臺灣

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.

為了解「螞蟻吊大象」課程中脆弱的火柴棒如何撐起六、七瓶礦泉水，我們設計實驗包括三根木棒的粗細或長度改變、木棒接觸面的材質、載重系統的整體環境等，探討承載架運用什麼方法撐起重物、如何增加承載架負重能力，發現改變各種變因能影響承載架負重效果：當木棒纖維強度不足時，承載架倒塌的原因為木棒斷裂，當木棒纖維強度足夠時，會因繩子受力拉長，最終導致傾斜倒塌。在實驗過程中了解承載架載重原理，嘗試應用於生活之中，設計能夠隨處掛起的環保杯袋，並且對力學有更深入的了解。

此研究的目的是要設計出一套完整編輯顯現數學式、加以計算，並求出解的一套方法與成品。而這項工作的執行者，在此稱之Equatetor 。一般的數學式子，若要計算的話，普通的計算機是不足夠的。原因是它們沒有辦法表現出數學式的「原貌」，例如分號、指數、函數、根號等數學符號混在一起時的情況。於是，我便擬定了一個研究，希望設計出一套更方便且實用的方法。換句話說，我要設計出一個功能強大的工程計算機程式。其中，自然牽扯到數學式子的顯現方式（以MathML 實現），以及計算機科學的演算法及資料結構。我主要的目的有四：(1) 顯示數學式(2) 方便編輯數學式(3) 計算數學式(4) 處理可以以不同形式輸出解答的計算（如輸出分數、根號、函數解等）。研究結果中，成功地運用XML 中的MathML 與二分逼近分數等演算法及若干資料結構，達到了以下實用的幾點：(1) 結構化的數學式編輯(2) 完整地顯示數學式(3) 正確運算並輸出運算式的答案(4) 提供一般數學形式之解（非小數之解）;The object of this study is to design a method and processor which is able to edit, display a mathematical expression representing a number, calculate and output the answer. The executor of this task is called Equatetor. Normal calculators are not adequate for this kind of task. The main reason is that they can’t reveal the original expression, such as fractions, radicals, exponents or mathematic functions. Therefore, a simple and convenient method is needed. To perform the possible way of handling those tasks, a computer program has been written. Several techniques were used, such as MathML, computing algorithms, data structures, and so on. Following are main purposes: (1) Displaying mathematical expressions. (2) Editing mathematical expressions simply. (3) Calculating mathematical expressions. (4) Outputting the answers(in different expressions). And the achievements:(1) Structured methods of editing of mathematical expressions. (2) Displaying mathematical expressions completely. (3) Calculating mathematical expressions precisely. (4) Offering answers in different expressions.

Earthquakes are results of rapid sliding of two crystal blocks around fault inducing seismic motions. Huge disasters caused by large earthquakes as the Ji-Ji Earthquakes occurred on 21* September 1999 show importance of earthquakes forecast. In our country and foreign countries , there appeared not a small number of reports suggesting there are clear precursors of ground water and electro- magnetic changes amount other numerous phenomena. Recently there are reports that point out the possibilities to investigate slight motion of ground water near active faults using electro- magnetic instruments. In order to investigate the problem more in detail a simple laboratory experiment is designed to study the electric field induced by the simulated water flow. The electric field changes are compared with at without water flow. It is shown that there appeared electric potential changes of an order larger than measurement limits water motion during earthquakes occurrence process, and that monitoring the flow of ground water near active faults is useful method in the earthquake prediction.近年來科學家從事地震研究，發現地震前斷層附近地下水流以及電磁場會發生變化。但或因位置不確定，或因變化量甚小而不易量測。本研究真對上述地震預警中兩項重要的關鍵 - 水及電，嘗試製作電極，並利用室內模擬地下水流動而野外斷層的電位量測，檢測斷層活動期間電場的變化。其結果顯示，當地下水因地殼受擠壓而流動時，可明顯觀察到電場的變化。這表示借由本實驗測量地震前發生的電位變化，可監測地震前版塊應力的改變，進而提供地震可能發生的資訊。

This study investigates the possibility that “Digital Buses” would actually be used in real life. In addition to the basic mathematics knowledge that I have acquired over the years, I have used “Microsoft Visual Basic” and “LEGO ROBOLAB SOFTWARE” to implement the idea as a program. It simulates the way in which a digital bus travels in a city with a rectangular grid. Various plans are tested to find the best paths for providing the most efficient, convenient and speedy transportation. This study has not only shown that “Digital Buses” are sure to be used in a modern city when wireless communication networks has developed to a certain point, but also supplied a framework for future researchers who may wish to study the optimal way in which more than one digital buses could efficiently run in cities according to their population distributions and road arguments, in order to overcome the traffic problems from the current bus systems. 本研究探討數位公車在人類未來生活中實際運行的可行性。本人以所學的數學知識進行公車路徑規劃，並透過「樂高機器人控制系統」以及Microsoft Visual Basic 軟體程式之撰寫，在棋盤式城市區域中模擬公車行駛情境，靈活搭配各種方案找出最佳路徑，達到便利快捷的高運輸效能。本研究顯示當現代化都市無線通訊網路發達到一定的程度時，數位公車的發展是可以預期的。本研究之結果可提供後續研究者繼續探討多台數位公車在實際都市中依人口分佈、道路狀況來規劃最佳行駛路徑，以解決現今機械公車無法克服之繁雜交通困境。

ELVES (Emissions of Light and VLF perturbation due to EMP Sources) is a transient luminous phenomenon of ionosphere induced by the electromagnetic pulse of lightning. In this report, we use the data of ISUAL science payload of FORMOSAT-2 to investigate the luminosities and the stepped-leader signals of the different kinds of ELVES.淘氣精靈全名Emissions of Light and VLF perturbation due to EMP Sources簡稱ELVES，為閃電的電磁脈衝波引發電離層短暫發光的現象，本研究是分析福爾摩沙衛星二號上科學酬載ISUAL的光度資料，以探討淘氣精靈類型與光度訊號強度以及閃電前導訊號的關係。

瓦斯熱水爐使用大火時廢氣的CO 濃度非常高是導致一氧化碳中毒事件的關鍵原因，要解決這個問題觸媒轉化是一種可行的方式。影響觸媒性能的因素中以活性中心的種類最為重要，我們發現對轉化一氧化碳為二氧化碳的反應而言鈷有最好的催化效果，其次分別為：鎳、銅、鐵。最好的載體是三氧化二鋁，鈷的含量使用10％，煅燒溫度使用300℃可兼顧性能與成本。 本研究中所研發的 Co/Al2O3 觸媒具備有實用的潛力，可以在空間速度高達1000min-1 的情況下將濃度14,632ppm 的CO 百分之百轉化為CO2，而僅需233℃的反應溫度。因此，應該可以應用在瓦斯熱水爐上以降低一氧化碳中毒的風險。 The incorrect usage of a natural gas powered water heater always generates high carbon monoxide concentration in a closed environment. The dangerous CO gas can be fatal to the careless user of the water heater. Catalytic conversion of CO to CO2 can be a convenient method to solve this problem. The effect of the support, the supported metal, loading of the metal, reaction temperature, gas concentration, and reactants flow rate on the performance of the CO oxidation catalysts have been investigated. X-ray diffraction, gas adsorption and Infrared spectroscopy were applied to study the characteristics of catalysts. A 100% conversion of CO to CO2 can be achieved when 1.46% CO/6% oxygen/N2 reactants was catalyzed by a 10% Co/Al2O3 catalyst at 233℃ with a space velocity of 1000min-1 . This reaction condition is sufficient to remove the entire CO generated by a family-sized natural gas water heater.

本研究以b04課程中的巴斯卡三角形為研究對象，將原先巴斯卡以「1」為首、「+」為運算符號的規律三角形，改為以「-1」及「ω 」為首、「×」為運算符號，分別就其產生的新三角形作探討，發現其中似乎隱藏著原先三角形所沒有的規律性。為了更瞭解這種規律，藉由電腦軟體繪出其圖形，圖形顯示出如碎形般的複製關係，不論放大或縮小，其中的遞迴關係並未改變，頗令人好奇，因此著手研究。研究過程中對於圖形的規律性採用先臆測、接著歸納、最後給予證明的方式呈現。得到以下的結論：一、分別以數列呈現新三角形圖形的規律性。二、分別將新三角形中每一列中的某數字（如-1、ω 或ω 2 ）的個數予以通式表之。三、分別推算出新三角形第n 列第j 行的數是「1」或「?1」及「1」或「ω 」或「ω 2 」。四、相同的模式，在特定的圖形範圍中，不斷重複出現。許多研究將巴斯卡三角形中的所有數，以某數為模的餘數紀錄下，去探討其餘數在新產生的巴斯卡三角形中的分布情形；而在碎形的研究中，大部份著重如何畫出碎形。本研究著重圖形其規律性的探討，提供上述研究不同角度的詮釋與探討。 This research subject is based on Pascal’ s triangle in senior high school curriculum. The regular triangle begins with「1」and use「+」as operation. Let 「1」 be replaced with「-1」and「ω 」, the operation sign「+」be changed into「×」. I do research on the new triangle and discover the seemingly hidden regularity which doesn’t exist in the original one. To understand more about this regularity, I draw figures through the computer. The figures show the relationship of reproduction as fractal. Whether the figure is enlarged or minimized, it’s surprising curious the recursive relationship doesn’t change, so we begin to work on research. In the process of the research, we make careful observations, assumptions and deductions about the regularity of the figure. Finally, we come to some conclusions by means of giving proofs:（1）Present the regularity of the new triangle figure with progression.（2） Present such numbers as「-1」, 「ω 」, 「ω 2 」 in each row of the new triangle with formulas separately. （3）Figure out the number in the row n and in the column j of the new triangle is「1」or「-1」,and「1」or「ω 」or「ω 2 」. （4）The same model appears again and again in the specific range of figure. Many researches record Pascal’s triangle modulo certain number to explore the distribution of remainders in the new triangle. In the research of fractal, how to draw fractal is mostly focused on. The exploration of this research emphasizes the regularity of figure, offering the interpretation and exploration of researches above from different angles.

有二系統A和B，A中一開始有2k個物體，，B中有0個物體。在一個單位時間內，兩系統可以互相轉移最多一個物體。當B中物體的個數為 i-1，i∈{1,2,...,k+1}，我們稱其為狀態 i，從狀態1﹝初態﹞開始計時，到達狀態 k+1﹝相同態﹞便即刻停止實驗，經過之時間為一隨機變數T，稱之為實驗時間。問當兩個系統的物體數剛好相等時，經過的實驗時間之分佈為何？本文將以上述問題為核心，分別探討不同條件下系統的實驗時間所反映出來的現象，如機率、期望值、變異數等等。 Define two systems, A includes 2k objects, and B has none. They can transfer at most one object from one system to another in a time unit. When the number of objects in B is i-1, i∈{1,2,...,k+1} , we say the system is at state i. As soon as system transfer form state 1 ( initial state ) to state k+1 ( the same state ), the experiment stop. Random variable T, called the experiment time, is the time before stop. What would be the distribution of the experiment time if all systems have the same amount of objects within? This article will focus on the described question and discuss what property the experiment time of the system under various conditions has, such as probability, mean, and variance.

DNA感測器近年來蓬勃發展,應用層面包括基因工程,醫學及藥物的開發等,然而目前較常使用的感測方法,需要繁瑣耗時的標定過程,且所使用的化學藥劑對環境容易造成傷害,鑒於以上方法的不完善處,我們決定設計一套新的感測系統,此研究結合了氮化鎵奈米線(GaN Nanowires)及延伸場效電晶體(EGFET)的優點,成功的發展出創新的DNA感測系統,氮化鎵奈米線的高生物匹配性及高感測面積,能有效提高靈敏度,延伸式場效電晶體的設計,史感測器具由免標定及時感測的特性,且易於組裝及操作,我們將探針DNA(probe DNA)修是在氮化鎵奈米線作為之延伸閘極上,由於DNA在中性水溶液中帶負電,且DNA之間具有強烈的互補特性,因此當目標DNA(target DNA)與探針DNA接合,形成雙股DNA,氮化鎵奈米線(閘極)的表面電位即會有所變化,並造成FET特性的改變,藉由此性質及能成功感測DNA,研究結果顯示,此研究所發展出的DNA感測器,愈有相當高的靈敏度(10-18),相較於其他以FET技術所設計出的DNA感測器,靈敏度提升了三個數量極,此外此感測器亦具有高選擇性,即使單一鹼基對的突變也能成功辨別;-hybridization based detection techniques are widely developed due to their promising applications in genetics, medicine and drug discovery. However, current DNA detection techniques based on labels or reagents are time-consuming, environmentally-harmful and complex to implement. In this study, we have successfully demonstrated a label-free extended-gate-field-effect-transistor (EGFET) sensor utilizing a GaN-nanowires electrode with DNA probes immobilized, capable of specific DNA sequence identification. The principle behind the design is based on the change in surface potential and charge transfer after hybridization. GaN nanowires, being bio-compatible, provide direct transfer path and high surface area, thus offer an unprecedented opportunity of DNA sensing with high sensitivity. In addition, our EGFET design facilitates easy assembly and operation of DNA detection. Comparative studies on complementary and non-complementary DNA were performed to verify the specificity of the sensor. By adapting GaN nanowires structure, the assay time of DNA was shorten to within thirty minutes. Moreover, our sensor displayed an ultra-high sensitivity in the level of attoM: three orders of magnitude higher in resolution than that of other FET-based DNA detection methods.