2004年

本實驗是控制奈米碳管的成長條件，研究奈米碳管的成長機制、電子場發射特性。奈米碳管的物理性質會因捲曲度(helicity)、管壁厚度(單層或多層)、管徑所影響，而不同的捲曲度，會形成不同電性(金屬性或半導體性)的奈米碳管。由此可知，探討奈米碳管的成長機制，以控制奈米碳管的穩定成長，及如何長出電性或光學性質相近的奈米碳管，是極為重要之事。為了研究奈米碳管的成長機制，我們使用微波電漿輔助化學氣相沈積法 (Microwave plasma ehanced chemical vapor deposition) ，在市售的縫衣針針尖上，成長奈米碳管，這個技術能夠經由吸收微波達到局部加熱針尖的方式，再透過控制微波功率、通入氣體的種類、壓力的變化以及催化劑的使用，能夠達到有效控制奈米碳管的成長條件。我們改變三個參數：催化劑的使用、氣體種類(Ar+CH4 或N2+CH4)及壓力，之後利用SEM 觀察奈米碳管的成長情形；再測量場發射(測量電性)，討論不同成長的條件與場發射電流關係。

In this study, we try to know how ectopic eye genes: eyeless(ey), eye gone(eyg), twin of eyeless(toy), twin of eye gone(toe) act cooperatively, and look for some unknown genes which affect the function of eyg. First, through human trans gene screening, we find two human genes change the phenotype of ey>eyg into dorsal out-growth when they co-express with eyg (ey>eyg+X). It means the two genes may relate to cell proliferation. Second, by sequencing the insert genes of mutant fly which was found by EP screening, the result shows the site of the insertion is the same as effete (eff) gene. eff translated wrong proteins which differ from functional ubiquitin-conjugating enzyme may be the major cause of the mutant eye . 本研究係探討果蠅複眼異位基因eyeless(ey)、eye gone(eyg)、twin of eyeless(toy)、 twin of eye gone(toe)間的協同作用，並尋找與eyg 有交互作用的基因、突變株。藉由人類基因轉殖篩選，找到兩株人類基因轉殖株，當其與eyg 共同表現時(ey>eyg+X)，會改變ey>eyg 的複眼性狀，造成dorsal out-growth，顯示這兩個基因可能與細胞增生有關，此外，藉由EP screening 複眼發生突變的果蠅之UAS 下游基因經比對後，位置與effete（eff）部分契合，推測複眼發生突變的原因是eff 的功能發生異常，致使細胞內蛋白質代謝失常所致。

本研究中，我們將提出一些新穎結果，著重討論其在三角中的應用；同時，找出其遞迴關係式，得出三角展開式與其所對應之多項式分解式，進而討論出多種的規律性及所涵蓋的內容及推廣性質，我得到很多高中數學公式無法推導出在【4】和【8】中的漂亮公式及創新的結果，且這些等式都是由我們不太瞭解的無理數所構成的。 主要是討論我們在【7】中所得到的收穫與經驗；複數是三角、幾何、代數互動的橋樑，我是以不同的角度及嶄新的方法來綜合探討在【6】中相關的應用。提出關於正整數平方的倒數和公式更為精簡且基本的證明，將 sin−2 x 表示成級數形式的部分分式，進而應用在(a,b) = 1的機率問題上；並研究相關的等式，直接透過三角與代數來研究關於 2p 次方的倒數之求和問題，得出級數 之和的有用遞迴公式，並與最重要的常數扯上關係。 For one thing, we present diverse methods to evaluate finite trigonometric summation and related sums. Trigonometric summations over the angles equally divided on the upper half plane are investigated systematically. Several related trigonometric identities are also exhibited. What is more, we use methods of calculus, and make several surprising and unexpected transformations. A useful recursive formula for obtaining the infinite sums of even order harmonic series, infinite sums of a few even order harmonic series, which are calculated using the recursive formulas, are tabulated for easy references. Furthermore, is there any interesting results and applications？ Finally, the purpose of this paper is to develop a new proof of and related identities, but their derivations are more complicated. The following studies are completed under the instruction of the professor.

Sicherman 已經找出與兩顆六面的正常骰子有相同機率分布的Sicherman 骰子，並進一步獲得與三顆六面的正常骰子有相同機率分布的骰子必為一對Sicherman 骰子與一顆六面的正常骰子之結果，我們試圖由已知的Sicherman 六面骰子的處理方法出發，透過對割圓多項式的分析來累積足夠的相關資料，以處理由兩顆四面骰子至兩顆三十面骰子，處理由三顆四面骰子至三顆三十面骰子的各種Sicherman 骰子的答案，來探索兩顆與三顆的n 面Sicherman骰子存在的充要條件與求法，並進一步將所得之結果分類，得到 ”有相同標準分解式的類型的數n，會具有相同組數的Sicherman 骰子”之猜測結果與特殊情形下的證明。 Sicherman has found out the Sicherman dice which have the same probability distribution as the normal two six-sides dice. Furthermore , he also found out a pair of Sicherman dice and a normal six-sides dice has the same result as 3 normal six-sides dice . We try to begin with the given algorithm of six-sides Sicherman dice , through the analysis of Cyclotomic Polynomials to accumulate sufficient related information then to come up with the solution from discussion of 2 four-sides dice to 2 thirty-sides dice , from 3 four-sides dice to 3 thirty-sides dice to explore the existence of necessary and sufficient condition and solution of 2 n-sides Sicherman dice and 3- sides Sicherman dice , and even to classify the results to come to a conclusion of the guessing results and proofs under special cases about “the numbers n which have the same Canonical Prime Factorization will have the same numbers of n-sides Sicherman dice.”

A vast amount of research has been conducted on various ant species such as Monomonum pharaonis, Formica rufa, and Lasius niger, demonstrating the coexistence of polygyny and monogyny colonies. In polygyny colony, the high heredity variability of filial generation could be expected, but what could the monogyny colony do to hold the high heredity variability in order to increase the fitness? I hope I can account the sex ratio in the colony of spiny weaver ants, Polyrhachis dives, and compare the different colony with different reproductive strategies. I also want to check by V8 that the colony can form a polygyny colony and virgin queens can mate with many males of the same colony in the artificial nest. The results suggest that in the colony of spiny weaver ants, the higher the number of the dealate queens, the lower the number of the male. In the monogyny colony, workers control the sex ratio. According to the observation, we can see the alate adult mate in the artificial nest, and multimating can be recorded for the first time. The following study was there for undertaken to examine what’s the aftereffect made by the Reproductive strategies of polygyny colony and monogyny colony.在多后聚落內，子代變異度高是可以預期的，但是單后聚落中，又如何維持遺傳的變異度以增加其對環境的適應力呢？我們希望能計算黑棘蟻聚落組成，比較不同生殖策略的聚落之各種性比，並且錄影證實黑棘蟻聚落可以為多后聚落並進行巢內自交。我們發現：黑棘蟻聚落內，蟻后數愈高，則雄蟻比例較低；單后聚落之性比決定於工蟻；而根據錄影觀察，聚落中的有翅生殖族可在人工蟻巢中完成交配，多次交配的現象首次被實地紀錄，並且佔所有交配新生蟻后的92.8%。本實驗可利用黑棘蟻來了解單后與多后聚落的生殖策略對其族群發展的影響。

Hamiltonian和Hiroimono路徑問題都有百年以上的歷史，且沒有直接解決方法，可能因為是題目本身的條件在討論時尚不足解決問題，現階段只能用電腦去跑。

The World Trade Center in New York City was collapsed after attacked by the terrorist. Although the design of this building did not consider the attack by the terrorist, however, this event also exposed the weakness of a high-rise building. This study is aimed at examining the cause of the collapse of the World Trade Center. A series of experimental studies was carried out to examine the strength of steel material under elevated temperature. Experimental studies were also performed on model steel frames under fire to simulate the situation of World Trade Center under fire. It is found that the strength of steel structure decayed under fire event. The upper stories lost its support from the floor that was subjected to fire load and the collapse of the floor under fire induced impact load from the upper stories. Progressive failure occurred on the subsequent floors due to the impact from the upper stories. This phenomenon was also observed in the experimental study of the model frame tests. This study has successful reproduced the failure mode of the World Trade Center in New York City. 紐約世界貿易中心大樓在遭遇恐怖份子攻擊後倒塌，雖然大樓之設計可能並未考慮恐怖份子的攻擊，但此次事件亦暴露超高層大樓的脆弱，本研究乃探討紐約世貿大樓破壞之原因，研究過程中首先以一系列之試驗探討鋼鐵材料在高溫下之行為，尤其是高溫對鋼材強度之影響。其次並進行鋼骨模型骨架受火燒之破壞試驗，發現在高溫燒烤下鋼骨軟化而失去承載能力，而無法承載上方樓層之重量，上方樓層倒塌後往下形成一衝擊力，並造成往下連續之衝擊，最後導致整體結構倒塌，模型結構試驗亦證實世貿大樓之破壞模式

Generally speaking in order for a exotic plant life to dominate over the local ecology, the following factors must hold true: 1. A close proximity of the environment (including geographical and climatic factors) 2. A lack of nature enemy and competitor 3. A strong reproductive and adaptability capacity. Base on the above factors, We will be using Field Observation record, Sample placement, virtual environment factor experiment and other methods to conducing our investigation. This study shown the African Touch-Me-Not（Impatiens wallerana） has a strong reproductive and adaptability capacity. Even under adverse condition the African Touch-Me-Not survive for a period of time. It can produce flowers then fruits all year round, within each fruit there is on average 45 seeds with, under the right condition, near 100% germination rate. It can also reproduce asexually via cutting. Taiwan’s warm and humid geographical condition is similar to its origin of Africa. And so far haven’t found any obvious natural enemy. In the future this plant will be likely to spread on the low to mid. level mountain region. It also can be seen that the divergence within its habitat is low. Therefore it will decrease the variety, the density and the diversification of the local eco-system. Here to advise the government’s forestry and agriculture department, to study the relevant ecological information on this species, when they are considering popularization this plant. Using the information to evaluate the impact of this plant may have on the environment, and use it as a guideline for their plant conservation policy. 一般而言，外來植物入侵本地原生植群成功的條件有：一、相似的環境（包括地理、氣候等因素）。二、缺乏天敵及競爭對手。三、旺盛的繁殖力和適應力。針對上述條件，利用野外觀察記錄、樣區設置及模擬環境因子實驗等方法，來探討非洲大鳳仙未來是否會在臺灣蔓延、擴展進而影響本土的生態系。結果顯示非洲大鳳仙有旺盛的繁殖力和適應力，?使在不利的環境下，短時間不會死亡。一年四季皆可開花結果，每粒果實平均有四十五粒種子。環境適宜時，有接近百分之百的萌發率，亦可用莖進行無性繁殖。另外，臺灣溫暖多雨的地理環境亦與其原產地非洲相似，且未發現明顯天敵，未來極有可能在中低海拔山區蔓延。調查也發現它生長的地區岐異度明顯偏低，使其他植物種類、密度減少，生物多樣性降低。因此建議政府、森林、園藝和農業工作人員在推廣時，多吸取相關物種的生態學資訊，評估其對環境可能造成之影響，以作為植物保育之重要參考。

The purpose of this experiment is to determine whether or not wood can be used as an alternative testing method for sunscreens and which species of wood are good for this objective. This will be accomplished by applying varying strengths, or SPFs, of sunscreens onto thin wood veneers. They will then be exposed using a weatherometer, in which real light and sun conditions will be simulated. Using a device called a Pulmac, the samples of wood will be pulled apart from the centre at zero span. Based on the consistency of the strengths, it can be determined how the wood reacts to the sunscreen and whether that species of wood is suitable as a testing medium. Trees are an important commodity which enrich the lives of many people, particularly those who live in British Columbia. They provide the means of living and recreation for numerous people, whether it is employment, business, housing, or camping. Since trees are a renewable resource, they are convenient and realistic to use for testing. There are two possible extensions to this project. If the active ingredients in sunscreens can be determined, then we may be able to use these elements to create a new type of stain for fences and other structures. This could make the necessity for painting less frequent, creating cheaper options for the homeowner. The second possible extension of this project is to use the results to as an initiative to reduce the amount of animal and human testing done by manufacturers. This is important, as animal testing not only causes unnecessary pain, but often the results are not very accurate. Overall, I determined that this method of testing sunscreens would work quite well, especially with the following species, listed in decreasing order. 1) Yellow Cedar 2) Yellow Poplar 3) Maple 4) Hemlock These results were based on how tightly grouped together the means of the strength values were for each species. The closer they were, the more consistent that type of wood and therefore the better they are for testing. Overall, I think this method of testing sunscreens would work quite well, particularly with the yellow cedar, maple, yellow poplar and hemlock, as they resulted in fairly consistent strength values. Generally, the sunscreens with a high SPF, or Sun Protection Factor, resulted in a lower strength loss than the sunscreen with SPF 15. In addition to proving that sunscreen is a good method for preventing UV rays from reaching the skin, this experiment has also confirmed that there are other methods of testing sunscreens, which can be researched further. Along with my main presentation I will be showing various graphs, statistics, and pictures. They will be supplemented by a booklet of “Commonly Asked Questions and Answers” and species descriptions for each type of wood.

本實驗是以實際探勘的地質及泉水資料和文獻為基礎，對於幾個可能造成冷泉降溫的原因(岩石種類、泉水pH值、流通氣體之壓力、流速)進行實驗。我們製作了一個模擬地下泉水流動的實驗管路，此管路並可同時觀察紀錄氣壓、氣體流速，以及實驗前後模擬管路的溫度變化。透過對實驗管路的熱容量校正，我們可以找出各變因對泉水降溫的關係，以建立出一個模型，期望可套用於實際冷泉的狀況，進而推論出更多冷泉的性質。This experiment uses data and bibliography from real exploration as bases to find the possibilities of why the cool spring drops in temperature. (Mineral types, spring water's pH value, air flow pressure, and movement flow.) We created a model of underground spring water for the simulation. From this model, we could observe the air pressure, movement, and the spring's change of temperature before and after the tests. By adjusting the thermal capacity in the model, we could find the direct cause of the spring's temperature drop. And hopefully be able to adopt this model to the realistic problem, increase the effort of analyzing the natural cool spring's properties.