The World Trade Center in New York City was collapsed after attacked by the terrorist. Although the design of this building did not consider the attack by the terrorist, however, this event also exposed the weakness of a high-rise building. This study is aimed at examining the cause of the collapse of the World Trade Center. A series of experimental studies was carried out to examine the strength of steel material under elevated temperature. Experimental studies were also performed on model steel frames under fire to simulate the situation of World Trade Center under fire. It is found that the strength of steel structure decayed under fire event. The upper stories lost its support from the floor that was subjected to fire load and the collapse of the floor under fire induced impact load from the upper stories. Progressive failure occurred on the subsequent floors due to the impact from the upper stories. This phenomenon was also observed in the experimental study of the model frame tests. This study has successful reproduced the failure mode of the World Trade Center in New York City. 紐約世界貿易中心大樓在遭遇恐怖份子攻擊後倒塌，雖然大樓之設計可能並未考慮恐怖份子的攻擊，但此次事件亦暴露超高層大樓的脆弱，本研究乃探討紐約世貿大樓破壞之原因，研究過程中首先以一系列之試驗探討鋼鐵材料在高溫下之行為，尤其是高溫對鋼材強度之影響。其次並進行鋼骨模型骨架受火燒之破壞試驗，發現在高溫燒烤下鋼骨軟化而失去承載能力，而無法承載上方樓層之重量，上方樓層倒塌後往下形成一衝擊力，並造成往下連續之衝擊，最後導致整體結構倒塌，模型結構試驗亦證實世貿大樓之破壞模式

本研究的目的在於探討蜻蜓兩對翅膀在不同的相位差之下對升力有什麼影響。在觀察蜻蜓及察閱相關網站、研究後發現蜻蜓前後翅的相為差有相差0.5 週期、相差0.25 週期、同週期三種不同振翅方式。在界定欲實驗的種類和評估現有的能力及資源後，決定研究加上相差為0.125 週期的四種振翅方式，於無風條件、相同的振翅頻率下進行實驗，測量其升力的變化週期。測量結果參照前人的文獻後發現，0.5週期產生的升力雖最小，但最平穩，所以為蜻蜓最常用的飛行方式。而0.25 週期升力會疊加，往下的力被抵銷，故為向上加速時使用。 ;The purpose of this study is to investigate the phase-shift between the front-pair and rear-pair wings on the maximum lift of a dragonfly. As observing the flight of a dragonfly and the literature survey from web sides, it has been observed that the general phase-shift modes of the dragonfly are in-phase-shift, 1/2 period and 1/4 period. It has been decided to include a 1/8 period phase-shift mode into the known three modes under the no wind condition with a fixed flapping frequency, the cyclic lift force of the dragonfly wing model has been measured. When it is flapping, we put the model on an electronic scale for measuring the weight of the model. After that we minus the original weight of the model, knowing the increasing or decreasing weight and the extra weight is the lift force. The results show that 1/2 period phase-shift mode produces the least lift force; however, it is the most stable flight, and is being adopted by the dragonfly for level flight. The in-phase-shift mode can produce more lift force on the flapping processes. The 1/4 period phase-shift mode produce the most acceleration, being adopted by the dragonfly for the climb flight.

This study investigates the possibility that “Digital Buses” would actually be used in real life. In addition to the basic mathematics knowledge that I have acquired over the years, I have used “Microsoft Visual Basic” and “LEGO ROBOLAB SOFTWARE” to implement the idea as a program. It simulates the way in which a digital bus travels in a city with a rectangular grid. Various plans are tested to find the best paths for providing the most efficient, convenient and speedy transportation. This study has not only shown that “Digital Buses” are sure to be used in a modern city when wireless communication networks has developed to a certain point, but also supplied a framework for future researchers who may wish to study the optimal way in which more than one digital buses could efficiently run in cities according to their population distributions and road arguments, in order to overcome the traffic problems from the current bus systems. 本研究探討數位公車在人類未來生活中實際運行的可行性。本人以所學的數學知識進行公車路徑規劃，並透過「樂高機器人控制系統」以及Microsoft Visual Basic 軟體程式之撰寫，在棋盤式城市區域中模擬公車行駛情境，靈活搭配各種方案找出最佳路徑，達到便利快捷的高運輸效能。本研究顯示當現代化都市無線通訊網路發達到一定的程度時，數位公車的發展是可以預期的。本研究之結果可提供後續研究者繼續探討多台數位公車在實際都市中依人口分佈、道路狀況來規劃最佳行駛路徑，以解決現今機械公車無法克服之繁雜交通困境。

從小習染之餘，對篆刻藝術的濃厚興趣及對電腦程式之熱愛，萌生將篆刻藝術與電腦 科技結合，於是應用PHP（Professional Home Page）的文字圖形（Text Image）處理功能 將中華文化之篆刻藝術透過網際網路推廣到世界各角落。本研究規劃建置了一個 FreeBSD Server 可完善處理PHP 功能的作業平台、應用PHP 的文字圖形處理功能，編 寫可在線上DIY 設計印章的程式，以及藉由Java Script 的技術在Client 端建立一個人 性化且相容性高之使用者界面網頁，達到提供多語系、多功能、依使用者偏好作調整 印章及輸出分享的功能。為使非漢語系國家能深刻體驗中華篆刻藝術，本研究同時建 立一個超過三萬筆之由英文名音譯中文名的資料庫，提供給使用者切身的服務。 Inspired by the interest of the art of seal engraving and the love for the computer programming beginning from my childhood, I combine the art of seal engraving and computer technology, and apply the Text-Image's function of PHP to promote the seal-engraving art of Chinese culture via the Internet to everywhere around the world. This project constructs a FreeBSD Server to process PHP platform perfectly, applies the Text-Image's function of PHP to write a program for online DIY pattern design, and uses Java Script to establish a human and compatible user-interface web page for clients to provide multi-language, multi-function, and being able to adjust pattern according to the user's preference and output sharing functions. This project also sets up a database of English-Chinese translation of over thirty thousand English terms to help people who are not Chinese to experience the art of seal engraving.

Cultures of bacteria were analyzed using fractal geometry and statistics to provide a method for predicting organism growth, paving the way for a better design of treatment drugs. Images of three cultures of isolated Bacillus subtilis were taken at time intervals of two to three hours for eight days. The images were processed using the IDOLON program and quantitatively described using three statistical formulas: fractal dimension D, Renyi dimension and Hausdorff-Besicovitch dimension. The three variables were integrated to compute the maximum of the distribution and were used as coordinates for a 3-dimensional graph f. A 2-dimensional graph g containing the maximum of a distribution under time analysis was also constructed. Topological properties of the graphs, including slope, direction and area were used to determine the interrelationship of the three fractal values. The two graphs, described as φ - : X -? P1 where X is the smooth algebraic assimilation of the four variables under time analysis, was extended using Java. A computer-aided prediction model of the graphs f and g were made which combined the topology of f and g at infinity. The computed fractal values showed the existence of a fractal pattern in the growth of Bacillus subtilis with fractal dimension ranging from 0.900 to 4.000, indicating a linear iteration. This was supported by the values of the Renyi dimension, which showed a horizontal growth pattern of the bacterial cultures, establishing the growth of the bacteria to be inclined to go towards the North East direction. There was consistency in the computed fractal values, maximum of distribution and topographical computations of all three cultures which also indicated the existence of a pattern of growth which could be extended to tinfinity, thereby allowing prediction of the direction and rate of growth of the bacterial colonies. The fractal patterns in the growth of bacteria, in this case Bacillus subtilis, yielded the direction and rate of growth of the bacteria as shown by the analysis of the fractal patterns and statistical values, showing that the growth of harmful organisms can therefore be predicted, making it possible to improve on the design of drugs for the control of perilous cells. By preventing the growth of insidious cells, the potential effects of virulent organisms may be avoided, and treatment may be made more possible.

本研究為首次由台灣本地作者進行的擬蠍研究，擬蠍歐美稱書蠍(Book scorpion)，在中國又稱偽蠍，屬蛛形綱的節肢動物，體型微小約2-5mm，台灣目前已知8屬10種，作者收集整理過去相關文獻，並對作者所採集到的加氏赭擬蠍Ochrochernes galatheae，長指地擬蠍Geogarypus longidigitatus，及緩步威擬蠍Withius piger進行描述、拍照與繪圖，並首次記錄大衛天牛(Batocera davidi)的鞘翅下的緩步威擬蠍與雙首冠擬蠍(Lophochernes bicarinatus)。另外還採集到1種暴擬蠍(Tyrannochthonius sp.)與1種小肉擬蠍(Microcreagris sp.)待後續研究。

電風扇在炙熱的夏日中為冷器以外不可或缺的生活用品。一個典型的電風扇是由架在可調高度鐵柱上的馬達及風扇構成。現行傳統電風扇有幾個缺點，一、馬達風扇(即重心)位置高，有易傾覆的缺點。二、風力分散，風速不高。三、吹出不可調室溫溫度的風。四、外觀呆板，傳統無奇。五、多噪音等。本研究根據這幾點傳統電風扇缺點，試著設計新的電風扇。首先將柱子移除使重心降至接近地面處。接著根據連續方程式(continuity equationρ1A1V1 ＝ρ2A2V2)製作圓錐狀「號角」裝置套於電風扇上以集中風力並減少噪音。最後企圖使用熱電半導體的致冷器降低輸出風的溫度。研究結果發現號角裝置有效達到預期的集中風力增加範圍目的。不幸發現以熱電半導體降溫的方式效率低且耗損過多能量所以可行性較低。雖然沒有降溫功能，本電風扇仍較傳統電風扇多出許多好處，例如加強的安全性、集中的風和強大擴充性。號角裝置可包含空氣清淨甚至音箱功能充當喇叭。Electric fans are a necessity during summer, especially in a hot and humid place such as Taiwan. A typical electric fan is primarily composed of an electric motor with fans mounted on a strut with user adjustable elevations. This setup presents several problems, including (a) the danger of an accidental tip-over due to the fan's elevated weight center (the heavy motor), (b) high wind dispersal rates, (c) room temperature winds, (d) excessive noise and (e) old, antiquated exterior appearance. This particular study attempts to alleviate all these problems. First the weight center is lowered to ground level by removing the entire strut and placing the motor close to the floor. Next by using calculations from the continuity equation(continuity equationρ1A1V1 ＝ρ2A2V2)a cone shaped “horn” device is placed over the fan in order to concentrate the wind, effectively increasing its speed while decreasing the audible noise level. Finally, an attempt was made to lower the temperature of the air in the interior of the horn by the placement of a thermoelectric semi-conductor cooling device. Our results were that the horn device worked, significantly lowered the wind dispersal rate and achieved an important objective. However, the thermoelectric cooling solution proved to be highly inefficient unless accompanied by precise wind speeds. Even without the cooling function, this new electric fan still has many distinct advantages over traditional fans such as improved safety, concentrated winds and high expandability. For instance, filters can be integrated to purify air, even an audio speaker can be made into the form of this fan.

我一直在想，為什麼植物的美麗不能永恆呢？美麗的花朵，伴隨答淡雅的香氣，往往能美化環境，更能淨化人心，自小生長在鄉間的我，更能感受到這份來自花草的神奇力量，因此深深愛上這花草世界．但為何花朵的美麗總是短暫，為了想讓植物開花的時間長久，於是，我著手進行在自然科技雜誌及網路上搜尋相關的資料及訊息，但是找到的大多都是使生長速率變快的報告，卻找不到使生長速率變慢的報告。終於，曾經有人運用圓周運動的原理，而成功的使動物的生長速率變慢，於是，我針對直線運動及圓周運動分別依速度快及速度慢來分成四組，以及一組靜止狀態的綠豆，將五組實驗後的數據相互作比較，結果發現，除了陽光、水、空氣、土壤、養分及本身具有的胚胎外，在不同的運動狀態下也會影響到植物的生長速率 ·I was thinking about the reason why the beauty of plants couldn’t last forever. The beauty of flowers that accompanied with sweet-smelling could beautify the landscapes and purify our heart. I felt strongly about the magic power of the plant because I lived in the country in my childhood. Therefore, I loved plants deeply. Why was the beauty of flowers transient? As a result. I started to search for the related data and information on science and technology magazines and Internet. Most of the reports increase the growth rate of plants, but I cou1dn find the reports about slowing down the growth rate.At last, someone had successfully used the principle of circumference movement to slow down the growth rate of animals. Therefore, I focused on linear and circumference movement and divided them into four groups and one group of green beans with still state. I compared the data of five groups, and found that different movement affected the growth rate of plants m addition to sun, water, air, soil, and embryo.

The starting point of this experiment is to study the structure of soap-film. By changing the height of the triangular prisms, cuboids and pentagonal prisms, I observed the patterns set by the soap within the frameworks. It is surprised that when the proportion of prism is in a specific range, the phase in the middle of the structure will overturn 90 degree and then transmitted into another kind of balance pattern. I named this process “phase transition”. According to the experiment ,we can conclude the change of film patterns within variable prisms are all applied to this regular cycle:： We know the soap films are forever attempting to minimize their energy. It stands to reason that surface tension tend to set up the film in its minimal surface. From the point of Mathematic, each structure should have only one single balance pattern, which is set up on the base of Fermat point and this pattern should stand to the minimize of it’s energy. However, we discovered that in some specific cases, one structure can allowed two kinds of balance films-patterns to exist. In these cases, any small vibration can cause the happening of “phase transition”. To sum up, I presume some structures have two different types of balance film-patterns: one of which stands to the local minimum (in this condition the pattern’s surface area isn’t the smallest); the other stands to the absolute minimum (in this condition the pattern’s surface area is the smallest). There is an energy valley separate local minimum from absolute minimum. The second pattern (local minimum) will appear when the structure is blocked from attaining its absolute minimum, but surface intention is not powerful enough to support the film jumping over the energy valley. In this condition, if we works on the structure (such as blowing), which would provide the film of energy to cross the valley, and then phase transition take place. Vice versa, we can also force the film to jump from absolute minimum to local minimum and phase transition will occur as well. In a word, phase transition can happen in each two way, which connects the two types of balance pattern. This report lays stress to find out the condition of phase transition. We also analyze the structure of soap-film by its included angles and surface area in hope to go deep into the science of soap-film. 我們實驗的出發點在於研究泡膜的立體結構。藉由改變正立方柱的高，觀察其平衡薄膜形式，意外的發現當正立方柱的邊長比在某個範圍時，泡膜結構中央會瞬間90 度翻轉，形成另一種平衡型式，我們將這個過程命名為面轉變(Phase Transition)。為了進一步了解面轉變發生的相關因素，我們設計了一連串的實驗，針對正三角柱、正四角柱、正五角柱、正六角柱發生面轉變的時機和條件分析討論。此外，我們還分析了泡膜結構中膜與膜夾角的特性、最小表面積和表面能之間的相關性，對於泡膜的立體結構做了一系列深入的探討。

Generally speaking in order for a exotic plant life to dominate over the local ecology, the following factors must hold true: 1. A close proximity of the environment (including geographical and climatic factors) 2. A lack of nature enemy and competitor 3. A strong reproductive and adaptability capacity. Base on the above factors, We will be using Field Observation record, Sample placement, virtual environment factor experiment and other methods to conducing our investigation. This study shown the African Touch-Me-Not（Impatiens wallerana） has a strong reproductive and adaptability capacity. Even under adverse condition the African Touch-Me-Not survive for a period of time. It can produce flowers then fruits all year round, within each fruit there is on average 45 seeds with, under the right condition, near 100% germination rate. It can also reproduce asexually via cutting. Taiwan’s warm and humid geographical condition is similar to its origin of Africa. And so far haven’t found any obvious natural enemy. In the future this plant will be likely to spread on the low to mid. level mountain region. It also can be seen that the divergence within its habitat is low. Therefore it will decrease the variety, the density and the diversification of the local eco-system. Here to advise the government’s forestry and agriculture department, to study the relevant ecological information on this species, when they are considering popularization this plant. Using the information to evaluate the impact of this plant may have on the environment, and use it as a guideline for their plant conservation policy. 一般而言，外來植物入侵本地原生植群成功的條件有：一、相似的環境（包括地理、氣候等因素）。二、缺乏天敵及競爭對手。三、旺盛的繁殖力和適應力。針對上述條件，利用野外觀察記錄、樣區設置及模擬環境因子實驗等方法，來探討非洲大鳳仙未來是否會在臺灣蔓延、擴展進而影響本土的生態系。結果顯示非洲大鳳仙有旺盛的繁殖力和適應力，?使在不利的環境下，短時間不會死亡。一年四季皆可開花結果，每粒果實平均有四十五粒種子。環境適宜時，有接近百分之百的萌發率，亦可用莖進行無性繁殖。另外，臺灣溫暖多雨的地理環境亦與其原產地非洲相似，且未發現明顯天敵，未來極有可能在中低海拔山區蔓延。調查也發現它生長的地區岐異度明顯偏低，使其他植物種類、密度減少，生物多樣性降低。因此建議政府、森林、園藝和農業工作人員在推廣時，多吸取相關物種的生態學資訊，評估其對環境可能造成之影響，以作為植物保育之重要參考。

在實驗中學2007 年校內科展，參展作品《三角形中的切圓》的研究中，研究三角形內的切圓時，發現連續切圓的圓心與拋物線的軌跡有關。於是去查資料，在偶然的情況下，翻閱《平面幾何中的小花》時，接觸了「六圓定理」。因為覺得這問題非常有趣，於是便著手證明（見報告內文）。 又發現，當移動六個圓中的起始圓時，總是在某種情況下，六個圓會重合成三個圓。繼續研究其重合的狀況，發現了馬爾法蒂問題（Malfatti's Problem）的一種代數解法。 當我試著推廣六圓定理至多邊形時，發現奇數邊的多邊形似乎也有如六圓定理般圓循環的狀況，於是著手證明，但目前尚未證明成功。而偶數邊的多邊形則無類似的結果。 ;In 2007 National Experimental High School Science Exhibition, one of the exhibit works, "Inscribed Circles in Triangles", shows that the centers of the consecutive inscribed circles has something to do with the parabola's trajectory. To learn more about inscribed circles and parabolas, I referred to literature. By accident, I am faced with the problem on six circles theorem, in the book The Small Flower of Plane Geometry(平面幾何中的小花). Out of my interest in this problem, I tried to prove it. The other results are as follows: With the initial circle of six circles moved, in certain circumstances, the six circles merge into three. Further in studying this coincidence leads to an algebraic method to solve the Malfatti's Problem. Applying six circles theorem to the odd-number-sided polygons exists the same characteristic. It indicates that the inscribed circles will form a cycle. However, it hasn’t been successfully proven. The even-number-sided polygons show no similar results.

"Nitrates and phosphates cause eutrophication when present in high concentrations.\r This project aims to employ macrophytes to reduce such macronutrients in water bodies via growth and kinetic studies, which is a unique fusion of methodologies. It also involves a novel design and analysis of several enclosure prototypes to introduce macrophytes into waterways and their effects on the waterway’s ability to convey storm water rapidly away from flood-prone areas.\r Tropical macrophytes (emergent macrophytes Typha angustifolia and Cyperus haspan, submerged macrophytes Hydrilla verticillata and Cabomba aquatica, floating macrophytes Lemna minor) were grown in simulated wastewater with high nitrate and phosphate concentrations. Analysis of the growth and uptake kinetics of the macrophytes showed a correlation between high growth rate and high nitrates and phosphates uptake. C. aquatica had the highest uptake rate for nitrates and phosphates as well as the highest growth rate of 6.11 ± 1.2 % day-1 . The remaining macrophytes were proven to exhibit good phytoremediative properties, with emergent macrophytes C. haspan and T. angustifolia having great affinity (as indicated by a low Km value) for phosphate and nitrate respectively. An analysis of the phytoremediative abilities of each macrophyte was done to provide recommendations for growth in different aquatic areas.\r A total of eight nettings, made from different materials-linen and plastic, and pore sizes were used to design the enclosure prototypes. These enclosures possess a metal skeletal structure for greater stability. Results show that a combination of 2 different nettings provided the best trade-off between ensuring that the macrophytes were contained within the enclosures and minimising the enclosure’s impact on the flow velocity of the waterways. Enclosures could then be attached to existing infrastructure like the float booms as a platform for large scale phytoremediation locally."