一等獎

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。

The apricot kernel is believed to have a great medicinal value in many cultures. However, literature and research indicates that this belief still remains extremely controversial and conclusions regarding the medicinal value are ambiguous due to the presence of cyanide in the kernel. The focus of this research was to evaluate two objectives through the use of several integrated technologies and modified methods: (a) To successfully remove the cyanide from the apricot kernel using an adapted method; (b) To determine the effects of the cyanide free apricot kernel extracts on Helicobacter pylori and Streptococcus pyogenes bacteria. Procedures The apricot kernels were removed from the pits and then ground using a food processor. The kernels were then tested for cyanide using a cyanide test kit and Cyantesmo test tape. These tests indicated that cyanide was present. A novel approach was devised to remove the cyanide and when retested, the kernels tested negative for cyanide. This result was confirmed with Infrared Spectroscopy. The cyanide free kernels were then extracted using a Soxhlet Extractor with methanol for 24 hours. In addition to the methanol extraction, three other techniques were used to obtain kernel extracts: (a) Celite filtration, (b) Infusion Method A, (c) Infusion Method B. The Kirby Bauer method was modified for the microbiology aspect of this project. The Helicobacter pylori and Streptococcus pyogenes bacteria were plated using a 0.5 McFarland Standard. Paper filter discs containing 20µL of each extract were placed onto the inoculated plates in replicates of nine. After 48 hours of incubation, the zones of inhibition were read for each plate. Data The results were extremely encouraging and therefore to ensure the accuracy and preciseness of the data collected, four statistical analyses were completed. These include Confidence Intervals (CI), Standard Deviation (STDEV), T-Tests, and Chi Tests. The methanol extract was significantly different from the control in all trials. The Chi test also yielded a Chi Square value of 223, which was significantly greater than the critical value of 15.507, indicating that the results observed were not due to coincidence. Conclusion Literature evidence has indicated that the apricot kernel has been and is still used for medicinal purposes. Studies have shown that the presence of cyanide and the risks associated with this compound outweigh any benefits gained from the kernel. It has also been suggested that previous bacterial testing resulting in positive inhibition may have been due to the presence of cyanide. However, in this study, I was able to remove the cyanide through an innovative method to prove that the biological activity observed was highly unlikely to be due to cyanide. This indicates that there are other compound(s) in the apricot kernel that have specific antibacterial properties. The potential to improve the quality of life through the application of the apricot kernel appears to be supported, and further studies justified at this time.

異族效應可能是造成種族歧視的原因。本研究透過按鍵反應及腦波儀的形式，對本國人及高加索人兩族群進行受試。實驗中，我們給予受試者兩種族群、正反兩種方向和七種情緒的刺激材料，請受試者辨識情緒，受試完畢後再利用ANOVA、EEG lab等分析行為實驗數據及腦波圖。分析結果發現：按鍵反應方面，高加索人較會辨認情緒，也表現出較強的同理心；本國人對兩種族皆產生面部倒置效應、高加索人則僅對於本國人產生；高加索人判斷正臉情緒時會有異族效應，本國人判斷時則正反皆無。腦波儀方面，每一種情緒的異族效應是相似的，就腦內影響的區域而言，本國人面部倒反效應多由枕葉影響，高加索人則多由額葉影響，本國人異族效應由右腦影響，且僅出現在刺激後150～200毫秒，高加索人則未呈現異族效應。另外，異族效應與面部倒反效應間具有交互作用，於是在臉部辨識上的正反差異就會呈現不同結果。將上述結果進一層地推論，可得知異族效應是後天學習行為，而面部倒反效應則是受本能與後天學習共同影響而產生。 期望本研究結果未來能運用在社會議題或心理學研究上，減少異族效應可能產生的負面影響。

這份研究是關於一個「數形合一」的問題，研究的主要目的是找出同時具有兩種圖形數身分以上的數。研究結果發現雙重多角數必定存在，但個數可能有限個也可能無限多個，有些雙重中心多角數是有限多個，有些雙重中心多角數是無限多個，但令人意外的是同時是K角數和中心K角數的數卻皆是永遠是無限多個，我對其模式進行了探究並加以具體分類，並說明原因。研究過程中發現遞推關係可以大大簡化計算的步驟，可簡潔快速的求出這些數。我也證明了同時是三、四、五角數的數只有 1。此外，我將研究應用在熱門的平衡數(balancing numbers)和NSW數(NSW numbers)等上面，應用多角數的研究解決一些熱門的問題和找出了圖形上不證自明的結果。

本實驗將小型塑膠圓片置於水中釋放模擬落葉的運動模式，發現圓片與水平之夾角呈現週期性變化，變化範圍會隨著時間改變。在運動幾個週期後，變化範圍會被限制，此時為穩定狀態。在水中加入鋁粉以觀察圓片運動時流場的變化，提出分流模型與最短時間原理，發現此模型可以解釋圓片的轉動機制。

本實驗主要是透過及程式模擬分析，探討變形之阿特午機 在一般狀況下及過渡期 的運動過 程。透實驗，我們找出不同的初始條件對於運動結果影響 ，如質量比、繩長 等。我們透過實驗和數值分析建構變形之阿特午機的模型 。因為 摩擦力和空氣阻對於運動 的影響皆不可忽略，因此 我們 也設計阿特午機和鉛直圓周運動的 實驗以求出兩個影響因素參數， 並將其結果統整於理論分析中。這份研究有助我們了解力學的過程目前我們 也正在進行更詳細的數值分析， 我們也希望能在之 後將變形之阿特午機的理論與實驗結 果合，預測不同變因的實驗結果。

本研究以熱激活化延遲螢光（Thermally Activated Delayed Fluorescence, TADF)材料之第三代有機發光二極體（OLED）為主軸，利用吖啶（acridine）作為電子予體、間位及臨位之雙CN苯環（phenylene, Ph）為電子受體，透過有機合成製備DMAC-m2CNPh及DMAC-o2CNPh分子。此外，我們檢測發現DMAC-o2CNPh具有極高的外部量子效率，並將此分子結合透明電極，經由熱蒸鍍製作出透明有機發光元件，探討元件的放光效率及應用性。本研究製作出吸光波長在可見光範圍外的分子，因此蒸鍍在透明基板上後可製作出透明的有機發光元件。將研究成果能應用在生活中，如展示櫥窗顯示新聞、汽車玻璃作為顯示器等，以期能夠提升生活的便利性及運用性。