In this work I make the analysis of the possibility of the existence of the number system with non-natural base & its investigation. The question examined in my work is totally opened:\r ‧ making the list of new characteristics, rules of the translation of the numbers, and also rules of the simple calculating operations, checked the operations of subtraction & division;\r ‧ checked the Euclidean algorithm, its characteristics by means of estimating the coefficients;\r ‧ found the practical appliance of new method in compiling & solving of the tasks.\r Investigation I’ve suggested stipulates for independence of new system & its appliance in type of tasks, that is beyond the course of school program & also beyond the whole system of school education.

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。

A pair of bacterial two-component system RssB-RssA was cooperated into Serratia marcescens for toxicity phenolic compound detection. First step of this study, E coli was used to accept the plasmid and certified by fluorescent. Then transfer the system from E coli into Serratia marcescens. Finally, 7 kinds of chemical, included phenol, benzene, toluene, xylenes, 4-chlorotoluene, 2-nitrotoluene, and kerosene, were used to check the sensitivity of this gene modified Serratia marcescens line. The results showed that this gene modified Serratia marcescens line had good performances and responses to those chemicals. 本實驗是以一受到二元訊號傳遞系統調控的發光基因重組質體，送入黏質色拉雷菌中，並以製備好的菌株進行毒性化合物之測試。在實驗的第一階段，我們將重組質體送入大腸桿菌內，並以其發光的有無來判斷是否達到送入的目的，其後再以電泳法確認各基因片段是否正確。第二階段再以相同的方法將選殖好的重組發光質體送入黏質色拉雷菌。第三階段，以發光重組菌針對酚、苯、甲苯、二甲苯、4-氯甲苯、2-硝基甲苯及煤油進行發光測試。結果方面，我們發現黏質色拉雷菌發光重組菌對於這一系列的酚環類化合物的確具有相當高的敏感度。

資訊時代的來臨，促使我們的社會型態大幅改變，無一不朝數位化的方向邁進。網際網路與資訊科技的快速發展，近年來影像資料庫和數位圖書館大量的成立，關於影像資料檢索的研究已漸漸成為一門極為重要的研究議題。在本研究報告中，我們提出一種植基於向量量化編碼法的灰階影像檢索技術。向量量化編碼法是一種極為簡單的影像壓縮技術。我們應用這個編碼法，來萃取出灰階影像內容的特徵值。同時我們也計算出整張影像與影像中間位置的像素平均值，作為日後檢索影像時過濾掉影像資料庫中不需要比對特徵值的依據。\r 我們所提出的方法能有效地萃取影像內容的特徵值並且讓使用者可以快速且正確地查詢到所需要的影像。當影像資料庫中存在與查詢影像完全相同的影像時，我們的檢索技術都能在第一時間第一順位檢索出這張影像。即便影像資料庫中不存在與查詢影像完全相同的影像時，我們的檢索技術平均74.3%也能在第一時間前五個順位檢索出最相似的影像。\r \r With the coming of the information age, our sociological system change extensively, and everything has moves toward digitization. Due to the rapid development of Internet, information technology, the rapid growth of image databases and digital libraries recently, the related researches of image retrieval have become a very important issue. In this memoir, we propose an image retrieval scheme based on the vector quantization to retrieve similar images from the image database according to the pre-collected image features. Vector quantization is a very simple image compression scheme. We have applied vector quantization to extract features from grayscale image. In order to speed up the retrieval process, we also calculated the mean pixel values of whole images and the central part of the image to filter the images, which are significantly dissimilar to the query image.\r The experimental results show that our proposed approaches can effectively extract features from the image and enable users to retrieve images from image database quickly and accurately. When images stored in image database match query image, the proposed scheme can instantly retrieve the stored image at the first rank. Even though images stored in image database query image exactly, the proposed scheme can instantly retrieve the stored image over 74.3% at the first five ranks.

In order to facilitate a paradigm shift from traditional high volume chemical experiments to an environmentally friendly microdose experiment; I had to innovate and overcome a lot of difficulties. After six generations of experiment design I successfully reduced the volume of the combined reactants to a single drop. I utilized many recycled components to build my apparatus including a vintage computer, a simple CD disk, optical sensors and a transistor from a common computer mouse. By using a CCD monitor with an external camera feed, the single drop chemical reaction can be observed in real time and a recording of the event can be made. I chose the focus of the experiment to be the reaction of sodium thiosulfate and hydrochloric acid to create a colloidal solution of sulfonium nanoparticles. By employing a custom-made transparency target to achieve a higher precision of measurement I have also conducted deeper research into the reaction order and the rate constants. 為了將傳統高劑量的化學實驗順利的推向顯微液滴的化學實驗上，今年我們更是創新突破了很多困難的關卡。 儀器設計由第一代減量研究到第六代的減量設計，目前已能成功的運用報廢的光碟片、報廢的電腦、報廢滑鼠內的感光二極體元件及電晶體來自製設計出兩反應物各一滴溶液做自動偵測反應的記錄。透過顯微鏡加裝的CCD電子螢幕目視觀看、拍成電子影片檔由電腦播放的目標。 因此，我選定了硫代硫酸鈉溶液和鹽酸溶液反應可產生硫奈米微粒的膠態溶液作為實驗的主軸及設計可較精確定量的投影片載液面，我們也企圖對其反應速率式的級數及反應速率常數做更深入的探討。

The first aim of my project is to learn more about mushrooms: their lifecycle, their structures, the nutritional value of mushrooms, the medicinal values of mushrooms as well as the biological importance of mushrooms.\r The second aim of my project was to find how mushroom are cultivated in the world and specifically how they are cultivated in Namibia, where climatic conditions are rather harsh for mushrooms. Through interviews, I aimed to understand why mushroom cultivation is not widely practiced in Namibia and what are direct economic advantages of mushroom cultivation in Namibia.\r The third aim of my project was to see whether I could find cheap and economic methods of cultivating mushrooms in Namibia, a semi arid country where humidity is so scarce.

In this experiment, we hope to produce appropriate-sized nano particles of by using the chitin. By mixing the particles with the metal of Ti, Fe and Zn of proper proportions and therefore narrow their band gaps. Thus, the Bacteriostasis of LightPhotocatalysts could appear under the environment where the energy is lower than ultraviolet ray. We use de-acetylated chitin in three ways -- chelating agent, surfactant and protecter. Then we put a thin layer of the mixture of chitin and metal nano particles on a piece of glass, and afterwards, sintering the mixture on the glass. Next, we scan the surface of the glass with AFM(Atomic Force Microscopy) to measure its particle size. The result we got showed that the surface-roughness of the Ti-Fe nano particles was 30.642nm, the best solution of all the samples. Yet, in this experiment, Fe was not suitable. Therefore we should choose the sample of Ti-Zn mixture, which is slightly smaller in roughness. According to the result we got from the experiment, we found that, under the yellow light, the survivable strain-number ratio of the sintered Ti-Fe-Zn mixture on the glass and empty glass was 0.09±0.06. This was much better than the survivable strain-number ratio of 0.17±0.06, the result we got out from the glass of pure Ti and empty glass. From the measurement, we found that the proportion of mixture could lower the excitation energy Ti needs. Through this experiment, we hope to create a layer of film containing nano particles, and by applying it to daily-use products, we could prevent harmful bacteria. 本實驗的目的，就是希望可以利用幾丁質製作出適當粒徑大小的金屬奈米顆粒，混合適當比例的鈦、鐵、鋅金屬，使其能隙變窄，讓我們能在低於紫外光能量的光譜下，產生奈米光觸媒的抑菌效果。筆者在實驗中利用去乙醯化之幾丁質在本實驗中扮演三種角色:螯合劑、介面活性劑及保護劑，以將幾丁質與金屬奈米顆粒均勻塗抹於玻璃上，並以燒結玻璃的方式進行實驗。並且利用AFM掃描玻璃表面，確認其表面尺度，驗證的結果Ti-Fe混合比例的奈米顆粒之表面粗糙度為30.642nm，為最佳狀態，但在本實驗中Fe並不適用，故應以粗糙度僅次於Ti-Fe的Ti-Zn混合比例為主。根據實驗的結果，在綠光下，混合比例的Ti-Fe-Zn玻璃與空白玻璃的菌落數比，菌落存活率為0.09±0.06，相較於純Ti的0.17±0.06來的低，代表混合比例可降低Ti所需之激發能量。經過此實驗未來筆者希望可以以幾丁質製作出一層含奈米顆粒的薄膜，應用到各種生活用品防止細菌的危害。

三角形的邊上取任意多個點，我們可以把這塊大三角形沿著切割線切割成較小塊的三角形，但切割線必須是點（或頂點）和點的連線，而且必須切割三角形，同時可以切任意大小的三角形，如圖（1）與圖（2）。但不可以一開始就取走整個三角形。定義拿到最後一塊三角形的人獲勝，而在多邊型中的玩法與在三角形中相同。 我們分A、B、C三種規則來討論，其中A規則即是上面提到的玩法，B規則大部分的玩法和A規則都相同，唯一不同的地方在於：A規則中，只要有一方取到剩下的圖形為三角形，另一方就可以直接取走剩下的三角形，而B規則規定即使剩下的圖形已經是三角形，也必須取到剩下的圖形邊上都沒有分點為止。C規則是限制玩家一次所能取的三角形數來進行遊戲。 我們完成了A、B、C規則中三角形與多邊形的必勝策略，並找出必勝策略之間的關聯。 ;Given any numbers of points on the sides of a triangle, the players can cut this triangle into pieces. Each cutting line has to be one, linked between two points given from two different sides. And the player can’t have to cut smaller triangles out of the original triangle. The out-cut triangles can be chosen randomly without any restriction in size, just like what’s shown in picture（1）and（2）. Meanwhile the first player can’t cut the original triangle exactly all out in the very beginning process. We define the player as the winner, who gets the last triangle. And the above way we play can be applies to any multi-side shapes. We discussed the question respectively in three rules, A, B, and C. Rule A is what we mention above. Rule B is generally the same as rule A, except for the only difference：The rule A , if there is any triangle left , the next player can get it directly, but while in rule B, the every next player has to cut out smaller triangles until no point is left on sides. Rule C proceeds on conditions that there is a limitation to a certain number of triangles cut out at a time. We has finished the winning tactic respectively in rule A, B, and C in the games with a triangle and multi-side shapes. Furthermore, we find the connection between the winning tactives.

The natural fruits of soap berry are worth-while detergent in the aspect of environmental conservation. It has been shown that the soap berry fruits can reduce the itching of head and inhibit the growth of fungi. Here we would like to test the inhibitory activity of soap berry fruits on the bacteria. This might benefit to the further application of the soap berry fruits. First,the soap berry extract was prepared and mixed with E.coli or S. aureaus. The number of bacteria was counted to realize the inhibitory activity of the soap berries. We found that the soap berry extract can inhibit the growth of E.coli and S. aureaus. Higher concentration of the soap berry extract and longer duration for the mixture make better inhibitory activities. 天然的無患子果實是一種極具環保價值的清潔劑，已知它有抑制黴菌生長的能力，可以 去頭皮屑、止頭皮癢。因此，我們想進一步探討無患子果實對於細菌生長的抑制能力，以期 了解無患子清潔劑在廣泛推廣上的應用價值。 在實驗設計上，我們自製無患子萃取液，並選擇日常生活中常見的大腸桿菌及金黃色葡 萄球菌，並然後使菌液與適量的無患子萃取液混合，計算菌液在加入無患子之前、後的細菌 個數，藉以了解無患子的殺菌力。我們發現無患子萃取液對大腸桿菌及金黃色葡萄菌有明顯 的殺菌力，且無患子濃度愈高、作用時間愈長，殺菌力愈好。

筆者利用自製的幾丁質與不同金屬的混合溶液而燒結出的奈米顆粒成效極佳，不但粒徑大小符合，在燒結的過程中也不需經過物理研磨及介面活性劑的輔助，並且在低溫下即可燒結，可以增加實用性以及商業價值。此外，在分解亞甲藍方面也有不錯的效率，並進一步從金屬氧化物之奈米膠體混合溶液比例的不同，決定其粗糙度（以AFM測定）及能隙改變，在陽光下有更高的應用效率。而在實驗的延伸研究上，希望應用在防菌、除污、甚至光電池。 We make use of self-made chitin with the mixed solutions of different metals to solder nano particles, and the result is excellent. The particle radius not only matches up to the size, but in the process of soldering nano particles, it doesn’t need any physical pulverizing or surfactant assistance. Also, it can solder in low temperature. And we could raise its practicality and the business value. What’s more, there is a good efficiency in decomposing Methylene Blue. We can further decide the roughness (measured with AFM) and the variation of the band gap from nano colloid of different metal oxide mixed ratios.Our experiment in the extending research aims to apply it to the defense of bacteria and pollution, and even photoelectric cell.