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].
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。
由Brocard Point 發現幾何不等式
本研究報告以Brocard Point 為核心，所用到的性質均先證明，以確認其正確性，並推演出一些其他的性質，藉由這些性質導出幾何不等式。內容可概分為四部份：(1)以Brocard Angle 及已知的或推演出的基本性質，導出一些不等式。(2)結合「法格乃諾問題」、「費馬點」、「尤拉公式」導出幾個幾何不等式。尤其是三角形邊長與面積，外接、內切圓半徑與邊長間的不等關係，頗為有趣。(3)以向量為工具，分別計算內、重、垂心與Brocard Point 間的距離，並導出邊長的不等關係。其中由內心及重心所導出的不等式，清楚俐落；垂心所導出的不等式則較為複雜。(4)以Brocard Cirle 與內、重心間的關係，導出一系列的不等式。其中Weitgenberk 不等式的無意發現，令我們印象深刻。The Discovery of Geometry Inequalities by Brocard Point This paper takes Brocard Point as a core. We proved some properties about Brocard geometry to confirm its accuracy, and deduce some other properties, and then derive some geometry inequalities by these properties. The content may divide into four parts: a) Derives geometry inequality by Brocard Angle, Crux Mathematicorum and properties which known or deduced. b) Unifies "Fagnano problem", "Fermat Point", "Euler formula" to derive several geometry inequalities. In particular the inequalities between triangle area and length of side, or circumradius inradius and the length of side, is quite interesting. c) Derives geometry inequalities about length of sides in triangle by the distances between incenter centroid circumcenter and Brocard Point. Especially, these inequalities were elegant which derived by incenter and centroid, but it was complicated derived by orthocenter. d) According to the relation about incenter centroid and Brocard Circle derives a series of inequalities. Discover Weitgenberk inequality makes us excited.
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.
Dioscorin 對塵?造成氣管上皮細胞傷害的保護性之研究
古籍上記載山藥益肺氣，養肺陰，且最近研究報告發現山藥含有珍貴的dioscorin，其為山藥貯存養分的重要蛋白質，有抑制胰蛋白水解?之活性。而塵?糞便、屍體中的消化蛋白?會破壞呼吸道上皮細胞緊密連接處引起過敏氣喘反應。我對此甚感興趣，進而利用山藥的萃取蛋白dioscorin、塵?粗萃取蛋白及呼吸道上皮癌細胞A549，藉細胞培養、免疫螢光染色、螢光顯微攝影來實驗山藥是否真能保護上皮細胞緊密連接處。再利用膠體電泳、西方墨點法中抗體的高專一性、二抗的高靈敏度來確知我之前的實驗。另外也用ELISA 來實驗dioscorin或塵?引起A549 發炎的情況是如何。由實驗得知，dioscorin 可抑制及預防塵?引起的過敏氣喘反應；而經由ELISA 實驗發現，dioscorin 對於塵?刺激A549分泌發炎物質Eotaxin 並沒有助長或是降低的效果。It was believed that Chinese yam have benefits in treating asthma. Recently, it was found that the valuable dioscorin can be isolated from Chinese yam. The major function of dioscorin is nutrition-storage, however, it also have activities in inhibiting trypsin-like protease. This inhibitory activities trigger my interests. Because the major allergens, mites, and their stool may destroy the tight junctions of airway epithelium cells through their trypsin-protease activities. I therefore carry out an in vitro study to identify whether dioscorin can be used in protecting epithelium from the attack of mites. My results showed that dioscorin can protect the tight junctions of A549 cells from the attack of mite crude extract protein. I believed that dioscorin can be a good candidate in pharmacology application. The genetic and proteomic information are my further focus. On the other hand, we also investigated the possible activity of dioscorin in inhibiting mites-induced inflammation through using A549 as a model and employing ELISA. We found dioscorin neither inhibited nor enhanced the eotaxin being secreted from A549 under the stimulation of mites.
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.
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.