I came up with the idea to build a small submarine after researching the internet and discovering the problems in which divers had to face in dangerous and time consuming tasks. The Remotely Operated Vessel (ROV) was designed to perform hull inspections on boats to look for hull damage and leakage of contaminates such as oil or other chemicals into the water. Search, rescue and recovery, are also common tasks which need to be carried out by the police when searching for objects and items. The ROV has been constructed at a reasonably low cost for submersing in depths down to 10 metres. It is remotely operated therefore needing a tether cable to link up between the computer and the vessel. I built a computer case-top from parts that I already had to eliminate the need for an expensive laptop. A program that I wrote in QBASIC interprets input data from the operator and sends out signals to the various operations on the vessel such as to dive, surface, propel, etc. The entire project consisted of five individual technology processes. Key processes such as Propulsion, Maneuverability, Dive & Surface capability, Imaging system, and the Control system. Each process required a cost effective and practical solution but still needing to function efficiently and be low maintenance. Through continuous testing and trial & error I feel I came up with the best possible solutions with the limited amount of time and money I had to spend. I wouldn’t have got as far as I have without the help and support from friends, family and local businesses. They helped with ideas and advice from time to time, help with funding, and the sponsorship of materials and tools. Now that the ROV is complete, I have been able to trial and test it in a swimming pool. Apart from discovering a few minor leaks in the hull and ‘bugs’ in the computer program, I was able to witness the success of the vessel under operation and find any improvements that could be done to make it work better in future. With further more tests at greater depths the ROV will soon be at the stage where it can perform hull inspections of boats and find lost objects and items underwater. I feel it has the opportunity to be a marketable device to underwater industries all over the world.

本研究首度發現人類肺癌A549細胞會促進其所浸潤的樹突細胞分泌Resistin，而更深入地探究獲悉Resistin會透過活化WHSC1/Twist途徑促進肺癌A549細胞惡化，此惡化過程包括誘導癌細胞上皮間質轉化(epithelial-to-mesenchymal transition; EMT)及提升癌細胞的移行(migration)和入侵(invasion)能力。為確認Resistin在臨床的重要性，透過肺癌病患檢體分析發現，相較於健康捐贈者，肺癌病人的血清可測的較高濃度的Resistin；更甚之，比較非腫瘤組織部位之CD11c+樹突細胞，浸潤於腫瘤組織部位之CD11c+樹突細胞會呈現高量的Resistin。接續探討Resistin對肺癌細胞的影響機制，實驗結果發現Resistin會增加A549細胞表現histone methyltransferase WHSC1的表現，而WHSC1在Twist啟動子的H3組蛋白lysine 36位置進行dimethylation修飾，並降低H3組蛋白lysine 27位置的trimethylation進而促進Twist的表現，促使A549細胞進行EMT和增加癌細胞移行和入侵。因此，Resistin可作為肺癌診斷分子及藥物發展的重要標靶。

何謂無限解？若n位正整數B ，滿足xm xp mod 10n，則稱B 是xm＝xp的n位數解。例:2494＝3844124001、2492＝62001，所以249為x4＝x2的一個三位數解。當n→∞時，則稱B 是xm＝xp的一個無限位數解，簡稱為無限解。本研究主要在探討方程式x2＝x、x3＝x、x4＝x、、、、xm＝x、xm＝xp無限解的規律性及各方程式無限解的個數，並加以證明。幸運地，我們利用任意數次方後其個位數每四個循環一次的特性，藉由整數論定理的推導，並佐以Mathematica軟體輔助計算，得到以下令人振奮的結論！在Xm＝Xp的無限解中：(1)若m－p＋1為4k-2或4k(即m－p＋1為偶數)k N，則其必僅有兩個無限解。(2)若m－p＋1為4k-1，k N，則其必僅有七個無限解。(3)若m－p＋1為4k+1，k N，則其必僅有十三個無限解。

物理課做水波槽實驗時，重疊的波紋引起我們極大的興趣。於是老師介紹我們看一篇( The Physics Teacher)雜誌中有關Moire' Pattern 的文章。Moire' Pattern 的特徵是當有寬度的條紋彼此重疊時，會出現一些新的圓形，我們對於這些富於變化，又具有規則性的圖形，感到興奮不已，就開始研究了。

近年來，由於科技的進步，導致合成性高分子材料大量開發利用，雖然便利 了人們的生活，卻造成許多環保問題，例如：資源的消耗，以及對環境的污染。 然而「生物可降解人工合成的聚乳酸高分子」和「天然的幾丁聚醣高分子」均具 有優良的生物可相容性及生物可分解性，添加無機層狀蒙脫土可補強其機械性質 之不足。本實驗之目的是以生物可分解之合成性高分子聚乳酸作為主體，再和經 有機化改質後的蒙脫土摻混而製備出聚乳酸/蒙脫土之奈米複合材料。 本實驗主要分為三大部分： (一)以界面活性劑對蒙脫土進行改質 (二)製備聚乳酸/蒙脫土奈米複合材料試片 (三)對試片進行生物降解性測試 此外，本實驗以X-ray 繞射儀（XRD）檢測改質後蒙脫土層間距離的變化； 場發射電子顯微鏡（FE-SEM）觀察生物降解後複材之表面型態；膠體色層分析 儀（GPC）檢測生物分解前後複合材料之分子量的變化；DMA 檢測複合材料之 機械性質；TGA 檢測複合材料之熱穩定性Thanks to the development and advance of modern technology, the synthetic polymers have been put in wide use. Though the synthetic polymers provide convenience for our lives, they also bring about many environmental problems, such as consumption of natural resources and environmental pollution. Nevertheless, both biodegradable man-made PLA（Poly Lactic Acid）and natural chitosan contain good biocompatibility and biodegradability. Else, adding MMT（Montmorillonite）into PLA can modify the mechanical properties. Our experiment aimed to prepare the PLA （Poly Lactic Acid）/ Montmorillonite Nanocomposites by adding organo-modified MMT into the biodegradable PLA. The experiment underwent three phases：（1） modifying MMT by means of CTAB(n-Hexadecyl Trimethyl-ammonium Bromide, CTAB ) and chitosan （2）preparing PLA（Poly Lactic Acid）/ Montmorillonite Nanocomposites （3）testing the biodegradability of the Nanocomposites we prepared. While conducting the experiments, we made use of the XRD（X-ray Diffraction）to examine the change in MMT’s layer thickness. The SEM（Scanning Electron Microscope）was also employed to observe the surface pattern of the Nanocomposites, and used Gel Permeation Chromatography （GPC）to examine the decrease of the Nanocomposites’ molecular weight. Moreover, we also used Dynamic Mechanical Analysis （DMA）to test the mechanical properties of the Nanocomposites（Tensile testing）. Last, we test the thermal stability of the Nanocomposites by using Thermogravimetric Analysis (TGA).

The study aimed to compare the electricity generated from the fruit extracts of calamansi, camias and starfruit. Unripe fruits were extracted and varied percentage compositions of each extract were prepared.Wires wereconnected to a multi-tester (voltmeter or ammeter) to measure voltage or current that passes through. Results revealed, that amount of voltage and electric current generated are its lowest reading at 25% and are its highest reading at 100%. Nonetheless, of the three fruit extracts, it’s the calamansi that has the highest amount of voltage generated of0.97 volt while camias has the highest amount of electric current generated of 13.98 mA. Using ANOVA at 0.05 level of significance on the amount of voltage generated among varied percentage compositions of three extracts. However, there’s a significant difference on the amount of electric generated among varied percentage compositions. Results of ANOVA statistically signify that the three different extracts could either be used as a source of voltage and that camias extract should be preferably used over the other two fruit extracts in generating electric current. In all compositions, produced voltage is between 0.88 and 0.97 volts and current is between 3.28 and 13.98 mA. These currents produced are not enough to turn on a small light bulb having a smallest voltage capacity of 1.2 volt, but can be able to turn on a light-emitting diode (LED) that require such amount of current.

NO donors are an emerging class of pharmaceutical compounds, with many important functions in the cardiovascular, nervous and immune systems. With great therapeutic potential, the development of new NO donor compounds would be of great medicinal value, potentially opening a whole class of drugs to be used to treat various ailments. This project studies a specific class of compounds, substituted cyclic oxime ethers, which have proven to be useful intermediates in fields such as medicine and biochemistry. The cyclic structure along with a determinable substitutable group at the C3 position is highly valuable, as it allows the oxime ether to act as a convenient precursor for a variety of useful products, playing key components in many drugs. And with a substituted nitrate group, which is an O-nucleophile, the oxime ether has the potential to become an NO-donor, and hence become a possible intermediate in a wide array of NO donor drugs. Co(NO)3 was used in the synthesis of the cyclic oxime ether, directly from a phenyl substituted bis(oxy)enamine intermediate, producing an entirely new compound: α-hydroxyoxime nitrates, the oxime ether being substituted with a nitrate group. This new reaction of the synthesis of α-hydroxyoxime nitrates was further studied for optimization purposes, in order to open a new class of NO donor precursors. In addition, other nucleophiles were also explored in this class of reactions, forming important bonds such as C-N and C-S bonds, with key structures for other types of synthesis intermediates and precursors. Different metal nitrates, or various other nucleophiles in place of the nitrates, were used in reaction with bis(oxy)enamine, and the yield and structure of the final products were determined by NMR spectra. Successful optimization of the synthesis of α-hydroxyoxime nitrates has been achieved, where the conditions for optimum synthesis involve using Cr(NO3)3•9H2O which achieved a high yield of 76%, dissolved in THF with the bis(oxy)enamine starting compound. It has been determined that the metal in the salt affects the reaction pathway, as the nature of the metal cation affects its efficiency to cleave the N-O bond in the starting compound (with d-block elements being the best performing), and H+ ions can promote the reaction as well. Also, the reaction proceeds with different types of bis(oxy)enamines, meaning the substrate scope can be expanded to give a variety of products. The reaction can also proceed to form other products with different nucleophiles other than the nitrate group, where the C-N and C-S bonds were successfully formed in the reactions from bis(oxy)enamine to oxime ether. Thus, this class of reaction in converting the bis(oxy)enamine to a cyclic oxime ether has potentially opened a new class of NO donor compounds, and further possesses the potential to form a wide variety of products to be used in other important synthesis procedures.

The purpose of this research was to challenge misconceptions about what attracts teenaged boys to girls. It has been observed that some teenaged girls hold stereotypes about boys and believe boys are only attracted to superficial qualities like beautiful hair. The aim is to investigate differences between what girls believe boys find attractive about them and what boys actually find attractive about girls. Hypothesis: There is a significant difference between what teenaged boys find attractive in girls and what teenaged girls think boys find attractive. Procedure Background reading was done to discover which characteristics are commonly used to measure attractiveness among teenagers. A survey questionnaire was used for gathering data. To gather information for the construction of the questionnaire, 4 focus groups were interviewed. The groups were asked to determine indicators of attraction and repulsion. Two separate questionnaires were designed (one for boys and one for girls), based on focus group information, with similar questions which could be used to compare results. Questions were related to personality and looks. The research was representative as 399 teenagers participated in the final survey. Results were collated in Excel tables. Percentages were calculated by using a scientific calculator and Excel. A bivariate analysis was created to examine the main question: ranking qualities that attract boys to girls. A comparison was made between boys’ and girls’ opinions from different age categories. Mean averages were calculated for this question. Other questions were analysed using mode averages translated into percentage of each gender. Graphs were designed using the values calculated. Observations/Data/Results 72% of boys prefer a girl with average looks and an awesome personality but only 37% of girls believed that to be true. The average boys from 12-14, 15-17 and 18-20 year old categories agree that confidence, humour, a nice body, politeness and intelligence are the five most attractive qualities in a girl they would consider dating. The order of these five change across the age groups but are constantly the top five, however confidence and humour always trump a “nice body”. The average 12-14 and 15-17 year old girl overrates a nice body and underrates politeness and intelligence but confidence and humour feature in their top five. The average 18-20 year old girl agrees with the boys priorities. When defining what makes a girl beautiful, 68% of boys highlight personality traits and 59% of boys mentioned physical features. When noting what repulses boys about pretty girls, more than 50% of both sexes agree that smelling bad was most off putting. 52% of boys mentioned taking drugs as unattractive yet only 23% of girls recognized this as repulsive. Conclusions The data supports the hypothesis. Confidence and humour are more important to the average boy than a nice body across all age groups. The younger the girl, the less she understands what attracts boys. 63% of teenaged girls believe that looks are more important to boys than personality. This is clearly not true. 72% of boys value a great personality more highly than good looks.

我們發現 l+ 2+…+n=n(n+l)/2這個公式可用下列這種積木堆積方式證明：我們先將其式子看成如下的積木排列數：如〔 圖(一)〕 這時，我們將另一塊形狀大小完全相同的積木組合，與圖(一)疊合如圖(二)。 ∴很明頭地，疊合成的積木組合為一矩形，積木數 2S=n(n+l) ∴S=n(n+1)/2 即 l+2+…+n＝n(n+l)/2

原題目是環球城市盃中，一個圖論的問題。而題目提供了一個證明，是證 明此種連線都是偶數的圖形，一定會在三的倍數邊形成立。在經過一番思考過 後，我們希望能將原本的偶數連線性質加以驗證，並確定奇存在性。此時，我們 也不禁聯想到：奇數是否也有所特別的性質。因此，我們也向奇數連線做研究。 就在平面得到了部分結論的同時，我們想到這個問題是否可以推廣至三維 空間。然而在推至三維空間的過程中，我們又聯想到，另一種平面：球面。在球 面上放點，能否也找到一些不同的性質。因此，我們分別從平面、球面、立體圖 下手。 基本上，探討平面和立體問題的方法，是以土法煉鋼的方式來求出結果。 然而這種圖論的問題，不可能嘗試到無限多點的情形。因此，我們是著找出一個 關鍵的key，那就是結合性質和外接合性質。以這兩種方法，我們可以將一個簡 單的基本圖形，推向無限多點和無限多邊的情況。 接下來，還有討論一些特殊狀況，例如： deg v＝3n+1，探討其結果。 最後得到的結論是： 1、平面偶圖成立的條件為：此多邊形為三倍數邊形， 而且除了內 部一、二、四點以外， 其他點數都可以成為偶圖。 2、平面奇圖成立的條件為：奇數邊形的情形下，除了三點以外，其 他的內部奇數點的都可以成為奇圖。偶數情形下， 除了四 點以外， 其他的內部奇數點的都可以成為偶圖。 3、三角形平面圖，d eg n 皆為m 成立的條件：2＜ m＜ 6( m? N ) 4、三角形內外任意點d eg 皆為3n ( n ? N )的成立條件： 三角形內部4 x+1 個點( x ? N )。 5、三角形內外任意點d eg 皆為3n+1 ( n ? N )的成立條件： 三角形內部3 x 個點( x ? N )。 6、立體偶圖n 頂點(n＞4)面體的成立條件為： 內部點數為5m+ n- 3、5m+ n- 1、5m+ n、5m+ n +1、5m+ n +3。(m 為大於或等於零的整數) 7、立體奇圖四面體的成立條件為： 內部點數為偶數皆存在。 The original problem is a question of Graph Theory in IMTOT ,which provides\r a proof that proving the figure which its linking-line number is even ,should also be\r contented in the triple-sides figure. After profound consideration ,we try to make sure\r the existence of the properties the we mentioned above. Meanwhile ,it also occurs to\r us that whether the properties would be contented ,in the figure which its linking-line\r number is odd. So we make our way to it. Additionally ,three-dimensional and\r spherical figures are part of our research as well.\r Basically ,we discuss the problem in two-dimensional and three-dimensional\r aspects with the simplest method .However ,it is impossible to discuss the problem in\r unlimited dots .Hence , we are going to find a “key” to solve this problem .As a\r result ,we can find a simple basic-picture , and expand to infinite-multiple lateral\r pictures.\r Next step ,we also discussed some special situations , for example: for each\r point v , deg v=3n+1.\r At last the conclusion is following:\r 1、The conditions of linking-line number is even: triple-sides. And the amount of\r points inside the figure is without 1,2,and 3.\r 2、The conditions of linking-line number is odd: In the odd-sides figure , all number\r of the points inside the figure can be content without 3 point. In the even-sides\r figure , all number of the points inside the figure can be content without 4 point.\r 3、In a triangle , each point’s deg is the same number m: 2

對於轉向次數K→∞且轉向角ɵ為任意角時，各收斂點P於坐標平面上恰形成圓C：。已知U為x軸上任一點且坐標為(u,0)，當ɵ改變時，p1p2與UP之交點S的軌跡為圓錐曲線（點、直線、拋物線、橢圓、雙曲線）。當U=c 時，交點S的軌跡為橢圓，此橢圓的長軸長為圓C半徑（r/1-r2 ），且焦點為P1(1,0)與C(1/1-r2,0)。各轉向點Pn(nÎN)位於一個方程式為，定角為之等角螺線上；同時繪出轉向次數k在不同值時，瓢蟲行進終點之軌跡，以驗證當k愈來愈大時，各終點形成的軌跡會趨近於一個圓。當k=2時，圖形為蚶線並證明其經平移後之極坐標方程式為R=r+2r2cosɵ。最後我們展示行進公比 r→1-，r=1 ， r→1+ 時所呈現的終點軌跡，並對此軌跡所呈現出的意象與自然界連結，而其實質關聯性則有待未來研究。

本研究探討象鼻蟲製作捲葉前在葉面上戳洞行為與圓柱狀捲葉關係。研究過程中測量葉面上孔洞記號的連接距離，發現可呈現許多相似等腰三角形，將所畫出的三角形組合成七邊形後，再利用三角函數及餘弦定理來驗證孔洞與捲葉間數學的規律。探討全等性質的等腰三角形及相似等腰三角形面積關係，並以手作摺紙及GSP軟體繪製圖形觀察。結果可以得知： (一)在一面積相等的正七邊形中，全等三角形合併時（內部為中心點）與相似等腰三角形合併時（內部為任意點）的面積公式為a/2(h1+h2+...hn)=n*a/4(cosθ/2)2*sin2π/n ，則可知兩者面積相等。 (二)我們利用餘弦定理進行演算，結果發現等腰三角形頂角約為 ，底角約為 ，與正七邊形內角相近，所以可得知捲葉搖籃內部約為正七邊形，而有接近圓的模式，符合捲葉搖籃的外觀形態。