“熱巧克力效應”是當你將巧克力粉加入裝有熱水之馬克杯後用湯匙輕敲杯壁，可以聽出攪拌前後敲擊所得聲音頻率明顯不同，攪拌後巧克力粉溶解頻率會較高。一般論文的解答是「當粉末溶解的時候，藏在粉末裡的空氣就會跑出來，在空氣與水混合的環境裡，音速比在水裡低。當水裡不斷有空氣與水混進去時，這個容器的共振頻率和它裡面的音速有關，所以也會降低。因此你會聽到較低之音調，直到空氣全跑光。」但根據我的實驗我覺得這樣的解釋並不對。我們提出新的模型來解釋“熱巧克力效應”。When we put an ounce of dry chocolate powder into a mug filled with hot water, then tapping the side with your spoon will generate a sound. The pitch of this sound will rise after stirring. This is called “the hot chocolate effect”. According to a published paper, the explanation is “The air trapped in the powder is released as the powder dissolves. Since the speed of sound is lower in air than that in water, the speed of sound in the air-water mixture is lower than that in pure water. During that period while the air escapes the container, the resonant frequencies of the water, which depend directly on the speed of sound, will also be lower. Hence, you hear a lower tone until the air escapes”. However, our experiments clearly demonstrated that the explanation is plainly wrong. A new theoretical model is also proposed for the observed phenomenon.

大氣圈、水圈與土壤圈是構成自然環境的三大領域，三者之間相互的影響，原本這些空間都具有極大的包容力，亦所謂「自淨能力」，許多的物質進入其中皆會被氧化分解或稀釋而消失於無形。近年來由於工業發展、人口增加，產生大量的廢棄物，長期、密集且迅速的堆積於環境中，使得天然的自淨能力無法應付而失去功能，造成嚴重的後果。就土壤而言，雖有較佳的自淨能力，但是一受污染，除了嚴重破壞土壤品質之外，同時也會直接或間接污染水源 (如:地下水)及空氣，對動植物造成危害，並且難以回復，實不容忽視。本實驗探討:一、土壤淨化能力是否受到不同地區、不同土壤性質的影響。二、同樣的土壤，對不同的污染物(色素、肥料、重金屬)淨化能力強弱的影響。實驗結果顯示大肚山土壤過濾溶液中的色素、磷、及重金屬中的鉻、鎳、銅的能力較中寮及大甲土壤強，只有氮與鉀的過濾能力較大甲土壤差，所以這次實驗中大肚山土壤有最好的污染淨化能力。實驗結果將來也許可以應用於土壤處理場址之適宜性評估。The air, water and soil are three parts of the nature. They affect each other. In fact, they have the "self-purity ability" - they can disassemble many polluted thing by this kind of self-purity ability. These years, because the industry development and the population explosion make lots of waste, the self-purity ability cannot do its best. The soil has better self-purity ability, but if it is polluted, it will not only pollute the water (ex: underground water) and the air, but also damage the animals and plants. We cannot ignore the serious result. This experiment will discuss:1. If the soil self-purity ability is affected by different area and different soil specificity? 2. The different purified results according to the different pollutant (ex: color, fertilizer and heavy metal) in the same soil. Results showed that Da-Du-San soil had strong ability then Chung-Liao and Da-Cha soil in filtrated color, phosphor, chromium, nickel and copper in the solution, but had weak ability then Da-Cha soil in filtrated nitrogen and potassium. Therefore, Da-Du-San soil had the beast pollution-purity ability in this experiment. In the future, results may be applied to the suitability evoluation of the soil treatment place.

本文由三個結合 tan−1 與費波那契數列的等式及其所搭配的無字證明圖形出發, 做出和盧卡斯數列有關的圖形, 並由數學歸納法找出並證明 tan−1 與盧卡斯數列及一般二階線性遞迴數列的全新等式： This paper startes with three equations of tan−1 and the Fibonacci sequence combined with the diagrams used to prove the three equations without words. According to the principle of mathematical induction, we continued to find out the similar equations of the Lucas numbers and the second-order liner recursive sequences as follows.

安德遜蠅虎的卵期和幼蛛期共約需 22~26 天，需經歷 6 齡（6 次脫皮）而成年，每齡需要時間為23~32 天，從卵期到成蛛約3~4 個月左右，成蛛約可再活 3~5 個月，為不完全變態。安德遜蠅虎喜歡在食物充足和陰暗的草叢和牆壁底層活動，能適應的溫度範圍在 15~33℃之間。安德遜蠅虎的行為項目目前已知 14 種，其中 4 種與捕食行為有關（例如：頭胸部升降、潛行、撲擊、迂迴），3 種與爭鬥行為有關（例如：Z形舞蹈1、前足斜舉、奔逃）；5 種與求偶行為有關（例如：觸肢擺動、前足斜舉、繞行、Z 形舞蹈 2、交尾） 。但牠不獵捕比自己體型過大的獵物，主要以小型蠅類或彈尾蟲為食，其捕食獵物主要靠視覺或感覺毛，中前眼最遠可看到超過12cm距離的東西，跳躍力最遠可跳出15cm 的距離。對於蠅虎的分佈區域就觀察提出【蠅虎集中發散推論】 ：一區域內的各種蠅虎，必有其集中地。各種蠅虎由其集中地向外發散、擴張形成發散地，並與其他種蠅虎勢力範圍重合，形成多種蠅虎共存的共存區。Hasarius adansoni’s egg development and postembryonic development require 22~26 days. It takes 6 stadiums to become adults. Every stadium needs 23~32 days . The adults can live to about 3~5 months . There are 3~4 months from egg development to adult. Hasarius adansoni like to move in grass and at the bottom of wall where there is plenty of food and no light.The scope of temperature is 15℃ to 33℃.There are 14 elements of behaviors known for Hasarius adansoni, including 4 predatory elements（such as Raise andlowered cephalothorax、Stalk、Leap and bit、Detour） , 3 agonistic behavior elements （such as Zigzag dance 1、First leg erect、Suddenly run and leap）, and 5 courtship behavior elements（such as Palp waving、First leg erect、Circular detour、Zigzag dance 2、Copulation）.But they don’t catch captures which are bigger than themselves；their main captures are little flies and Homidia sp. Relying on their vision and sensation hair，Hasarius adansoni’s Anterior Median eyes can identify for up to 12cm；long jump can for up to 12cm. The inference of jumping spider’s distribution could be that different species of jumping spiders in an area are sure to have their respective center habitats. They spread from the center habitats to disseminated areas. Then they overlap with those of their species and form a shared section of multiple species.

作者受考題（ International Mathematics Tournament of the Towns, Senior A-Level Paper, Fall 2009, No. 7 ）?發而展開此研究。經搜尋文獻發現，這系列命題可追溯自 Scientific American （ Feb 1979 ）中 Martin Gardner 的文章 The Rotating Table 。\r 命題之操作原在正方形桌上執行，後被Ted Lewis & Stephen Willard 推廣至正多邊形（1980），又再被Richard Ehrenborg & Chris M. Skinner推廣至任意置換群（1995）。\r 本文從均勻多面體的情形出發，藉諸自創的證明方式，重新詮釋上述論文之結果，給出較簡潔自然的證明。同時，作者改變命題裡的關鍵限制，發展全新的研究方向；並針對不同的情形（多邊形、多面體、置換群）分別求出各變數之上、下限。\r 本文使用到的技巧包括：群論、歸納法、組合設計。充分性之證明過程提供的演算法能應用於同步連絡管道，允許匿名用戶之間建立連線。

因國際原油價格上漲，因此對研究及發展具潛力的生質柴油引起高度興趣。傳統以加熱方式在適當觸媒下將低碳數醇類與油脂轉酯化生成生質柴油。但以強鹼為觸媒使用過量會讓部分反應轉為皂化。而利用微波，使微波腔在極短的時間內產生電場，使具有電偶極的分子朝向電場方向迅速排列而產生轉動，快速地增加分子間的碰撞頻率而加速反應，但不破壞分子結構。也嘗試利用超音波來生產生質柴油。試驗方法為利用SD-22 柴油引擎測試所生產的生質柴油，並收集廢氣檢驗，評估其污染性。實驗後發現，微波能將一般加熱所需的60 分鐘大幅縮短至4 分鐘，甲醇溶液能生產較多的生質柴油。其中1.40%氫氧化鉀甲醇溶液且油與醇莫耳比1：9 效果較佳。氫氧化鉀甲醇溶液0.80%且油與醇莫耳比1：5 效果亦佳。製成的生質柴油能讓引擎發動，廢氣處理後經分光光度計檢驗氮氧化物，生質柴油確實能有效減少氮氧化物污染。 Due to the fact that the price of international crude oil raises , people look for alternative energy resources actively. Therefore, I have great interests in doing researching and developing the biodiesel through many ways. The traditional way is to transesterify the low carbon alcohols and fats with the suitable catalysts by means of generally heating. However, the overuse of strong bases as catalysts may turn the experiment result into saponification reaction. This study made good use of the microwave to generate electric fields in the microwave cavity in an extremely short time. Owing to the effect electric fields exerted, the molecules with electric dipole momentum rearranged to rotate rapidly .Consequently, the frequency of collision among the molecules increased without destroying the molecule structures. Also, I applied SD-22 diesel engine to test the produced biodiesel and examined the collected exhaust to evaluate its pollutant. According to the results of these experiments, the conclusion was as following: the microwave could shorten the Transesterification reaction time from 60 minutes to 4 minutes. The methanol solution could produce more biodiesel than the ethanol solution. Besides, the 1.40 wt ％ Potassium hydroxide solution with the molar ratio of oil and methanol 1:9 had the best efficiency in producing biodiesel. On the other hand , the 0.80 wt ％ Sodium hydroxide solution with the molar ratio of oil and methanol 1:5 also had the great efficiency. All the biodiesel we produced enabled the diesel engine to run smoothly. The exhaust inspected from the examination of Spectrophotometer resulted that the biodiesel did less NOx pollution to the environment indeed.

Purpose of Research\r Colour blind individuals make up a large part of the population but are not usually considered. I aim to design an interactive guide that can be used when designing websites, social networking pages and various digital presentations to ensure that they are legible to colour blind individuals, by determining which colours generally confuse both red-green and blue-yellow colour blind people.\r Procedures\r I e-mailed my test, which consisted of 240 slides depicting every possible combination of the 16 basic web colours in the form of a frame, a heading-appropriate sized text and a paragraph-appropriate sized text, to a group of red-green and blue-yellow colour blind individuals, as well as an equally sized control group. I asked them to flip through the slides at a comfortable pace and note the slides that were difficult to read offhand, thus getting an idea of which colour combinations are not suitable for colour blind individuals, as well as the combinations that are not visible to those with normal colour vision.\r Data\r I wrote up my results using tables and stacked column graphs to determine which colour combinations were not visible to an unusually great number of test subjects. I then represented the information I collected in the form of a flash guide. This interactive guide allows one to choose a background colour from a wheel of 16 colours, and then be given a choice of appropriate text colours. The user is also presented with an example of the combination that was chosen, showing how the text appears on the background. The guide is easy to navigate and understand, can be posted on the internet or e-mailed, and is not overly technical so it can be used by designers as well as ordinary internet users.\r Conclusion\r Colour blind people are easily confused by colour combinations which might seem clear to us. My hypothesis was proved as I was able to set up a guide that would make it possible for both colour blind individuals and those with normal colour vision to read the text on websites, social networking pages and digital presentations.

Aims of the project Prevent youth from the -reckless use of the road .shoulder .Reduce the congested roads - Reduce accidents resulting - from the wrong use of the road .shoulder Idea of the Project The control system based road shoulder constantly and actors vis notice of the existence of any prejudice to the safety of road users to take the necessary action against them The beneficiaries of the System With health-Bouts With emergency situations The way the system works When any vehicle parked on the road shoulder remote sensors sensing the vehicle body and the issuance of the initial reference point against the vehicle on the shoulder of a road..And after a period of time known by the concerned and at the same time the system to identify the site and send information to the authority concerned in turn, take the necessary

此研究之重點在於如何建構一套人工智慧方法，人工智慧含多種進行方式，例如以類神經網路訓練近似於人腦之結構，而專家系統係於不同的科學領域內以自己之所知判斷。我們先以 John Holland 的 Genetic Algorithm （暫譯基因演算法，以下暫稱GA）的理論來實作出一套人工智慧系統之方法。Genetic Programming 係以ＧＡ為基礎之實作方法，主要的內容不出基本的演化定義；在這次的試驗中，首要為先定出程式欲演化成何種類型，在此我們先定義為排序型的演算法，經過分析實際程式之結構後定出適合基因元件的資料結構，分化為兩個部份進行，一為產生器，亦為突變，交配器，一為評審程式，亦為執行器，兩者使用相同之基本元件，再以不斷的交配和突變以達到全域最佳化。我們將兩種部份完成後，加上現有的PVM 分散運算函式庫來增加演算的速度。 Abstract The research mainly discusses AI. AI, involves in several types, for example, neural network(NN),which adopts human-like training method; Expert systems determine and make decision by what it has known. We will use John Koza's Genetic Programming theory to implement an AI system.Genetic Programming theory is based on GA. In our experiments, we have to define what kind of applications we want : a sorting application, which is divided into two parts - a producer (along with crossover and mutation operations) and an executor (along with judging operations), is an easyimplemented algorithm. Our program, also with PVM, will approaches global optimal after evolutions.

無疣蝎虎（Hemidactylus bowringii）與蝎虎（Hemidactylus freuatus）分類上屬蜥蜴目守宮科蝎虎屬，為本島住家附近常見且生態地位相近的壁虎，近年來因人為因素使原本有地理區隔的兩種壁虎在北部地區產生共域現象。本研究利用問卷來調查兩種壁虎分佈狀況，並用「體型大小」、「食物競爭能力」兩種指標，設計實驗評估種間競爭程度，來探討兩種居家壁虎種間競爭程度。問卷調查及物種採集結果顯示，在台北市各行政區確實存在共域現象，且分佈數量互有消長。體型大小比較上，蝎虎體型較無疣蝎虎稍大，但在統計上無顯著差異。食物競爭能力強弱比較上，以斷尾後尾巴增長量為指標，結果兩者大致相等，無顯著差異。綜合以上研究結果，顯示兩者共域後會出現種間競爭現象，程度大致相等，有互相消長現象。Hemidactylus bowringii and Hemidactylus freuatus are commonly seen in Taiwan, and their habitats are very near the area people live. Recently, two species have inhabited the same or overlapped geographical areas in northern Taiwan. This sympatric phenomenon resulted from the geographical isolation being broken by people. This research investigated their distributions in Taipei city by using questionnaire, and evaluated the degree of interspecific competitions by using indexes of the body size comparison and the food competition to design our experiments.According to results of questionnaire and animal sampling, two geckos did inhabit closely in some areas in Taipei city, and their population distributions were changing with time. According to the result of the body size comparison, Hemidactylus freuatus is bigger than Hemidactylus bowringii. But there is not a statistically significant difference between two species. The degree of food competition of two species was all square. In summary, it was occurred the interspecific competition between Hemidactylus bowringii and Hemidactylus freuatus, and the degree of competitions was almost equal.

在我們週遭環境中常可見到許多種類的植物，然而可以叫出名字的卻少之又少，或許我們可以查閱植物百之類的書籍，但是這類書籍通常多不在手邊，就算有了植物百科，也不易翻到顯示該種植物的正確章節。假如我們可以將想要認識的植物葉片影像取得後，透過網路將該影像傳送至植物葉片資料庫查詢，經過電腦的自動分析辨識後，再將結果傳送回來，這樣不是比查閱植物百科方便多了嗎？本研究提出一種利用輸入葉片的影像來進行植物資料庫辨識查詢的方法，藉著兩階段處理的策略及最佳權重組合式的特徵值來調校系統，以達到較佳的整體辨識效能，從實驗測試的結果得知，我們的策略與方法確實有效，有82%的查詢葉片可以被精確的辨識出來，而每次查詢的平均反應時間只要17.22 秒。In our living environment, there are many kinds of plants, but we can only name a few. We may consult an encyclopedia about plants, we always can’t find any encyclopedia with us. Besides, even if we have one, it won’t be easy to find out the proper section or the exact page immediately. How should we solve this problem? One significant improvement can be expected if the plant recognition can be carried out by a computer. First, we take a picture of the unknown plant’s leaf. Then, we transmit this image into a leaf database to recognize. After the recognition we will get the answer easily. By using a computer-aided leaf recognition system, non-professionals can also identify many plant species. Isn’t it much more convenient than checking the encyclopedia? In this study, we present an efficient method for leaf database retrieval by inputting leaf images. We use a two-stage approach and combined features with optimized weight to adjust the system to get the best system performance. The result of the experiment shows that our approach is workable and efficient. 82% leaves of the query images can be recognized accurately. And in general, the average response time only takes 17.22 sec per query.

1. 碘酒的配製 碘是非金屬元素，符號為I、而碘分子為I2，具有消毒殺菌作用。碘(I2)不溶於水，在酒精中的溶解速率慢，但非常容易溶於含有碘離子(I－)的水溶液，因I2容易與I－構成錯離子 ，易溶於水。因此要配製碘酒時，要先將1.0克的碘化鉀溶於10毫升的蒸餾水後，加入碘2.5克與酒精50毫升，攪拌使碘完全融解，再加蒸餾水配成100毫升，即成為常用的皮膚消毒劑。 2.碘酒不適於消毒傷口 碘酒與雙氧水一樣，是醫師用來消毒無傷口的皮膚以便進行手術的，因為傷口經不起任何刺激，過於刺激會抑制傷口癒合，有時還會造成疤痕。傷口的消毒最好使用無菌的生理食鹽水沖洗。 3.碘酒與紅藥水不能混用 因為碘酒含有碘(I2)，而紅藥水含有汞(Hg)，兩者相遇會產生碘化汞(HgI2)，碘化汞為劇毒物質，對皮膚黏膜有強烈的刺激作用，可能會引起黏膜潰瘍，所以碘酒和紅藥水不能混用或先後使用。 4.碘酒可用於檢驗澱粉 碘與澱粉的反應非常靈敏，一般稱為碘－澱粉反應。衛生單位曾利用碘－澱粉反應以檢驗餐館碗盤的清潔。碘－澱粉反應的呈色可能是藍、藍紫、棕、甚至粉紅，太濃時可能成黑色。澱粉的組成大約可分為兩類，直鏈澱粉與支鏈澱粉。例如：可溶性澱粉含直鏈澱粉的成分較多，可溶於熱水形成膠體溶液，與碘酒作用則呈現藍色。澱粉遇碘酒會呈現什麼顏色，取決於澱粉中的直鏈澱粉與支鏈澱粉的比例。有的豆類所含的澱粉，幾乎是直鏈的，遇碘酒呈藍色，而糯米中的澱粉幾乎是支鏈的，遇碘酒則呈現紫色。 【動手做】 1.取急救箱的碘酒5滴，加水20滴後攪拌均勻，得黃褐色的碘酒稀溶液，作為檢驗澱粉之用。 2.取一粒生米，搗成粉末後，滴碘酒稀溶液於粉末上，觀察有何變化？ 3.另取一粒飯(熟米)後滴一滴碘酒稀溶液於飯粒上，比較與生米有何不同？ 4.以同樣的方式檢驗家裡的食物，例如：稀飯汁、餅乾、玉米等仔細觀察其顏色的異同。