最後留下數字會是多少？該問題在台灣的全國中小學科學展覽出現多次。而資訊界演算法大師Donlad E. Knuth 在其著作The Art of Programing，CONCRETE MATHEMATICS （具體數學），針對該數列作詳細的說明；但是，不論是歷屆全國中小學科學展覽或是大師著作，對於該問題，都只是談及殺1 留β或是殺α留1。本研究利用獨創α分類、n 及k 分類、d 函數、b 函數及循環、n 及y 分類、碎形數列和演變關係，將約瑟夫問題探討範圍提升至殺α(個數)留β(個數)，直到剩下最後1 個數時就不能再殺了，遊戲終止，倒數第k 個留下的自然數是多少？同時，本研究在殺α(個數)留β(個數)下，指定自然數y 為酋長，酋長不能被殺，殺到酋長時遊戲停止，求剩下的自然數有幾個？會發生什麼情形？The Josephus problem refers to what will be remaining when arranging n natural numbers in a circle and starting killing one and leaving the next one alive. The problem has been on display for many times in Taiwan National Primary and High School Science Exhibitions (as shown in Table 1). And, the information algorithm master, Donald E. Knuth has elaborated on the array in his works The Art of Programming, CONCRETE MATHEMATICS. However, both the past science exhibitions and the master’s works are limited to discussions on cases of killing 1 leaving β or killing α and leaving 1. This research employs uniquely created α classification, n and k classifications, d function, b function and loop theory to extend the Josephus problem scope to killing α leaving β to find out what the remaining natural number is by No. k counted recursively. Meanwhile, this research designates natural number y as the chieftain, which can never be killed. The game is over when the chieftain is to be killed. The problem is to work out how many natural numbers are remaining. And what happened?

On account of the rapid development of human activities, much more fossil fuel is burnt and thus a greater amount of greenhouse gases are emitted to the atmosphere including carbon dioxide (CO2). CO2, is considered as the major cause of the exacerbating global warming. “Geo-engineering”, literally, means the options that would involve large-scale engineering of our environment in order to combat or counteract the effects of changes in our atmosphere. As a carbon neutral CO2 scrubber is proposed to be a large-scale scheme to fix carbon globally through reducing the CO2 emitted to the atmosphere and our ultimate goal is to implement the CO2 scrubber scheme to the whole globe, that is, a large-scale scheme to our environment, it is a project of geo-engineering. The procedures of the project are as the following: (a)Investigating on the absorption of CO2 produced by calcium carbonate (CaCO3), using different basic substances at different temperatures (b)Investigating the absorption of CO2 in car exhaust produced by combustion of petrol in car engine using basic solid (c)Feasibility of using a prototype of CO2 scrubber in exhaust pipe of car (d)Feasibility of fixing carbon by turning CO2 into dry ice and stored in deep water (e)Feasibility of growing plant in used basic solution Results: 1.The CO2 scrubber prototype had an average CO2 removal ability over 50%, which was considered to be efficient. The concentration of CO2 (561ppm) was even lower than that in the ambient air (CO2 612ppm). During the experiment, the prototype was closely attached to the exhaust pipe and did not fall down. Thus, a CO2 scrubber was feasible to be used in the vehicles. Besides, our prototype was more energy efficient than LM2500 PE simple cycle gas turbine (consumed 21MW electricity) though our prototype had a lower CO2 removal efficiency. The cost of our prototype would be much lower than membrane technology as the production cost of the membrane was high. 2.Unlike existing CO2 scrubber prototype installed in open area (with electric fan installed), our CO2 scrubbers installed in the chimneys of power stations and exhaust pipes of cars are carbon neutral as exhaust gas has high kinetic energy and would pass into the scrubber. 3.dry ice would not evolve carbon dioxide gas at high water pressure such as at the bottom of the ocean. 4.Plants grew well in alkaline environment, it was feasible to grow plants in basic solution. Conclusion: CO2 scrubber is a suitable choice in combating the climate change through absorbing the excess carbon dioxide, with the utilization of the carbonates produced in the reaction, it is hoped that the climate change can be relieved using an environmentally-friendly device.

\r The idea for my steering system started from a discussion with my Tech teacher about a wheel the Mechatronics and Robotics Research group of Massey University were working on. It featured precision shaped rollers at 45 degrees to the wheel’s axle. The idea was that with a number of these wheels a vehicle could go in any direction, depending on the rate that each wheel was revolving. \r

A polysiloxane elastomeric lens was formed by mixing a silicone elastomeric base and silicone elastomer curing agent. It was molded from a +100 glass lens attached to a milled Plexiglas mold. The changing focal length as a result of the application of different degrees and ways of applying strain was observed with the help of a diverging laser beam and 28 and 30- diopter lenses. The shortening of the focal length as a function of applied strain using weights was observed for two treatments namely low weight and high weight. The focal lengths were measured using a vernier caliper and an adjustable white board on which the laser beam was reflected. Data for the experiment involving weights showed that there is a general decrease in the length of the foci of the elastomeric lenses as more weights were added to the set-up. This can be attributed to the increase in curvature of the lenses as more weights were added. Data for the experiment involving spring balances showed that there is a general increase in the length of the foci of the elastomeric lenses as the spring balances are pulled harder. This can be attributed to the flattening or decrease in curvature of the lenses as the spring balances are pulled harder. A stretchable lens can be used to replace intraocular lenses in cataract extraction. By changing the focal length, the lens can work for a wide range of distances, and therefore serve as the definite solution to the development of cataracts and other conditions that affect visual activity.

我們的研究重心是設計簡便的裝置來檢測生活周邊的用水 · 利用生物對於環境污染的生理特徵、活動力、忍受極限 … 等變化，作觀察、實驗之後，將紀錄結果分析、做成表格，進而形成明確、簡易的指標，以供給一般人更容易的了解用水的品質。本實驗不必使用昂貴的儀器來檢測河水與用水，成本低廉的水生生物為本實驗的最佳選擇 · 可於任何地點完成，作為大及化的檢測方法，本實驗參考水樣急性檢測方法一水蚤靜水式，以水蚤在不同眾屬離子、酸鹼值溶液中的實驗結果，用以做為分析水質的標準，佐證我們生活圈附近的水質現況。Our point of study is design the simple and convenient device to measure the water with peripheral life. Utilize the living beings to the physiological characteristic , energy of the environmental pollution, stand limit. Wait for and change, after making observation , experiment. noting down the result will be analysed , make into the form , and then form the clear , simple and easy index , in order to supply common people with the quality of easier understanding water. This experiment needn’t use the expensive instrument to measure river and water . the best choice of the experiment that the cost is based on living beings cheap aquatically. Can finish in any place , as the popular detection method. This experiment consults the acute detection method of water sample — Water flea’s quiet ability of swimming. with the experimental result in different metal and ion sour soda value solution of water flea, use the standard taking making as water quality of analysis, prove the present situation of water quality of adjacent place of our life range.

The research is about the optimal on parallel processing. Through boot disk – which will automatically finish booting configuration, .it is efficient and quick to build high performance PC clusters. The advantage of parallel computing could be applied to massive image processing. By sharing processing and breaking huge processing load into lots of pieces, we could get more efficient result. It is also possible to optimal parallel system through some special means such as dynamic configuration. Through the means, the system could distribute work loading itself. It could also adjust itself to get the highest performance and the most stable environment. 本研究之目的在於探討平行處理中的計算資源的最佳化，透過自動完成開機設定的Boot Disk 來有效快速建製出高效率的PC Clusters 環境，並透過動態配置與類神經網路的校調，使整體叢集的運算能自動調整至最佳化。平行處理優勢，可以應用在耗費極大量的運算資源的影像處理上。透過運算資源分享，可以以很高的效率將極為龐大的運算工作分散成許多較小的程序，使影像處理速度加快。經由平行演算法及實際應用的調整，可對已成形之平行系統作效能上的加強。使用類神經網路的方式訓練，使其系統能夠自我分配運算工作量，且隨著各平行化程式與各節點的不同，能自我校調至最佳化，達到高效率且穩定的運算環境。\r 本研究透過高效率且能自我調校的運算環境，可用於優化其本身結構，以達到\r 演化出更進一步系統，具有相當大的發展潛力。

The main reason for the creation of the project was looking for the uncondutuinal support for the entire handicap people that reside in the whole world. \r In all the communities there are barriers that oppse the total development of these people, and what currently exists can not help achieve a full lige for example: it's hard to have a basic education, a productive employment, or in their case to have a simple normal life.\r at the present time there is a serious problem of inequality, this is presented beacuse there has not been a mechanism that has been albe to please 100% of its real demand. That's way what we seek with this prototype, to be able to help them to have and live a better quality of life, it has the function of warning them when an object is near or before them emitting a brief sound that dose not cease until the way is completely free of obstacles, it is also sought to prevent accidents lkie falls, trips, among other, and also to help create more accsess possibilities to help any people that suffer any kind of handicap.\r This is a prototype that is able to help blind people, by heping them become able to move from one place to an other more faster and more securely, these is trying to make them more sure and reliable on them self, also the project is very economical and it was created due to the high quantity of blind men and women that exist in the whole world

高分子發光二極體為導電高分子之熱門研究課題，因其有低成本、製程簡易、可大面積化之優點為無機高分子發光二極體所缺乏，所以受到學術界與工業界之注目。由於高分子發光二極體其有廣視角、高答應速度、低驅動電壓、可製成撓曲式元件等特質，極具成為下一世代顯示器之潛力。高分子聚苯胺為高分子發光材料中，具有低驅動電壓與高發光效率之優點，故本研究將之選為電洞傳遞層材料。但唯一缺點就是不易溶於溶劑中，所以在實驗驗中有安排質子酸摻雜的步驟，就是為了要改變高分子的電性、磁性、光學性質或結構，同時導電度也隨之增加。本研究以ITO基板改質及無電極電鍍為研究主軸，以此來增加其之性能。改質ITO基板目的，是希望使得ITO陽極表面平坦化且可促使電洞注入，進而增加發光層材料附著力與阻隔電子直接導入陽極之特性，故可增加元件之發光亮度。而使用無電極電鍍法，因為其不須通電就能進行電鍍的反應，行成的薄膜也很均勻。所以採用無電極電鍍法，來完成電鍍的步驟。The polymer light emitting diodes is one of the most important study projects in the field of the conducting polymer due to the low production costs、 simple production process、great surface products that the organic light emitting diodes can not achieved. The purpose of this study is try to utilize the polyaniline as the electric hole transfer layer, and the MEH-PPV as the light emitting layer. The disadvantages of the polyaniline are the low solubility in solvents that was improved by doping proton acids. The performance of the indium-tin oxide was improved by the self-assembling method that made the surface of the ITO became more smooth to help the electric hole injection of electrions. And the aluminum cathode was produced by the electrode less plating.

此研究是探討光合細菌對污染水中油脂的影響。利用光合細菌(Photosynthesis Bacteria; PSB)來探討對油脂分解的能力，實驗使用的油脂4種，分別是柴油、沙拉油、橄欖油和豬油4種油脂來做為實驗對象。然後取4種不同的油脂各2克分別加入光合菌液98公克做為實驗組，對照組則取4種不同的油脂各2克分別加入海水98公克作為空白對照（不另添加光合菌），每組皆為2重覆實驗，以純光合菌液98公克作為校正組，再利用索氏萃取裝置分離光合菌和水中的油脂，進行油脂回收，實驗進行4週，計算油脂的減少量和油脂分解率作為評估光合細菌對4種不同油脂分解的能力。

For this research, the nocturnal perching habits of the lizard, Japalura Polygonata Xantbostona, were examined. Nighttime observations were made from July 2002 to March 2003 in the area along the mountain brook in the south valley of the King-Mien Mountain in Nei-Hu District. The study comprised a series of analysis with discussion of the lizard’s (Japalura Polygonata Xantbostona) perch based on the temperature of living environment and the manner of perch including the dissimilarity between male and female, adults and juvenile lizards in selecting their perch conditions. During the period of study 452 lizards were marked and examined. 163 were female, 168 were male, and 121 were young lizards. The study considered four particulars: (1) orientation, (2) angle, (3) manner of perch, and (4) height of the perch above ground. As for the orientation, most of the lizards chose to perch in an inward (towards the tree) and in an upward direction; the angle of perch was mainly within 1°~ 45° and slanted to 180°. Second, the manner of perch chosen by most of the lizards was holding the stem or trunk by arms. All four groups of lizards exhibited no difference in the orientation, angle and manner of perch. However, male lizards tended to perch at a greater height above ground than the female and juvenile lizards did. The study produced other findings as well: A tendency correlation curve was plotted showing that temperature related with the number of lizards taking perch, and from the curve the optimal temperature of the living environment was determined to be approximately within the range of 19° ~24°. Additionally, there was a relationship between temperature of living environment and the size of lizard and the number of lizards taking perch. A further positive relationship was observed between temperature and the height of perch above ground. Also, the study showed an apparent positive relationship between the temperature of sample living area and the snout-vent length(SVL) of the lizard. Finally, the Japalura Polygonata Xantbostona tended to take their nocturnal perches within a rather fixed home range. 本研究由2002 年7 月至2003 年3 月，於臺北市內湖區金面山南麓溪谷進行黃口攀蜥夜 晚停棲策略研究，以溫度和各項停棲行為進行來分析探討，包括黃口攀蜥的成幼蜥、雌雄蜥 停棲選擇上的差異。 研究期間，共標記到452 隻攀蜥，其中雌蜥163 隻、雄蜥168 隻、幼蜥121 隻。將停棲 的情況分為方向、角度、停棲型態、離地高度四項來分析，在方向上多以朝內、向上為主； 角度多以小角度的1°~45°及180°為主；在停棲型式多以環抱莖枝為主。進一步分析成幼蜥、 雌雄蜥不論在方向、角度、停棲型式的選擇上皆無差異。離地高度的部分則以成蜥及雄蜥的 停棲高度較高；以溫度分析黃口攀蜥的成幼蜥出現停棲隻次、停棲高度、出現停棲攀蜥體型 的相關性，溫度對出現停棲隻次可以做出趨勢相關曲線，估算攀蜥的停棲有一最適宜溫度範 圍約在19~24℃間；溫度與其停棲高度呈現正相關性；每次測得樣區溫度與出現停棲攀蜥平 均吻肛長有顯著的正相關。而黃口攀蜥夜晚婷棲時則會傾向於較固定的範圍內。

This study is to discuss the reason that interfere the fish schooling behavior " adult fish surround the young fish ". I use mathematic simulation, to observe the result when the fishes are stimulated, due to the body size , the speed of swimming , the difference of sensitivity will make different reaction. We predict the motion dots of fish when the hunter appears on the block paper, then analyzes the motion of adult fish and young fish in dot to determine if the result remind "adult fish surround the young fish "structure. The conclusion shown that natural reaction physiologically on fish will show "Adult fish surround the young fish "results, so, the factor that interfere the structure of fish group is not so called "group defense by ethnologist".本研究目的，在探討影響魚群「成魚圍繞著幼魚游」的行為。本研究是以數學模擬法，依觀察結果，設定魚在受到刺激後，因體型大小、游速的快慢、靈敏度的差異等，所產生的不同的反應。再在方格紙上模擬魚群在捕食者出現時，游開的動線。最後分析成魚幼魚的動線分布情形，是否仍是「成魚游在幼魚外圍」的魚群結構。研究結果發現，依魚類的生理條件所設定的條件下模擬，自然形成「成魚游在幼魚外圍」的魚群結構。所以，影響魚群結構的因素，的確不是行為學家所說的防禦行為。