去氧核糖核酸水解?，(deoxyribonuclease,簡稱DNase)為一種核酸內切?。目前研究得最透徹的去氧核糖核酸水解?為牛胰臟的DNase I，有四種以上的同功?存在。而牛和雞的DNA序列有極高的相似度，由之前的研究中在等電點焦集電泳法顯示雞胰臟DNase I 具A、B 兩種同功?，本實驗則希望能進一步了解兩種同功?的差異原因。在抽取RNA 後，以RT-PCR 方法合成cDNA，將其以限制?切割，再以大腸桿菌作為載體進行轉殖及繁殖培養，最後將其DNA 定序後進行分析比較。目前已完成第一次定序，但因引子接合過程中有部分位置錯亂造成殖體無法進行表現。另外在此次所得之序列中有發現一個胺基酸的轉變，而其是否為多型性之表現則有待進一步的實驗證實。The most advanced research on deoxyribonuclease in current states is on the bovine pancreatic DNase I, more than four of which isoforms have been found. It is shown that the DNA sequences of chicken and bovine have relatively high similarity. In addition, according to the result of isoelectric focusing from previous researches, chicken pancreatic DNaseI has two isoforms (A and B.) In this research, the author expects to establish more knowledge on the differences on the isoforms and the causes. After receiving the RNA, the RT-PCR is preformed to incorporate the cDNA, which is later cleaved by restriction enzyme and inserted into the plasmid DNA of the E. coli host cell to be cloned. So far a polynucleotide sequence has been deduced from clones of the cDNA, but it cannot be expressed successfully in E.coli due to few random mistaken splicing. There is an alternation of one amino acid, and whether it is the actual state of isoform or not still requires further proof.

本研究從理想城鎮(Ideal City)街道開始，討論平面上相異n 點到某一點的最短距離和。經研究後發現：當n 為偶數時，則到相異n 點的最短距離和所形成的區域可能是一個點、一個線段或是一個矩形；當n 為奇數時，則相異n 點的最短距離和所形成的區域將會退化成一個點。此外，本研究將理想城鎮的街道換成正三角形的街道幾何平面，同樣是討論平面上相異n 點到某一點的最短距離和。經研究後發現：當n 為偶數時，則相異n 點的最短距離和所形成的區域可能為一個點、一個線段、一個四邊形、一個五邊形及一個六邊形；當n 為奇數時，相異n 點的最短距離和所形成的區域則可能為點、三角形的情況。假使考量各點重要性的比重，分別加權後再求最小點。研究發現無論在理想城鎮或正三角形幾何平面上，皆可將各點視為多個權數相同之點重疊於此點上，便可利用先前的方式求得最小點區域。透過這次的研究，可以利用n 個相異點到某一點的最短距離和實際應用在貨物運送的問題或是消防設施配置等問題。The present study was intended to start with the Ideal City and proceed to discuss the sum of the shortest distance between a point and n different points on a plane. After the discussion, it was found that if n is even, the formed region could be a point, a line segment, or a rectangle. If n is odd, then the formed region must be a mere point. Further, the current study transformed the Ideal City into the geometric plane of an equilateral triangle. Similar to the previous discussion, if n is even, the formed region could be a point, a line segment, a quadrangle, a pentagon, or a hexagon. On the other hand, if n is odd, then the formed region could be a point, or a triangle. The result of this study, which investigated the sum of the shortest distance of a certain point to n different points can be applied to the real life situation, such as transporting goods or distributing fire control facilities.

My school requires year 13 students to complete a year long project of a topic of their choice, culminating in the presentation of a thesis, a display and speech to a public audience. Many different topics appealed, but in the end I decided to build a micro wind-turbine. I have always been fascinated with mechanics, mathematics, engineering, aerodynamics and electricity. A wind turbine is a mixture of these technologies, with the overall goal of electricity production. In a world that is starting to see the true costs of fossil fuels, renewable energy seems to be increasingly popular and the demand for electricity is always growing.\r I was aware that building a wind-turbine from the foundations up wouldn’t be easy. Many of the experts I contacted in the early days cautioned me against trying such a complex thing in one year, at the same time as completing a full Year 13 course. There were, however, people prepared to support me. Michael Lawley, who builds micro wind turbines in New Plymouth was very helpful, just full of priceless knowledge and gave me a few basic parts to start with. The knowledge gained from Doug Clark, who also builds his own 11 kW wind turbines, was such an inspiration. Later I had practical help from Wilson Springford and Darron Matthews.\r I investigated and documented the history of and current state of wind technology, as well as my own experience and learning in the design, construction and testing process. I thought it would be interesting to find out how the electrical and mechanical side works.\r The generator, a washing machine motor, needed to be completely rewired, and converted to DC (direct current) from AC (alternating current). I built my own 3-phase AC to DC converter.\r Other parts like the disc brakes and bearings had to be found. The rest was hand-made and every part, to a certain extent, had to be modified. Probably more than twenty braking system design attempts led to the final decision to incorporate the wind-activated hydraulic disc brake where the wind paddle starts to ease the brake on over a certain wind speed.\r I studied the dynamics of wind turbine blades, their shape, the material they were made from and how this affected their performance. The decision to make my own blades helped me gain a great sense of achievement and knowledge of blade design. I found some New Zealand made 100% recycled plastic pipe, an added bonus because I wanted to have minimal environmental impact. I designed the turbine with three blades to give better starting torque along with a lower top speed, perfect for how I wired the generator.\r I designed the swivel, the part of the wind turbine that enables the power cables to get from the turbine down the tower without twisting up and has the job of carrying the whole turbine, which is mostly made from recycled aluminium. The steel and bearings used to create the swivel were all second-hand parts and materials. The power from the turbine passes through the swivel into the cables and down the tower. The main mast of the tower is a little over 4.7 metres and pivots on two shorter supporting poles which go down around 2.6 metres to the bottom of the reinforced concrete foundation.\r I managed to, design and construct an operational prototype micro wind-turbine, incorporating recycled and recyclable materials as much as possible, with the end result surpassing all expectations.

In this research, we investigated the interactions between goldfish’ (Carassius auratus) sensory experiences (electric shock, high osmotic pressure and colors). We separated the sensory experiences into two parts. One of them, we used different kinds of environmental color-models to analyze goldfish’s environmental preference behavior and different kinds of stress experience(electric shock and high osmotic pressure) to build the animal model of environmental preference behavior. We found that goldfish prefer brown-colored environment (compared with white) and different stress has different effects on fish’s environmental preference behavior. It proves that fish has the ability to learn and memorize the stress experience and shows that there are complicated interactions among environmental stimulus, memories of stress and behaviors caused by different kinds of stress. Also, we investigated the interactions between spatial memory and color distinction. We measured the duration of goldfish getting through the color-marked barriers driven by regular electric shock. We found that goldfish spend less time to get through color-marked barriers than those unmarked. It shows that there are some interactions between spatial memory and color distinction. In conclusion, the research proves that different sensory experiences can affect goldfish’s behaviors.本實驗利用感官經驗(電擊、高滲透壓、色彩)，探討與朱文錦(Carassius auratus)行為調控的交互作用。我們將感官經驗分成兩模式：利用環境色彩特徵的差異，探討不同逆境刺激經驗(施予電擊或高滲透壓環境)，與魚類環境偏好行為的交互作用，建立朱文錦環境偏好行為之動物模式。我們發現朱文錦偏好土色環境(相對於白色環境)，而不同性質的逆境經驗，對魚類的環境偏好行為具有不同的影響，顯示魚類具有記憶逆境環境的學習能力，且證明「環境刺激—經驗(記憶)—行為表現」三者之間具複雜的交互作用。另外，我們亦探討空間記憶與色彩辨識的交互作用，利用規律的電擊刺激使朱文錦通過有色彩標示的關卡，以研究色彩差異與空間變化對朱文錦通過關卡能力的影響。我們發現色彩的標示可降低通過關卡的時間，且不同的色彩具不同程度的效果，顯示空間記憶與色彩辨識具交互作用。本實驗證明了不同的感官經驗或刺激，對朱文錦的行為調控具質與量的差異。

YWHAZ(14-3-3δ)蛋白被證實在肺腺癌中會引發上皮-間葉的轉變作用(epithelial - mesenchymal transition ; EMT)導致癌轉移，然而其分子機制卻不清楚。先前實驗室利用cDNA微陣列技術(microarray)發現肺腺癌細胞大量表現YWHAZ蛋白會導致Wnt訊息傳遞路徑之相關基因大量表現。因此，本研究目的是探討YWHAZ蛋白在肺腺癌細胞中是否會活化Wnt途徑而引發EMT。\r 本研究結果發現大量表現YWHAZ蛋白除了會增加細胞質中β-catenin的表現量，也會增加細胞核內 β-catenin 和TCF4 的蛋白表現量，並且在細胞核中與β-catenin和TCF4形成複合體；而臨床肺腺癌病患檢體中發現，相較於正常肺葉組織，YWHAZ蛋白與β-catenin在肺癌組織的檢體有較高的表現量，同時少部分會進入細胞核內。經由以上結果，我們推測YWHAZ蛋白可能會結合β-catenin與TCF4蛋白並活化Wnt途徑，因而引發EMT之產生，而促進肺癌轉移。說明YHWAZ蛋白有潛力成為日後診斷肺腺癌的指標蛋白(marker protein)，同時亦成為治療肺腺癌的標的蛋白(target protein)。\r 重要性\r 1.提出YWHAZ可能在肺腺癌細胞中活化Wnt訊息傳遞路徑(Wnt signaling pathway)而導致癌轉移。\r 2.再度指出YWHAZ在腫瘤生物學的重要性。\r 3.對於肺腺癌轉移提供了臨床診斷及治療的另一種選擇 ─ YWHAZ。

本研究中，我們將提出一些新穎結果，著重討論其在三角中的應用；同時，找出其遞迴關係式，得出三角展開式與其所對應之多項式分解式，進而討論出多種的規律性及所涵蓋的內容及推廣性質，我得到很多高中數學公式無法推導出在【4】和【8】中的漂亮公式及創新的結果，且這些等式都是由我們不太瞭解的無理數所構成的。 主要是討論我們在【7】中所得到的收穫與經驗；複數是三角、幾何、代數互動的橋樑，我是以不同的角度及嶄新的方法來綜合探討在【6】中相關的應用。提出關於正整數平方的倒數和公式更為精簡且基本的證明，將 sin−2 x 表示成級數形式的部分分式，進而應用在(a,b) = 1的機率問題上；並研究相關的等式，直接透過三角與代數來研究關於 2p 次方的倒數之求和問題，得出級數 之和的有用遞迴公式，並與最重要的常數扯上關係。 For one thing, we present diverse methods to evaluate finite trigonometric summation and related sums. Trigonometric summations over the angles equally divided on the upper half plane are investigated systematically. Several related trigonometric identities are also exhibited. What is more, we use methods of calculus, and make several surprising and unexpected transformations. A useful recursive formula for obtaining the infinite sums of even order harmonic series, infinite sums of a few even order harmonic series, which are calculated using the recursive formulas, are tabulated for easy references. Furthermore, is there any interesting results and applications？ Finally, the purpose of this paper is to develop a new proof of and related identities, but their derivations are more complicated. The following studies are completed under the instruction of the professor.

本研究以高頻阻抗分析儀，針對自製的電容器，以不同比率的三氧化二鐵加二氧化矽混合後所製成的電容器，對頻率、電容直及正切損耗能量直從事研究。實驗結果發現，在低頻率直到60Hz以內，其 Cp及D值變化非常大，明顯的下降，60Hz到1000Hz Cp及D值變化很小。由參考資料中電容器中的損失因數是介電材料是否適合於絕緣材料用途之最基本的準則，一般均希望具有低介電率。即使在最小的空間內也希望有高電容值，如電視、收音機中在介電材料的高頻應用。是故我們所製作的電容器以二氧化矽添加三氧化二鐵後高頻值其Cp值、D值較小，是適合於高頻需求的應用上。We report on the study of high frequency dielectric spetra. On the capacitance, it is made by mnyself. At various mixed ratio value of Fe?O? pius Sio?. In order to understand the frequency capacitance value Cp and tangent loss energy analysis D. The results of our work provide a large of low frequency in o Hz TO 60 Hz in Cp and D. It is obviously descend a small various frequence is 60 Hz to 1000Hz. From reference, we know capacitance energy loss factor is a purpose of suitable an insulator rule. In dielectric constant. We hope a low dielectric value and high capacitance. Even it is a small distance. For example TV. Radio. Etc. it is used to high frequency. So we made a capacitance in difference of Fe?o? pius Sio?. To provide the Cp and D. the value is small. So it can be used in high frequence demand.

鹼性電池使用的電解液均為強鹼，電池中的鋅極會與其發生腐蝕反應，使得電池放電壽命降低，並產生氫氣，而大量氫氣使得電池有爆裂的危險，為了改善上述問題，我們自行設計了氣體觀測儀器，用來檢測銀鋅電池充放電與靜置時之氣體產生量，更藉由探討影響變因的過程找出銀鋅電池較合適之使用條件，其中包含電解液種類及濃度之選擇、電極面積與充電電流對使用效果之影響，並改善電池腐蝕程度；我們將鋅極以浸鍍處理(Sn:Pb ＝1:1 )並搭配電解液添加物(KOH:Zn(OH)42 －＝ 2:1) 可效率地抑制氣體產生；更用氯化銀粉末取代傳統氧化銀極片為正極，發現氯化銀可代替氧化銀電極，且有不錯的放電效果。;As we know, the electrolyte solution used in an alkalinebattery is a concentrated alkaline solution, which corrodes the zinc electrode in a battery of this kind. The corrosive reaction not only reduces the lifespan of the battery but also produces hydrogen, causing the battery to explode. This study is intended to help us design a device to measure the quantity of hydrogen gas generated in the charging of a zinc-silver battery. We have studied several factors affecting zinc-silver battery, including the variety of electrolyte, the concentration of alkaline solution, the surface of electrode, and the density of charging current, etc. To reduce the corrosion of zinc electrode, we plate the zinc electrode by the immersion electroless plating method, using several kinds of low-polluting anti-corrosive additives (metallic compounds such as lead and tin). We also add zincate ion into electrolyte solution to further reduce the quantity of hydrogen produced. The experiments show a zinc-silver alkaline battery works most efficiently, if the powder of silver chloride is used instead of silver oxide.

微孔珊瑚是優良的生物氣候記錄器，可準確記錄海水表面水溫、陸源沉積物通量和其他微量海水組成等，已成為熱帶氣候變遷研究的重要工具。然而，珊瑚成長速率則顯著受限於海水表溫影響（邱景星，1999）。太陽是地表能量最主要來源，其活動狀態能深遠掌控地球氣候變化，因此其週期性變動規律，已成為近期地球科學家探討環境變遷的重要資訊。 本研究以台灣東南外海綠島採集的微孔珊瑚骨骼樣本，藉由X-ray精確測量其年平均生長速率及觀察骨骼內微量腐殖酸螢光特性，並透過比對太陽輻射量、珊瑚生長與太陽黑子數目的相關性分析，以推倒百年來控制地表氣候變遷的主要因素。 本研究經由頻譜分析、主變量計算、平均標準差和太陽輻射角修正，獲得正確太陽黑子數目、地區性輻射、海水表面溫度和珊瑚生長速率等資料，並討論其間的相互關係。 結果顯示，太陽輻射、海水表面溫度和氣溫有高度正相關（r2>0.62），證實太陽對地球氣候系統的重要性。太陽黑子與輻射資料，則因大氣折射、日照時數等因素影響，正設法解決這些干擾效應；而珊瑚生長速率與海水表面溫度的相關性，則涉及雙極化效應（註）及其他未知因素影響，尚待進一步釐清。 （註）：雙極化效應指珊瑚在過高或過低的環境下，生長速率皆會停止 The skeleton of Porites corals is one of the most useful biogenic recorders, which provide relevant information of abrupt climate change, such as sea surface temperatures (SSTs), riverine sedimentary flux, and seawater compositional variations. Information retrieved from coral skeleton, therefore, has become a powerful tool for studying tropical climate change. The annual growth rate of Porites corals, however, was affected strongly by local SSTs (Chiu, 1999). On the other hand, the climatic condition on Earth surface is regulated significantly by solar activity. Subsequently any intensity or periodicity variation in sunspot activity will cause major global environmental changes. This research aims to study coral skeleton collected from the Orchid Island (Lan-yu) offshore southeastern Taiwan for precise measurement of annual growth rate using X-ray density bands, as well as the luminous characteristics of trace humic acids in skeleton. A systematic comparison among solar irradiation, SSTs and coral growth rate will provide critical information on major factors that may affect environmental changes occurred during the last millennium. In this study, we apply spectrum analyses, principal component, mean standard error method, and modified sun irradiation angle to correct biases presented in the available data of observed sunspot number, local irradiation, SSTs and coral annual growth rate and to examine possible relationships among these factors. We have found excellent correlation coefficient (r2>0.62) in solar irradiation, SSTs and air-temperature, which support the importance of solar irradiation to the earth surface climate. However, effects on cloud and length of sun irradiation need further investigation to emphasize the importance of sunspot activity to the annual growth rate of Porites corals. No straight forward relationships were observed between coral growth rate and local SSTs due to complicated biological effect (1*) or other unknown factors, waits for further investigation in the near future. 1* Complicated biological effect means that coral may stop growing their skeletons when the temperature it lives in is over range for growth.

將一個集合{1,2,...,n}分成數個非空的集合（組，區塊），稱為此集合的一個分割。如果可以找到1 ≦ a 已知無孤立點無交錯分割以Riordan 數{rn}n≥0 =1,0,1,1,3,6,15,36,... 來計數。在這篇文章中我們研究無孤立點無交錯分割的一些性質。 首先我們考慮無孤立點的無交錯分割按區塊的細分。我們得出：集合{1,2,...,n}恰含k個區塊的無孤立點的無交錯分割的個數為： 其次，我們證明bn,k和多邊形的剖分有令人訝異的關連。令dn,k是用不相交對角線將凸n 邊形分成k 塊的方法。我們用代數方法證出 bn,k = dn+2−k ,k，也給了一個新的組合證明。 最後，透過對應的方法，我們找出了七個嶄新的組合結構，這些結構都是以Riordan 數來計數。 Partition the set {1,2,...,n} into several nonempty sets (blocks) and call it a partition. If there exists 1 ≦ a It is known that the nonsingleton noncrossing partitions are counted by Riordan numbers {rn}n≥0 =1,0,1,1,3,6,15,36,... In this paper we study the properties of them. First we consider the enumeration of nonsingleton noncrossing partitions in respect to the blocks. We prove that the number of nonsingleton noncrossing partitions of {1,2,...,n} with k blocks is Then we give a connection between nonsingleton noncrossing partitions and polygon dissections. Let dn,k be the ways to dissect an n –gon with noncrossing diagonals. We prove that bn,k = dn+2−k ,k We also give a combinatorial proof. Furthermore, by way of the technic of bijection, we find 7 new combinatorial structures counted by Riordan numbers.

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。

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。