本次科展作品由三角邊形的魔方陣出發，設定規則如下；在 n 階三角形魔方陣中填入給定數字，使其三個 1n ? 階三角形數字和相等。我們得出如何從 n 階魔方陣推至(n+1)階魔方陣，與給定任意一個 n 階魔方陣，如何填出一組解的方法。遵循著三角形魔方陣的填法，我們可將其推廣在平面任意 m 邊形及正四面體上。前者，我們得到給定任意 n 階 m 邊形填出一組解的方法。後者，則是可由 n 階立體魔方陣推至(n+1)階立體魔方陣；當給定偶數階立體魔方陣時，可利用自創的圓形圖進行求解，文末亦討論了具有特殊性質點的個數。

當人體缺乏乳糖?時，未被分解的乳糖在小腸中產生吸水作用，於是發生水瀉的情形；到了大腸更會被細菌分解、發酵，產生大量的乳酸、二氧化碳及氫氣，使人腹脹、放屁，還會使腸道蠕動過快，誘發痙攣腹痛以及腹鳴，稱之為「乳糖不耐症」。乳糖?會將乳糖分解為葡萄糖和半乳糖。我們利用尿糖試紙測量葡萄糖的含量，以進一步瞭解乳糖?分解不同乳品中乳糖之情況以及模擬消化系統中不同酸鹼質環境，觀察乳糖?的作用是否受到影響。結果發現不同乳品在添加乳糖?後，葡萄糖含量隨時間而增加，而乳糖?在模擬胃中酸鹼值為2 之牛乳中完全失去活性，無法分解乳糖。

我們以投影片為底，分別塗上導電膠、導電碳膠、鎳絲、不同粒徑的石墨粉或石墨烯等導電材料製作可彎曲的導電片，用它們來取代價格昂貴的ITO(銦錫氧化物)透光導電玻璃片，以製作染料敏化太陽電池(簡稱DSSC)。自製的DSSC的兩極中間塗了奈米級TiO2 (14 nm)晶粒，並以紫羅藍花(乙醇當溶劑)為染劑，再以鹿角萵苣(溶於乙二醇的溶劑中)作為電解液。實驗結果發現，最好的導電材料首推「石墨烯」，並發現以「投影片/鋁膠帶/石墨烯」組合作正極，以可透光的「投影片/導電膠」作為負極，可獲得較高的發電效率。自製的太陽電池不僅製作成本很便宜，而且還可以彎曲喔！

Innovative, inexpensive, sustainable fuel for cooking and light can be produced with an anaerobic digestion biogas system. A biodigester was designed from parts that are locally available to purchase and maintain in a developing nation. The prototype was designed, built and the engineering was approved and tested. Research and testing of techniques used to produce biogas were recorded and analyzed. The digester successfully produced enough biogas to connect to a stove and burn. Research and testing continued on different ways to pressurize the biogas. A burn time of eleven minutes was recorded. A Bunsen burner was designed, again from locally available parts, in order to enhance the flame to use for cooking. The designed digester and burner worked satisfactorily to burn the biogas collected in the system. Using small scale tests, additional research and testing continued on the most efficient production of the biogas. Figure 1 shows the results of the small scale biogas testing. The results from the small scale testing showed that the best variables for producing biogas are using school compost, ie apples, bananas, oranges, cucumbers, grapefruit, grapes etc, which has been blended to acquire the most surface area with a 1:1 ratio. Figure 3 shows the results of a sample of methane (first three peaks) and of the biogas that was produced (last two peaks). The first peak is the nitrogen and the oxygen in the sample. The second peak is the methane and the third peak is carbon dioxide. The first biogas sample that was tested had no methane so there was an absence of the second peak. This was similar for Figures 4 and 5. Figure 6 shows a sample of the final biogas product which is producing methane as shown by the blue circle. Figures 3 through 5 lack a methane peak due to leaks in the biogas system and limited time within testing periods. The hypothesis was proved correct. An innovative, inexpensive, sustainable fuel for cooking and light using an anaerobic digestion system that can be built completely in developing nations such as Honduras was created. The biogas was ignited using a stove which provided heat for cooking. The biogas was not tested using a light; however, since the biogas can burn, this is theoretically possible. The final system achieved these goals.

核四如果停建後，必須另尋其他替代方案。題目中提及立即有效且環保，在選項裡面只有A. 節約能源 最能立即顯現效果，例如節能減碳計畫、節約用電、使用綠色環保標章的低耗電產品、購買綠建築可以減少用電需求、隨手拔插頭等等，在個人的日常生活中即可實行。\r 在未來勢必要選項B. 發展再生能源，例如太陽能、風力、地熱、潮汐能等等，再生能源目前還在研發如何量產，還不能立即全面推廣，不符合題目中提及的立即有效方案。\r 火力發電廠會產生大量二氧化碳，加劇溫室效應使地球增溫。火力發電使用的石化燃料煤或石油，會產生硫化物質，形成酸雨的來源。也會造成空氣污染。所以火力發電廠是不符合題目中提及的環保替代方案。

在市而上有許多電子廠商，均已出售電話放大器之零件或成品，本校六十三年校慶時，老師也要我們作電話放大器、電子鳥、電子琴等各式各樣的電子成品展覽，以供參加校慶的來賓參觀，於是我們就在想，電話漏磁既然可以放大，若加一適當的處理，當然也可以作為遙控電子設備或使用電力的大型機械，因之，引起了我們對該方而研究的動機。

In recent years, sandstorms have seriously attacked Taiwan day by day. Combining with the observations of Central Weather Bureau and the satellite images of NASA, the study has been collected the data of suspension grain in decades. And the study hopes the sandstorms’ information could be observed in early period. Still it hopes to find out the possible transmission paths in the atmosphere. Then we know how to cope with sandstorms in early time. Sandstorms attack Taiwan frequently in alternation of the spring, the autumn, and the winter. Compared with thecharts of sandstorms and the satellite images, we could broadly aware hat the moving paths of sandstorms are related to the currents and the characteristics of the atmosphere. When El Nino happens, the times of sandstorms attacking Taiwan decrease, and that increase when La Lina happens. From the observation data of acid rain, when sandstorms attack Taiwan, acid rain would diminish. Combining actual Measures and satellite data in the future, maybe we can establish a prediction mechanism of sandstorms.近年來，大陸沙塵暴侵襲台灣的情況日趨嚴重影響。本研究中收集了近十年來懸浮顆粒資料，配合中央氣象局所觀測的資料與美國太空總署的衛星影像資料，希望能夠在早期觀測發現大陸地區沙塵暴訊息，和沙塵暴所帶至大氣中的懸浮顆粒可能傳輸的路徑期能早期應映。發生沙塵暴侵臺事件的季節，主要在秋冬及冬春兩季交替期間發生的次數為最多。由沙塵暴監測氣候圖表及美國太空總署的衛星影像進行綜合比對之後，可大致瞭解大陸沙塵可能的移動路徑與大氣環流及特徵有關。聖嬰現象（El Nino）發生時，侵襲臺灣的沙塵暴次數會減少。在「反聖嬰現象」（La Lina）發生時，侵襲臺灣的次數相對增加。由酸雨中得知大陸沙 塵暴侵襲台灣時，酸雨情況會減緩。未來結合實測及衛星資料或許我們可以預報大陸沙塵暴的侵襲。

當流體由圓管流下，在碰撞到物體後水流會產生類似駐波的形狀。為瞭解此現象的產生機制，及影響此現象的變因，我們改變流體的表面張力、流速及與碰撞物體間的距離，以探討各變因對波形所產生的影響，進而研究此現象的成因。由實驗結果發現波形會因流速加快、擋板距離增加、表面張力減少而有波長變短的趨勢，且可以用表面張力波的理論解釋。由理論推導的結果，可測量液體表面張力。由於圓球狀的外型使表面積增大，可增加液體之散熱的面積，因此可應用在水冷系統方面。A phenomenon similar to the standing wave, which occurs when a slow-velocity fluid jet collides with an obstacle, was observed. Because the free surface profile was observed to be stable, the phenomenon was not considered as standing wave. To understand the mechanism of this phenomenon and the factors that can affect the free surface profile, the surface tension of the fluid, jet velocity and the distance between the exit of the tube and the obstacle are varied to study their influences on the free surface profile. According to our experiment, the wave length is shortened when the jet velocity or the distance between the tube and the obstacle increases or when the surface tension decreases. The tendency of the investigated phenomenon can be explained by the capillary wave theory. Based on Bernoulli’s principle, continuity principle and surface tension\r equation, an ODE (ordinary differential equation) could be formulated. By using numerical method to solve this ODE, we predict the free surface profile which could match the experimental photo well. The tendency of the phenomenon can also be explained by the ODE. In order to measure the surface tension of the fluid, we wish to minimize the experiment apparatus. To enhance our assumption we use laser to locate the individual particle that we add in the fluid and calculate the velocity field of the flow jet.

水平感應發電機是一個結構簡單的發電方式，如何使水平發感應電機產生最大電力，並\r 將發電的電力應用於生活上，本研究主要的內容，磁鐵排列方式能產生電力，線圈圈數與發\r 電力大小、線圈的大小與發電，線圈的形狀與發電，漆包線的粗細與發電，磁鐵與漆包線距\r 離與發電大小，磁鐵數量轉換次數與電量大小，線圈的串並聯的應用以增加電力的大小，磁\r 鐵磁力大小與發電量，線圈中加入鐵塊所產生的電力大小，水平感應發電機應用在腳踏車的\r 照明。

噹！噹！噹！ 下課的鐘聲又響起，我們一群人吆暍著衝向操場，正準備打球時，忽然間，其中有一位小朋友不小心被榕樹打到頭，在撥開樹枝的同時，卻發現樹枝上長有形狀怪異的葉子，葉子上還有一點一點的小紅點，此時，平時便有「好奇寶寶」之稱的何同學提議找老師幫忙解決疑問，這才明白裡頭住著一種其貌不揚，人稱捲葉高手的小動物─榕管薊馬，而那些在榕樹葉上的紅色斑點稱為「蟲x」，是榕管薊馬蓋房子的主要工具。於是，我們仔細觀察學校裡的榕樹都有薊馬的寄生，可是對榕樹也沒有什麼傷害和影響，想一想有這麼多現成的小薊馬，正好可以拿來做為今年的自然科課外研究，這篇報告就是今年研究薊馬的記錄與發現 。

本實驗利用五種瓜類蔬菜，分別為南瓜、苦瓜、絲瓜、冬瓜及小黃瓜等為試驗材料，將所取得之萃取液以濾紙圓片擴散法（disk diffusion technique）進行抑菌試驗，其試驗菌株以3株細菌為對象。初步試驗結果顯示南瓜具最佳抑菌活性，次為苦瓜、絲瓜、小黃瓜、冬瓜。進一步探討不同溫度、pH值對其抑菌活性之影響。結果顯示，五種瓜類萃取液經121℃，20分鐘加熱處理並不會破壞其抑菌成份；萃取液則因pH值不同而改變抑菌活性，各組實驗皆在pH值較低情形下得到較好抑菌活性。由初步試驗中得到南瓜萃取液具有最佳抑菌活性，因此進一步進行食物模式研究，添加不同濃度之南瓜類萃取液於4℃市售柳橙汁、鮮乳、奶茶及豆干中儲存5天，其生菌數皆低於控制組。

縱觀同餘方程理論的發展，雖已有十分輝煌的成就，但二次剩餘卻還僅止於有無解的判別，而沒有良好的求解方法，有之，僅是以嘗試法，逐一代入求解（如李恭晴先生著整數論第 61、61 頁解 X =21mod 37 )，或以逐步捨棄法，去其不可能數，待數目較小，計算不太麻煩時，直接代入試驗得之（如數論導引第 48 頁，解 X=73 mod 127 ) ，這些方法在理論上，雖非站不住腳，但其不夠完美乃人盡皆知，尤其是數字一大，困難更是接踵而來；至於一次同餘式，目前更有多種形式的解法，那些理論雖稱完備，但其演算過程，都不夠單純明快，更由於不能一氣呵成，所以，也很難避免不必要的失誤，有鑑於此，而研究一次同餘式的連分解法，及中國餘數定理研究，以及二次剩餘的二次非剩餘解法和平方試驗法，這些方法及名稱，均為作者自己假設，希望能彌補時下理論之不足，並願以此新的嘗試，為您帶來一段思考的愉快時光。