所謂約瑟夫數列，就是有n 個數排成一環狀，從頭開始，殺1(個數)留1(個數)，求倒數第k 個留下的數會是多少？約瑟夫數列在台灣的全國中小學科學展覽出現多次（如下表）。全國科學展覽與本題類似的作品 資訊界演算法大師Donlad E. Knuth 在其著作The Art of Programing，CONCRETE MATHEMATICS，也針對該數列作詳細的說明。唯，不論是歷屆科學展覽或是大師的著作，對於該數列，都只是談及殺1 留β或是殺α留1。 筆者則在2005 年暑假，曾經提交於全國國小組比賽作品「老師無法解決的難題」討論到n 個人排成一圈經過殺α留β，最後留下來的情形。 本研究是將α、β、k 和n 作為變數，求：當有n 個數排成一環狀，從頭開始，殺α(個數) 留β(個數)，則倒數第k 個留下的數會是多少？ 需符合α、β、k、n 皆∈N，且n≧k 1.直觀觀察:發現在每一個循環中，當n 等差α時，Aα,β,n,k 則等差α+β、n- Aα,β,n,k 則等差β。 2.分類:將其分類為cα,n，使當中有規律可求。 3.循環觀察:發現每個循環的尾數n- Aα,β,n,k 都小於β。 4.循環尾數:設計公式求出每個循環節的尾數n、留下數Aα,β,n,k 及n-Aα,β,n,k 。 5.倒推:由與循環節中有等差的性質，則可以由循環節的尾數，推論出循環節中的任意一數。 Joseph Sequence is the problem that discussed the situation of eliminating1 and retaining1 in the circle formed by n people. Joseph Sequence has appeared a number of times in National Elementary School and Middle School Science Fair in Taiwan (as shown in the table below). Past national science fairs and researches on Joseph Sequence The publications，The Art of Programing，CONCRETE MATHEMATICS ，by the expert of mathematical calculation in the IT industry，Donlad E. Knuth，has provided detailed explanation on it. However, all of those only discussed eliminating 1 and retaining β or eliminating α and retaining 1. The researcher proposed “Problems unsolved by teachers” in the national competition, and discussed the situation of eliminating α and retaining β in the circle formed by n people. This study continued the summer project of 2005, and conducted research on the question of when is the last kth person eliminated in a circle formed by n people. In the paper, α, β, n and k were independent variables and the research process was as follows: 1. Direct observation: the series shows equal difference in each cycle. 2. Classification: to search the pattern of the series based on cα,n classification. 3. Use the end number of each cycle to obtain the pattern. 4. Reverse induction: use the equal difference of each cycle to induce when the kth person would be eliminated.

伏打電池中，若兩極的電極種類及溶液種類均相同，僅是兩極的溶液濃度或溶液溫度不同，兩極間就有電位差，稱為濃差電池及溫差電池。典型的濃差電池中 ( 電極為電解液正離子的金屬片 )，濃度大的一端電位較高，電池電壓與兩杯溶液濃度比值的對數值成正比，且在相同濃度比值時，硝酸銀濃差電池的電壓最大，其次為硝酸銅、硫酸銅，硫酸鋅濃差電池的電壓最小。硫酸銅溫差電池，若電極為銅片，則電池電壓與兩杯溶液溫度差成正比，且溫度高的一端電位較高。 我們將硫酸銅溫差電池製成太陽能電池，在太陽下曝曬3 小時，電壓可達 13.6mV， 電流可達0.76mA，因此只要串聯數個電池以提高電壓，再對鉛蓄電池充電，就可以達到方便、實用與重複使用的目的。 In a voltaic cell, if the kinds of both electrodes and electrolytes are the same, but the molality or the temperature of the solutions are different, there will be potential difference between the two electrodes. We can them molality-difference cells and temperature-difference cells. In a typical molality-difference cells－its electrode is a piece of metal which is the same kind of metal with the cation electrolyte.－the electrode with the higher molality has the higher potential, and the potential and the log of the fraction of the molality of the two glasses of solution are directly proportional, and when the fraction is the same, AgNO3 has the highest potential and then Cu(NO3)2 and CuSO4, and ZnSO4 has the lowest potential. In a CuSO4 temperature-difference cell, if its electrode is a piece of cuprum, then the potential and the temperature- difference of the two glasses of electarolytes are directly proportional, and the electrode with the higher temperature has higher potential. We use CuSO4 temperature cell to make a solar cell, and put it under the sun for 3 hours, the potential can be 13.6 m V, and the current can be 0.76m A. Therefore we can make several of them series to get higher potential and charge a lead storage battery. By this way, we can make a convenient, practical and recycled battery.

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.

原產於西非的「神秘果」，嘗了之後，30~200 分內，所有酸苦的東西嘗起來都是甜的。在深入蒐集相關資料後，我們發現神秘果有多種特殊效果，僅擷取以下幾種感興趣之方向來研究。〈1〉使酸苦的感覺變甜〈2〉解酒〈3〉消除蚊蟲叮咬之腫、癢〈4〉抗氧化能力極強。用食鹽水可萃取出miraculin 這種醣蛋白，經由生化實驗，推測使酸味變甜為其cover 舌尖甜味味蕾之結果，分子量約為40000 左右；但在檢測過程中，發現對咖啡、黃連和肉桂，都沒有太顯著的效果，只有酸味有顯著的改變，和以往所閱讀的研究報告有出入，因此懷 疑有氧化還原等其他化學效果，將再做深一層研究。消除蚊蟲叮咬之腫癢的成分確定為小分子所致。經由Prolox 當量測定法檢測神秘果抗氧化能力數值高達4974g/nmol，比一般中草藥及蔬菜多3000 左右。使酸變甜的原因若深入研究對糖尿病患者和減肥者都是一大福音，塗抹蚊蟲叮咬藥膏也可用天然物質製作，而抗氧化能力高更對人體健康有所幫助。當台灣已大量栽植，相對於日本及美國因地寒而無法培育成功，神秘果研究可成為另一項產業發展契機。 "Miracle fruit” is a fruit from West Africa. Though it's not sweet itself, if you eat anything that is sour or bitter after eating miracle fruit, the taste will turn sweet. After researching further material, we discovered that there are many amazing functions in miracle fruit, and decided to pick up some of which to study. (1) Turning the sour and bitter tastes into sweetness (2) Relieving alcohol (3) Relieving the hurt from mosquitoes and bugs (4) An excellent antioxidant. We can extract the miraculin that changes the taste from NaCl (aq), and through the biological experiment, we guess that's because miraculin covers the sweet sensor. The molecular weight of miraculin is about 40000.According to the experiment, we found out that miraculin doesn't have a great effect on the taste other than sourness, such as the bitterness of black coffee, Coptis chinensis, and cinnamon. . It is much more different from the former report we read. So we doubt that there are some other reactions. The thing, which relieves the hurt from mosquitoes and bugs, are sure to be a simple molecule, not a protein. By the Prolox equivalent weight experiment, we found that the ability of antioxidation got to 4974g/nmol, which is much higher than the normal vegetables and fruits. The effect of taste changing is really good news for diabetics and weight reducers. And the medicine can also be made by natural material. The excellent antioxidation is helpful for our health, too. Since Japan and America cannot grow the miracle fruit because of the cold weather, developing the functions of miracle fruit seems to be another chance for Taiwan to stand out in the world.

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.

自從九二一集集大地震以後，中、小學對於防震教育是更加的重視，一次又一次的防震演習\r 還不夠，還讓學生到地震演練室去體會更逼真的地震實境。在地震演練室的下面就有一個六\r 軸動感平台，六軸動感平台的運作是各軸的伸縮長度不同而模擬地震的，而用彈簧製成的震\r 動台也可以達到模擬地震的效果，去做一些關於地震的研究實驗。地震有各種不同的震動方\r 式，多半是垂直的上下移動或是水平移動，不同的地震對於相同的建築物的影響也有所不同；\r 而地面上有各式各樣的建築物，有的高有的低，所以相同的地震對於不同的建築物的影響也\r 會有差別。\r Since the disastrous Earthquake 921 happened three years ago, the primary schools and junior high\r schools have stressed on the anti-earthquake education and training. Except for the anti-earthquake\r drills they take the students to an earthquake show room to experience more realistic earthquakes.\r Beneath the earthquake show room there’s a 6 degree of freedom Steward platform. The platform\r simulates the earthquakes by varying the length of the 6 axis. We also designed a platform by springs to\r simulate the earthquakes. There’re several types of earthquakes mostly horizontal or vertical .\r Different earthquakes have different effects on the same buildings. Earthquakes of the same amplitude\r will have different effects on different buildings.

Refer to Figure 1. Suppose ABCD is a trapezoid and . Passing the intersection M of and we construct a parallel line intersecting and at E and F, respectively. We obtain that , and then we can generalize the result. 如(圖一)，若ABCD為梯形且，過 和交點M 分別作平行線交、 於E 、F ，可得 的關係，再加以推廣。

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.

本研究利用蛋白質的環保、生物活性，金奈米粒子的低毒性，及蛋白質金奈米粒子的螢光特性，合成可應用於生物體內之螢光蛋白質金奈米粒子，從而利於標靶藥物研究。本研究選擇與眾多疾病相關的胰島素，以最佳方式合成紅色螢光胰島素金奈米粒子，有助於探討糖尿病相關機制。並嘗試以養晶得到結晶狀的胰島素金奈米粒子；經由離子測試發現胰島素金奈米粒子十分穩定，更可應用於細胞內微量氰離子檢測；根據CD光譜，確認胰島素金奈米粒子與胰島素的蛋白質二級結構相似。之後利用MTT測試細胞毒性，並將胰島素金奈米粒子餵入細胞，並取得細胞螢光影像，證明胰島素金奈米粒子可經由細胞表面之胰島素受體進入細胞內，且呈現紅色螢光，證明胰島素金奈米粒子可用於生物體內顯影追蹤。利用老鼠實驗證明胰島素金奈米粒子具有胰島素降血糖之功用。

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.

本研究利用偏振片、量角器為刻度盤、雷射光為光源，及照度計為偵測器，組裝一個簡易且可靠的旋光度計。我們利用單位時間旋光度的變化量當作反應速率，來測量蔗糖的水解速率，同時求出蔗糖水解反應的反應級數、速率常數(k)。利用糖類的旋光度具有加成性之特性，找出不同混合比例時的旋光度，追蹤實際蔗糖水解的每個狀態，找出最後平衡狀態，同時將蔗糖水解平衡結果顯示，旋光度與濃度有線性關係，而蔗糖水解反應對蔗糖而言為一級反應。接著，我們在蔗糖水溶液中加入不同種類的酸，探討催化劑的種類與蔗糖水解反應速率的關係。 In this research, in order to measure the optical rotation accurately without expensive equipments or complex process, we assembled a polarimeter by ourselves. With simple materials which can be found in ordinary senior high school laboratories, including a calibrated scale, a simple Luxmeter, a laser as the photo source, and other side devices. The Polarimeter ended up operating fluently and accurately. We put the laser under a tube, which has two pieces of polar screens on the top of it and on the bottom of it, ,and put a luxmeter just above the tube. When we slowly rotate the polar screen on the top, the figure shown on the luxmeter changes. By numerical analysis, we can get information about the hydrolysis of polarized substance. Secondary, we measured the optical rotation of glucose, fructose, malt sugar, galactose, and sucrose to get their specific rotation. Then we measured the optical rotation of sucrose every five minutes. By doing this, we could keep track of the hydrolysis rate of sucrose, figure out the order of reaction, and the rate constant (k) and the equilibrium constant (K). Thirdly, we used different kinds of acids into sucrose solution as the catalyst, and observed the effect. The result showed that hydrochloric acid is a better catalyst to this reaction than sulfuric acid and nitric acid. The polarimeter of this research can be used in science education of junior and senior high school. By teaching students to assemble and operate the self-made polarimeter, students can know better about optical rotation and polarized substance. Also, the interest in this experiement will add to students’ motivation to do science research.

由於台灣山區溪流短小陡急，土石流災害嚴重，透過式防砂壩攔阻工法為現\r 今之趨勢，而帄面透水柵具有一般透過式壩的優點，不但能將土石流轉化為水砂\r 流，還可以減低土石流衝擊力造成的損壞及改善上游儲砂空間不足的問題。本研\r 究採用改良式帄面柵，在下游處增設分流河道，可改善分離出之細顆粒土砂水與\r 大礫石再度結合之危險。此工法於2003 年引進台灣後，尚未廣泛應用，主要原因\r 為缺乏設計之經驗式，因此本研究針對透水柵的柵棒長度（L/ Dmax）、棒淨間距\r （b/ Dmax）、柵面架設方式、柵面篩分角度（θ）等多項重要因子進行室內渠槽\r 試驗，最後提出土砂篩分比與攔阻率的趨勢方程式，設計時以總攔阻率（R）高為\r 原則，輔以篩分比（S）與貯砂率（R1）高，即可有良好之成效，期望能作為國內\r 外現場工程施做時之參考，結果如下所示。