本研究針對東北角鼻頭港海域中主要的珊瑚品種──萼柱珊瑚（Stylophora pistillata）進行實地觀察、實驗研究，藉以探究其與共生藻(zooxanthellae)之關係。透過複式顯微鏡觀察共生藻和珊瑚蟲。使用細胞計數器計算共生藻數量，再除以珊瑚分枝面積可得共生藻密度。影響珊瑚白化最劇烈的因子是海水溫度的極端高低溫變化。因此，測量棲地水溫為本研究監測對象。實驗驗證：短時間內水溫劇烈降低或稍長時間溫度穩定上升超出珊瑚適應範圍，共生藻密度隨之減少，造成白化。實驗綜合浮潛觀察，發現鼻頭海域的萼柱珊瑚在2010年7~8月可見白化的現象。

三角形的邊上取任意多個點，我們可以把這塊大三角形沿著切割線切割成較小塊的三角形，但切割線必須是點（或頂點）和點的連線，而且必須切割三角形，同時可以切任意大小的三角形，如圖（1）與圖（2）。但不可以一開始就取走整個三角形。定義拿到最後一塊三角形的人獲勝，而在多邊型中的玩法與在三角形中相同。 我們分A、B、C三種規則來討論，其中A規則即是上面提到的玩法，B規則大部分的玩法和A規則都相同，唯一不同的地方在於：A規則中，只要有一方取到剩下的圖形為三角形，另一方就可以直接取走剩下的三角形，而B規則規定即使剩下的圖形已經是三角形，也必須取到剩下的圖形邊上都沒有分點為止。C規則是限制玩家一次所能取的三角形數來進行遊戲。 我們完成了A、B、C規則中三角形與多邊形的必勝策略，並找出必勝策略之間的關聯。 ;Given any numbers of points on the sides of a triangle, the players can cut this triangle into pieces. Each cutting line has to be one, linked between two points given from two different sides. And the player can’t have to cut smaller triangles out of the original triangle. The out-cut triangles can be chosen randomly without any restriction in size, just like what’s shown in picture（1）and（2）. Meanwhile the first player can’t cut the original triangle exactly all out in the very beginning process. We define the player as the winner, who gets the last triangle. And the above way we play can be applies to any multi-side shapes. We discussed the question respectively in three rules, A, B, and C. Rule A is what we mention above. Rule B is generally the same as rule A, except for the only difference：The rule A , if there is any triangle left , the next player can get it directly, but while in rule B, the every next player has to cut out smaller triangles until no point is left on sides. Rule C proceeds on conditions that there is a limitation to a certain number of triangles cut out at a time. We has finished the winning tactic respectively in rule A, B, and C in the games with a triangle and multi-side shapes. Furthermore, we find the connection between the winning tactives.

隨著科技的發達，工業廢棄物應運而生，在地小人稠的台灣，每年就產生約6000 公噸的廢觸媒，為了讓環境免於遭受廢棄物的污染，本實驗著重於廢觸媒的再利用，探討廢觸媒作為混凝土中礦物摻料對水泥(砂)漿流動性的影響。 本實驗所採用的廢觸媒來自石油裂解廠的靜電集塵廢觸媒，主要由SiO2 及Al2O3 所組成且具有部份非結晶相和卜作嵐材料之特性，外觀為乳灰白色粉末、含水量2.8﹪，溶於水中有放熱現象，pH 值為3.85。廢觸媒對水的親和力大，添加至水泥(砂)漿中會使得漿體的流動性減小，因此必須藉由提昇強塑劑劑量才能提高工作度。 在水膠比(W/B)為0.42 時，隨著強塑劑HPC-1000 劑量的增加，水泥漿的流度明顯增加，而且適當量的廢觸媒取代水泥，能維持水泥漿一定的流度。當強塑劑HPC-1000 劑量為3.0﹪、砂/水泥＝2.75 時，隨著水灰比(W/C)的增加，水泥漿的流度也明顯增加，而同條件下，不論水膠比(W/B)0.485 或0.55 時，廢觸媒取代水泥之水泥砂漿的流度比飛灰、爐石、高嶺土好，與矽灰相當，其最佳取代水泥量為15﹪。 As technology continues to develop, a considerable amount of industrial wastes have been produced.In Taiwan, over 6,000 tons of spent catalysts were brought out yearly. If such wastes can be reused in some ways, it may be helpful to protect our environment from being polluted. This study was taken to determine the influence of spent catalysts on the flowability of mortar while the catalysts were used as mineral additives for concrete. Since the catalysts could reduce the flowability of cement pastes because of the affinity between the catalysts and water, it was necessary to have superplasticizers added to improve the fluidity of the mortar. The spent catalysts used in this study were spent electrostatic precipitator cracking catalysts, called Epcat, which were provided by petroleum refining companies. Comprising mainly silicon oxide and aluminum oxide, the off-white catalyst powder present water content of 2.8%, pH value of 3.85 and exothermic reaction with water. In this study, it was found that while the ratio of water to binder (W/B) was 0.42, the flowability of the cement pastes increased with the increasing addition of superplasticizers. Besides, the flowability of cement pastes kept steady while a proper amount of Epcat was used to replace cement.When the ratio of sand to cement (W/C) was 2.75, with 3.0% superplasticizers HPC-1000 added,the flowability of the mortars markedly increased while the W/C increased, and the replacement with spent catalysts made the mortars show similar flowability as silica fume but better flowability than fly ash, slag and kaolinite, no matter the W/B value of the cement pastes was 0.485 or 0.55. In fact, the best Epcat replacement for cement was 15%.

隨著工商業發展，環境污染日益嚴重，對多數生長在這塊土地上的人，無疑造成了非常嚴重的影響。但若想要監控目前環境中的空氣品質，則必須具備專業的訓練，及昂貴的實驗設備，對一般民眾而言，根本就做不到。\r 藉由指標植物對所生長環境的高度敏感性，可以發展出一套純天然且免費的環境污染偵測器，不但方便、免攜帶、無須高級儀器協助、更不需要專業的分析技術。為此，我們以對二氧化硫等空氣污染物極為敏感的地衣作為指標植物，對其進行生態與環境污染關係的一系列觀察，並設計相關的實驗，找出環境污染物對地衣的實際影響，使其能夠實際的應用於日常生活，並可加以推廣，讓人人都可以利用地衣來了解自己所處的環境是否遭受污染，為自己家園的環境優劣把關。\r \r 文摘要 :\r With the development of industry and business , environmental pollutions become more and more serious . Undoubtedly , those pollutions have a great effect on us.\r However , by the means of the indicator plant which is highly sensitive to its environment , we can develop a set of natural and free environmental pollution detectors . In this project , we use lichenes,which are very sensitive to air pollution , to do a series of observations and to find out the influence the pollutants have on lichenes . If we can apply this to our regular lives , everyone can use lichenes to see if their environment is polluted or not .

Lotus self-cleaning effect arises because the leaves have the superhydrophobic surfaces. When rain falls onto a lotus leaf, water beads up as a result of surface tension. The water drops promptly roll off the surface, taking every dirt with them. This phenomenon is called the lotus effect. With the aid of a light microscope and an Environmental Scanning Electron Microscope, we observe and describe the morphology of the leaves of Nelumbo nucifera in detail. We successfully observe the real interface between air, water droplets and the papillae of a lotus leaf, and find the evidence of a composite surface that is formed by epicuticular wax crystals and air. These observations improve our understanding of the two-level composite surfaces that are formed by micro-scale papillae, nano-scale epicuticular wax crystals and air. We try the method of using the critical angle of a static drop beginning to roll on inclined surface to evaluate the self-cleaning ability. We then find out that it may be a more precise criterion compared to using the static contact angle for the evaluation of the lotus effect. Literature review shows that the earlier investigation lacks the height(H) and interval(I) of the projections on the lotus leaf surface. A close relationship between the self-cleaning property and the H/I ratio is found. In this study, we present the experimental data of the height and interval of the projections on four different species of plant leaves that all have lotus effect, which may be of great help to technological applications. 蓮花效應是指蓮葉表面具有超疏水性與自我潔淨的能力，當雨水落在葉面，因為表面張力的作用形成水珠，水滴迅速滾離葉面，把灰塵一起帶走。本實驗以光學顯微鏡和環境式掃描式電子顯微鏡觀察蓮葉，詳細描述其表面形態，成功的發現空氣、水滴和蓮葉乳突真實的接觸界面以及表面蠟和空氣構成複合表面的證據。實驗結果可以使乳突、奈米表面臘質和空氣構成的雙層次複合表面更容易被了解。我們嘗試以水滴傾斜滾動臨界角來評估自潔能力強弱，實驗結果比傳統使用靜止接觸角更為準確。表面高度和間距的比值與蓮花效應有很大的關係，查閱文獻顯示蓮葉缺乏這些資料，本研究提出四種有自潔能力的葉子的實驗數據，這些數據應該對科技應用有很大的幫助。

目的：1. 以地理資訊系統分析臺北市靜水生態系的分布狀況；2. 分析靜水生態系的連接度。過程和結果：我實地踏察了臺北市區的381 個地點，在其中187 處發現224 個靜水生態系，首次統整出臺北市區靜水生態系的現況資料。靜水生態系的平均密度為0.82 個/km2，其密度與人口密度成正比。以 GIS 軟體標定這些水池，發現它們成任意或叢生分布。再以 VisualBasic 程式語言設計程式，以預測移動能力不同的濕地生物在這些靜水生態系間移動的情形。結論：由程式模擬可知，能在所紀錄地點間自由移動的濕地生物種類很少，顯示都市化對靜水生態系的隔絕效應。In a city, still water ecosystems (ponds and lakes) are divided by buildings and roads, so they are not continuous in the space. I surveyed 381 sites in Taipei City and found 224 ponds and lakes at 187 sites. The density of still water ecosystems is 0.82 per square kilometer. The density of still water ecosystems is higher in areas where more people live. I use a geographical information system software to mark the locations of these ponds. Their distribution is either random or clumped. I use Visual Basic to design a program to predict how do wetland creatures move among these sites. My program tells that very few creatures can move freely, indicating still water ecosystems in this city are quite isolated.

Surfactants have a great effect on decreasing the surface tension in aqueous solution and thus they are important components in detergents. The present study aims to explore the cleaning mechanisms of the substances for greasy subjects such as bowls and clothes. The roles of various surfactants that have on the changes in the surface tension of aqueous solution in the presence and absence of additives such as tea and salt have been carefully studied by using a lab-made equipment. We carefully observed the changes in the oil droplets after pushing oil in a syringe to the aqueous\r solution containing surfactants and additives. With decreasing the surface tension of the aqueous solution, the size of the droplet becomes smaller. By using this simple lab-made equipment, we are able to determine the critical micelle concentration (CMC) of sodium dodecyl sulfate (SDS), with a result of 0.0079 M at 20 ℃. The result is in a good agreement with the literature (0.0077M). With decreasing temperature and adding salts such as sodium sulfate, the decreases in the surface tension have been confirmed by our simple experiments. This simple equipment also allows study of the effects of impure additives such as salt, tea, vinegar that have on the changes in the surface tension of aqueous solution containing commercial detergents. We have found that most of the additives have a great effect on reducing the surface tension of the aqueous solution. The present study results suggest that the simple experimental set-up is practical for measuring the CMC of surfactants and for exploring the effects of additives on changes in the cleaning ability of commercial detergents.界面活劑性可有效降低水溶液的表面張力，因此，他們是清潔劑的重要成份。該實驗主\r 要在探討各種物質的清潔機制。利用自製的實驗裝置，針對各種不同的界面活性劑在添加了鹽類或茶水後界面張力的改變量，作詳盡的探討。我們將含有不同濃度界面活性劑以及添加物的水溶液裝入容器中，在推擠針筒使其的油通過針頭並進入該溶液後，我們仔細的觀察紀錄油滴大小的改變。結果顯示界面張力的降低會使得油滴變小。藉這個自製的裝置，在20℃下，本實驗所測得的陰離子型界面活性劑-十二烷基硫酸鈉之臨界微胞濃度0.0079M。結果幾乎與過去的文獻0.0077M 值符合。該實驗同時也證實了降低溫度，添加了鹽類後，可有效的降低界面張力。此外，此實驗裝置也可以用來測量市面上販售的清潔劑在添加了不純的物質後，其界面張力的改變量。我們發現大多數的添加物都能有效降低界面張力。目前的實驗結果顯示，這項實驗裝置在測定臨界微胞上有很高的實用性，同時也可以探討不同的添加物對市面上販售的清潔劑之洗淨力的影響。

Every year more soluble and insoluble substances are added to the oceans by runoff. This process slowly increases the salinity of the oceans. As the salinity of the oceans increase, what effect will this have on our climate? The purpose of this investigation is to determine how an increase in salt concentration affects the evaporation of sea water. Four ten liter aquaria were filled with six liters of distilled water in each aquarium. One aquarium contained only water. The other three aquaria had different amounts of Kosher salt added as follows: 120. grams, 240.grams and 480.grams. Measurements of the level of water in each tank were taken over a period of two months. The tank with the highest concentration of salt had the smallest rate of evaporation. In the feature with less evaporation of sea water the atmosphere will receive less moisture. This could result in fewer clouds and less rain fall for the planet.

我們就單純的數學方法研究向日葵原基排列的規則列出以下的研究目的:一、費氏數列與原基緊密排列之關係 二、螺旋結構的產生、方向與螺線數目的關係三、向日葵雙螺旋結構的特性兩原基相切的關係式 p2＝1－2×(cosmφ＋1)/(amφ＋1/amφ＋2)初始原基標示為A0，設Am 為後續第m個產生的原基，與A0 相切，切點為T， 則p2＝1－2×(cosmφ＋1)/(amφ＋1/amφ＋2)《以餘弦得證》費氏數列與原基相切之關係如下：(一)若生成螺線方程式為r＝aθ, 0＜a＜1，則必存在n嘁，使得Q(a)＝Pa(Fn)。(三)原基相切會讓向日葵形成螺旋結構，而且螺線的數目必為費氏數列的某一項Fn。若n 為奇數，則螺旋方向為逆時針；若n 為偶數，則為順時針。(四)原基緊密的排列形成雙螺旋結構，使向日葵花頭最密實。

This paper describes the investigation of a fascinating physical phenomenon called the “floating water bridge”. Despite the fact that water is undoubtedly the most important chemical substance on earth, it is practically ubiquitous and it still represents one of the best explored substances, still not all characteristics are well-understood. There are some phenomena like the “floating water bridge”, which cannot be explained. If high voltage is applied to two beakers, which are arranged close to each other and which are filled with deionized water, a connection forms spontaneously, giving the impression of a floating water bridge. For the experiment discussed in this paper, two beakers with a diameter of 50 mm and a height of 80 mm are filled with triply deionized water. Platinum electrodes are submerged in the center of the beakers, one set to ground potential (anode), the other one on high voltage, up to 25 kV dc. Within the scope of this work, an experimental setup was developed, which enables measuring and demonstrating the most important parameters like voltage, current, length and temperature of the water bridge as well as the mass transfer between the beakers. In addition the correlation between the different parameters and the influence on the water bridge could be estimated. Once the beakers are separated, the bridge remains stable for several hours up to a length of 2.5 cm. With platinum electrodes and no electrolysis observed, a small current (≈300µA), a mass flow from anode to cathode and forces were measured. Pictures, taken with an infrared camera and a new developed method to record "infrared-videos", enabled to visualize the heat flow in the water bridge. Furthermore the conversion of energy and the dependence of charge and mass transfer could be estimated roughly. In the course of the investigations it was also tried to prove the water bridge with other liquids like castor oil, olive oil, a mixture of glycol and water as well as tap water - for some of them for the first time. Supplementary the experimental setup was varied by using different electrodes with different sizes and different material as well as beakers of different sizes and materials. In addition, a qualitative explanation was developed. The results of this work enable a better understanding of the floating water bridge and provide a basis for further research as well as for development of future practical applications. One of these applications could be an improved waste water treatment process.

由於低廉成本、無毒及其他原因，由二氧化鈦、有機染料及電解液所製造的光敏有機太陽能電池(DSC)被預測即將成為一種大規模廣泛流行的太陽能電池。本實驗比較合成染料(像紅汞和疊氮離子)及成本較低且無毒的天然植物染料用於太陽能電池的效能。有些天然植物染料的效能大於合成染料的效能，像是紫色高麗菜、地瓜……等。在研製太陽能電池的過程中, 本研究利用自製的幾丁質燒結出的奈米顆粒成效極佳，不但粒徑大小符合，在燒結的過程中也不需經過物理研磨及介面活性劑的輔助，並且在低溫下即可燒結，並由BET 和SEM 測得幾丁質燒結的TiO2 的孔隙度大於標準燒結的TiO2 的孔隙度，因此本實驗決定利用去乙醯化之幾丁質扮演太陽能電池的二種角色:介面活性劑及保護劑。在本實驗中，部分的電池效能不盡理想，或許是因為所有的太陽電池樣本均使用相同的電解液(I3-)。要找到每種太陽能電池最適合的電解液則需要更多的研究。Because of the desirable features of low cost, non-toxin, and other reasons a dye-sensitized nanostructured solar cell (DSC) composed of nanocrystalline TiO2, organic dyes and electroiytes is expected to be in prevalent use. This study compared the differences in the functioning of different dyes in the solar cells, specifically those between the synthetic dyes, such as Merchrochronate and Polypyridyl complexes of ruthenium (N3-), and dyes made of natural plants which cost less and are not toxic. Some natural dyes, such as purple cabbage, sweet potato, etc, were found to have better efficiency than the synthetic dyes. The study makes use of self-made chitin to sinter nano particles, and the result is excellent. First, the particle radius meets the size requirements. Second, in the process of sintering nano particles, no physical pulverizing or surfactant assistance was needed. Third, the nano particles can be sintered at a low temperature. Fourth, from BET and SEM measurements, the degree of aperture of TiO2 sintered with chitin is superior to that sintered with Triton X-100. For these reasons, the de-acetylated chitin was chosen to serve as surfactant assistance and protector in the solar cells in this study. The study also found that some solar cells were not efficient enough. Maybe it is because all the samples of solar cells in this study were produced with the same electrolyte (I3-). Further study is needed to figure out the most suitable electrolytes for each solar cell.

傳統的畢氏定理三元二次不定方程x² + y² = z²有一組漂亮的整數解為(m² - n²、2mn、m² + n² )；中國數學家嚴鎮軍、盛立人所著的從勾股定理談起一書中記載四元二次不定方程x² + y² + z² = w²的整數解為(mn、m² + mn、mn + n²、m²+ mn + n² )，這組解被我們發現有多處遺漏，本文以擴展的畢氏定理做基礎修正了他的整數解公式，並推廣取得N 元二次不定方程的整數解公式。 There is a beautiful integer solution formula for the Pythagorean theorem equation, x² + y² = z² , such as (m² - n² , 2mn ,m² + n² ). The “m＂ and “n＂ of the solution formula are integer number. A book written by two Chinese mathematicians, Yen Chen-chun and Sheng Li-jen who expanded the Pythagorean theorem equation to the four variables squares’ indeterminate equation, x² + y² + z² = w² . They claimed that they found its integer solution formula, such as (mn , m² + mn , mn + n² , m² + mn + n² ) for any integer “m＂ and “n＂. But we found it losses many solutions. This paper corrected their faults due to the expanded Pythagorean theorem built by ourselves. Further more, we derived a general formula of N variables squares’ indeterminate equation. Now, we can get integer solutions of the equation, (for all natural number “n＂) easily by choosing integers m1 , m2 , m3 ,……, mn−1 up to you.