臺灣

在一次偶然的機會中，我們在科學月刊上讀到一篇探討骨牌排列 (Domino Tiling) 問題的文章。文中骨牌排列問題看似單純，但其中卻有許多有趣的性質，因此，我們想對此進行更深入的研究。\r 我們將1x2的骨牌填入特別的方格中，考慮填入的順序並計算其排列情形的數量。由定義的兩個模型SDT(Standard Dominos Tableau) 與「缺一格」的GDT(Good Dominos Tableau) 為基礎，嘗試尋找它們之間的關連性，藉由對應(bijection)的方法，得知在高度的限制為奇數的情況下，SDT與GDT的數量相同，並且，兩者之間的結構有密切關聯。\r 除此之外，在這個研究中，針對SDT在高度不超過三排時，我們建構出了骨牌排列情形與我們架構的「廣義Motkzin路徑」的對應操作流程。接著，我們嘗試探討一般化的SDT與此結果的關聯性，由對應過程的想法，架構出高維度的「廣義Motkzin路徑」，並推測此路徑與SDT之間有緊密的相關性！

為了了解淡黃蝶Catopsilia pomona無紋型crocale-like及銀紋型pomona-like中間受到環境因子的差異。先比對兩型的粒線體ＤＮＡ，之後模擬夏季和冬季自然環境進行實驗。得知兩型為同種。另一方面進行溫度和光週期的實驗，顯示淡黃蝶幼蟲和成蟲雌雄個體各部位會受到此兩環境因子的影響。In order to realize if Catopsilia Pomona and Catosilia crocale are the same species, we analyzed and compared the DNA sequences of Mitochondria, and the result revealed they are indeed the same species. Then we observed the developmental process of the butterfly, and inspected the effects of different factors: photoperiod and temperature were shown to affect the phenotype of the butterfly; lower temperature and shorter day resulted in phenotypic shift from crocale-like to pomona-like, and vice versa. Also, the conflicting factors produced intermediated form. (e.g. lower temperature with longer day) Not only changed the phenotypes of adult with photoperiod and temperature, those of larvae also did. However, the mechanism how photoperiod and temperature affect the phenotype of the butterfly is unknown.

秋颱引發共伴效應時，台灣西北方有高壓產生東北季風，風速因外圍環流和東北季風合流增強，並帶來強烈降水。本研究利用侵臺颱風資料庫，整理西元1958~2010年間曾引發共伴效應的秋颱，發現第五、六、九路徑最易引發共伴效應。此外，由於颱風位置的關係，各個路徑共伴效應颱風對台灣各地造成的降雨量大小不一。取出第五、六、九路徑秋季共伴效應颱風，比較其逐時雨量，發現此三個路徑颱風各在特定位置引發最強共伴效應，颱風中心位置大略為台灣西南方、東北方和東部海面。比較第五、六、九路徑秋季颱風產生共伴效應者和一般颱風對台灣各地造成的雨量、風速，發現在秋季共伴效應發生時，颱風對台灣北部、東部的降雨量影響較大；而第六、九路徑秋季共伴效應颱風只會影響台灣北部的風速，但五號路徑颱風對全台各地的風速皆有影響，且使台灣北部的風向由東南風轉為東北風。

上體育課的時候看到同學投空心球（籃球在沒有碰著籃框的情況下進入籃中），覺得好厲害。因此，我們利用相關的數學知識與運動原理來討論籃球投出後的運行軌跡，以及影響其命中率的相關因素。我們得知籃球的運行軌跡是一條拋物線，並求出其二次方程式；並利用標準籃球直徑與籃框直徑找出籃球進入籃框的最小入射角。若要提高命中率，必須考慮籃球投出時的投射角、初速度、籃球投出時的高度以及籃球與籃框水平距離之間的相關影響。此外，我們藉由電腦軟體列出相關數據提供作為實際投籃時的參考，並藉此進一步分析上述因素如何影響籃球運行軌跡以及如何提高投籃的命中率。Those who always shoot nothing but the net in basketball games were always heroes to me. I have being thinking for a long time how to become a person of that kind. For this, we investigated the trajectory of shooting a basketball and the factors to increasing the field goal percentages through our knowledge on mathematics and physics. We have obtained that the trajectory is in fact a parabola and, we further, found its quadratic equation. We also derived the minimal incident angle from the diameters of the standard basketball and hoop as well as the quadratic equation we have found. To raise the field goal percentages, some important factors must be taken into consideration, such as the vertical and horizontal distance between the basketball and the hoop, the incident angle and the initial velocity of shooting. Finally, we provide some concerning data for reference, and analyzed how the important factors we have mentioned above have affected our basketball trajectory and how, of the most importance, to increase the field goal percentages

政府最近公佈在東沙群島設立第一個國家海洋公園，顯示國人重視海洋資源的保育與復育；但是東沙島特殊的自然景觀「會擺動的沙嘴」—龍擺尾，卻因興建八座消波塊構築的突堤而消散停擺。本研究以一個高中生的觀點，設計及進行一系列的模型實驗，探討東沙島的形成機制、各種環境因素對海灘及龍擺尾的演化、驗證龍擺尾的現況及如何讓龍擺尾復活，再由東沙島海灘復育看世界的海岸問題。雖然設備很克難，但都能完成預定的目標，證實東沙島的海灘演化。希望此次對東沙島海灘的研究成果與初步探討，能應用於世界上遭受侵蝕而需復育的海岸。In 2007, our government proclaimed Dongsha archipelago as the first national marine park, signifying her emphasis on the conservation and restoration of marine resources. However, the sand spit on Dongsha island, a unique natural wonder commonly referred to as the “swaying dragon tail”, has become motionless since the construction of a total of eight groins along its SE and NE coast during the period between 1993 and 1996. This study has conducted a series of model experiments to verify several fundamental issues, ranging from the formation and the factors affecting the stability and the status quo of Dongsha island and its spit. The experimental results find several favorably outcomes, giving the coast evolving evidences of Dongsha island. Furthermore, strategy to stabilize the coast and revitalize the spit are then considered, which could hopefully benefit the coast suffering erosion on the world’s coastline.

在炎炎夏日總希望來點可以「降火氣」的食品，依據古籍記載某些中藥材具有降火氣的效應，而中醫所謂的降火氣與西醫的抗發炎反應密切相關。本實驗利用巨噬細胞株受到LPS (Lipopolysaccharide，革蘭氏陰性菌細胞壁表面所含有的脂多醣體)刺激後，會分泌發炎介質的現象，再分別加入各項傳統認為可降火氣(以菊花、薏仁、仙草作為樣品)或上火氣(選用龍眼作為樣品)的中藥食材，來評估中藥材對巨噬細胞分泌發炎介質能力的影響。經由實驗，我們發現市售的『降火氣』中藥食材，在適當的濃度下，確實具有降低IL-6、TNF-α 分泌量的能力，但濃度過高時卻會造成細胞凋亡。另外，傳統以水熬煮的方式比冷凍乾燥取得的樣品有更好的降低IL-6、TNF-α 分泌量的能力。 我們期望以此一系列的實驗，來建立篩選『降火氣』食材的抗發炎效用的研究模式，並在後續實驗中可用以篩選出更多具抗發炎效應的中藥材。In summer, people always consider eating some special things to refresh themselves. According to ancient books, there are some Chinese herbal medicines that were recorded to have the function of cooling us down, which is related to anti-inflammation in the Western. Macrophage cell lines can be stimulated by LPS (Lipopolysaccharide) and secrete proinflammatory mediators. Thus, it is often used to evaluate the anti-inflammatory effects of different herbs. In our experiment, we also use macrophage cell lines to test different anti-inflammatory effects between chrysanthemum, Job’s tears and grass jelly. In addition, some Chinese herbs such as longan that can parch us are also tested in our experiment. In our results, we found these herbs that are available indeed have ability to anti-inflame in appropriate consistency; however, high dose does harm to cells. In addition, the samples that are poached in ancient ways have better ability to show the low dose of IL-6 and TNF-α. Finally, we would set up a model to test the anti-inflammatory ability of different herbs that were said to be able to cool us down, and then we could test more herbs in the future.

吹長笛時，按同一按鍵，以大小不同的力量去吹，會引發不同頻率的泛音，而通常越用力吹，引發泛音的頻率越高，所以我們想了解為什麼越用力，泛音的頻率會高，其間的關係究竟是什麼？風經過管口會產生各種頻率的噪音，其中某些特定頻率的聲音會因為會在管內形成駐波而放大，所以我們只能聽到某些特定頻率的聲音。當風速增加時，會在管口形成渦漩逸放的紊流現象。其渦漩頻率與流速成正比（註一）。我們以塑膠管實驗。發現以特定的風速引發該基音後，繼續增加風速，當風速達某一定強度時，才會躍遷為下一個泛音的頻率。這個現象告訴我們：在一封閉管下，風速與泛音的關係並非「線性遞增」，而是越「躍遷遞增」的關係。另一個實驗測量不同管長、其諧音之頻率的關係，我們可以得知，越短的管子，因為相鄰兩泛音間頻率差較大，越不易激發更高階泛音。經由這些實驗結果，我們能夠推論：當管子越長、基音頻率越低時，諧音間頻率的差距相對越小，繪出的風速－頻率關係圖應更加顯示了風速與頻率呈正比關係。未來我們可以以閃頻器觀測紊流渦漩的產生，再變化至不同吹入角度，及各式管口造形，這些實驗能協助我們更進一步了解樂器的發聲原理，甚至開發一個以聲音頻率測量風速的儀器。註一：林婉如、張?文2006 國際科工程組佳作作品。When we press the same key and blow a flute using different strengths, we can get different overtones. Usually, the harder we blow the flute, the high the frequency we get. We want to understand why we get a higher frequency when we blow harder into the flute and to understand the relationship between them. When wind passes through the mouthpiece, many kinds of noises will be produced. Some of the frequencies will expand because they will form standing waves in the tube. Therefore, we can only hear certain frequencies. As wind speed increases, a turbulence of the vortex shedding will be formed. The frequency of the vortex shedding and wind speed will be in a direct ratio. We experiment with plastic tubes. When we increase the wind speed and get certain magnitudes, the frequency will jump to the next overtone. The phenomenon shows that the relation, in a closed tube, between wind speed and harmonics is not a linear increase but a transition increase. In another experiment, we measured the relationship between wind speed and different lengths of tubes. We can infer that the shorter the tube, the higher high-frequency harmonics can be produced. Through these experiments, we come to the conclusion that the longer the tube, the lower frequency of the fundamental tone we get and the discrepancy in frequency between harmonics is smaller. Then we make a diagram between wind speed and frequency that indicates that there is a direct ratio between wind speed and frequency. In the future, we can use “” to observe the production of turbulence. Then we can switch to different angles when we blow into flutes. Otherwise, we can experiment with different shapes of mouthpieces. These experiments can assist us to understand more how the instrument sounds. We can develop a device measuring wind speed with frequency.

由於本身有頭皮屑的煩惱，在使用各種洗髮精之後，一方面覺得大部分的洗髮精效果不是很好，另一方面也擔心抗屑洗髮精的成分對人體有害。所以有了研究頭皮屑的念頭，希望能找出減少頭皮屑的方法。\r 在與幾位皮膚科專門醫師討論後，醫師們都不建議在直接人體上進行減少頭皮屑的實驗。於是我們將研究的重點放在〝皮屑芽孢菌生長之探討〞，希望對皮屑芽孢菌有更深入的瞭解。除了洗髮精之外，我們也將研究各種廣為流傳的民間偏方是否能有效抑制皮屑芽孢菌生長。在這些民間偏方的蒐集可兩大類：一類是在日常生活中可以很容易取得的物質，如鹽、醋、大蒜、生薑、洋蔥等；另一類則是台灣特有的物質，如無患子、茶籽粉、竹醋液等。\r 我們希望透過研究方法能瞭解\r (一) 溫度、濕度、酸鹼度、油脂對皮屑芽孢菌生長的影響\r (二) 哪些物質可以抑制皮屑芽孢菌的生長\r (三) 不同稀釋濃度的物質抑制皮屑芽孢菌的生長的效果\r 為了避免繁複的數量計算(如菌數計算)，我們採用較多的對照比較(如抑制圈大小)。同時，我們設計了一個簡易的觀察與測量方法(稀釋法與抑菌指數)，來比較各種民間偏方\r 的抑菌效果。\r 研究與實驗分為四大項進行:\r (一) 基本生長環境之探討：溫度、濕度、酸鹼度、油脂對皮屑芽孢菌生長的影響\r (二) 民間偏方抑制效果之探討：鹽、醋、大蒜、生薑、洋蔥是否能抑制抑制皮屑芽孢菌的生長\r (三) 民間偏方抑制效果之比較(抑制圈)：比較各種物質的抑制圈大小\r (四) 民間偏方抑制效果之比較(稀釋法)：利用抑菌指數來比較各種物質的抑菌能力\r 經過研究，我們所蒐集到的民間偏方都有某種程度的抑菌效果，大致可以分為強效(蒜液、竹醋液、茶樹精油)、有效(食鹽水、食用醋、洋蔥液、檜木芬多精、茶籽粉)及普通(薑汁、無患子)三種效果。\r \r Since I have the serious dandruff problem, I try to seek, except the shampoo, the natural materials to decrease the dandruff. After consulting with some dermatologists, they suggest I can focus my research on the “Malassezia Furfur”, which is the major bacteria causing the dandruff.\r This project is designed for finding the materials which have the most powerful inhibition capability for the “Malassezia Furfur”. I collect some folk prescriptions from the internet that salt, vinegar, garlic and onion can decrease the dandruff. The problem is “Do they have good inhibition capability for the Malassezia Furfur too?”\r The goals of the research are as followed.\r (1) The exploration of the basic environmental factors for the growth of Malassezia Furfur, such as temperature, humidity, acidity & alkalinity.\r (2) What kinds of material have the good inhibition capability?\r (3) The comparison of inhibition capability of the different material with different consistency.\r We especially design a method called “Dilution metering and index” to compare the inhibition capability of the different material. By using very simple observation, this method will transfer the simple “Qualitative Analysis” to the result of complicated “Quantitative Analysis”. The “Dilution metering and index” is the major achievement of this project, and it is also the good way for the projects which are not equipped with the precision instrument for bacteria inhibition capability measurement.

氣候暖化是一個地球目前正面臨的一大議題，造成地球暖化的主要原因是長期大量使用的化石性燃料所產生的二氧化碳等溫室氣體因此尋找一個替代性的能源是一個當今十分重要的問題。本研究將可見光光觸媒Bi20TiO32、CuFeO2粉體及鐵絲網懸浮於內照式光觸媒觸媒反應器內，當受激發之光觸媒粉體與鐵絲網發生碰撞，則可使光生電子-電洞經金屬-半導體異相介面傳遞至另一光觸媒之活性位置，藉此有效地分離光生電子-電洞而提高光觸媒水分解之產氫速率。本研究發現，利用此一光生電子-電洞傳遞途徑，在293 K下CuFeO2之光觸媒活性可達8.38 mL H2/min‧g。然而，本研究中光觸媒水分解之產氫速率在沒有氣體壓縮器的協助下，未能有效地驅動質子交換膜燃料電池。本研究亦探討質子交換膜燃料電池之最佳化條件，發現在333 K下，以100 mL/min純氫作為進料，可使質子交換膜燃料電池在0.6 V之操作電壓下，輸出0.78 W之電能。在未來，將本研究發展之光觸媒反應系統與質子交換膜燃料電池結合成光電能轉換系統，則可能夠在日常生活中有效地被運用。

直接乙醇燃料電池以酒精與氧氣透過氧化還原反應產生電能，但化學反應緩慢，需利用觸媒以增加其速率。本實驗目的在於盡可能找出一個表現最佳的觸媒。本實驗利用活性碳粉作為觸媒（鉑、錫）的載體，以酸性（HNO3）與鹼性（NaOH）環境分別處理碳粉，再以含浸法與多元醇含浸法將觸媒還原。我們得到以HNO3 處理的碳粉無法保有原碳粉的型態，較利用NaOH 處理為差。在觸媒製備方面，多元醇含浸法還原效果比含浸法可得到較小的觸媒尺寸，在本實驗中，溶液中鉑與加入的碳粉重量比為3:7 時，可得到最大的反應面積。此外，當鉑與錫原子數比為4:1 時，可得到最大的乙醇氧化電流。Direct ethanol fuel cell is a kind of power source which generates electrical power by a redox reaction involving ethanol fuel and oxygen. However, this reaction takes place slowly; therefore, catalyst is needed to improve its activity. The goal of this project is to get an optimize catalysts ratio to obtain the best catalyst activity. Activated carbon is used as the support of catalyst (platinum and tin) particles in this project, which is pre-treated in acid (HNO3) and alkaline (NaOH) solutions respectively. Then, the precursor is reduced by impregnation and EG-impregnation. We learned that activated carbon pre-treated with NaOH activates better than which pre-treated with HNO3 because the latter bear less resemblance than the former. As for the catalyst, the results of EG-impregnation show smaller size of catalyst particles than those of impregnation. In this project, when the ratio of the weight of platinum and activated carbon added into the solution is 3:7, we can get the largest surface area. In addition, when the ratio of the amount of platinum and tin atoms is 4:1, we can get the largest current of ethanol oxidation.