我們研究的主題是曲率，且以高中所學的函數為主。雖然大學已有曲率公式，但我們將其表示成高中生較易了解的型式，並且以f(x) 的方式呈現。我們在函數曲線上取不共線三點，構成一個三角形，並求出此三角形的外接圓半徑。再將所取三點逼近，所求之半徑即為特定點的密切圓，也就是曲率半徑。而此曲率半徑的倒數，就是所求的曲率，同時我們將公式帶入高中各常見函數，以導出函數上各點曲率。;Our study is about curvature, especially about the fuctions we learn in senior high school. In university, there is a certain formula for curvature, but we hope to change it into a form that can be easily accepted by senior high school students, and express the formula with f(x), the symbol of functions. We pick three incollinear points from the curve of a function, making the three points into a triangle, and figure out the circumradius of this triangle. Then, we approximate the three points to one of them, and the circumradius will also be the radius of the osculating circle of the point. We define the radius as radius of curvature. The reciprocal of the radius of curvature will be the curvature. Then, we use the formula to figure out the curvature of the functions we learn in senior high school.

本實驗希望發展簡易光降解有機物的裝置以降低分解一些實驗室中常見的有機廢液，實驗中採用Pyrex 玻璃取代昂貴的石英材質反應槽，使用空氣打氣機取代純氧氣的輸送，以TiO? 在分解甲基橙的水溶液中可測得反應速率為二級，利用二級反應速率推得甲基橙降解半生期約44.5小時。本實驗中並嘗試以不同的反應初濃度探討甲基橙降解效果，發現甲基橙在愈稀薄的溶液中，分解效果較佳。;We hope that the experiment can help us develop an equipment to reduce the common organic waste in some laboratories. We will use Pyrex glasses to replace the expansive quartz reactor and the air pump to increase air flow instead of pumping pure oxygen. The results show that our reaction equipment is good decomposition efficiency. The phtodegradation in methyl orange is second order reaction, and the half of livetime is 44.5 hour. We find that the photodegradative rate of the methyl orange is much effective in a thinner solution.

本研究討論一條線和兩條線打成死結或活結的原因，再探討有寬度的線段（?帶）翻轉不同度數後黏合的情形，與由橡皮筋衍伸出的各種圖形有哪些規律與特色，最後我們也探討了一些和拓樸有關的遊戲並研究發明其他遊戲或魔術。從這次的研究中，我們發現生活中不起眼的繩子、紙帶與橡皮筋，竟然也隱含了數學的拓樸原理，而且從簡單的拓樸性質-物體或圖形在不割裂、破壞孔洞下，可任意伸縮及變形，就可以衍伸出許多神奇有趣的遊戲。

此研究以設計自動化發票對獎的系統（Award-checking System,簡稱ACS）為目標。架設網路攝影機拍攝發票上的數字，經由自製的二值化演算法、雜訊處理以及字元切割方法，將數字逐一取出，擷取影像中特徵向量，經過訓練完成的「支持向量機」模組判讀影像中的數字，進而對獎。其中為了達到自動化對獎的效果，以微控制器操控機械手臂翻取發票，與電腦端使用遠端程序呼叫的通訊協定，進行系統整合。 實驗後得知於此系統上，以顏色為依據的二值化方法之正確率為Otsu（最大類間方差法）演算法的2.88倍；且自製的光學數字字符識別（Optical Digital Character Recognition, 簡稱ODCR）較一般OCR(Optical Character Recognition)程式高出約18%的正確率。

奈米技術在 20 世紀後期蓬勃發展，而具有奈米及孔洞的超分子更為化學家所積極尋求合成上的突破與挑戰， 超分子化學用來探討一些分子間較弱、可恢復性的作用力，以期製備一系列具有功能性的孔洞材料 。 其主 要分為以下六種： 1. 凡德瓦力 (van der Waals forces，energy -1) 2. π-π堆疊作用力 (π-π stacking interactions ，energy= 0~50kJ‧mol-1) 3. 氫鍵 (hydrogen bonds，energy energy = 4~50kJ‧mol -1) 4. 偶極 -偶極作用力 (dipole -dipole interactions，energy= 5~50kJ ‧mol -1) 5. 陽離子-π作用力 (cation interactions， energy = 5~80kJ ‧mol -1) 6. 離子 -偶極作用力 (ion-dipole interactions，energy= 50~200kJ ‧mol -1) 而分子自組裝即利用這些作力， 依熱學最安定的合發生然排列現象可應用於分離、化學感氣體儲存子交換導熱以及光電性。 本研究主要利用混合掌性異構物的酒石酸鉀鈉與硝酸鈣或鎂，在水酒精的環境下進行自組裝，利用簡單與無毒的自組裝合成法，讓右旋酒 石酸分子鎂金屬配位而左石酸分子與鈣金屬配位，別得到掌性聚合物除了將兩種 掌性異構物分離，也 實踐綠色化學中無毒與環保的概念 。

Islands far from lands use the underground or surface water as the water for living. The population of the islands is growing fast and the amount of water usage is increasing year after year. However, the amount of water usage is limited, so that people who live in islands have trouble using water. To compensate this problem, underground water is drawn from deeper underground sites. If this matter occurs continuously, sea-level may rise and then we cannot use underground water. Seawater desalination is a way to solve the water shortage, but it requires a lot of energy. It is difficult for island far away from lands to supply a lot of energy. It is considered the eco-friendly way to minimize the use of energy on the island. In order to solve the problem of water shortage on the island, it is considered fog that on the island occur frequently. It is an attempt to create water from fog, but it is a lack of research of efficiency of fog-catching nets to create water from fog. In this research, I have studied the efficiency of the fog-catching nets, a way to increase the efficiency, the amount of water that is created on the island, usage of discarded fishing net for fog-catching nets. Through this research, I found a kind of fog which can be changed into water and the difference in efficiency due to the difference in the size of the mesh size of the fog-catching nets, wind direction, wind speed, water absorption capacity of thread of fog-catching nets, installation direction of fog-catching nets, a way of installation of fog-catching nets. Also I found fog-catching nets of discarded fishing nets on the island and the possibility of usage for everyday life that the amount of water are created for a day or a month during dry season on the island.

由於奈米科技之進步發展神速，許多難以偵測的奈米污染物可能對生物體造成不可預知的負面影響，然而傳統之感測方法主要針對氣體分子，可能不適用於感測粒狀奈米污染物質。因此，本研究之主要目的是探討(也建立一套)奈米污染物簡易感測方法之可行性。利用二至三個塑膠瓶、塑膠管組裝簡易感測實驗，並且使用非常少量(約0.05 mL)之綠色溶劑(離子熔液)，實驗結果顯示奈米ZnO 及螢光粉塵灰(2 或奈米CuO 反而使電阻增加；未通過過濾材料之螢光粉塵灰(2 and phosphor particulates was conducted in a home-made nanopollutant sensing system. Experimentally, abstraction of nano ZnO into the IL caused a reduction of the IL resistance. Similarly, decreasing of the IL resistance was also observed in the abstraction of phosphor particles with particles sizes of 2 particles was found. Abstraction of nano CuO in the IL also led to a slight increase of the IL resistance. The determined characteristic resistances of the IL for abstraction of select nano particles such as nano ZnO, nano CuO, nano TiO2 and phosphor particulates may be used in the development of novel nanopollutants sensors.

本實驗是利用二氧化矽分子篩保護奈米銀的方法，有別於市面上奈米銀產品大都以有機溶劑浸泡，且保護劑均是採取界面活性劑，該項產品浸在純水中除了不會改變溶液性質外，又能以分子篩特性讓奈米銀漸進式釋放而達到長效性效果。 針對棉衫吸附奈米銀實驗非常成功，經過十次以上洗滌且放置時間長達一個月以上，對於抗菌效果也有長效性的功能，為本次實驗重大突破。 The experiment is to use SiO2 molecular sieve protected nano Ag method , different from nano Ag popular product which is organic solvent-soak, and the protectant are all surfactant. This product will not change solvent’s proterty in pure water , beside , molecular sieve generally release nano Ag and achieve long-term effect . The experiment for cotton clothes adsorptive nano Ag is very successful , and achieve long-term effect in antibacterial property , that is the most significant .

在一次意外的發現中，我觀察到以鱷魚夾夾住的鎂帶在海水中竟然不斷的冒出氣泡，引起了我一探究竟的興趣。經由一系列的探索和實驗，我驗證了此種奇特電化學行為的反應機制，並且藉著此種機制，我嘗試尋找可以產生最大電流、電壓的伏打電池組合，以便製出一個又產電、又生氫的新式伏打電池，一方面可作為直流電的電源，另一方面產生的氫氣又可作為燃料電池的燃料來源。 In one accidental discovery, I’ve observed that there were continuously bubbles coming out when a magnesium stripe was attached by the metal clip in the sea water. This incident aroused my curiosity to find out the reason. Through a series of searching and experiments, I have proved the mechanic reaction of this spectacular electronic chemical behavior. Then I tried to search for a combination which can produce the greatest electronic current and voltage in order to produce a new type of voltage battery that can produce electricity and hydrogen. In one way, it can be the source of producing the direct-current. On the other way, the hydrogen it produced can also be the source of a fuel battery.

Data and records show accidents caused by loose bolts or nuts often occur in building or mechanical structures all over the world. They may be train derailments, parts falling off amusement rides, escalator breakdowns or wheels coming off automobiles. These incidents can often cause serious casualties and should not be ignored. At present, the only devices used to prevent screws loose are spring washer and nylon locking nuts, but they are not readily detectable with the naked eye when they failed to tighten. Based on simple mechanics and spring principled, our “Smart Washer” has been designed to detect loosen screws. Whenever the bolt or nut gets even slightly loose, the lower part of the washer will spring up, this is a sign to alert and remind the user to carry out maintenance and re-tighten the loosen screw before serious accidents occur.

NO donors are an emerging class of pharmaceutical compounds, with many important functions in the cardiovascular, nervous and immune systems. With great therapeutic potential, the development of new NO donor compounds would be of great medicinal value, potentially opening a whole class of drugs to be used to treat various ailments. This project studies a specific class of compounds, substituted cyclic oxime ethers, which have proven to be useful intermediates in fields such as medicine and biochemistry. The cyclic structure along with a determinable substitutable group at the C3 position is highly valuable, as it allows the oxime ether to act as a convenient precursor for a variety of useful products, playing key components in many drugs. And with a substituted nitrate group, which is an O-nucleophile, the oxime ether has the potential to become an NO-donor, and hence become a possible intermediate in a wide array of NO donor drugs. Co(NO)3 was used in the synthesis of the cyclic oxime ether, directly from a phenyl substituted bis(oxy)enamine intermediate, producing an entirely new compound: α-hydroxyoxime nitrates, the oxime ether being substituted with a nitrate group. This new reaction of the synthesis of α-hydroxyoxime nitrates was further studied for optimization purposes, in order to open a new class of NO donor precursors. In addition, other nucleophiles were also explored in this class of reactions, forming important bonds such as C-N and C-S bonds, with key structures for other types of synthesis intermediates and precursors. Different metal nitrates, or various other nucleophiles in place of the nitrates, were used in reaction with bis(oxy)enamine, and the yield and structure of the final products were determined by NMR spectra. Successful optimization of the synthesis of α-hydroxyoxime nitrates has been achieved, where the conditions for optimum synthesis involve using Cr(NO3)3•9H2O which achieved a high yield of 76%, dissolved in THF with the bis(oxy)enamine starting compound. It has been determined that the metal in the salt affects the reaction pathway, as the nature of the metal cation affects its efficiency to cleave the N-O bond in the starting compound (with d-block elements being the best performing), and H+ ions can promote the reaction as well. Also, the reaction proceeds with different types of bis(oxy)enamines, meaning the substrate scope can be expanded to give a variety of products. The reaction can also proceed to form other products with different nucleophiles other than the nitrate group, where the C-N and C-S bonds were successfully formed in the reactions from bis(oxy)enamine to oxime ether. Thus, this class of reaction in converting the bis(oxy)enamine to a cyclic oxime ether has potentially opened a new class of NO donor compounds, and further possesses the potential to form a wide variety of products to be used in other important synthesis procedures.

This study of health diagnosis based on using computer signal analysis technology. In order to make health management more perfect. The main points of this study are wrist pulse and body temperature information, remit to the database of the computer, analyze with the computer. With the internet network , transmit it to the medical center in order to carry and control, seek medical advice, prevent infective disease from spreading, defending healthy purposes of people, this research system includes the following six functions:（1） Automation measured: Can prevent popular disease from spreading , and ensure the medical personnel to avoid being infected.（2） The heart and lungs function warning system:When the pulse beats too fast or slowly, computer will send out warning signal immediately .（3） The body temperature is unusually warning system: When the body temperature is too high or too low, will send out warning signal immediately.（4） Pathology analyzed: Will pick and fetch the pulse wave form, which use the computer procedure to carry on frequency spectrum in order to analyze, then compared with database, with the purpose of analyze pathology. （5） The health managed: Remit the physiological information that quantity examines to the database of computer, offer pathology analysis, carry on the prevention of the disease. （6） Analysis results of the human exercise: With the operation of the database, we can analyze and obtain the effect that all previous sports accumulate .本研究係運用電腦訊號分析科技、資料庫軟體，使健康管理更為完善。研究重點為擷取人體手腕脈象、體溫生理訊息，匯入電腦資料庫，以電腦進行分析。藉由網際網路，傳輸至醫療單位，達到遠端監控、緊急就醫、防止傳染性疾病蔓延，守護國民健康之目的，本研究系統包含下列六大功能：（1） 自動化檢測：可防止流行疾病蔓延，並保障醫護人員避免遭受感染。（2） 心肺功能異常警示：脈搏跳動過快或過慢，立即發出警示。（3） 體溫異常警示：當體溫過高或過低，會發出警示。（4） 病理分析：將擷取脈搏波形，運用電腦程式進行頻譜分析，與資料庫比對，藉以分析病理。（5） 健康管理：將量測之生理訊息匯入電腦資料庫，提供病理分析，進行疾病之預防。（6） 運動成效分析：藉由資料庫之運作，可解析獲得歷次運動累積之成效。