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，

These days we hardly see fireflies, the Milky way, and rainbow. What’s the reason of that?\r We think the reason is related to air pollution but the concrete reason is unknown to us. Thus the purpose of this research is to see the relation between air pollution and rainbow with Aerosol. In this research we approached in some ways about why rainbow didn't appear in polluted atmosphere.

My aim was to test the effectiveness of coolboxes under different\r conditions, to use this information to do comparisons using commercially\r available coolboxes and finally to build an effective and cheaper coolbox\r appropriate to Namibia\r The general method used to compare different coolboxes involved\r measuring the rate at which ice melted inside the cool boxes under\r different conditions.

本研究探討不同的控制變因，對磁性流體薄膜在水平磁場下有序結構的影響。我們發現，外加水平磁場於磁流體薄膜時，會形成一維有序磁鍊排列，磁鍊間距除會隨著磁場增強而變小外，另外其條件值如磁場強度、流體濃度、磁增率、薄膜寬度及厚度等也影響磁鍊間距。其中磁增率及磁流體濃度增加會使磁鍊間距變小，而凹槽寬度及薄膜厚度增加會使磁鍊間距變大等現象。至於其形成磁鍊的物理作用，我們假設薄膜有三種能量交互作用，即(1)磁鍊與外加磁場間的磁能UdH。(2)兩條同方向磁化的磁鍊間相互排斥所造成的磁能Udd。(3)熱能Uther等。藉由系統能量Udh+Udd+Uther最小化，我們導出了磁鍊間距和外加磁場之間理論上的關係，並比較實驗結果確實具有相當的一致性。因這些有序結構會引發許多的光學性質，將來這些特殊的光學性質預料應可製成可調式光柵、光開關及顯示器等光電元件，使磁流體在奈米世界及光電領域裡扮演重要角色。We investigate experimentally the structure of the magnetic chains formed in the magnetic fluid thin film under the influence of the external magnetic field parallel to the film surface. A one-dimensional ordered structure forced by magnetic chains can be obtain in the magnetic fluid film. It is worth noting that the ordered structure can be manipulated by changing the control parameters such as the magnetic field, concentration of magnetic fluid, the thickness of the film, the width of the film, and the dH/dt. On the other hand, the physical mechanism of forming the ordered structure can be also studied theoretically. These magnetic chains are regarded as magnetic dipoles and three possible interactions are condisered for the energy of the system: the attracting potential energy between the magnetic chain and H(denoted by UdH),the repulsive potential energy between two magnetic chains with parallel magnetizations(denoted by Udd), and the thermal energy Uther. The relationship between the chain distance △x and the applied magnetic field H was derived by minimizing the total energy of the system with respect to the chain distance. The experimental data is consistent with the theoretical results.

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.

本研究主要是探討翼端小翼對飛機飛行的影響，翼端小翼在現在不少的飛機上都有這種設計，假設小翼可以阻止飛機機翼末端的氣流上旋，進而增加升力與推力，讓飛機能提高飛行時的效率，為了驗證這個假設，因此製作了簡易風洞對小翼的升力與阻力進行定性和定量的探討。升力與阻力的定性定量探討是經由10 組主機翼與五個小翼組合，共有2000 次的測試記錄，再轉化成折線圖予以比較研究，而得到一個穩定性數值結果。這測試實驗的數值結果顯示：小翼可以增加升力，但是也會增加阻力，為了降低阻力，小翼的剖面最好是有弧度。The purpose of this research is to find out the effect resulted from the winglet of the plane to the flight. Many a winglet is nowadays designed for the airplane. Assumes the winglet can stop the air of the tail section of the airplane to revolve up, further increase the force of the raise and the push, and uplift the efficiency of the flight. In order to proof this assumption is correct, so makes an easy air hole to do the research of qualitative and quantitative analysis for the force of the raise and resistance. After about 2000 records tested through the combination of ten sets of the main wing and five tiny wings, and transference of curve diagram , we get a steadily value result. This test result appear the first the winglet can increase the force of the raise, and so do the resistance, and the second to have the force of the resistance decreased, it might be better the section of the winglet is not straight but circular.

My project is about investigation on traditional medicines in\r Namibia. This is all about plants and different herbs that different\r people in Namibia use for medicinal purposes. The objective of this\r project is to inform the world of how valuable nature is and how we can\r try to conserve nature’s treasure so that valuable knowledge cannot pass\r away with olden experienced herbalists. Understandably the enquiry\r into indigenous medicinal herbs arose from the need to expand the\r possibilities of ones own medical practice. It was very important for me\r to satisfy our farmer’s thirst for knowledge, which is what I want to do\r with the rest of the world.\r In this project I have included most but not all of the plants that we\r use in Namibia for medicinal purposes. Seeing that some of these plants\r do not grow in certain parts of the country, I have also tried to clone it in\r other parts of the country. I have also made a powder from one of the\r plant’s leaves and tested it on several people within the country.\r To conclude my findings and experiments I would like to say, let us\r try to take these precious knowledge left for us from our ancestors and\r maybe one day in the future we might need it in some ways.

本研究以網路上Soft X-ray、UV195Å、K-Line、Ｈα波段太陽影像上黑子，光斑經度位置的逐時變量，試求太陽自光球層以上各層是否有越高層轉速越慢的現象？經試用數種方法求大量黑子、光斑位置，最後以省時，且誤差減小的＂由PhotoShop軟體讀出黑子、光斑在圖檔中位置，於EXCEL軟體中套用日面座標公式＂，以Peter Meadows的黑子定位程式抽樣對驗，來求其經緯度值。結果：在任何緯度，光球層以上各層轉速不同（徑向較差自轉現象），但並非越高層越慢，而是在大部分緯度處其各層速度變化呈 的快慢交替現象。

令Sn 為{1,2,…,n}任意排列所成的集合，π ? Sn 為其中的一個元素，我們記π = (π(1), π(2),…, π(n))。今給定π ? Sn ，若對所有i,1? i ? n，都有π (π (i)) = i 時，我們稱π 為involution。假設π ? Sn ，並給定σ ? Sm (m ? n)，當π 中任取m 項，其大小關係的順序都和σ 不同，我們稱π 避開σ，或稱π 是一個σ-avoiding 排列。在這篇報告中，我們主要分析了2143-avoiding involution，1234-avoiding involution，和3412-avoiding involution 中的一些統計量，給出了十數個結果與幾個猜想。Let Sn be the set of permutations on {1,2,…,n} and π ? Sn be an element in Sn. Denote π as π = (π(1), π(2),…, π(n)). We say that π is an involution if π(π(i)) = i for every i, 1? i ? n. Given π ? Sn and σ ? Sm (m ? n) , we say that π avoids σ (or π is an σ-avoiding permutation) if π does not contain any m-term subsequence in the order of σ. In this paper, we discuss some classic statistics on 2143-avoiding involutions, 1234-avoiding involutions and 3412-avoiding involutions. We get many new results in this field and give some interesting conjectures.

此項研究是用溶氧計連續偵測培養液中之溶氧量，藉以分析固氮\r 單胞藻RF-1 的光合韻律。實驗的結果清楚地看出RF-1 之光合韻律，\r 而且能夠清晰地觀察到其中光合作用、呼吸作用和固氮作用之間的相\r 互關係。研究中還發現：在不進行光合作用時，RF-1 的固氮作用也\r 會停止；另一方面，在有進行光合作用、但是停止固氮作用的狀況下，\r RF-1 光合作用之韻律現象會喪失。這些實驗結果值得未來更深入地\r 探討。報告中也包括了單胞藻PCC6803 的光合韻律實驗，藉以做為\r 有固氮能力與沒有固氮能力藍綠藻之間的對照。The variation of dissolved oxygen (DO) in the culture of the\r unicellular nitrogen-fixing cyanobacterium Synechococcus RF-1\r under diurnal light/dark condition was detected automatically by DO\r meter. The results indicated that the algae exhibited circadian\r photosynthetic rhythm. The results also revealed that a respiration\r rhythm occurred at dark phase when the culture was grown in\r nitrogen-free medium. There was correlation between the rhythm of\r photosynthesis and nitrogen fixation. The nitrogen-fixing activity\r could not be detected if the photosynthesis was stop by cultivated\r under continuous darkness. On the other hand, the rhythm of\r photosynthesis could not persist when the nitrogen-fixing activity\r was inhibited by NaNO3. In order to compare the difference\r between Synechococcus RF-1 and the cyanobacterium, which\r cannot fix nitrogen, the DO pattern of Synechocystis PCC6803 was\r also investigated.