上體育課的時候看到同學投空心球（籃球在沒有碰著籃框的情況下進入籃中），覺得好厲害。因此，我們利用相關的數學知識與運動原理來討論籃球投出後的運行軌跡，以及影響其命中率的相關因素。我們得知籃球的運行軌跡是一條拋物線，並求出其二次方程式；並利用標準籃球直徑與籃框直徑找出籃球進入籃框的最小入射角。若要提高命中率，必須考慮籃球投出時的投射角、初速度、籃球投出時的高度以及籃球與籃框水平距離之間的相關影響。此外，我們藉由電腦軟體列出相關數據提供作為實際投籃時的參考，並藉此進一步分析上述因素如何影響籃球運行軌跡以及如何提高投籃的命中率。Those who always shoot nothing but the net in basketball games were always heroes to me. I have being thinking for a long time how to become a person of that kind. For this, we investigated the trajectory of shooting a basketball and the factors to increasing the field goal percentages through our knowledge on mathematics and physics. We have obtained that the trajectory is in fact a parabola and, we further, found its quadratic equation. We also derived the minimal incident angle from the diameters of the standard basketball and hoop as well as the quadratic equation we have found. To raise the field goal percentages, some important factors must be taken into consideration, such as the vertical and horizontal distance between the basketball and the hoop, the incident angle and the initial velocity of shooting. Finally, we provide some concerning data for reference, and analyzed how the important factors we have mentioned above have affected our basketball trajectory and how, of the most importance, to increase the field goal percentages

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。

此篇報告中,主要是在敘述以單晶片8051為主體,運用其所具有之功能,製作成此作品,稱為記數抽籤機,又稱抽籤機,根據本篇報告結果,可歸納出以下結果:1.本實驗能讓初學者對單晶片8051之特性與功能有更深的了解,以增進實驗與成品實作的能力。2.此作品以便利為原則,故其體積不大,重量輕攜帶方便。3.使用之元件普遍,價格便宜,在電子材料行均可買的到,成本低。4.依本品之功能,可用於學校讓老師進行抽問,也可用於其他有抽籤或抽獎活動之場合,公平又公正。;In the report, we take the single chip 8051 as a main body, making use of function to do the counting drawing lots machine, which are also called drawing lots machine. According to the resultof this report, conclusions are as followings: 1. With the experiment, the beginners egt deeper understanding about the characteristics and the finished products. 2. This machine is light and its volume is small, so it is easy and convenient to carry with. 3. The essential elements are common,cheap and can easily be bought in the store which is sellong electronic materials. 4. The drawing lots machine can be used at schools when teachers want to pick out some students to ask or it can be used for some drawing lots occasion as well. The outcome is just and fair.

In the previous year study, we assumed that the fish basin as a column-shape model in order to exam and explain how the water spouting. This year, we established a reality-like situation of the fish basin to construct our theory base. At this point, round-waves and up-down waves are found as the beginning point of the water spouting. The sound from the basin is the frequency of the vibrations. Meanwhile, this process enables us to understand the causes of four, six, and eight waves. In addition, we tried to change the basin's positions, the capacities of water, the densities of liquids, and the sizes of the containers to demonstrate the theory. Furthermore, we used similar containers, such as high-heel cup and big magnetic bowl to experiment. The results are also corresponded with the theory. These results can also be used to explain the Chinese aeolian bell, clock, shaking bell, etc. That is a major innovation for us. Finally, we obtain better understanding of the abstractive theory though the simulation of the computerized photographs. 魚洗，也稱龍洗，傳說是中國唐宋時代皇帝洗臉的臉盆，內底四條魚紋，麟尾畢具。洗內盛水後，用手摩擦其兩個雙耳，立即發出響亮的嗡鳴聲，並出現美麗了漣漪，水珠四濺，摩擦越快，聲音越響，波浪翻騰，水珠越烈。對此在上一年度的研究中，是將洗盆視為圓柱狀，然後由圓柱狀所建立的模型去解釋水跳的原因，初步瞭解了水跳的原因。今年我們以洗盆真實的情況建立理論模型，在殼體產生共振的圓形駐波及上下駐波，此為水跳產生點，此時殼體發出的聲音就是共振的頻率。也瞭解了有四個、六個、八個、十個波腹的原因。並以改變殼體不同位置、水量、液體密度及洗盆大小等變因應證模型，結果與理論相符合。繼而以高腳杯、大磁碗等類似魚洗盆構造的容器，加以實驗應證，也能符合此理論。甚可推到中國古時候的編鐘、搖鈴、風鈴等器材。對於我們總認為碰撞就產生聲音的觀念實是一大突破。最後經由電腦動畫的模擬，讓此抽象的理論更容易瞭解。

當我們寫作電腦程式時，經常發現一個現象，就是：在某個時候會須要某種功能，但是我們正在使用的那種電腦語言（ ex : FORTRAN . BASIC ）沒有這種功能，而另一種語言有。因此我們便想到要學習一種功能最強大的語言，要能包容其他各種語言的所有重要功能的。但是我們找不到。於是退而求其次，希望能找到一種可以定義指令的語言，這樣我們就可以定義出我們想用的功能。 FORTH可以，但它只能作整數運算，作浮點運算時必須採用模擬的方法，定義起來太複雜。 LOGO可以，但它是Interpreter ，速度太慢。我們理想中的語言要有：Compiler 的速度 FORTRAN 的運算能力 PASCAL 的結構化 BASIC 的簡單易學 LOGO 的定義指令能力當我們 找不到這樣一個語言時，我們就自己動手來創造了。

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.

本報告的目的在：電腦Cabri 3D 軟體上模擬出「類球狀多面體」（圖1-8），\r 並實作其模型（圖9）與它們的星體（圖10）。「類球狀多面體」的定義如下：\r 可由「正多面體」切出之多面體，且需滿足以下性質：（1） 除「正多邊形」外，\r 其餘皆是「六邊形」。（2）鳥瞰每個「正多邊形」時，形狀皆保持不變。（3）\r 等長的稜數最多。\r 以「正十二面體」切出之「類球狀多面體」為例，（圖1）中兩個「正五邊形」\r 相距一個「六邊形」簡稱A1。（圖2-4）依序為A2、A3 與A5。正二十面體可切\r 得（圖5-6），正六面體可切得（圖7-8），......等。（圖9）為A2 的實體模型，\r （圖10）為A2 的星體模型。

The human eyes can adjust automatically the color of object under different illuminants. But digital camera does not have such mechanism, must join the white balance to simulate the color constancy of human eyes. There are many existing white balance methods. They can be categorized into two types. The first type utilizes the widespread assumption on the dealing natural scenery, which has the advantage of simplicity. Another type explores knowledge of the semantic content, which has the advantage of accuracy. In this study we modify and enhance the widespread assumption methods that can adopt the advantage of the simplicity and accuracy. Our proposed method is structured in two main parts: a color cast detector and a color cast remover. The detector first analyzes the color distribution of the image with simple statistical tools to determine whether or not the image has color cast. The remover, a modified and enhanced version of the widespread assumption methods ( gray world and max RGB ), is then applied on the color cast image. From the experiment results, it demonstrates the efficacy and performance of the proposed method.人類的視覺能夠自動修正因光線變化而改變的物體顏色，但是數位取像設備的感光元件卻不具有這樣的功能，必須加入白平衡的功能，才可模擬人眼維持色彩恆常的特性。現有的白平衡演算法可分為兩大類型，第一類型為廣泛假設型，具有運算速度快、與取像設備無關的特性，但是平均誤差會較大；另一類型為預知特性型，其特徵為準確性較高，但是運算較速度較慢、建立色彩特性資訊時所需的成本較高，本篇研究針對廣泛假設型的演算法做些修正與增強，使其具有較小的平均誤差以獲得較佳色彩品質的影像。我們將影像的色偏校正分為色偏偵測與色偏移除等兩個階段來進行，由於僅有被偵測出有色偏的影像才需要進行色偏的移除，所以可以避開將無色偏或固有色偏的影像做錯誤的修正，由實驗的結果看來，我們的方法確實有效，除了具有運算速度快、與取像設備無關的優點外，其色偏校正能力也較現有的方法好，使得影像色彩更能與人眼所見相近。

本研究是以數位科技改良生物實驗上的傳統比色法，並探討中國樹蟾及台北樹蛙的變色行為。有些兩棲類有變色行為，這是眾所皆知的現象，過去一向採用比色法判斷生物體的體色變化；然而，以人眼去測定色差，會有相當大的主觀誤差。本研究及是探討以數位科技量化並比較實驗對象的變色情形。在研究過程中，用電腦量化數位相機所拍攝的影像，以像素的方式呈現出來，得以取的準確且客觀的實驗數據，並加以解析，也經由此一實驗方式，交叉比較中國樹蟾及台北樹蛙在不同環境和不同時間下的變色情形。結果顯示：樹蛙變色和環境顏色及時間有密切關係，且在短時間內以數位量化的方式解析其變色行為的方法極為可行。The purpose of this study is to investigate the color variation behavior of tree frogs using an image processing technology. It is known that some of the amphibians have the ability to change their skin color under different circumstances. In the past, a conventional “color comparison” method was frequently used whenever it comes to analyzing the color variation of organisms. However, it is realized that evaluation of color difference by human eyes is extremely unreliable. An advanced image processing technology is thus suggested to quantify the variation of skin color of tree frogs under different conditions in this experiment. Accurate quantification can be determined from the pixel number of exhibited digital images during the experiment. The color variation of different species of frogs (Hyla chinensis & Rhacophorus taipeianus) is also compared under different parameters. It is found that the color variation of tree frogs is closely related to the color of back ground as well as time. The proposed digital quantification technique has been successfully demonstrated to be an effective method for analyzing the color variation of frogs within a very short time.

本研究利用雷射光、光感測計、偏振片、齒輪及馬達組裝成一個簡易、精確且可接於電腦的數位旋光度計。我們先藉由Arnao研究的ABTS/ H2O2/HRP分析系統，以不同濃度的維生素C與延遲時間畫圖作為標準曲線來測量總抗氧化活性，並比較奇異果、火龍果、聖女蕃茄、加州李四種水果，以微波、水煮及油浴三種方式測得熱處理後抗氧化活性的變化趨勢。之後，我們再利用自製旋光度計來求得水果經過熱處理後的旋光度與熱處理時間之關係。研究顯示，經熱處理後，此兩種方法有一致的趨勢，所以證明了我們成功地開發出一種可以利用旋光度來測定抗氧化的新方法。最後，我們進一步將此裝置應用於真假蜂蜜的檢驗，同時利用物質旋光度具有加成性，建立一套方法來計算蜂蜜中蔗糖、葡萄糖、果糖的含量。

多變色膽固醇型液晶面板為利用具雙穩態(Bistable)特性及因螺距不同而反射特定波長的膽固醇型液晶(CLC)。本研究創新作法為二：一、利用固化的方式使膽固醇型液晶螺距大小不同，使變色機制不同於一般電腦液晶面板，所製的液晶面板為以液晶的特性變色。二、將液晶螢幕中控制液晶的IPS 系統、側邊電極應用於液晶白板中。雙層液晶白板上層為混合E7(向列型液晶)+S811(旋光物質)的Bistable CLC，下層為混合RM82、CB15、BL006、I-369 的多變色(Multi-color)CLC 面板。The main purpose of the research plan lies in the application of the CLC. By using the Cholesteric －the bistable and the wavelength due to different pitch sizes－ we can make liquid crystal whiteboard. First, by heating and curing, we are able to cause the pitch sizes of CLC to be different. Unlike the commonly used LCD in computers, the features of CLC itself are applied to the color changing mechanism we make. Second, we apply the IPS horizontal electric field and flank electrode to our LCD whiteboard. In making the Multi-color CLC Display, we mix RM82, CB15 and BL006.

台灣北部和日本北海道地區皆位於板塊碰撞隱沒帶上，我們由ANSS 資料庫，下載這兩個地區近40年內的地震發生時間、經度、緯度、深度與規模大小等數據，加以整理，以電腦Excel程式繪製成震源、震央隨經緯度之分佈圖、規模大小、發生次數之折線圖、圓餅圖等；經過了一連串觀察、分析步驟，比較日本與台灣地震在時間與空間的表現，並以取log 值的方式處理地震發生次數繪出的圖形，以理解地震發生的規則，再比較兩地區累積能量隨時間釋放的型態。利用我們所繪製的圖形加以合併自己所學的知識，討論其中的差異。由能量釋放的不同表現、隱沒帶的地震深度、板塊在彎曲下插時的斜率、地震活動次數與深度等不同，比較分析北台灣和日北北海道地震的確有地域性差異的特質。