrier, and in conjunction with array transducer output. To improve the sound quality, We use the spectrum-Equalizer to adjust the frequency distribution of the origin signal. The EQ reduces the low-frequency amplitude, and boost high-frequency amplitude, which enables every frequency of the original signal to be properly modulated, achieving the best sound quality.

本實驗以吸附染料之二氧化鈦奈米結構電極層為承載基材的太陽能電池為研究對象，旨在增進其光電轉換效率，促使染料有效地吸收光能後造成電荷分離，再經由二氧化鈦傳導帶向外傳出而形成電流，即所謂染料敏化太陽能電池。實驗主軸共分三：1、合成染料N3：觀察吸附度與浸泡時間之關係，發現在18~20 小時電池有最佳吸附；改變電解液濃度，求得最佳電解液濃度範圍；酸化二氧化鈦極板。2、天然植物色素：改變溶劑，得出高極性之丙酮對電池最佳；酸、鹼化植物色素；觀察電池隨著光照時間增加，性質趨於穩定。3、混合色素與染料：此實驗旨在印證不同吸能範圍之染料在極板混合浸泡後，電池吸能帶是否有疊加、擴充的效果，並觀察分開浸泡與混合色素一起浸泡之不同效應，量測IPCE 以玆比較。實驗結果可知，確實對於電池吸光範圍有所增加，且分開浸泡之效果較好。This experiment is mainly about the phtosensitization of Ti02 solar cell, aiming at improving the energy conversion efficiency, promoting the electric charge to separate from TiO2 and spread out through after the dye absorbs light. That is so-called dye-sensitized solar cell. The experiment mainly divides into three parts: 1. Ruthenium(II): Observing the connection between adsorption and dipped-time, find out that solar cell has best to adsorb in 18 to 20 hours; change the concentration of electrolyte; acidification TiO2. 2. Photosynthetic pigments: Change solvent, and get the conclusion that pigment has better adsorption in high polar solvents such as acetone; acidification/basification pigments; observe the changing of energy conversion efficiency while the illumination time increases. 3. Mixed the dye and pigment: This experiment is aim at proofing that the absorption spectrum of soaked-TiO2 may mix after dipped in different dye and pigment. Furthermore, we compares the differences between TiO2 dipped in one mix solution and dipped in several solutions separately, measure its IPCE. According to the experiment, the spectrum of soaked-TiO2 is certainly larger, and dipping in solution separately has better effect to the battery.

由於台灣山區溪流短小陡急，土石流災害嚴重，透過式防砂壩攔阻工法為現\r 今之趨勢，而帄面透水柵具有一般透過式壩的優點，不但能將土石流轉化為水砂\r 流，還可以減低土石流衝擊力造成的損壞及改善上游儲砂空間不足的問題。本研\r 究採用改良式帄面柵，在下游處增設分流河道，可改善分離出之細顆粒土砂水與\r 大礫石再度結合之危險。此工法於2003 年引進台灣後，尚未廣泛應用，主要原因\r 為缺乏設計之經驗式，因此本研究針對透水柵的柵棒長度（L/ Dmax）、棒淨間距\r （b/ Dmax）、柵面架設方式、柵面篩分角度（θ）等多項重要因子進行室內渠槽\r 試驗，最後提出土砂篩分比與攔阻率的趨勢方程式，設計時以總攔阻率（R）高為\r 原則，輔以篩分比（S）與貯砂率（R1）高，即可有良好之成效，期望能作為國內\r 外現場工程施做時之參考，結果如下所示。

Refer to Figure 1. Suppose ABCD is a trapezoid and . Passing the intersection M of and we construct a parallel line intersecting and at E and F, respectively. We obtain that , and then we can generalize the result. 如(圖一)，若ABCD為梯形且，過 和交點M 分別作平行線交、 於E 、F ，可得 的關係，再加以推廣。

記得小時候常玩大富翁，在走步數之前常要由擲骰子來決定。又在上國中之後學到了有關機率的問題，所以讓我想起此事，想藉由此次的科展對大富翁內的機率做一番徹底的研究與了解。

磁粉探傷過程包含兩個重要的物理現象，其一是磁力線於工作瑕疵處的漏磁現象而形成邊緣磁場，其二是鐵粉顆粒受邊緣磁場的影響而向工作瑕疵處附近聚集現象分別反應出磁場在通過不同介質時所遵循的折射原哩，以及磁場分佈對鐵粉顆粒產生的磁力原理。本研究以電磁通電產生靜磁場，並利用兩電磁鐵間的氣隙來模擬工件瑕疵，因電磁鐵的磁導係數遠大於空氣之磁導係數而造成漏磁場方向機與漏磁面垂直，形成一單純的邊界條件使得邊緣磁通密度的解析解可直接利用馬克斯威爾方程式求得。我們亦導出空氣中的磁通分佈對微小的鐵粉顆粒所產生的磁力公式，發現鐵粉顆粒受靜磁力的大小與該顆粒的體積、磁通密度與磁通密度之梯度成正比，而其方向則與磁通密度之梯度一致，此結論與磁粉探傷過程中，鐵粉向工件瑕疵處聚集的現象吻合。實驗設計採用螢光粉混合鐵粉以獲致明顯的鐵粉顆粒運動軌跡，用數位錄影機紀錄後再擷取影像圖檔判讀其位置與時間之關係，進而反算鐵粉顆粒之位置與所受之靜磁力的關係，以定量的方式證實所推導的邊緣磁場分佈公式以及磁力公式。Two important physical phenomena are observed in the practice of magnetic particle inspection (MPI). The first one is that leakage flux is present in the defect area of the work-piece under inspection. The second one is that magnetic particles aggregate in the vicinity of the defect. These phenomena manifest the theory of flux refraction, which occurs in the intersection area of two different magnetic materials, and the theory of magneto-static force, which is experienced by the iron powder in a magnetic field distribution. Two electromagnets, made of cast steel, are aligned together such that the leakage flux in the air gap forms a fringing field distribution. It is this magnetic field distribution that simulates a defect area in a magnetized magnetic work-piece. Since the permeability of cast steel is far larger than that of air, the direction of the fringing field at the surface of the electromagnets is almost perpendicular to the surface. Such a simple geometry renders an analytical solution to the Maxwell’s equations. The magnetic force of the magneto-static field exerting on the magnetic particle, an iron powder in this case, can be derived by using the principle of virtual displacement. We obtain a formula of magnetic force, whose direction coincides with the gradient of the magnetic flux density and whose magnitude is proportional to the magnitude of the particle volume, the magnetic flux density and its gradient. This formula also agrees with the observation in MPI that the magnetic particles aggregate in the vicinity of the defect.

設Γ為一平面曲線而 P 為一定點 , 自P 向Γ所有的切線作對稱點，則所有對稱點所成的圖形Γ1 稱為曲線Γ對定點P 的double pedal curve , Γ1 對定點P 的double pedal curve Γ2 稱為曲線Γ對定點P 的2-th double pedal curve , Γ2 對定點P 的double pedal curve Γ3 稱為曲線 Γ對定點P 的3-th double pedal curve ,…… 。以下是本文主要的結果：結論A：當Γ為一圓形而P 為圓上一點時 , 計算其n−th double pedal curve 的方程式。結論B：當Γ為任意平滑的參數曲線而P 為任意一點時 , Γ的 double pedal curve 的切線性質。結論C：當Γ為任意平滑的參數曲線而P 為(0,0)時, 計算其n−th double pedal curve 的方程式。 Given a plane curve Γand a fixed point P ,the locus of the reflection of P about the tangent to the curveΓis called the double pedal curve of Γwith respect to P.We denote Γ1 as the double pedal curve of Γwith respect to P, Γ2 as the double pedal curve of Γ1 with respect to P , Γ3 as the double pedal curve of Γ2 with respect to P ,and so on , we call Γn the n-th double pedal curve of Γwith respect to P. If Γ is a circle, and P is a point on the circle, we got the parametric equation of the n−th double pedal curve of Γ with respect to P. And, for any parametric plane curve Γ; we got the method to draw the tangent of the double pedal curve of Γ.

去年(民國九十年)，我們在國中地科課本第六章「多變的天氣」中看到一段不懂的話:「颱風移到高緯度的海面以後，也會因低層水氣的供應變少變弱消失。」(104頁第二行)請教老師之後，疑惑未解。師長們幾番鼓勵之後，我們這群對大氣現象原本就充滿無限好奇的國中生便想試試能否一探問題真相，想到能夠挑戰學生心目中至高無上的課本，我們真的是非常興奮!\r 經過數週的資料蒐尋與交叉討論之後，我們發現這並不是件容易的事，事情並非我們想的那麼簡單。於是，在大家冷靜沉澱 想法之後，我們便把焦點放在颱風與地形的交互作用上，先從難度較低的項目開始學習。