化學中的數學與程式設計
When we were learning about organic compounds at school ,there was a unit discussing the isomers of alkane .Our teacher made us practice drawing all the structural formula of the isomers from hexane to nonane .We were much interested in the subject .However ,we often missed or duplicated some isomers .Thus , we began to think if it is possible to find a way by developing programs to let the computer calculate the exact number of the isomers of alkane . After discussion ,we set up a complete coding system .We numbered the isomers in the way that computers could decode and then wrote them in C language. Through computer execution ,the numbers of the isomers from C1 to C20 all match those on the reference website. According to the same concept , we also find a way to calculate the number of alkane with one substituted group . In the future,our goal will be focused on the research of multi- substituted alkane and cyclokane. In addition , the ionic crystal accumulation model are so variable. Take the double face-centered accumulation of NaCl for example, when the ion pairs are extended to the infinity , the potential energy of attractive field will approach a constant which is named as the Madelung Constant. We also managed to write a computer program with C language to approach this convergence with three models, including cube , octahedron , and sphere . The result turned out to be that the data of the sphere was less stable . In the other two models , when “n” is up to 43 layers , the data is identical with that on the reference website to the eight decimal point . 在學校裡學習有機化合物有關烷類異構物這個單元，老師讓我們練習畫出己烷~壬烷的所有異構物結構式，這引起我們極大的興趣！但常一不小心就漏掉或多出幾個，我們開始思考：能不能找到一個方法並設計成程式，讓電腦執行以找出烷類異構物？經過討論，我們建立了一套完整的編碼系統，將各異構物以電腦可解讀的方式編號，並以C 語言寫成程式。透過電腦執行，各碳數化合物自C1至C20都與參考網站吻合。依相同觀念，我們也設計出烷類含一個取代基的異構物數目。將來努力的目標為：多取代基及環烷類之研究！另外，離子晶體堆積模型變化多端，以NaCl 雙面心堆積為例，其引力場位能，當離子對延伸至無限大時，這個值將趨近於一個常數，又稱為馬德隆常數。我們嘗試以C 語言設計電腦程式，用三種模型（正立方體、正八面體、圓球）來逼近並求得這個收斂值。執行結果是：圓球數據較不穩定；而另二種模型到n=43 層以上，其數值大小與參考網路上的數值，在小數點以下8 位完全相同。
台北盆地的熱島效應及其對環境的影響
本研究主要是以台北市中心的氣溫觀測站，以及市區外圍東邊的汐止，南邊的屈尺，以及西邊的山佳等三個氣溫觀測站，從1998 年至2004 年的七年期間的氣溫資料中，來探討台北地區的熱島效應現象。這個研究的結果發現，台北市區與周遭鄰近地區確實會因為熱島效應的影響而產生1~2℃的溫差。這個溫差在白天時不甚明顯，在中午過後，便由台北市中心逐漸向郊區遞減，形成類似同心圓狀的分布。溫差最大值發生在夜晚，使得台北地區晚間宛如一座夜晚增溫的城市，同時夏季的熱島效應又較冬季顯著，氣溫又逐年遞升，造成夏季台北市區的高溫屢創新高，將是未來都市發展的危機。This study is focused on the urban heat island effect of Taipei Basin, northern Taiwan. The hourly temperatures of Taipei meteorological station and three rural sites eastern Hsi-Chih, southern Cyu-Chih and western San-Chia, were compared from 1998 through 2004 to illustrate the temperature differences between city center and surrounding country areas. The results show that a difference of 1~2℃ exists between city center and surrounding country areas, indicating the extent of urban heat island effect in the Taipei Basin. The daily temperature contours show a clear high-temperature bull’s eye at the city center during the midnight, implying the high latent heat trapped by the dense and high rise buildings. This phenomenon is not sharp in the high noon due to the reduction of temperature difference between city center and surrounding country areas. The heat island effect is most prominent in the summer than that of the winter. Along with the increasing temperature-difference trend through years, the summer times often experience record-breaking heat waves and pose great risks for the city development in the future.
「從害羞到大方需要多少時間」(環境因子對含羞草開葉時間的影響)
含羞草會因為受到各種不同外界刺激(光照、外力等等)，而造成膨壓改變。外 觀上表現出葉片閉合或有葉柄下垂的現象。其中含羞草處在黑暗的環境下一段時 間後，會做出睡眠運動。當它重新暴露於光照之中，將會需要一段時間以恢復原 先葉片張開的樣子。這個實驗是研究不同類型的環境因子(主要是光照和溼度)在打 破睡眠運動之後，對其葉片復原時間所造成的影響。我們針對上述環境因子在不 同狀況時，進行我們的實驗上百次，進一步得到了多項的數據。也在實驗中，為 了精確了解整個恢復的程序，而將恢復程序程序做成書面說明。以下是我們所紀 錄與分析完數據後的結果，以及我們在實驗期間，進行一些不同的實驗嘗試，所 發現不同於表面所見的驚人事實。 The mimosa can accept plenty of stimulation (light, force, etc), which results in the change of turgor pressure, and on outward appearance, it shows the phenomenon that the leaves become closed or that the stalks get pendent. Among the stimulation, the mimosa will undergo nyctinasty when it is left in the dark for a period of time, in order to enable it to be exposed to the light once more, which requires certain time. This experiment is based on how different kinds of elements of the environment (primarily light and hydro level) effects the rehabilitation time after the nyctinasty is broken. A large number of data are gained after experimenting on it for hundreds of times. Steps of habilitation are also made into illustration in writing, so as to understand the whole steps accurately in the experiment. Below are our records and analysis based on the data, including a few special experimental tries during our working time, in which some surprising facts that were discovered are different from what are seen on the surface.
打破語言隔閡-以圖點餐之數位餐廳
本次研究利用Web Sevrice軟體系統和Microsoft SQL Server的全文搜尋(Full-Text search)並藉由使用者選擇的圖片組合排列從系統資料庫中檢索比對，篩檢出正確或者最相似的餐點。Web Service 是建立於網際網路上之系統架構，且為一個具開放性、分散式的軟體元件，其基礎建立在HTTP、XML、SOAP、WSDL和UDDI等標準協定上，此研究即是透過Web Service系統與資料庫伺服器的連結進行。很多數位化資訊是以沒有結構化的文字資料，存成純文字檔及格式化的文件。這一類的文字資料儲存在檔案系統，而許多組織現在將這一類資料儲存到關聯式資料庫。這樣做就可以廣泛利用資料庫的好處-包括高效能存取、查詢能力、對使用者而言簡單的應用程式使用者介面，以及安全的遠端存取、查詢能力、對使用者而言簡單的應用程式使用者介面，以及安全的遠端存取。運用此功能即可在配對完成時搜尋最佳的結果並加以排名。「打破語言隔閡-以圖點餐之數位餐廳 」不只消除語言隔閡，更讓點餐手續方便許多，並讓錯誤的可能性降低。另外圖片資料庫的增減簡單快速、介面明瞭易懂。希望這些應用及創新能讓人們用餐方便及餐廳事業蓬勃發展。This research uses Web Service software system and Microsoft SQL Server. To choose the correct or the most similar meals by checking the combination and arrangement of the pictures chosen by users form the system data banks. Web-Service is a system structure establishes at the Internet. And its an open, dispersed software part. Its foundation is established at the standard agreement of HTTP,XML,SOAP,WSDL, and UDDI. The research proceeds by linking Web Service system and data-bank server lots of digital data are stored as words files and stylization documents without any structural words data. This kid of ward data are stored at file system, and many organized systems now store them at connected data banks. By doing this, people can make the most advantage of data banks- including efficient access, inquiry abilities, simple applies user’ interface, and safe remote access. People can find the best results and place them when this function finishes matching. It can not only eliminate language barriers but also make order procedure more convenient. It can also lower the mistake possibilities. In addition, we can increase or decrease pictures of data banks easily and fast. We can make the interface understood easily. We hope the applications and innovations can make it more convenient for people to order meals. And the business of restaurant can be developed successfully.
Amazing Fairy Chess －討論多元方形鏈的數量
在這篇研究報告中，我們討論的是一種方形集合圖形的數量。”多元方形鏈”約略在 60 年代被提出，衍生出一系列的問題和遊戲，例如熟知的電玩軟體 『 俄羅斯方塊 』 ，或是 『 益智積木 』 的遊戲，都是多元方形鏈的應用。在這些問題當中，最令人頭痛的難題就是 n 元方形鏈的圖形總數。為了解決這道難題，我們採用一種轉換方法將圖形轉換成序組，並且給出序組的性質，再據此寫成 C 語言的程式；反覆地修改程式以增進執行效率及速度，最後利用該程式成功地統計出圖形總數。 In this report, we discussed the amount of polyominoes, the graphs of a set of squares. “Polyominoes” has been brought up in 1960s, and later developed into a series of questions and games, such as a well-known video game — Tetrix, and the game of puzzle blocks. Both are the applications of polyominoes. Among those questions, the toughest one is the amount of n-polyominoes. To solve this problem, we used a method which transforms the graphs into sequences. By looking into the properties of those sequences, we obtain a set of rules that can be used to determine the quantity of n-polyomines. The rules are implemented into computer codes in C language with proper modifications made to speed up the efficiency of our algorithm. The computational results show that the amount has been successfully calculated.
彩色蠶繭之研究
近幾年來，蠶繭彩色化已引起廣泛的注意，日本與中國大陸紛紛投入此研究領域。我們用食用色素、酸性染料和活體染色劑中性紅等色素水溶液，以沾附於桑葉餵食、浸泡蠶體、注射入蠶體血腔等方法，使白色繭品系的家蠶生產出多種顏色的彩色蠶繭，其中以附於桑葉餵食最有效率，我們就此法找出投與色素的有效期間，可以比日本、中國的方法更節省色素。同法處理黃色品系的家蠶則產生黃色與所加色素的混合色蠶繭。由於這樣得到的彩色蠶繭放久了都會褪色，我們試用奈米色素餵食家蠶所得彩色蠶繭，與一般食用色素所製成的彩色蠶繭比較，發現對各種光照、清潔劑清洗等處理，用奈米色素所得蠶繭明顯較用一般食用色素所得蠶繭不易褪色。這樣用奈米色素生產的彩色蠶繭，因為解決了褪色的問題而更具有潛在的產業價值。To make silkworm cocoons with different colors has received a great attention recently. Japan and China have invested great resources in this field of the study. In order to let white cocoon silkworms produce cocoons of different colors, we used the aqueous solutions of food dyes, acid dyes and neutral red, and fed the worms with mulberry leaves immersed with such aqueous solutions, or directly soaked or injected them with the solutions. We found that using mulberry leaves immersed in the dye solutions was the best approach. We improved this approach by finding a critical, effective time of applying dyes. It saved the dyes and labor than those of Japan and China. We also found that yellow cocoon silkworms produced yellow and mixing colored cocoons by the mulberry leaf feeding method with the same dyes. Because all colors of the cocoons mentioned above faded easily, we furthermore tested nano-dye and found that colors of the cocoons had better resistant to fading away in washing with detergents under various types and intensities of light illumination. This result suggested that nano-dye has a potential in solving the fading problem of the colored cocoons.