臺灣

想像一下，原來固定的一個黑色大正方形(以下我們簡稱S1)四個角經過較小之正方形(以下簡稱S2)遮蓋後旋轉，為什麼會有放大縮小的感覺呢?(圖一) 我們猜測這是因為未被遮蓋部分(以下簡稱S3)的面積改變了，所造成的結果。令S1的邊長為 r，S2的一個小正方形邊長為n，k=r-n，θ為旋轉角度，我們實際算出了旋轉角度θ對S3的面積函數，

細胞凋亡具有控制生物體細胞數目之功能，能讓特定的細胞走向死亡，因此若能掌握其作用機制，便可能藉由調控細胞凋亡的發生，進而應用於癌症治療。前人研究（2.）指出，經基因重組技術純化之口蹄疫病毒鞘蛋白rVP1，會導致BHK-21的Akt 蛋白質去活化，引起細胞凋亡的現象。然而在其後續的研究中，卻發現到在BHK-21中大量表現磷酸化的Akt 蛋白質，並無法反轉由rVP1 所誘發之細胞凋亡。因此本實驗利用二維蛋白質電泳，尋找Akt pathway 以外之細胞凋亡相關蛋白質。目前已證明Prohibitin 此一蛋白質，在由rVP1 所引起之細胞凋亡中，有自細胞核移動至細胞質的現象。此外，亦經由實驗排除Prohibitin 位於Akt pathway 的可能性。Western Blot 之結果更顯示，經rVP1 處理後，Prohibitin 在很短的時間內便出現遷移的現象，故推測其具有調控細胞凋亡上游反應的功能。Apoptosis can lead some specific cells to programmed death, thus, it is a major way for creatures to control their cells amounts. If we can command the mechanism of apoptosis, we may use it as a therapy for cancer by artificial regulation of apoptosis. VP1 is one of the capsid proteins of Foot and Mouth Disease Virus (FMDV). A research (2.) has indicated that the recombinant VP1 (rVP1) can result in dephosphorylation of Akt in BHK-21, and then lead the cells to apoptosis. However, in their follow-up experiments, they discovered that even if they expressed great amount of phospho-Akt in BHK-21, it still couldn’t reverse the apoptosis induced by rVP1. Therefore, this experiment takes the advantage of two-dimension protein electrophoresis (2D) in order to find apoptotic proteins excluded from the Akt pathway. I have found that Prohibitin exports from nucleus to cytosol after rVP1 treatment. Furthermore, I eliminate the possibility that Prohibitin’s may be located in Akt pathway. The results of Western Blot also shows that protein amount of Prohibitin in BHK-21 increase after rVP1 treatment, hence the purpose of nuclear export of Prohibitin might not be to degrade it. It might have some much more important function in the process of exportation. Besides, Prohibitin exports to cytosol in quite a short time after rVP1 treatment. According to this phenomenon, I suppose that Prohibitin has a role as a regulator of apoptotic up-stream reactions.

一 Motivation and Purpose: In this study, we want to completely know about “The number abc…de, which times m/n, 1≦n≦m≦9?N can get ed… cba?”, and also expect to find out “The good rule within them”. 二 Procedure:Using method of enumeration, induction to collect sample of all and beginning from two digits to get information “good rule”. When get some useful idea, put them into the following research for the step easy go on, the method try and error is a very tiresome works, especially when we deal higher digits. till enough information is obtained, we solve problem and find new one, then likewise again research steps, just the basic science research ways, we are glad have the key of these problem. 三 Result and conclusion :Those number we named “converse No.” There are two groups: S=m+n=10 and 11 S=11, then Q=m/n=9/2,8/3,7/4,6/5=4.5,2.6,1.75,1.2 S=10, then Q=m/n=9/1,8/2,7/3,6/4=9,4,2.3,1.5 Each group have four type. When S=11,Q=7/4=1.75,if converse No.each digit is a multiple of 3, then can cancellation or extension of fraction to get another 3 or 4. Growth up rule: Converse No. = type factor x heritable factor x growth factor=rx hx g S=11,r=2~5,h=9, s=10, r=1~4, h=99 一 研究目的：盼能找出”顛倒一族”的族譜。二 研究過程：確定研究題目為ab…cde×m/n=edc...ba,0≦n≦m≦9?N 求ab… cde？以窮舉法收集觀察資料，歸納演繹尋求規律。1.先觀察兩位數，分析共有顛倒對36對。2.建立乘數Q=m/n一覽表，共有27個3.設計顛倒對大/小及其商一覽表，以利觀察、歸納獲得規律。4.接著觀察三位數，共有360對，綜合二、三位數規律，找出選擇式窮舉法：9之倍數法。5.再接著找出四位數，再綜合而知另有 全調法 重現法 半調法 GCD遺傳基因法等來繁衍高位數顛倒數。6.於是依諸法找得六位數資料，得知GCD遺傳基因法為繁衍通則，完成族譜建立模式。7.研究顛倒數位數與其個數間關係式，完成研究。研究結論：1.顛倒一族有兩大類：S=10與S=11 S=m+n。2.每一大類有四型： S=10中，Q =9/1,8/2,7/3,6/4(9,4,2.3,1.5)S=11中，Q =9/2,8/3,7/4,6/5(4.5,2.6,1.75,1.2)3.每一型均有一個顛倒數，除了S=11中，Q=7/4=1.75者可約、擴分而得3or4個。4.顛倒數原則上均為9之倍數，除了Q=7/4經約、擴分可能得非9倍數者。

灰色理論近來廣泛應用於各行各業的管理資訊科學上，本研究乃應用灰色理論的一階微分中輸入變數為一項之 GM ( 1 , 1 ）模型，來預測台灣中部地區土石流主要因素雨量的月平均量值。本文運用三筆以上的歷史資料，作最近一年歷史性資料的預測，藉以驗證獲得其誤差（±△e）之校止參考依據值，比利用殘差檢驗所得的誤差校止數據，更能修止出精確的預測值，接著再做台灣中部雨量未來之預測，以作為未來雨水、土石流防治之參考 · 為了能迅速產生所要的灰色預測值，研究中並以 VB 程式語言及以Petri-net分析其動態處理行為，藉 GM ( 1 , 1 ）模型的專屬處理支援程式，以做為未來雨輦自動化處理警示與預測之支援機制。Recently Grey Theory has been widely applied to management information science in all kinds of areas. This research applies the first Level differential of the Grey Theory to put a variable in GM( 1,1) model to forecast the monthly average value of the most common precipitation, in the midland Taiwan earth-stone flood zone. This paper uses more than three historical data to forecast the most recent year’s historical data, which can be used to verify and acquire referential correction data of its errors ( ±△e). The aforementioned method can correct forecast data more precisely than the differential inspection. In addition, this method can then forecast future precipitation in midland Taiwan earth-stone flood zone and the results can serve as reference for future precipitation control. To rapidly receive the needed Grey forecast values, the research analyzes its dynamic process method by utilizing VB program and Petri-net to build a dedicated process-support program of GM( I , 1) model. This program will serve as a support mechanism for future automatic precipitation warning and forecast.

If we place a block in continuous, steadily flowing water, some periodic eddy currents will appear behind it. In my report, I would like to introduce a new way to explain how the periodical movement of eddy currents would help to triggering El Nino. According to my experiment, these eddy currents have a certain life cycle, and the eddy current give a force, which drag water form the area they just went by. It will cause water level became lowest for a period of time. These phenomena are also shown in the real data of “Sea Surface Height Anomaly”, it is a quiescence period, and then changes into the highest one it is interesting that highest one always follows by the starting of El Nino. Another important result from my experiment is that, in the same fluid, the frequency of eddy currents is controlled by 2 variables: Size of the block and velocity of the flow, From this result, then get the frequency of eddy current-occur every 3.2 years. It is just correspond with frequency of historical data the El Nino from the 70’s to the present. 本報告嘗試以南極繞極環流在南美洲南端產生週期性渦流脫離的現象來解釋聖嬰的發生根據水槽實驗的結果，水流在通過障礙物後渦流脫離瞬間，會形成一水位低的空區，之後在周圍的水大量湧入，水位突然升高，並有一段時間的振盪。另外，實驗結果也顯示，渦流形成和脫離頻率大致上和注水流速成正比，且和障礙物的大小成反比。根據此結果，對照實驗結果，我認為1993 年3-4 月，1996 年1-6 月及2001 年7-10 月三個「海平面高度異常」的最低值密集帶，此極可能是渦流脫離的時段。且對照「海平面高度異常」實際資料後，發現「海平面高度異常」的「最低值密集帶」後均伴隨水面「寧靜期」，接著就出現周圍暖水流大量湧入的「最高值密集帶」，此時南美洲東南側海水溫度驟增，接著馬上接續著聖嬰的到來。「海平面高度異常」分析的結果，指示渦流脫離的「最低值密集帶」和顯示著聖嬰到來的「最高密值密集帶」間約間隔半年左右。我們推算水的史托爾數約為1，以這個值代入實際南極繞極環流通過南美洲南端，得到渦流脫離的頻率約每3.2 年一次，和長期聖嬰發生的平均頻率非常接近。

This study was to explore the nature of two basic constitutes of the regular pentagon,With these two constitutes, the regular pentagon could be multiplied into any times in size. We used four multiplication methodsto show how the regular pentagon enlarge and to verify that the enlarged regular pentagons derived from computer did exist. By integrating these four multiplication rules, we were able to arrange regular pentagon of any length of side, and evidenced the equation was ( If m,n is the number of A,B of a regular pentagon respectively ) When we tried to verify if any regular pentagon could be constituted by other smaller regular pentagons, we found that it was un-dividable only if the length of pentagon side were (the number of A, B were the 2n and 2n-1 item of Lucas Sequence), otherwise, any regular pentagon is able to be constituted by other smaller regular pentagons. The divided forms could be multiple. We also found that any pentagon could be divided by two successive un-dividable pentagons, which is called “standard division rule”. We expected to derive all kinds of division by analysis of two successive un-dividable pentagons in standard division rule. 這個研究起源於一個拼圖玩具：利用兩種黃金三角形排出指定大小的正五邊形。我們的研究動機是：一、 假如無限量供應A 和B，能夠拼出哪些邊長的正五邊形？二、 哪些拼好的正五邊形不能拆成一些較小的正五邊形？我們將研究的主要結果分述如下：

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

Motivated by Napoleon theorem, we study the properties of the triangles obtained by moving the midpoint of each side of a given trianle along the perpendicular bisector of corresponding sides, and extend the results to the case of quadrilaterals. On the other hand ,we consider the method of erecting a regular M-gon to each side of a given N-gon and joint the N centers of these M-gons to form a new N-gon. (abbreviated as CRG method),and get the following results. 1. We characterize some kinds of N-gons that can be transformed to regular N-gons via CRG method. 2. Of M,N are nature numbers with M|N, then it is possible to find a N-gon that can be transformed to a regular N-gon by CRG method. \r 3. If a polygon P is symmetric with respect to a fixed point or a fixed line, then P can be transformed by CRG to a polygon with similar symmetries. 4. If a polygon P is transformed by CRG to ′P,there exists a commonpoint G such that ΣGA=0 andΣGB=0, where A and B runs through vertices of and P′P, respectively. 本研究將拿破崙定理加以延伸。先探討由各邊中點沿中垂線延伸得出之三角形的性質並推廣至四邊形之情形條列式報告成果。另一個推廣是將給定的多邊形的每邊外接一個正多邊形，再以這些外接的正多邊形的中心為頂點造出一個新的多邊形。我們發現此幾何變換具有以下性質：（1） 「哪些多邊形能被變換成正多邊形呢?」，我們觀察出能被變換成正多邊形的多邊形其限制條件隨邊數增加而增多，並進一步區分了哪些多邊形可以被變換成正多邊形。 （2） 在將非正N邊形做變換時，不一定須外接正N邊形才能得到正N邊形，我們區分出可外接哪些正多邊形而得到正多邊形。 （3） 對給定的多邊形作此變換時，若原多邊形有點對稱或線對稱等性質，則新多邊形也將具有相同的性質。 （4） 此變換得到的新多邊形會與原多邊形共重心，亦即新舊兩多邊形內到各自的頂點向量和為0的點會是同一點。

本研究利用佛手瓜的卷鬚探討向觸性的原理。本研究大致分為兩部份，一方面我們在卷鬚中發現了含量極為豐富的構造，此一螺旋狀構造分布於維管束中，且用雙縮?詴劑檢測後發現其含有蛋白質，且不具有運輸水分的功能；並發現此一構造的分布疏密，會影響到螺旋內側外側以及切割後片段泡溫水的彎曲方向。此外，在進行卷鬚蛋白質電泳的過程中，我們發現使用含尿素的緩衝液萃取蛋白質的效果最佳，1克的卷鬚乾重約可萃取到5毫克的蛋白質，且蛋白質總量會隨著卷鬚的成熟而遞減。利用軟體比對及質譜分析八個蛋白質點，得知此八點的蛋白質為：malate dehydrogenase, oxygen-evolving enhancer protein 1, oxyen-evolving enhancer protein 2, calreticulin, peroxidase, stromal 70 kDa heat shock-related protein, and AP2/ERF and B3 domain-containing transcription repressor。由此可知，向觸性為植物經過一連串訊號傳遞後，對外界刺激的順應。

從小習染之餘，對篆刻藝術的濃厚興趣及對電腦程式之熱愛，萌生將篆刻藝術與電腦 科技結合，於是應用PHP（Professional Home Page）的文字圖形（Text Image）處理功能 將中華文化之篆刻藝術透過網際網路推廣到世界各角落。本研究規劃建置了一個 FreeBSD Server 可完善處理PHP 功能的作業平台、應用PHP 的文字圖形處理功能，編 寫可在線上DIY 設計印章的程式，以及藉由Java Script 的技術在Client 端建立一個人 性化且相容性高之使用者界面網頁，達到提供多語系、多功能、依使用者偏好作調整 印章及輸出分享的功能。為使非漢語系國家能深刻體驗中華篆刻藝術，本研究同時建 立一個超過三萬筆之由英文名音譯中文名的資料庫，提供給使用者切身的服務。 Inspired by the interest of the art of seal engraving and the love for the computer programming beginning from my childhood, I combine the art of seal engraving and computer technology, and apply the Text-Image's function of PHP to promote the seal-engraving art of Chinese culture via the Internet to everywhere around the world. This project constructs a FreeBSD Server to process PHP platform perfectly, applies the Text-Image's function of PHP to write a program for online DIY pattern design, and uses Java Script to establish a human and compatible user-interface web page for clients to provide multi-language, multi-function, and being able to adjust pattern according to the user's preference and output sharing functions. This project also sets up a database of English-Chinese translation of over thirty thousand English terms to help people who are not Chinese to experience the art of seal engraving.