費曼曾說：There is plenty of room at the bottom。喬治亞理工大學的Mostafa El-Sayed 教授發表的癌細胞辨識、與科學月刊報導『台大抗煞一號』引發我們對膠體金粒子的興趣。膠體的性質主要是由界達電位 (zeta potential)決定。參考台科大、成大、中山…等超音波應用研究，提出改良篩選物理法製造之膠體金粒子的儀器設計與製作。經沉降過濾可達平均粒徑 100 nm；而離心式篩選機與超音波管式篩選機可達平均粒徑30 nm。篩選後的膠體粒子以電容原理調控膠體金粒子之界達電位 (zeta potential)，成功地從-30 mV 提升至-59 mV，並發展成電容超音波界達電位控制儀(Capacitor Ultrasonic Zeta Potential Controller)。以膠體金粒子與蛋白質鍵結量來測試調控界達電位的效果，發現蛋白質鍵結量之增加曲線與界達電位的增加曲線的增加趨勢相似；此功能的發現對於生物科技方面的應用應會有很大的幫助。透過界達電位控制系統，本研究達到費曼先生所期望的「在原子或分子的尺度上來加工材料和製造設備」。“There is plenty room at the bottom.” The words of Mr. Feynman are the beginning of nano technology. Mostafa El-Sayed, a professor of Georgia Institute Technology, identified cancer cells through nano gold-antibody complex. So, our study focuses on the zeta potential of colloidal gold particles. At first, the filtering method and equipments were developed. The theories were based on the ultrasonic studies of universities such as National Taiwan University of Science and Technology. Then the colloidal gold’s sizes were filtered to100 nm through settling. At last, by using Continual-Filtering Centrifuge (CoCe.) and Tube Well Mass (TW-MS), the mean particles sizes can be filtered to 30 nm. The most important results are: Zeta potential of the gold colloid was controlled with Capacitor Ultrasonic Zeta Potential Controller. The zeta potential can be raised from -30 mV up to -59 mV, which is -20 mV higher than the conventional pH-changing way. The function of zeta potential to protein binding quantity was tested. The increasing curves of zeta potential and protein binding quantity were similar. This property would be a significance of biotechnology. Thourgh Capacitor Ultrasonic Zeta Potential Control system, the zeta potential’s limitation of gold colliod, which is produced by SANSS (Submerged Arc Nanoparticles Synthesis System), can be controled in a wilder range. The study which is focused on nano-scale, like the wish of Mr. Feynman – “To manufacture material and produce equipment in atom and molecular scale”.

本文藉由模糊數學理論所提的分類方式，來設計一套對於DNA序列的分類方法，並利用了40筆人工已分完的樣本，分別作為測試及學習樣本。\r 發現可以順利的將每筆DNA序列中的鹼基每3個一組轉成胺基酸序列，再利用模糊分類方式將所有胺基酸序列進行分類，最後並利用原先滾動方式的環狀排列方式，來對同一筆鹼基的3組胺基酸資料進行檢核，發現可以有效提高分類的正確性。\r 之後我們再利用182筆自然樣本進行檢檢，也發現模糊分類方式亦可正確完成此次分類結果。

實驗發現，在高溫並排鋸條之齒面上可以形成懸浮水珠，而水珠具有爬坡的現象。當鋸條齒面溫度達四百度且鋸條傾斜角低於二十度時，水滴均可向上爬坡，特別的是，角度在十二度內，大小水滴的爬升速度皆有隨著角度提高而變快的趨勢，且質量較小的水珠爬升速率較快。 水珠之所以能向上爬坡與其表面受熱快速蒸發和齒廓曲線有關。首先，水珠因受熱在周圍形成一層很薄的蒸氣層，阻隔熱的傳遞，使得在鋸齒面上可以形成懸浮水珠，持續一段時間而不會立即蒸發；而水珠爬坡的現象，肇因於蒸氣壓力和蒸發所產生的反向動量，配合不對稱的齒廓曲線，造成水珠會受到一個沿斜坡向上之淨力，進而可以爬坡。綜合前述的原因，我們可以合理的解釋各項實驗結果。

由於台灣山區溪流短小陡急，土石流災害嚴重，透過式防砂壩攔阻工法為現\r 今之趨勢，而帄面透水柵具有一般透過式壩的優點，不但能將土石流轉化為水砂\r 流，還可以減低土石流衝擊力造成的損壞及改善上游儲砂空間不足的問題。本研\r 究採用改良式帄面柵，在下游處增設分流河道，可改善分離出之細顆粒土砂水與\r 大礫石再度結合之危險。此工法於2003 年引進台灣後，尚未廣泛應用，主要原因\r 為缺乏設計之經驗式，因此本研究針對透水柵的柵棒長度（L/ Dmax）、棒淨間距\r （b/ Dmax）、柵面架設方式、柵面篩分角度（θ）等多項重要因子進行室內渠槽\r 試驗，最後提出土砂篩分比與攔阻率的趨勢方程式，設計時以總攔阻率（R）高為\r 原則，輔以篩分比（S）與貯砂率（R1）高，即可有良好之成效，期望能作為國內\r 外現場工程施做時之參考，結果如下所示。

We consider a game played with chips on a strip of squares. The squares are labeled, left to right, with 1, 2, 3, . . ., and there are k chips initially placed on distinct squares. Two players take turns to move one of these chips to the next empty square to its left. In this project, we study four different games according to the following \r rules: Game A: the player who places a chip on square 1 wins;Game B: the player who places a chip on square 1 loses;Game C: the player who finishes up with chips on 12 . . . k wins;Game D: the player who finishes up with chips on 12 . . . k loses. After studying the cases k = 3, 4,5 and 6 for Game A and the relation among these four games, we are led to discover the winning strategy of each game for any positive integer k. The strategies of Games A, B and C are closely related through a forward or backward shifting in position. We also found that such strategies are similar to the type of Nim game that awards the player taking the last chip. Game D is totally different from the rest. To solve this game, we investigate the Nim game that declares the player taking the last chips loser. Amazingly, the strategies of two Nim games can be concisely linked by two equations. Through these two Nim games, we not only find the winning strategy of Game D but also the precise relation between Game D and all others.\r 去年我研究一個遊戲：有一列n個的方格中，從左至右依序編號為1,2,3,....n。在X1個、第X2個、第X3個格子中各放置一個棋子。甲乙二個人按照下列規則輪流移動棋子：\r 一、甲乙兩個人每次只能動一個棋子(三個棋子中任選一個)。遊戲開始由甲先移動動棋子。二、甲乙兩個人每次移動某一個棋子時，只能將這個棋子移至左邊最近的空格(若前面連續有P個棋時可以跳過前面的P個棋子而且只能跳一次)，而且每個方格中最多只能放一個棋子。\r 研究這個遊戲問題時，我討論四種不同"輸贏結果"的規定：甲乙兩個人中，A誰先將三個棋子中任意一個棋子移到第一個方格，誰就是贏家。B誰先將三個棋子中任意一個棋子移到第一個方格，誰就是輸家。C誰先不能再移動任何棋子，誰就是輸家。D誰先不能再移動任何棋子，誰就是贏家。\r 當"輸贏結果"的規定採用ABCD時─我們稱為遊戲ABCD。今年我將把這個遊戲問題中棋子的個數由三個推廣到一般K個情形之後，再繼續研究遊戲的致勝策略，同時也將研究遊戲ABCD之間的關係。

本研究之目的，乃針對氫氣及沼氣發酵的結合，建立『氫化-甲烷化』程序的厭氧發酵產能系統，取代傳統『酸化-甲烷化』的厭氧發酵程序，以期提升整體厭氧處理的產能效率。研究以蔗糖、畜產廢棄物（豬羊兔糞）、鳳梨皮廢棄物為基質，先個別以產氫菌35℃發酵收集氫及產甲烷菌40℃發酵收集沼氣，進一步再將產氫廢液進行二次發酵收集沼氣。試驗結果顯示，經過氫化-甲烷化的二次發酵後，能量總產值較傳統酸化-甲烷化發酵程序的產能提升，提升倍數分別為蔗糖基質：1.16倍；滅菌鳳梨皮基質：1.17-1.27倍；未滅菌鳳梨皮基質：2.62倍。以畜產廢棄物為基質，進行產氫菌及產甲烷菌靜置與連續流培養，以兔糞基質氫氣與甲烷產量最高。酸性的產氫廢液經二次發酵後，pH值皆有趨向中性偏鹼的變化。

演奏樂器時，是使發聲體產生駐波而發出各式各樣悠揚的聲音及音調；樂器主要分成振動體(發聲體)及共鳴器兩部分，依發音方式分為弦樂器(使弦振動產生駐波)、管樂器(利用空氣柱振動產生駐波) 及打擊樂器(利用板、膜或磚等彈性材料的固有頻率振動產生駐波)。聲音有三要素：振幅、頻率及波型，響度取決於振幅大小、音調與頻率有關、波型則由不同的頻率及響度組成。樂音多變的主因是音色及音調。音色是發聲體的發音特性，取決於該發聲體的聲波波型。音調即聲音的高低，與發聲體的振動頻率材質息息相關，頻率愈高，其音調愈高，而樂曲中的音階高低則是由音調高低所構成。樂曲的製作及演奏必涉及到律制，從駐波的產生、律制的探討、頻率的測量和琴鍵的振動模型建立與波形的觀察，我們使用計頻器、示波器及有限元素ANSYS 軟體、數學計算Mathematica 軟體，我們設計一系列實驗，企圖對樂器聲波操作技巧有更進一步的認知。從實地走訪樂器製造廠，了解到設計與改良仍是樂器工藝家重要課題，本文的實驗方法可提供大型演奏會現場調音、樂器調音師或樂器工藝家設計製造樂器時參考用，對於發展文化產業期待提供更經濟與實用的建議。;Playing musical instrument is to make sounding part produce stationary wave so as to give off various gentle sounds and tones. According to different modes of sound producing, musical instruments which comprise vibrator (sounding part) and resonator can be divided into stringed instruments (which vibrate the strings to produce stationary wave), wind instruments (which produce stationary wave with vibration of the air column) and percussion instruments (which produce stationary wave with natural frequency of boards, films or bricks). Three Essentials of sound include amplitude, frequency and waveform, in which the amplitude decides the volume, tones are related to frequency and the waveforms are composed of different frequency and volume. Various musical sounds are mainly due to different timbres and tones. Timbres, sounding characteristics of sounding part, is decided by waveform of the sounding part. Tone means pitch of the sound and is closely related to vibrating frequency of sounding part. Higher frequency makes higher tones and pitch of a musical scale is decided by different tones. Music composing and playing is necessarily connected with music temperament including producing of stationary wave, discussion of temperament, measurement of frequency, establishment of vibrating mode of keys and observation of waveform. We adopted frequency counter, wave inspector, ANSYS software and Mathematica software and designed a series of experiment to get further knowledge of technique of handling musical instrument wave. After visiting musical instrument manufacturers, we learnt that design and improvement are still the essential subjects for instrument craftsmen. Experimental method in his article can provide reference for on-the-spot tuning of large concert, musical instrument tuner and musical instrument designing and manufacturing by craftsmen, and more economic and practical suggestion for cultural industry development.

溶液和水置於同一容器中，當溶液中的溶質向上擴散時，溶液的濃度會隨著\r 高度改變，形成濃度梯度以及折射率梯度dy/dn。\r 寬度a 的透明方形盒，下方盛溶液，上方加入水，雷射光照射和鉛直成45°\r 的玻璃棒，再照射方形盒時，由於溶液的折射率梯度，雷射光在屏上形成鐘形曲\r 線，向下偏Z 的距離，r 為容器至?的距離，ar/Z=dy/dn 。\r 兩液原始交界處(y=0)鐘形曲線最低位置(Z)隨著時間(t)改變，測量Z 及t 作1/Z平方-t圖，由其斜率可算出擴散係數D。\r 濃度較高的二元混合液，例如甘油水溶液，當其重量百分率濃度未超過70％\r 時，擴散係數仍不隨濃度改變；但在屏上所形成的鐘形曲線，其最大偏折點不但\r 逐漸上升，還向甘油方偏移。測量偏移點所對應的液高(y)，以及經歷時間(t)；\r y平方= 2Dt，作y-√?? 圖，由其斜率亦可算出甘油的擴散係數。

本研究探討肥皂膜與肥皂水的共振現象。在肥皂膜共振方面，我們以實驗探討皂膜的共 振模式與頻率的關係；並配合共振理論模型求出薄膜厚度，再與體積密度-厚度測量方法比 較。而又發現皂膜在共振時，皂膜保存時間較平常久，故進行皂膜生命期與頻率、強度的關 係。在進行肥皂膜實驗時，肥皂水滴落在喇叭上，振動出奇特的形狀，進而探討皂水共振的 特性並嘗試建立其數學模式。 ;The research is about the resonance of soap film and soapsuds. For the resonante of soap film, we tried to find out the relation between the resonant pattern and frequency by experiment; according to the resonante model, we measured the thickness of soap film, which was compaired with volume-dencity method. We found that the life-time of the resonant soap film is longer than the normal one, so we proceeded to study the relation between the life-time, frequency, and power. We observed special resonant pattern while the soapsuds fell down on the speaker. So we studied the characteristics of resonant soapsuds, trying to make the mathematical pattern of resonant soapsuds.

本研究計畫之目的在建立一個家蠶自動注射系統，並應用此系統讓家蠶生產具特定抗菌蛋白之蠶絲，製成抗菌繃帶。使用家蠶為載體生產特定基因工程蛋白，具有成本低廉、產量大、品質較好等優點，而家蠶自動注射系統可以大幅增加其生產基因工程蛋白蠶絲的效率。本研究中先進行家蠶表皮組織之研究，找出家蠶的最佳注射點。其次使用電流變液做為介質，設計了可控快速家蠶固定系統，並使用單一攝影機進行影像辨識，進行注射器之雙軸定位。接著發展出小液量之微量注射器，每次注射量可低至2 l。系統中並設計一圓盤式輸送系統，可快速運送家蠶至定點接受注射。研究後段以實驗控制桿狀病毒之濃度，讓家蠶產出具特定抗菌蛋白之蠶絲，並使用該蠶絲製成抗菌繃帶，可有效保護傷口免於特定細菌之感染。