臺灣

在夏日的午後，在炎熱的柏油路面上很容易可觀察到遠方的 路面上，出現如鏡子般的倒影，看起來彷彿前方有一灘水，但當 我們向前進一些時，倒影卻突然消失了，這個現象，一般稱為海 市蜃樓。 一般解釋海市蜃樓的成因，都是由於在上層的低溫空氣，和 在下層靠近路面的高溫空氣，因密度的不同，以致於折射率的漸 層差異，繼而產生全反射。 但我們觀察發現，地面與上層空氣的溫差，並非柏油路面上 假積水現象及倒影出現的必要條件；反而和入射光的角度、路面 的平坦程度及路面的性質有關。我們提出了粗糙面在入射光的入 射角接近90度時，可發生單向反射的模型。並由實驗來驗證假積 水現象及倒影主要的成因是「柏油路面的單向反射」而非「空氣 的折射與全反射」。 Under the scorching sunshine, we can see the reflection on the tarmac in the distance just like a water puddle on the road. And the water also reflects the people and object nearby. But, in fact, the tarmac road over there is very hot and dry. Therefore we call the phenomenon as the “false water puddle on the tarmac.” According to the textbook , the main reason for “false water puddle on the tarmac” is that the temperature difference leads to the refraction of the light and causes the phenomenon. However, from our observation, the theory still can’t explain some phenomenon, For example, the “false water puddle on the tarmac” remains to appear when the wind blows fiercely. Even with little temperature different at night the phenomenon is still obvious. Therefore, in our opinion, the temperature different of the air is not a necessary condition of “ the false water puddle on the tarmac.” We bring up the model to explain the phenomenon that when the incident angle of the light approach 90 degrees, the light will result in one-way reflection. According to the model, furthermore, we make experiments at midnight and at dawn. The result of the experiment assures us the hypothesis of the model, Consequently, we hold the ideal that the main condition of the “false water puddle on the tarmac.” Is not because of the refraction and the total reflection but because the light reflects off the road and result in the one-way reflection on the tarmac road.

蜜蜂(Apis mellifera) 可以透過視覺經驗的累積與學習，增加辨識影像的正確率，這種透過先前學習過的經驗而增進視覺辨識的能力，與一般所熟知在視覺上是由眼睛將影像訊號傳至大腦進行辨識的過程恰好相反，因此被稱為top-down process。 \r 我們以Y型迷宮進行蜜蜂的行為實驗，制約訓練蜜蜂辨識文字影像。蜜蜂能在訓練後成功地辨識文字，並建立所謂top-down process的現象：無法直接辨識複雜的文字影像→經過提出的簡單影像特徵進行訓練後→能顯著地辨識原來的複雜影像。可見蜜蜂能夠藉由經驗中的提示訊息辨識影像。 \r 若以「提示形狀」、「提示位置」、「提示正確端」及「提示錯誤端」等不同影像特徵進行實驗，則發現蜜蜂會擷取形狀或正確影像的訊息，在記憶中形成較深刻的經驗，增強辨識能力。 \r 蜜蜂能夠辨識文字，且能在短時間內擷取重要的影像特徵，做為執行top-down process的經驗。蜜蜂只用不到1 mm3的腦部處理複雜的視覺訊息，牠們的行為與神經機制值得我們繼續深入探討。

「翻車」事件令人怵目驚心，輕則車毀，重則人亡。減少翻車事件，可減少悲劇的發生。而翻車絕大多數均發生在轉彎的路段，且伴隨著超速發生。因此，本研究乃針對汽車過彎行駛，探討其翻覆的原因以及改進之道 · 本研究乃利用實驗分析法以及理論驗證法進行研究，實驗中變化不同的汽車質量，車軸寬、車身高以及車軸寬/車身高，質量重心寬、高以及寬/高、傾斜度以及迴轉半徑等九種參數 · 於自製的紅外線偵測變頻式可調迴轉模擬機上以八部模型試驗車測試其翻覆轉速，並換算為翻覆速度後逐一分析討論之。經由實驗結果，本研究得到以下結論：一、汽車轉彎翻覆與離心力有關，當離心力大於臨界側向推力時，汽車即翻覆。臨界側向推力公式為 F = mg ( tanθ + K?) / ( l -K? tanθ ) 二、最大容許車速平方與轉彎半徑及質量中心寬高比相乘積成正比；而在定車速下，飲小客許轉彎半徑與質量中心寬高比成反比．前述各項皆與質量大小無關．三、提高轉彎路面傾斜度對防止汽車翻覆有確實的效果。而最佳的過彎防止翻覆方法是降低車行速度，提高轉彎半徑，增加路面外側傾斜度，以及提高汽車質量中心寬高比”四、汽車過彎不致翻覆的最大極限速度 Vc 以及最小轉彎半徑rc分別為 vc=〔 rg ( tan θ + K ?）/ ( l 一 K ? tanθ ) ]; rc =（ V2 / g ) ( l 一 K?tanθ ) / ( tanθ + K? ) 五、本實驗所設計紅外線偵測變頻式可調迴轉模擬機，可有效的模擬汽車過彎翻覆，適用於中等學校物理、力學等學科的實驗課程。The accident of overturning a car always results in both destroying the car body and the death of the people. This project is to investigate what factors would have an effect on overturning a car and how to prevent a car from overturning.This project explores the factors by varying the mass of the cars, the distance between axes, the height of the car body, the ratio between the axis distance and the car height, the central gravity, and the declination. We test and record different overturning rotating speeds of eight model cars by a self-made adjustable simulator with a varying frequency infra-red detector. According to the experiment, the following results are obtained. I. The overturning occurrence is as a result of the eccentric force over the critical lateral force. The critical lateral force is F=mg(tanθ +K?)/(l—K?tan θ) 2. The square of allowable maximum speed is in proportion to the product of turning radius and ration of width to height for the center of mass; however, the allowable minimum turning radius is inversely proportional to the ration of width to height for the center of mass under constant vehicle speed. The above inference is independent of the mass of vehicle. 3. Increasing the declination can prevent a car from overturning. 4. The maximum speed for a car turning without overturning is Vc. The minimum turning radius is r. Both are expressed as follows:Vc=[rg(tanθ +K2)/(1—K?tanθ );rc=(’V2/g)( I —K?tanθ )/(tanθ +K?)5. The self-made adjustable simulator with a varying frequency infra-red detector can be used in the experiments of the middle school science curriculum.

塑膠一向被認為絕緣體。但Heeger，MacDiarmid，以及Shirakawa證實，塑膠可以被改製成電的良導體。這須在高分子合成的過程中，使碳鏈呈現單、雙鍵交錯排列情形。此外，高分子也須加以摻雜(doped)，換言之，電子必須在氧化過程中被移除或在還原過程中被加進聚合物。電子移除所留下的電洞，或新加進的電子則可自由在分子鏈上移動，形成導電性。我們所要製備的導電高分子二次電池就是由這個原理完成的。所謂的二次電池(Secondary Cell)簡單的定義就是「可反覆充電、放電，循環使用的電池」，我們將會將其與市售電池比較，並改良出合適商品化的高分子二次電池。我們將以聚苯胺做為我們電池的正極，並用鋅片(原本我們要用鋰金屬的，但其再空氣中即易氧化，因此改採鋅)做為負極，製成一聚苯胺二次電池。The plastics is thought to be a insulator, but Heeger, MacDiarmid, and Shirakawa had proved that conductivity of plastics can be improved by doping other media. The conjugated polymers such as polyacetylene、polyaniline have the interlaced single-double bonds that electrons can move from one side to another side caused the production of electric currents. The purpose of this study is try to study the application of the conjugated polymer polyaniline to make a secondary battery. First, we use the chemical and electrochemical method to compose the polyaniline. Then we test the conductivity of the produced polyaniline and test the current and electrical potential of the polymer battery. The battery that we made from our laboratory has the electric potential about 0.5 volts and the electric current is greater than 50 microamperes. Finally, we also try to use the lithium as cathode to improve the performance of the polyaniline battery.

When we were learning about organic compounds at school ,there was a unit discussing the isomers of alkane .Our teacher made us practice drawing all the structural formula of the isomers from hexane to nonane .We were much interested in the subject .However ,we often missed or duplicated some isomers .Thus , we began to think if it is possible to find a way by developing programs to let the computer calculate the exact number of the isomers of alkane . After discussion ,we set up a complete coding system .We numbered the isomers in the way that computers could decode and then wrote them in C language. Through computer execution ,the numbers of the isomers from C1 to C20 all match those on the reference website. According to the same concept , we also find a way to calculate the number of alkane with one substituted group . In the future,our goal will be focused on the research of multi- substituted alkane and cyclokane. In addition , the ionic crystal accumulation model are so variable. Take the double face-centered accumulation of NaCl for example, when the ion pairs are extended to the infinity , the potential energy of attractive field will approach a constant which is named as the Madelung Constant. We also managed to write a computer program with C language to approach this convergence with three models, including cube , octahedron , and sphere . The result turned out to be that the data of the sphere was less stable . In the other two models , when “n” is up to 43 layers , the data is identical with that on the reference website to the eight decimal point . 在學校裡學習有機化合物有關烷類異構物這個單元，老師讓我們練習畫出己烷~壬烷的所有異構物結構式，這引起我們極大的興趣！但常一不小心就漏掉或多出幾個，我們開始思考：能不能找到一個方法並設計成程式，讓電腦執行以找出烷類異構物？經過討論，我們建立了一套完整的編碼系統，將各異構物以電腦可解讀的方式編號，並以C 語言寫成程式。透過電腦執行，各碳數化合物自C1至C20都與參考網站吻合。依相同觀念，我們也設計出烷類含一個取代基的異構物數目。將來努力的目標為：多取代基及環烷類之研究！另外，離子晶體堆積模型變化多端，以NaCl 雙面心堆積為例，其引力場位能，當離子對延伸至無限大時，這個值將趨近於一個常數，又稱為馬德隆常數。我們嘗試以C 語言設計電腦程式，用三種模型（正立方體、正八面體、圓球）來逼近並求得這個收斂值。執行結果是：圓球數據較不穩定；而另二種模型到n=43 層以上，其數值大小與參考網路上的數值，在小數點以下8 位完全相同。

本研究探討在給定範圍的面積下，以最省錢的方式用籬笆圍出最大的矩形土地，其中矩形的邊長為正整數，且矩形對邊使用相同單價之材質的籬笆，但相鄰邊使用不同單價之材質的籬笆。我們希望透過轉換，將單價不同的情況回歸到單價相同的情況，以便完整的解決這個問題。\r 藉由改變邊長，將 轉換成 ，使問題轉換成相鄰邊之單價相同的情況；但是經過運算找出的最佳解 轉換回 後卻不一定符合「整數邊長」的要求(即 和 不一定是整數)。為了解決這點，我們重新以不同的角度探討單價相同的情形，以找出整數的最佳解。\r 最後我們發現，若 和 切線斜率的差值大於或等於1，則 坐標愈近 的解愈佳，而在差值小於1的範圍內，我們提出一個檢驗法，可以找到整個問題的最佳解，同時讓此最佳解 轉換回 後仍符合「整數邊長」的要求，進而解決問題。

給定一個P∈(0,1),令k0=0, p0=p，定義k1為能使 的最小正整數k，而 ; 相同的，對於給定的kn-1, kn 為能使的最小正整數k, 。若存在kn 使得，則稱p∈ In; 若對於所有n 與kn ，，則稱p∈ I∞。如此區間(0,1)可分解成集合I1,I2,…,I∞。

有毒重金屬是一個全球矚目的環境污染問題，為了解決這問題，人們常使用沈澱法和螯合劑兩種主要化學手段來吸附重金屬物質，這些方法的缺點是在某些情況下(如:酸雨)，重金屬可能會再溶出污染環境。本研究旨在提出一個低成本且環境友善，能整治重金屬污染的新方法，使用牛糞來吸附重金屬離子，再將此已經吸附重金屬的牛糞回收製成觸媒。研究發現摘要如下: (1).磷酸鹽適合作為吸附劑，以穩定重金屬離子。 (2).發酵處理的牛糞由於微生物分解有機質，使成分中磷酸鹽含量變高，牛糞磷酸鹽愈高吸附重金屬離子的效果愈好。 (3).牛糞置於Cu2+、Ni2+水溶液，能有效吸附Cu2+、Ni2+離子，在應用上可預防重金屬污染地下水源。 (4).模擬土壤淋融的實驗中，超過99%的金屬離子可被牛糞固定於土壤中。 (5).回收吸附的重金屬離子牛糞，製作成活性碳觸媒，可進行脫色實驗，達到回收利用的目的。

In the previous year study, we assumed that the fish basin as a column-shape model in order to exam and explain how the water spouting. This year, we established a reality-like situation of the fish basin to construct our theory base. At this point, round-waves and up-down waves are found as the beginning point of the water spouting. The sound from the basin is the frequency of the vibrations. Meanwhile, this process enables us to understand the causes of four, six, and eight waves. In addition, we tried to change the basin's positions, the capacities of water, the densities of liquids, and the sizes of the containers to demonstrate the theory. Furthermore, we used similar containers, such as high-heel cup and big magnetic bowl to experiment. The results are also corresponded with the theory. These results can also be used to explain the Chinese aeolian bell, clock, shaking bell, etc. That is a major innovation for us. Finally, we obtain better understanding of the abstractive theory though the simulation of the computerized photographs. 魚洗，也稱龍洗，傳說是中國唐宋時代皇帝洗臉的臉盆，內底四條魚紋，麟尾畢具。洗內盛水後，用手摩擦其兩個雙耳，立即發出響亮的嗡鳴聲，並出現美麗了漣漪，水珠四濺，摩擦越快，聲音越響，波浪翻騰，水珠越烈。對此在上一年度的研究中，是將洗盆視為圓柱狀，然後由圓柱狀所建立的模型去解釋水跳的原因，初步瞭解了水跳的原因。今年我們以洗盆真實的情況建立理論模型，在殼體產生共振的圓形駐波及上下駐波，此為水跳產生點，此時殼體發出的聲音就是共振的頻率。也瞭解了有四個、六個、八個、十個波腹的原因。並以改變殼體不同位置、水量、液體密度及洗盆大小等變因應證模型，結果與理論相符合。繼而以高腳杯、大磁碗等類似魚洗盆構造的容器，加以實驗應證，也能符合此理論。甚可推到中國古時候的編鐘、搖鈴、風鈴等器材。對於我們總認為碰撞就產生聲音的觀念實是一大突破。最後經由電腦動畫的模擬，讓此抽象的理論更容易瞭解。

George Sicherman discovered that it is possible to take a couple of 6-sided dice re-labeling them with different positive integers (1,2,2,3,3,4) and (1,3,4,5,6,8) having the same probability distribution as rolling a standard pair of 6-sided dice. Such unique pair of dice is calling Sicherman dice. The secret behind the Sicherman dice can be studied by combining the powerful mathematical tool “Generating functions” with the symbolic manipulation software “Derive 6”, The same procedure may be applied to studying the possibility of the generalized Sicherman dice along the consideration of :\r (1) Adding more dice. (2) Changing the number of faces. To this end, we introduce the concept of the Sicherman Bound. For a given integer n, the number of n-sided Sicherman dice is finite. We computed manually such numbers for n?50 based on the method of “Elimination of negative terms”. Sicherman Dice 就是一對點數配置與正常骰子(6 面正立方體，點數為1到6)不同的骰子，它所拋擲出的每一種不同點數和(2,3,4...,12) 的機率恰好與一對正常的骰子相同。這種骰子是美國的Col. George Sicherman 所發現的。 Sicherman 更進一步指出：在不使用Sicherman Dice 的情形下，不可能找到一組大於或等於三顆的非正常骰子，它們拋擲出的每一種不同點數和的機率恰好與一組同數量的正常骰子相同。本研究的目標在於1. 尋求計算「Sicherman Dice 的組合和正常的骰子有相同的出現機率」的方法2. 證明Sicherman 結論的真偽及是否適用於其他正多面體(4 面/ 8 面/12 面/ 20面) 的標準骰子3. 修正Sicherman 的結論，並定義Sicherman 極限(Sicherman Limit)。在假設n面正多面體(n 為自然數， n ? 50 )存在的情形下，探討每一個正多面體的Sicherman 極限4. Sicherman Dice (Crazy Dice) 的延伸探討(1) 不同面數骰子的組合，是否可以找到面數組合相同，但點數配置不同的Crazy Dice( 如4 面與6 面的標準骰子組合，找到4 面與6 面的Crazy Dice)(2) 多個面數相同或不同骰子的組合，是否可以找到面數、個數及點數配置皆不同的Crazy Dice ( 如3 個4 面標準骰子組合， 找到2 個8 面的Crazy Dice)在研究的過程中，我發現以下的現象：(1) Sicherman Dice 的產生，是生成函數因式重新組合的結果(2) Sicherman Dice 是否存在，則視上述重新組合的結果是否有負項產生由於上述的觀察，我使用自行發展的「負項消去」法來檢驗Sicherman 結論的正確性及求得n 面正多面體其對應的Sicherman 極限。同時我也和Col. George Sicherman 取得聯繫， 討論當年他發現Sicherman Dice 的經過及其結論的限制條件，作為本研究未來發展的參考。