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.

“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.

水生食蟲植物絲葉狸藻 (Utricularia gibba) 是非常獨特的，它不但跟其他植物一樣能行光合作用，且具備捕蟲囊捕捉水中小生物，補充生長所必需的營養元素。捕蟲囊的構造精密卻不複雜，消化吸收主要靠囊內壁上的四爪腺毛，目前尚未有文獻實際以追蹤物質描述出整個共質體輸送路徑。我們是最先以螢光染劑 (carboxyfluorescein) 及共軛焦雷射掃描顯微鏡(confocal laser scanning microscope) 成功地描繪出捕蟲囊共質體運輸路徑。同時我們也以對細胞無害的食用色素，進行相同的實驗觀察。發現食用色素不但成本低，且較螢光染劑有更多的優點，如觀察時間較不受限制等，非常適合用來研究捕蟲囊吸收物質的路徑，因此，本實驗的模式可以應用在其他水生植物運輸路徑的研究。;The aquatic carnivorous plant Utricularia gibba is very unique. It has not only the ability to undertake photosynthesis just like other plants, but also can trap and obtain the nutrients from the freshwater zooplankton. Its trapping organ is very sophisticate but not complicate. The digestion and absorption process inside the trap are mainly accomplished by the quadrifids structure. According to our knowledge, we are the first to introduce the phloem-mobile, fluorescent probe carboxyfluorescein (CF) and confocal laser scanning microscope (CLSM) to the study of the symplastic transport in the Utricularia trap. In addition, we use edible food colorings as tracers for this transport study. Both approaches turn out to be very successful in delineating the symplastic transport of the trap. But CF quenches rapidly so the observation time is restricted. On the contrary, food colorings don’t have these disadvantages; it is inexpensive, easy to perform, and the transport process is not fast. As a result, the study is easily to be completed. These methods will be very helpful in the studies of symplastic transport in other plants.

根據研究結果，溫室效應使全球暖化，海洋溫度溫差變大，對流速度加快；暖流由赤道向北流，鹽度增加，流速會變慢；冷流由北極向南流，因為鹽度增加，海水密度増大，冷流無法下沉，造成流速變慢。溫度越低，鹽度會增加，密度就會變大，所以洋流會往下沉，越往下鹽度越高，當冷水跟周圍達平衡時，就不再繼續往下沉，反而會沿水平方向移動。電影「明天過後」所描述的氣候現象是指北極冰棚融化後，由於北大西洋海水鹽度降低造成全球「大溫鹽循環」（thermohaline circulation）停止，海洋從低緯到高緯的熱傳輸能力降低，使地球進入冰期狀態，美洲北部全面冰封的情景。這樣的電影場景不可能在短時間內發生。

當我們在開車享受冷氣同時，此時冷氣水正一滴一滴的滴水，造成水資源的浪費，在環保意識抬頭的今天，我們即針對此一問題進行研究，主要將冷氣水回收起來，並運用在補充雨刷水箱或者提供引擎水箱或冷凝器降溫作用，是否達到提高引擎工作性能及降低冷氣冷房效果，進而達到「資源回收」的。實驗結果證明在補充雨刷水系統最符合環保概念；另在引擎水箱噴水作用時，可縮短風扇運時間並增加停止運轉時間，可增長風扇使用壽命，對下水管溫度亦可降低，可防引擎過熱；在冷凝器噴水作用中亦能明顯提升汽車冷房效果。When we enjoyed driving with cool air from air-conditioning, the condensed water from air-conditioning system is dripping from the system drop by drop. It caused the issues of the waste of water resource. Facing the greater public awareness of environmental protection issues in Taiwan, we are focusing on this issue to have further research. The idea is to re-cycle the air-conditioning condensed water and re-fill it in the water tank of wipers, the water cooling tank of engine or the cooling system of condenser. The purpose is to improve the performance of engine and enhance the cooling efficiency of air-conditioning system. It is helpful to meet the objective of water resource recycling. The result of experiment has shown that re-filling water in the water tank of wipers meet the goal of environmental protection well. Also, the water injection in the water cooling tank of engine could reduce each operation time of cooling fan and increase the idle time of cooling fan as well. It prolong the equipment life of cooling fan and lower the operation temperature of Low water pipe which prevent the engine overheating. Meanwhile, It is proved that the water injection in the cooling system of condenser can enhance the cooling efficiency of air-conditioning system.

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.

本研究主要利用油脂「皂化反應」的原理，設計六個部份實驗，試著從定性方面探討油脂的皂化反應及其產物的分離，包括(1)肥皂的鹽析(2)脂肪酸的鹽析(3)脂肪酸平均分子量的求法(4)肥皂的沉澱試驗(5)甘油的丙烯醛反應(6)甘油的銅複合物之形成。從定量方面：利用化學動力學研究油脂皂化反應的級數，及油脂的碘值、酸值、皂化值等問題，期望能在環保上對處理油污工作有所幫助。This research mainly applies the theory of lipid Saponification to design six experiments and try to study lipid Saponification and the division of the product, including (1)salting out of soap (2) salting out of fatty acid (3)study on the molecular weight in fatty acid (4) soap precipitation (5) acrolein reaction of glycerin (6). Glycerin’s Cu-complex formation of soap .From the aspect of assay use chemical kinetics to research the order of lipid Saponification and the problems of Iodel value, Acid value, Saponification number and so on, expecting to help dispose oil pollution in the environment.

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.

The purpose of this study is to set up a quick, easy and economical way to evaluate the ability of different concentration of various antibiotics to penetrate biofilm and establish the antimicrobial susceptibility patterns of various antibiotics. The susceptibility of five antibiotics upon sessile cultures of Bacillus subtlis ATCC 6633, Escherichia coli XL, Pseudomonas aeruginosa ATCC 27853, Staphylococcus aureus ATCC 29213 and Sarcina lutea ATCC 9341 were measured ATCC 27853, and S. aureus ATCC 29213 proved to be very difficult to eradicate, with only Gentamicin proving to effective at achievable drug concentrations, but the S. lutea ATCC 9341 biofilm was the most susceptible to the Penicillin. The results demonstrated that for biofilms of the same organisms, several hundred to thousand times the concentration of a certain antibiotic were often required for the antibiotic to be effect, while other antibiotics were found to be effective at the MICs. The concentration of antibiotic to penetrate the biofilm is proportional to the thickness of biofilm. Indeed, our research have already indicated that the use of MIC values to indicate antibiotics effectiveness is misleading, because MIC values can not represent the actual effect of anticbiotics on microbiologicals that have developed biofilm. The antimicrobial susceptibility patterns of antibiotics to various bacterial biofilm are different. The susceptibility of the mixed biofilm depends on the physical and biological change of biofilm. Our biofilm device offers a new technology for the rational evaluation of antibiotics effective against microbial biofilms and for the screening of new effective antibiotic drugs.此研究之目的是要建立一套操作簡便、快速且費用低廉之生物膜厚度產生方法，藉此探討不同生物膜厚度對抗生素抗菌之影響，進而完成抗生素對生物模之抗菌圖譜。本實驗將測試五種抗生素Bacillus subtilis ATCC6633，Escherichia coli XL，Pseudomonas aeruginosa ATCC27853，Staphylococcus aureus ATCC29213和Sarcina lutea ATCC9341之抗菌圖譜。試驗結果顯示Gentamicin對前四株試菌有較佳之穿透力，對S.lutea ATCC 9341則是Penicillin。實驗結果證明最小抑制濃度值確實無法實際有效地表達對已形成生物膜菌體之抗菌效果，要完全去除生物膜之抗生素濃度是為最小抑制濃度之數百倍到數千倍，而且抗生素用藥濃度隨著生物膜厚度增加而成比例增加。不同抗生素對不同菌株生物膜有不同之抗菌圖譜，混合菌株生物膜是否會促進或抑制抗生素之穿透力，端視其生物膜結構有無改變。本實驗方法可以做為一種快速檢定抗生素對細菌生物膜敏感性之新技術，同時亦可有效地篩選新的抗生素藥物對生物膜的抗菌效應。

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.

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.

Abstract (一)、 In our study, we discuss a m×n chess and any beginning square p finding a directed path of chessman from p moving to an end square in which the chessman moves to adjacent squares including only three directions which are right move, up move and diagonal left down move. A m×n chess is ruled into m columns and n rows creating the number of (m×n) squares (二)、 A chess directed path moves from any beginning square to end square in a m×n chess and every other square is visited just once. In the view of the beginning squares, the chess paths are solvable paths in a mxn chess and the corresponding squares are solutions. (三)、 First, we find out that some beginning squares are located in a special area with no any solvable directed paths. We define the special area be no-solution area. (四)、 According the 3-color theorem, we determine more than two thirds of no-solution area. (五)、 Then, we derive properties of reversibility and symmetry in solvable paths. i.e. A solvable path exist another solvable path by reversibility and symmetry respectively. (六)、 Utilizing the generalization of no-solution area which is extended from the concept of no-solution area provides judgment for the next moves effectively. The judgment is defined as effective move principle. (七)、 Furthermore, using the other theorem called rules of shift Hamiltonian path gets augment solutions. (八)、 According to the effective move principle finding a number of solvable directed paths, use the reversibility and rules of shift Hamiltonian paths to get augment solutions. Finally, utilize symmetry to find out all solvable paths in the m×n chess. (一)、研究規則：在m×n 的格子中，任取一格A 當作「起點格」，在起點格上放一顆棋子，只能往「上」、往「右」、往「左下」的方向移動。(二)、定義：若棋子從「起點格」，按照上述規則能不重複的通過所有m×n 格子到達某一「終點格」，則對於「起點格」而言，此移動路徑稱為m×n 的「有解路徑」，其任4一「終點格」稱為「起點格」的「路徑解」。(三)、我們先研究出「基本無解區」。(四)、根據遊戲規則我們利用三種顏色將n × n 方格塗滿，並判斷出大部分的「無解起點格」。(五)、利用遊戲規則得到兩重要性質：(1)[可逆性性質] (2) [對稱性性質](六)、利用「廣義基本無解區」，當作我們[有效移動]的判斷，讓「有解路徑」快速的找出。(七)、利用本研究所稱的「平移哈式鏈」，得到[擴充解]。(八)、根據[有效移動]求出部分「路徑解」，再利用[可逆性性質]、 [擴充解] ，最後利用[對稱性性質]完成所有「路徑解」的尋找。