猜牌術
This research mainly talks about how someone, by observing the non-congruent patterns on the backs of the playing cards and by working with the dealer on a pre-arranged lay out, can call out the cards as if he possessed the magic power to see through them. During the card-predicting game, one can use the patterns on the backs of the cards as visual clues （Observing whether it was places upside down or not）to help figure out the probability of where the card is going to show up. Suck a mathematical formula is known as the Pigeonhole Principle. Upon an analysis of the formula, we find that when given that the value of n is greater than 24, we can successfully call out a number of cards that is greater than 2n/3 . The possibility of such mathematical studies in other directions is endless. 中文摘要： 本研究主要探討利用橋牌非對稱的牌背，猜牌者經由和傳遞牌的人的一種事先約定的方 式（排法），彷彿（魔術）透視般的將一疊牌的花色逐步猜出。其猜牌過程是利用牌背 圖案的朝前朝後的指示，配合適當的猜牌張的分配，而運用到的數學法則包含鴿籠原 理，分析與討論歸納。最後我們得到一疊由四種花色張數相等所混合的n 張牌，可猜出 的張數恆大於 2n/3 （n>24 時）。後續可研究的方向仍然甚廣。
以簡易方法探討奈米銀的化學活性優於非奈米級銀粒子
A novel and simple method was developed to determine the activity of silver in nanometer particles more than in non-nanometer particles. The conductivity of conducting polymer, polyaniline (PANI) doped with different amount of nanometer silver particles was used to evaluated the activity of nanometer silver. In polymerization of polyaniline, hydrogen chloride solution usually used to increase the conductivity of polyaniline. When 1%(w/w) nanometer silver particles doped during the polymerization, the conductivity of polyaniline was down from 2.28 s/cm to 0.65 s/cm, then increased with increasing the amount of nanometer silver doped. The conductivity of polyaniline was changed from 2.28 s/cm to 0.47 s/cm when 3%(w/w) nanometer silver particles doped, but it is increased from 2.28 s/cm to 2.44 s/cm when was doped with 3%(w/w) micrometer silver particles. The conductivity of polyaniline changed due to the formation of silver chloride (AgCl) in doping nanometer silver. Some of the nanometer silver particles were formed to silver ion in hydrogen chloride solution for the high activity property of nanometer silver. This also can be proved from the spectra of XRD and FE-SEM. Therefore; determination the conductivity of conducting polymer by doping nanometer metal particles can be used to determine the activity of the nanometer particles. 本研究為開發一個新穎的檢測奈米金屬粒子化學活性大於非奈米金屬粒子的簡易方法。方法為利用導電高分子聚苯胺，於合成過程中添加不同濃度的奈米銀粒子，並分別偵測其成品的導電度，藉以評估奈米銀粒子的化學活性。由於聚苯胺在合成過程中通常加入鹽酸以提高其導電度，致活性較大的奈米銀粒子於氧化後，隨即與氯離子形成氯化銀的沉澱，而降低聚苯胺的導電度，如添加1﹪(w/w)奈米銀粒子的，其導電度由2.28 s/cm 降至0.65 s/cm，隨後隨著添加量的增加導電度先降後再稍回升。一般非奈米級銀粒子因氧化電位為負值，即化學活性小，而不易被氧化。由實驗結果，我們發現同樣添加3%(w/w)的奈米級銀粒子或微米級銀粒子，添加奈米級銀粒子的導電度由2.28 下降為0.47，添加微米級銀粒子的導電度卻由2.28 上升為2.44，此乃說明本方法確實足以證明奈米級金屬的化學活性的確遠大於微米級金屬，因相同條件下，微米級銀粒子未如同奈米級銀粒子一樣被氧化成銀離子。即奈米級銀粒子可以輕易的被氧化，而非奈米級銀粒子則不易被氧化。尤其也可由X 光繞射儀分析光譜圖和場發射式掃描電子顯微鏡拍攝圖證明。因此，我們可以採用添加3 %(w/w)奈米級金屬銀粒子及微米級金屬銀粒子於導電高分子的方法，並藉導電度的變化，證明奈米金屬粒子的高活潑性。
松鶴土石流災害初步調查分析
The heavy rain fall brought by Typhoon Mindulle in 2004 caused debris flows in the mountains of Taiwan. The most serious debris flows took place in the areas along the East-West Expressway. The area from Mt. Li to Tien Leng, namely, from the upper course to the middle course of River Da Chia. There was plenty of debris flowing to the courses of the rivers from the hot spring area in Ku Kuan to the starting place of East-West Expressway, Tien Leng. This situation caused the sedimentation of the river courses. According to the data issued by The Soil and Water Conservation Bureau of the R.O.C, on July 2nd debris flows erupted in the First and the Second branches of the river in Sung Ho Village and caused 1 death and 2 injuries, besides, the disaster destroyed 8 major roads causing transportation breakdown. On August 24th, the Typhoon Aere caused the heavy flow of the river which destroyed Po I Elementary School and Chun Chin Bridge. The researchers employed research reviews and field investigations as the research methodology with the research scope of Sung HoVillage in middle Taiwan and disaster of debris flow. The First and the Second branches of Sung Ho River belong to the category of high potentiality of danger of debris flows. The Chichi Earthquake had accumulated sufficient sedimentation of soil and stone. 2004 年敏督利颱風豐沛的雨量，引起台灣山區發生土石流，中橫公路沿線尤其嚴重。從 大甲溪上游的梨山到中游的天冷都有災情；谷關溫泉區至新中橫起點的天冷，大量土石，流 入溪中，造成河道淤積。據水土保持局的資料顯示，7 月2 日松鶴一、二溪爆發土石流，傷 亡各1 人，2 人失蹤，對外聯絡道路台8 省道崩塌中斷。8 月24 日艾莉颱風來襲，溪水暴漲， 沖毀博愛國小、長青橋及民房7 戶【1】。 本文以松鶴為試區，土石流災害為對象，使用文獻探討及現場調查的方法，進行研究。 結果顯示，松鶴一、二溪，均屬於土石流高危險潛勢溪流；肇因於九二一地震的崩塌地，提 供充足的土石堆積物。
棋子跳躍問題
This is a study about the solution to a chess flipping game. The game is based on a 4*4 game grid. First, place some chesses on the grid randomly to start a game. Move any chess by jumping over one or two neighboring chesses in the same row (left or right), same column (up or down), or on the same diagonal. Chesses which get jumped over should be flipped. The ultimate aim is to make all the chesses upside down. In this study, I try to find the rules of the beginning arrangement that ensure solution. Here are the steps I take: First, break the restriction of the 4*4 grid, and set the coordinate system. Second, find out a few “basic illustrations” that can be solved and moved in order to cope with certain complicated problems. Third, with “basic illustrations”, find the rules applying to games on n*n grid. 這是關於翻棋遊戲的可行解之探討。棋盤是一個4*4 的方格，遊戲開始時在棋盤上任意擺上一些棋子，均是正面朝上，利用相鄰棋子的水平、垂直、斜向跳躍，棋子被跳躍過一次則翻面一次，遊戲目的在於使所有的棋子都翻為反面。我要探討的是關於棋局可解不可解的問題，找出棋盤上可解棋局的規則。研究步驟大致如下：一、打破棋盤4*4 的限制，將棋盤座標化。二、找出若干個可解並可移動的「基本圖」。三、利用基本圖，找出n 列棋盤可解的規律。
雪山姑 翡翠嫂 順姑情 逆嫂意? 雪山隧道之地質環評與工程建設的恩怨情仇
實驗初期以膠體水晶模擬岩層，模擬雪山隧道水平傾斜約 1°，製作壓克力模型(實驗一)，證明是否如賈儀平教授所言《雪山隧道＝水脈改道》註3，同時此模型也證明隧道防水襯墊完工後，和隧道開挖時水力梯度的明顯變化。再加上訪問坪林到宜蘭圓通寺一帶居民結論是：1. 雪山隧道對翡翠水庫的影響不大，但對宜蘭方面影響很大2. 模型的數據證明『隧道剛開挖因為出水嚴重出現明顯梯度外，其餘二組都不再有特定梯度，即使隧道處也沒有明顯變化』。證明隧道的水平角度對水也沒有太大導引作用。因為隧道的比例對一座山而言相當小，不會有太大的影響。3. 證明隧道防水襯墊完工後，和施工前(隧道未開挖)是同一狀況。釐清對翡翠水庫影響不大後，重心改為宜蘭。此時我們綜合中興工程資料及地調所資料理出“交錯正斷層的破碎岩體”應是大漏水的原凶！1. 於是用實驗一模型加入“破碎岩體” (實驗二)證明破碎岩體水力梯度的明顯變化。2. 再加上訪問頭城附近社區，了解居民因應大漏水後改變取水層的應變措施。3. 於是再設計模型(實驗三)證明不同不透水層的相互關係。實驗末期再度訪問頭城附近社區，赫然發現水稻已開始種植(去年還荒蕪，居民抱怨連連)看到綠意盎然的稻田和笑逐顏開的居民，我們的照片和實驗數據願為雪山隧道工程做個平反！The experiment began by using gel-crystal model to simulate rock strata and the acrylic model to simulate the dip angle of 1° of the Syue Mountain Tunnel. The experiment aimed to prove if the building of the Syue Mountain tunnel will change the water tunnel as Professor Yi-Ping Jia has indicated. The model also shows the obvious change brought by the membrane lining layed on the Tunnel and the dip angle of the water power gradient when the Tunnel was built. The conclusion of our interiew with residents in the Ping-lin and Yuan-Tong Temple in I-lan is as following: 1. The building of the Syue Mountain Tunnel has more impact on the I-lan than Fei-Tsui Reservoir. 2. The statistics of the model proved that Syue Mountain only showed gradient in the beginning when it was built. The Tunnel itself did not show any obious change. The dip angle of Syue Mountain Tunnel did not draw water due to it is small in size compared to the Syue Mountain. 3. The Syue Mountain Tunnel remained unchanged after the membrane lining was layed. After we can clarify that the Syue Mountain Tunnel has less impact on the Fei-Tsui Reservoir, we turned our attention to I-lan. We combined the information provided by Zhong-Xing Construction and the Central Geological Survey, and found that the cross-normal fault if the cause of the leakage. 1. The second experiement was conducted by adding fractured stones to the previous model and proved these stones will cause the obvious change to the water power gradient. 2. We have conducted another to the communities around Tou-cheng and realized that residents have changed the water supply strata in response to the leakage. 3. Finally, we built another model in 3rd experiment to prove the relationship of 3 water proof stratas. At the end of our experiment, we returned to Tou-Cheng and found that residents have started to grow rice and started to have simle on their face. Our experiment and statistics can do Syue Mountain Tunnel justice.
綠色親善大使之誕生-生物可降解性奈米複合材料的研究
近年來，由於科技的進步，導致合成性高分子材料大量開發利用，雖然便利 了人們的生活，卻造成許多環保問題，例如：資源的消耗，以及對環境的污染。 然而「生物可降解人工合成的聚乳酸高分子」和「天然的幾丁聚醣高分子」均具 有優良的生物可相容性及生物可分解性，添加無機層狀蒙脫土可補強其機械性質 之不足。本實驗之目的是以生物可分解之合成性高分子聚乳酸作為主體，再和經 有機化改質後的蒙脫土摻混而製備出聚乳酸/蒙脫土之奈米複合材料。 本實驗主要分為三大部分： (一)以界面活性劑對蒙脫土進行改質 (二)製備聚乳酸/蒙脫土奈米複合材料試片 (三)對試片進行生物降解性測試 此外，本實驗以X-ray 繞射儀（XRD）檢測改質後蒙脫土層間距離的變化； 場發射電子顯微鏡（FE-SEM）觀察生物降解後複材之表面型態；膠體色層分析 儀（GPC）檢測生物分解前後複合材料之分子量的變化；DMA 檢測複合材料之 機械性質；TGA 檢測複合材料之熱穩定性Thanks to the development and advance of modern technology, the synthetic polymers have been put in wide use. Though the synthetic polymers provide convenience for our lives, they also bring about many environmental problems, such as consumption of natural resources and environmental pollution. Nevertheless, both biodegradable man-made PLA（Poly Lactic Acid）and natural chitosan contain good biocompatibility and biodegradability. Else, adding MMT（Montmorillonite）into PLA can modify the mechanical properties. Our experiment aimed to prepare the PLA （Poly Lactic Acid）/ Montmorillonite Nanocomposites by adding organo-modified MMT into the biodegradable PLA. The experiment underwent three phases：（1） modifying MMT by means of CTAB(n-Hexadecyl Trimethyl-ammonium Bromide, CTAB ) and chitosan （2）preparing PLA（Poly Lactic Acid）/ Montmorillonite Nanocomposites （3）testing the biodegradability of the Nanocomposites we prepared. While conducting the experiments, we made use of the XRD（X-ray Diffraction）to examine the change in MMT’s layer thickness. The SEM（Scanning Electron Microscope）was also employed to observe the surface pattern of the Nanocomposites, and used Gel Permeation Chromatography （GPC）to examine the decrease of the Nanocomposites’ molecular weight. Moreover, we also used Dynamic Mechanical Analysis （DMA）to test the mechanical properties of the Nanocomposites（Tensile testing）. Last, we test the thermal stability of the Nanocomposites by using Thermogravimetric Analysis (TGA).
可調式光電元件:奈米線與液晶的結合
藉由結合液晶與奈米線，本研究設計出新型的光電元件，我們發現這些新設計具有先前元件很難達到的新穎特性。首先，我們研究液晶分子與一維磁性奈米線之結合，很有趣的是磁性奈米線在液晶元件內，會沿著液晶方向作整齊排列，更重要的是經由一外加電場，即可調控磁性奈米線之磁場方向。藉由電場調控磁場，是很久以來許多科學家追求的目標，然而成效不彰，本研究提供了一個簡便的方法，克服了長久以來的障礙。第二個例子，我們研究液晶分子與一維半導體奈米線結合之元件，我們證實了半導體奈米線所發射瑩光之電場偏極方向，可以經由外加電場來調控，這個特性對於資訊科技的應用，將很有用處。本研究所觀測到之結果，皆可利用下列事實來理解，奈米線具有很大的表面積，因而增加了與液晶分子之交互作用，經由此增大的交互作用力，奈米線會沿著液晶分子方向排列。值得強調的是，本研究利用了已成熟的液晶顯示器技術，其未來應用性將有很大潛力。New devices based on the composites of liquid crystals and one dimensional nanowires have been designed, fabricated, and characterized. It is discovered that these novel devices own interesting properties that are very difficult to be obtained by conventional ones. As the first example, the liquid crystal device with built-in one dimensional magnetic nanowires has been studied. It is found that the magnetic nanowires can be well aligned along the orientation of liquid crystal molecules. Quite interestingly, the direction of the magnetization of magnetic nanowires can be easily manipulated by an external electric field at room temperature. The phenomenon of electric manipulation of magnetization has been studied since nineteen century, but the achievement is rather limited. Here, we provide a convenient alternative to overcome the long quest search. For the second example, the liquid crystal device with built-in semiconductor nanowires has been investigated. We demonstrate that the polarization of the emission arising from semiconductor nanowires can be easily controlled by an external electric field, which is one of the basic requirements for information technology. All of our observed results can be well understood in terms of the inherent nature of a large surface to volume ratio of one dimensional nanowires, which induces a strong interaction between embedded nanowires and liquid crystal molecules. Therefore, the nanowires can be driven along the orientation of liquid crystal molecules. It is stressed here that our newly designed devices are based on the well established liquid crystal display technology and therefore their practical application can be realized in the near future.