倍位元灰度影像產生器
本研究設計一新型的影像投射系統，可將影像顯示的灰度位元加倍，例如，顯示面板只需用4位元，即可顯示8位元的影像;亦能充分利用光路光源，增加光源使用率。此系統使用兩片相同灰度位元的顯示面板，此兩面板所顯示的影像經過灰度的重新處理，且各經由不同光源強度比值的光路合成後，其灰度分佈將可增為原來的平方倍。經模擬與實驗顯示，此種系統很輕易就能獲得預期目標。無論使用穿透式或反射式皆可應用於目前單片液晶面板之投影系統中;未來可望利用網板來表現灰度，應用於紅外線景物投射系統中，作為紅外線影像式尋標器靜態模擬時所需的高強度動態範圍與高解析度之影像產生器。In this study, a novel image generator utilized in a projecting system has been proposed; it can double the bits of gray-level for image display and enhance the efficiency of illumination of lamp in the optical path. With this system, a 4-bit display panel can achieve an 8-bit image display. Two display panels with same gray-level bits is adopted, images on them will be processed, and then go through different path with a proper intensity ratio. The gray level distribution of image displayed which the two images combined afterward, will be the square of that of original one. The results of simulations and experiments have approved to meet the requirements. No matter transmitting or reflective types can be applied to current projecting systems with single LCD panel. It is expected that a halftone-gray-level pattern will be suitable for this system to form an infrared scene projector, and to act as an image generator with high dynamic range and resolution for static simulation of infrared imaging seeker.
將錯就錯的knuth 河內塔
在這篇報告中，我們探索了「將錯就錯的Knuth 河內塔問題」。傳統河內塔問題在電腦科學上佔有重要的地位，是一個極具內涵的模型。由於這個模型的深厚數學內涵，使其和巴斯卡三角形建立了緊密的連結，且利用這個緊密的數學連結，設計出復原任意起始狀態的良好演算法。Knuth 河內塔起因於數學家Knuth 在論文[3]中，描述傳統的河內塔問題時所發生的一次筆誤。在這個新的規則之下，我們意外發現Knuth 河內塔存在著一個和傳統河內塔平行的模型，此模型在電腦科學及數學上有著完全不同於傳統河內塔的內涵。我們的研究主要如下：(分別為內文中的四大段)(一) 結構分析。移動環所需要的次數，如何移動環並分析每一次動作所動的環，及每個環何時被動到並給出演算法。(二) 正整數的分割。所有的移動步驟將正整數做了一個新的分割(Partition)；此分割模k之後有良好的循環性質。(三) 費波那契真分數的排序。這個正整數的分割形成一張表，這張表恰好就是分子分母皆為費波那契真分數之排序。(四) 隨意亂排的Knuth 河內塔復原演算法。在Knuth 河內塔的規定下將起始狀態改變，找出良好的復原演算法，並分析。 In this project we study the "Knuth Hanoi Tower", which is motivated by a typo in a paper of Knuth. This inadvertently typo leads to a new rule of moving the discs on the Hanoi Tower (see introduction below for definition). Although seemingly similar to the traditional Hanoi-Tower problem, it turns out that under this rule the "Knuth Hanoi Tower" problem consists of amazing properties, and is totally different from the traditional one. Our study focuses on the following directions: (1) Structure analyzing: We analysis the sequences recording the disc moving and offer enumeration results and recurrsive/non-recurrsive algorithms. (2) Partition of N: The moving sequence forms a partition (a table) of N, which has an amazing congruence property. (3) The order of Fibonacci proper fraction: The row/column of the partition table is, even more amazing, exactly the order when sorting the Fibonacci proper fraction with fixed denominator/numerator. (4) The Restoration of an arbitrary initial state: We offer an efficient algorithm for restoring any initial state of discs. We hope that our study on the "Knuth Hanoi Tower" offers a simple, neat, and new example on the theory of Algorithm, Number theory and Combinatorics.
半屏山之簷下姬鬼蛛的研究
The spiders, Neoscona nautica, often appear in groups, but individuals have their own sense of territory.They usually spin webs among branches during 6:00~ 8:00 in the evening. When building webs, they will first start with bridges and then spin Y-shaped spokes. Next, they spin meshe of net, silk frame, spokes, spirals and free-zone in order. After finishing webs, they will wait for prey on the free-zone or meshe of net. If they find something inanimate on the web, they will break the spiral attached with the inanimate object that is later removed. If the meshe of net is broken, they will fix it immediately. For them, the time to take webs back is during 2:30~ 6:00 in the morning. Most time they use the first pair and the second pair of legs to take webs back and swallow the webs. Sometimes, they break the spirals by the last pair of legs. The sequence to take webs back is : lower right section, lower middle section, lower left section, upper left section, and upper right section. At last, one thread of bridge will be left. Every early mornings they take webs back and swallow them. The next evening they rebuild webs. Possibly there are two reasons to explain why spiders eat their webs: (1).They swallow webs to get protein. (2).The web threads are easily polluted by dust and humidity and reduce stickiness. The web may also reduce the probability of capturing prey. The body length of them is not related to effective web dimensions. However, the web sizes depend on the width of web-building location. The study shows linear relation among body length, meshe of net and dimensions of free-zone. The linear relation represents that the meshe of net and free-zone have ecological or survival meaning for them. We expect that this study of Neoscona nautica can be helpful to build spider ecological database in Taiwan.簷下姬鬼蛛常成群出現，但個體卻有很強的領域性；常於下午6：00 至8：00 結網於樹枝間，結網時，先以橋絲為出發，織出一Y 形的縱絲，再由此依序織出中空網眼、絲框、縱絲、橫絲、棲息圈，網結好後，簷下姬鬼蛛則在棲息圈或網眼靜候獵物，若發現網上有非生物之異物，則將黏住異物的橫絲弄斷，再把網上的異物丟棄；若網眼被破壞，則會立即修補。收網時間為凌晨2：30 至凌晨6：00，收網時，大部分由第一、二對步足進行收網，偶爾會用最後一對步足將橫絲弄斷，一邊收網一邊將網吞食，收網的順序為：右下、中下、左下、左上、右上，最後留下一條橋絲。簷下姬鬼蛛每天清晨都會收網，並將網吃掉，翌日傍晚再重新結網，其可能原因有兩點：(1)將網吃掉以補充蛋白質。(2)蛛絲容易受灰塵、水氣之污染而減小黏性，降低獵捕功效。簷下姬鬼蛛體長與有效網面積無關，但網的大小視其結網地點寬敞程度而定。體長與網眼、棲息圈面積呈線性關係，表示網眼和棲息圈對簷下姬鬼蛛具有生態或生存意義。我們對簷下姬鬼蛛生態調查之結果，希望能幫助台灣的蜘蛛生態資料庫之建立。
外觀數列
The Look and Say sequence is produced by describing the appearance of the previous row. For example, start with “1,” which can be described as “one 1,” and therefore the second row is “11,” which is "two 1s," making the third row “21,” the fourth row “1211,”and so on. The main goal of this study is to work out the exact formula for this sequence, which means given the row number n, we can know at once what the n-th row is without having to start from the first row and doing the look-and-say iteration for n-1 times. Some of the methods used include dividing groups, repetition and cracks. The formula we derived speeds up the calculation and gives us a better understanding of the look and say sequence.「外觀數列」為依照外觀產生下一列的數列，第一列為「1」，第二列描述第一列「1 個1」而為「11」，第三列則描述第二列「2 個1」而為「21」，第四列「1211」，依此類推。本研究針對外觀數列的各項數學性質作研究探討，並由此推導出外觀數列的一般式，即給定第n 列就可知道該列的內容。我們運用了分組、重複性以及裂縫的方法分析數列，最後得到了其一般式，此一般式有助於運算速度的加快以及我們對數列性質的了解。
Wind Power
My school requires year 13 students to complete a year long project of a topic of their choice, culminating in the presentation of a thesis, a display and speech to a public audience. Many different topics appealed, but in the end I decided to build a micro wind-turbine. I have always been fascinated with mechanics, mathematics, engineering, aerodynamics and electricity. A wind turbine is a mixture of these technologies, with the overall goal of electricity production. In a world that is starting to see the true costs of fossil fuels, renewable energy seems to be increasingly popular and the demand for electricity is always growing.\r I was aware that building a wind-turbine from the foundations up wouldn’t be easy. Many of the experts I contacted in the early days cautioned me against trying such a complex thing in one year, at the same time as completing a full Year 13 course. There were, however, people prepared to support me. Michael Lawley, who builds micro wind turbines in New Plymouth was very helpful, just full of priceless knowledge and gave me a few basic parts to start with. The knowledge gained from Doug Clark, who also builds his own 11 kW wind turbines, was such an inspiration. Later I had practical help from Wilson Springford and Darron Matthews.\r I investigated and documented the history of and current state of wind technology, as well as my own experience and learning in the design, construction and testing process. I thought it would be interesting to find out how the electrical and mechanical side works.\r The generator, a washing machine motor, needed to be completely rewired, and converted to DC (direct current) from AC (alternating current). I built my own 3-phase AC to DC converter.\r Other parts like the disc brakes and bearings had to be found. The rest was hand-made and every part, to a certain extent, had to be modified. Probably more than twenty braking system design attempts led to the final decision to incorporate the wind-activated hydraulic disc brake where the wind paddle starts to ease the brake on over a certain wind speed.\r I studied the dynamics of wind turbine blades, their shape, the material they were made from and how this affected their performance. The decision to make my own blades helped me gain a great sense of achievement and knowledge of blade design. I found some New Zealand made 100% recycled plastic pipe, an added bonus because I wanted to have minimal environmental impact. I designed the turbine with three blades to give better starting torque along with a lower top speed, perfect for how I wired the generator.\r I designed the swivel, the part of the wind turbine that enables the power cables to get from the turbine down the tower without twisting up and has the job of carrying the whole turbine, which is mostly made from recycled aluminium. The steel and bearings used to create the swivel were all second-hand parts and materials. The power from the turbine passes through the swivel into the cables and down the tower. The main mast of the tower is a little over 4.7 metres and pivots on two shorter supporting poles which go down around 2.6 metres to the bottom of the reinforced concrete foundation.\r I managed to, design and construct an operational prototype micro wind-turbine, incorporating recycled and recyclable materials as much as possible, with the end result surpassing all expectations.