摺紙數列-相關問題探討
1. 遊戲規則：將1～ 2m × 2n的連續正整數，由上而下、由左而右依序填入 2m × 2n的方格內。操作規則允許將2m × 2n做往右或往左或往上或往下的完全對摺，直到操作至所有單位方格均疊成一行，此同時有數字也由上而下形成一數列。2. 本研究即是探討操作完成的數列之數量與數字間的關連性。3. 我們發現：(1) 數列之數量與巴斯卡三角形有關。(2) 形成的數列必符合內文的 [ R(L) 性質]、 [ D(U) 性質]、[ R&D 性質]、[D&R 性質]。
1. Rules of thegame: Fill in order the continuous positive integers 1~ 2m × 2n, from top to bottom and from left to right in the 2m × 2n check. The operational rule allows a complete fold of 2m × 2n either rightward or leftward, or upward or downward, until all the check units pile up in a line. At the same time, all the integers form a series from top to bottom. 2. This study explores the relationship between the number of the series and the integers after the operation. 3. Our findings are: (1) The number of the series is related to Pascal triangles. (2) The series formed meet the properties mentioned in the study: [the property of R(L)], [the property of D(U)], [the property of R & D], and [the property of D & R].
線鋁之情-以陽極氧化鋁模板製作氧化亞銅奈米線
我們使用陽極氧化鋁(AAO)模板來製備銅及其氧化物的奈米線。以硫酸銅和乳酸配製電鍍液，利用氫氧化鈉水溶液(NaOH)將其pH 值調整到12，供以不同電壓，可電鍍出銅及氧化亞銅奈米線。在較高電壓下可製備出銅奈米線，而在較低電壓下可製成氧化亞銅奈米線，若使用中間電壓則能製得銅及氧化亞銅的混合態。利用x 光繞射分析儀(XRD)來分析其結晶構造、使用場發射掃描式電子顯微鏡(SEM)以得知其表面形貌。電鍍出的奈米線直徑約60 nm。奈米線的長度可藉由調整電鍍時間或電壓來控制。在製作IC 內部導線方面，銅奈米線深具開發潛能；在提升太陽能電池的轉換效率、製作可見光光觸媒方面，氧化亞銅奈米線極具前瞻性。We electrodeposited copper and cuprous oxide (Cu2O) nanowires with anodic aluminum oxide (AAO) templates. Both Cu and Cu2O nanowires could be prepared with an alkaline cupric lactate solution, which was adjusted to pH 12 using a 6 M NaOH, when supplied with different electrolytic voltages. Cu nanowires could be prepared when a higher voltage was supplied, and Cu2O nanowires could be prepared with a lower voltage. A mixture of Cu and Cu2O nanowires could be prepared with a supply of a voltage in between. X-ray diffraction (XRD) is used to determine the phase composition, and scanning electron microscopy (SEM) is employed to characterize the morphology of the nanowires. The length of nanowires can be controlled by adjusting the time spent on electrodeposition and the voltage supplied. The resultant diameter of the nanowires was about 60 nm. Cu nanowires are promising materials for making the conductive wires in IC, and Cu2O nanowires hold great promise for improving the conversion efficiency of solar cells and manufacturing visible-light photocatalyst.
單細胞浮游藻類對紫外線防禦機制之探討
在先備知識中，我們知道在缺少營養鹽及紫外線傷害下，浮游藻類的葉綠體會因為過氧化物（R.O.S.）的增加而受到破壞，進而影響光合作用的進行，甚至導致死亡。所以確實了解常見浮游藻類生理狀態和環境的影響，以期待未來可利用大幅度提高浮游藻類生產力的方式有效降低溫室效應的影響為本實驗的主要目的。故實驗設計針對兩種常見的海洋種浮游藻類（Tetra、Ske），在不同紫外線光譜（UVAB、UVC）的照射下，觀察R.O.S.的產生量和T-T dimer的表現狀況，並對照兩者之間的關係。結果我們發現：綠藻（Tetra）和矽藻（Ske）在UVAB、UVC 的照射下皆會產生R.O.S.，且綠藻產生的量較少；但在UVC 照射下皆有DNA 損傷（產生T-T dimer）。故推估並不是綠藻（Tetra）擁有紫外線的特殊防禦機制，而是能較有效地代謝R.O.S.。As we know, under the condition of unorganized salt’s shortage and the harm of the ultraviolet ray, the phytoplankton’s chloroplast will be destroyed because of the increasing peroxide (R.O.S.). Furthermore, the ultraviolet ray will have an effect on the process of photosynthesis, and even result in the death of phytoplankton. So, we intend to promote the production of phytoplankton in order to lower the influence of greenhouse effect by probing into the environmental influence on the physiology of phytoplankton. The experimental is designed to observe two common marine phytoplankton: Tetra and Ske. By close observing Tetra and Ske exposed to different wavelength of ultraviolet way (UVAB and UVC ), we contrast the production of R.O.S. with the appearing of T-T dimer. We observe that both Tetra and Ske will produce R.O.S. after being exposed to UVAB and UVC , but Tetra produce less than Ske, and that UVC will do harm to both the DNA of Tetra and Ske (producing T-T dimer). Based on the result of the experiment we estimate that Tetra can catobolize R.O.S. efficiently instead of having a unique defensive mechanism against ultraviolet ray (UVAB and UVC under discussion in this experiment.)
同步現象的研究
In our daily life, objects and the contacts between objects they will have mutually affect each other, some initially chaotic systems after a sufficient amount of time will mutually correct each other, and finally achieve synchronization (example: the speed of bird and fish migration, market prices, infantry…), although some are unable to achieve this. We will illustrate and explain the synchronization system, its process and discover the conditions for synchronization. Using linking concepts, we will integrate the coupled map lattices with global coupling and coupled map lattices with intermediate-range models into a synchronization mode in order to simulate a synchronization system. We first used a small system of n≦50 to obtain results that will demonstrate the linking concepts: 1. The more chaotic a system, a longer period of time is required for synchronization. 2. An increase in the number of individual objects requires an increase in the range of concepts and the amount of time in order to achieve an in depth synchronization. 3. Initial concept values which randomly effect synchronization critical point conditions are not obvious in a mathematically incorrect graph. In a closer look, when we increased the synchronization to n≦400 and the number of times to t-->100,000 we discovered:1. Using the function G(x) we hoped the results from the graph after apply the function and correction able to overlap and test with “Scaling and Universality in Transition to Synchronous Chaos with Local-Global Interactions”, but the part which overlapped the measurements was not identical: 2. We can use the significance of the critical point and the Interactive Process to find the approximate value of the critical value up to 4 digits following the decimal point. 3. We can also use the approximate value to find out the range for the simultaneous conditions and the various points on the system itself, as well as obtain a negative correlation between them, and then it can be similarly expressed with using a curve. A computer can calculate values with this kind of enumerating method, even without any special resolution capabilities to quickly obtain large amounts of approximate values of simultaneous conditions, this is especially true when calculating unfamiliar systems. 日常生活中，物件與物件的接觸，彼此會互相影響，有些原本雜亂的系統再經過充裕時間的互相修正後，最後竟能達成同步(例如：鳥群、魚群遷徙的速度、市場價格、行軍步伐…)，有些則不能。因此，我們試著利用描述同步系統的模型，觀察系統同步的過程，並且找出同步的條件。由連結的觀點，我們將Coupled map lattices with global coupling 和Coupled map lattices with intermediate-range 模型的優點整合成Synchronization mode 去模擬同步系統。我們先用小系統(n≦50)得到能印證連結觀點的結果：(一)、系統越雜亂，就需要稍長的時間同步；(二)、個體數越多時，各點需要更大範圍的點數去影響於每單位時間內以及更深的影響才能同步；(三)、起始值隨機影響同步臨界條件並不明顯，在誤差範圍內。更進一步，我們將系統推向n≦400 點,t→100,000 次，我們發現：(一)、在”G(x)”我們希望能將圖形經過函數修正之後能疊和，驗證”Scaling and Universality In Transition to Synchronous Chaos with Local-Global Interactions ”中的結果，但只有部分疊和，尺度不相同；(二)、可以直接利用臨界點的意義用十分逼近法求出臨界值的近似值到小數後四位；(三)、我們用近似值也能發現同步條件與系統各點本身可跳躍的數值範圍是負相關，可用曲線去近似。這種窮舉方式，交由電腦運算，不需要特別的解析能力就能夠快速且大量求得同步條件的近似值，尤其在運算不熟悉的系統時。
整合型水族養殖系統研究與開發
本研究主要的目的是在開發二氧化碳製造、過濾與循環的整合型水族養殖系統。二氧化碳的產製是以基於發酵原理，並搭配具有純化二氧化碳作用的水濾裝置，發酵環境溫度以水族箱內的水來維持，循環過程中並搭配外部過濾器，所有容器均由保特瓶改裝完成，整合成一套價廉、環保且具有高效率的水族養殖系統。由實驗結果可得知，二砂糖發酵對於二氧化碳產生率而言，其最佳發酵環境溫度範圍25℃~35℃，一般水族箱的水溫即可保持在此一溫度範圍。過濾系統則使用光電比色計與一般市售過濾器相比較，亦有令人滿意的效果。本實驗除了研究以二砂糖發酵之外，還希望更進一步地朝向廚餘減量方面開發其他發酵材料，希望能為環保盡一份心力。;The purpose of this study is to develop an integrated system of aquatic breeding with the functions of producing carbon dioxide, filtering and circulating, where carbon dioxide is produced based on fermentative theorem and purified by the water filtering; the environmental temperature of fermentation is maintained by the water in the aquarium and circulating is through an external filter. All the containers are made of PET bottles and thus integrated a cheap, environmentally friendly and high efficient system of aquatic breeding. According to the experimental result, for the producing rate of carbon dioxide, the best fermentative temperature of NO.2 granulated sugar is 25℃~35℃. With a photocell colorimeter to compare the function of the self-made filter with that of the filters on the market, one can find it’s comparable. In addition to the fermentation of NO.2 granulated sugar, the study is also expected to develop other fermentative materials to reduce kitchen waste for environmental protection.
氣泡在黏滯性液體中的運動
本研究目的在探索不同大小之氣泡在不同黏滯性液體中運動情形。實驗結果發現大氣泡向上運動的速度較大，其下方會漸漸向內凹。並且觀察到氣泡間結合時的相互作用：氣泡在相同黏滯性膠水中上升時，若下方氣泡體積較大，其較快的速率會使距離縮短。此時小氣泡的下半向內凹，大氣泡的下半則向外呈現流線型尖端並且在接近小氣泡時速率增加，最後與小氣泡結合。若上方氣泡體積很小，與下方大氣泡的距離縮短至相互貼合，小氣泡會先停留在大氣泡的上半表面，再沿大氣泡表面下滑至大氣泡的下半才與大氣泡結合。This research traces the motions of bubble with different volume in viscid liquid. The experimental results show that the bigger bubble rises at faster speed. The shape of the small bubble is round. As the volume of the bubble increases, it turns hamburger-like. And if the bubble is big enough, its underside would be concaved. In viscid liquid, the speed of the bubble is not smooth but waved. The smaller the bubble is, the more the variation in speed is. The interaction of two bubbles is also studied. There are two types of the combination of two bubbles. While the big one closes to the small one, it is accelerated. The underside of the small one becomes concave. And the big one becomes streamline shape. If the difference in volume between two bubbles is significant, the small one slides along the surface of the big one, and goes into the concave beneath it, then combines with it.
熱線式渦流流量計
流量計在實驗室與工業領域裡是重要的儀器，如今已經有數十種依不同物理原理而發展出來的型式，可以配合多變的環境需求與測量條件而使用。然而，各種流量計所適用的範圍備受侷限。本研究主要目的在發展一種熱線式的渦流流量計，供給氣體之流量量測之用。透過自行製作儀器與設備：熱線測速儀(包括探針、探棒及電子處理器)和渦旋產生器(管道中含一三角形截面之鈍體，當流體通過時，在後方尾流產生週期性渦旋逸放)。由於熱線測速儀擁有偵測流體運動時高頻動態變化的能力(約為20000 Hz 以內)，因此結合熱線測速儀與渦旋產生器，經適當的設計與調校，可以測得在不同流體流速時渦旋產生器的三角截面鈍體後方渦旋逸放的頻率。由於渦旋產生器的截面面積為固定值，因此可以從而計算出流量與渦旋逸放頻率的關係。經由嚴格的校準與驗證步驟，本研究的結果顯示自製的熱線測速儀擁有極佳的渦旋頻率偵測能力，所量測到的校準曲線顯示渦旋產生器的三角形截面柱所產生的渦旋逸放頻率與流量成線性關係。為了降低誤差，建議在0 ~ 40 CMM 之量測範圍內分成三條方程式來代表不同範圍內的校準曲線，最大誤差僅在5%以下。若需使用在不同的流量範圍時，僅需改變渦流產生器和幾何尺寸，以使渦旋逸放頻率適合於熱線測速儀的動態響應範圍即可。倘若商品化之後，可以實際應用於風扇流量量測、引擎進氣埠流量的測量等等應用。熱線測速儀本身也可作為風速計，適用於各種場合之風速量測。Flow meter is a instrument that is vital to the laboratory as well as the industrial related field. Based on different physical principles, tens of models that work in harmony with the diverse environmental demands and measurement conditions are developed to date. However, the application of varied flow meters is still under severe restriction. The purpose of this study is to develop a hot-wire type of vortex shedding flow meter for the use of flow rate measurement. Through the home-made apparatus and device, the hot-wire anemometer (includes probe, stem and electronic processor) and the vortex generator. (duct that contains triangle’s section of the bluff body. When fluid passes through, the wake behind produces periodical vortex shedding.) The ability of hot-wire anemometer when it detects the fluid moving changes of high-frequent movement is within 2000Hz, after appropriate design and adjustment, the combination of hot-wire anemometer and vortex generator may investigate the frequency of different flow rate that generated from the vortex shedding behind the bluff body of triangle section. The section area of vortex generator is constant value, thus it can calculate the relationship of flow rate and the frequency of vortex shedding. By means of strict calibration and test procedure, the results reveal that home-made hot-wire anemometer has excellent ability to detect the frequency of vortex shedding. The calibration curve indicates a linear relationship between the frequency of vortex shedding and flow rate. In order to reduce inaccuracy, it is suggested to classify three formulas to represent the flow rate that ranges from 0 ~ 40 CMM. The greatest inaccuracy is under 5%. When applied to different flow rate range, it only has to change the size of vortex generator only if the response frequency of hot-wire anemometer suit for the range of frequency of vortex generator. After commercialization, it can be applied to measure the flow rate of fans, flow rate of intake valve of engine, etc. Hot-wire anemometer also served as anemometer, which can be applied to wind velocity measurement in any situation.
Peanut Hull as an Antioxidant in Metal Coats
A study was done to determine if the antioxidants found in peanut hulls could be used\r for lessening the corrosion rate of iron. Peanut hulls were ground then divided into two\r batches, P1 and P2, then oven-dried at temperatures of 50°C and 60°C, respectively. The\r moisture content of each batch was then determined before performing methanolic extraction\r to isolate the antioxidants. Eighteen iron strips of approximately the same surface areas were\r thoroughly cleaned and weighed, then divided into six groups. The iron strips in the first five\r groups were respectively coated with pure extract from batch P1; a 1:1 mixture of P1 extract\r and turpentine; pure P2 extract; a 1:1 mixture of P2 extract and turpentine; and pure\r turpentine. No treatment was done on the sixth group. All iron strips were exposed to air to\r allow formation of rust thru atmospheric corrosion. After 12 days, the iron strip were cleaned\r and weighed; then the individual corrosion rates of the metals were determined.\r The corrosion rates of the metals treated with pure P1 extract, the P1-Turpentine, and\r the P2-Turpentine mixtures were found to be significantly lower than the corrosion rates of\r the metals without treatment, at 5% level of significance in a t-Test for independent samples.\r The average corrosion rates of all the treated metals were found to be lower than that of\r metals treated with pure turpentine, though not significantly. The corrosion rate of the metals\r coated with turpentine was not significantly less than that of untreated metals. The corrosion\r rates of the metals were also found not to be dependent with the moisture as there was no\r significant difference in the mean corrosion rates of metals treated with P1 extract and those\r treated with P2 extract, with or without turpentine.\r The project has shown that peanut hull extracts can be used to lessen the production\r of rust on the surface of the metal. Moisture content of the hulls was not found to be a factor\r in lessening the corrosion rate.