本文主要在探討平面幾何學中的兩個重要結果—三角形中的『Menelaus定理』與『Ceva定理』推廣到任意的『球面n邊形』的相對應結果，對於任意的球面n邊形，我們分別找到了『球面n邊形的Menelaus共線定理』與『球面n邊形的Ceva共點定理』的一般化結果。

本研究利用碳酸鈣、硫酸鈣、二氧化鈦、樹脂、蠟、色素、蛋殼、粉筆灰等研發環保新粉筆，且透過自繪粉筆檢測裝置，測量其書寫狀況。研究發現碳酸鈣粉筆容易書寫、且清楚，但易掉粉。硫酸鈣粉筆：質輕堅硬、抗變性高。二氧化鈦粉筆容易書寫，寫灰度極高，但較軟易碎。碳酸鈣：硫酸鈣：二氧化鈦：水=3:1:11:8整體效果佳。添加樹脂、水溶性蠟可以提升粉筆的抗變性且使書寫清晰。使用各色顏料色素可調和粉筆顏色，其中薑黃粉的調色較果最好。與市售粉筆比較，自製粉筆的書寫的附著率、寫灰度、擦灰度皆為第一名具有良好的市場價值，而在自製粉筆中添加蛋殼、粉筆灰回收再製作，是環保可行的方法。

Infectious diseases caused by bacteria from biological pollutants pose a great burden in terms of diagnosis and treatment, and millions of people worldwide die from bacterial infections. Detection of bacteria plays a critical role in clinical diagnosis and control of contamination, but is not accessible due to the high cost, complex devices and equipment required. In the project, an alternative to existing methods, a paper-based biosensor for the detection of model organism E. coli bacteria, which is visible, low cost, easy to use, can be integrated with a smartphone, is based on rapid color change in the exposed environments, drinking and pool water, wastewater, beverage products. platforms were developed. For the specific detection of E.coli bacteria, two different biosensors have been developed that can perform colorimetric detection in a user-friendly origami design, minimizing microchip and processing steps based on antibody-bound PVDF membrane and filter paper-based immunological method. In the presence and absence of target bacteria E.coli, the lowest detection limit of the biosensors obtained by using paper-based platforms that create a distinctive color on them, depending on the concentration, was 0.9x103 bacteria/ml for origami biosensor, 2.7x103 bacteria/ml for microchip biosensor and the widest dynamic linear operating range was calculated as 103-107 bacteria/ml. With the biosensor platforms we have developed, the use of only one smartphone for both qualitative and quantitative, visible results and analysis within minutes constitutes the originality of our project. With these promising results, the biosensors we have developed can also be used for the detection of different biological pollutants, do not contain complex devices and can be easily produced in large scales. We believe that the biosensors we have developed for the detection of biological pollutants in water and beverages, especially in regions where test laboratory infrastructure is not available, will contribute to the literature, public health, health economy and sustainable development goals such as clean water and sanitation, health and quality life, and life in water.

為了瞭解銀腹蜘蛛屬蜘蛛結網角度為何常與地面成一角度且角度變異極大，我們以此屬的常見種類西里銀腹蛛為對象，針對野外族群測量結網角度、結網面積、蜘蛛體長、結網高度及結網方位，結果顯示結網角度可從9度到70度，以46 – 50度最常見，而且結網角度與結網面積、蜘蛛體長、結網高度及結網方位均無明顯相關性。 我們從結網角度與受風面及捕蟲率的關係來思考，結果發現，在結網角度與地面垂直時之捕蟲率比起水平時明顯來的高，但結網角度越大即越垂直於地面，受風面越大，故必須織出較強的絲，需花費較多能量；所以西里銀腹蛛可能需在花費較多能量編織強度較強的蜘蛛絲與捕蟲率上取得平衡，因此結網角度才會有如此大的差異。

本研究將以BiOCl、BiOBr以及Pd/BiOCl的晶體製備二氧化碳還原之光觸媒，用以還原二氧化碳，期許能製造出具有經濟價值的還原產物，以緩解全球暖化並利用可再生能源。此外，我們藉由探討此類晶體在二氧化碳還原中的差異，比較加入不同鹵族元素及是否摻入鈀金屬對於光催化還原二氧化碳效率及產物的影響。 合成晶體後，我們透過X射線衍射儀(XRD)、掃描式電子顯微鏡(SEM)、能量散射X射線譜(EDX)進行晶體的鑑定，也確定Pd/BiOCl的晶體結構是以BiOCl為主體，且Pd鑲嵌在其表面。我們也以X光光電子能譜儀(XPS)了解晶體的鍵結型態及推測不同晶體表面的OVs相對含量，並以紫外光/可見光光譜儀(UV-vis)檢測樣品的能隙，推測其光催化性能。 我們發現摻入鈀的BiOCl晶體結構為分散的片狀結構，是三種晶體中唯一的奈米晶體，且能隙為三者中最小(2.46eV)、表面OVs含量也增加；表面附著的Pd奈米金屬顆粒更可以協助主催化劑的電子-電洞對維持分離狀態，促進其光催化效率。 最後我們將合成的BiOCl、BiOBr以及Pd/BiOCl晶體應用於光催化還原二氧化碳，並以氣相層析熱導偵測器(GC-TCD)及氣相層析質譜儀(GC-MS)檢測產物種類及產率，發現還原出的氣體產物有H2、CO、CH4。而總還原產物及含碳還原產物的產率皆以Pd/BiOCl為最高。

本研究探討不同的溫降對史特林引擎做功的差異，結果發現以1300毫升的熱水，從95℃降到91℃、90℃降到87℃、85℃降到83℃時，史特林引擎分別做了 39.65、7.57、1.49焦耳的功。假設實驗室的數據能夠複製到實際大型的水體，則以宜蘭的仁澤溫泉每日抽取溫泉約20公噸來估算，若在其自然冷卻的過程中可以透過史特林引擎發電，當溫度從140℃降到90℃時，預計可發電23.2度，等於減少11.81公斤的二氧化碳排放量。本研究結果希望能讓讀者多了解利用熱質自然冷卻來產生電力，有助於改善我們的環境。

本研究主要想了解兩互溶流體間形成碎形圖案之機制，並找出實驗證據，經由將不同濃度的染色液滴滴到不同濃度的壓克力顏料溶液上，並使用iphone 8 手機以240fps拍攝液滴擴展過程，得知酒精液滴因表面張力小，而向外流動，且因流體間互溶之緣故，造成流速的不連續性(虎皮紋的流痕)，而在外圍產生不均勻的堆積(島紋)，當堆積過多時，便會發生突破(顯微攝影拍到突破瞬間)，而長出手指，同時堆積會由突破口轉移到手指指尖，當堆積夠多時，指尖又會再分裂出新的碎形手指，如此往復下去，就形成碎形圖案。 此外，碎形手指的圖案，跟利希滕貝格圖極為相似，經使用方格覆蓋法，計算出碎形維度約為1.82，與利希滕貝格圖的理論值1.71接近，確實是碎形圖案的一種。

平時我們總是會在各個角落看到螞蟻成群結隊的行走，牠們依靠彼此的觸角不斷溝通，彼此各司其職，建構出小型社會。深入觀察後，我們發現牠們似乎能夠敏銳地感知光線的方向。讓我們想進一步了解光線對牠們的行進路線是否會有影響，於是，我們展開了一系列實驗，探討不同環境及不同偏振光對螞蟻行進路線的影響。 此次實驗我們選用希氏巨山蟻及大黑巨山蟻分別進行環境測試、習性測試及偏光實驗，藉以探討螞蟻在黑、白兩種路徑上的偏好，以及在生長燈下旋轉偏光片改變不同偏振光，進而探討對螞蟻行進方向的影響。 研究結果顯示，在黑、白兩種環境中，螞蟻更偏好行走在黑色的環境，同時，我們也觀察到改變偏振光會對螞蟻的行進路線產生影響。

本研究驗證多霜蠟鼠婦及光滑鼠婦的交替性轉向反應行為，並探討何種因素會影響此反應。結果顯示，兩種鼠婦皆具有交替性轉向反應，在95%信心水準下，有80%以上呈現此反應。此外，這種反應可連續發生，約87%的鼠婦在3次轉向中，至少連續2次出現交替性轉向。我們進一步探討影響轉向的因素，發現當轉向後移動距離增加，反應頻率就愈低，並且證明沿牆行走會影響轉向方向。最後藉由步態分析證明，鼠婦轉向時的步態與直線移動不同，內側的胸肢站立期比率較外側高，此與前人所提出雙側不對稱腿部運動(BALM)的解釋不同，且為支持此假說的另一項有力證據。

手語為聾啞人士日常溝通的工具，但對一般人來說這是一種難以理解的溝通方式。本實驗使用深度學習的 Yolov3 與 Yolov4 模型訓練37個國語注音符號手勢，然後再驗證模型對圖片、影片、即時(Real time)攝影辨識的正確率。 實驗結果顯示：Yolo v3 圖片辨識度效果還不錯，但影片辨識度很差，而Yolo v4 不管在靜態的圖片或動態影片都有不錯的辨識率，另外在即時的影像辨識也有不錯的效果。 雖然有部分符號的辨識度很低，但這可能是訓練時照片拍攝的問題，如果可以改進拍攝的數量和技巧，相信可以大幅提升判讀的準確率。

With the introduction of the transformer architecture by Vaswani et al. (2017), contemporary Text Generation Models (TGMs) have shown incredible capabilities in generating neural text that, for humans, is nearly indistinguishable from human text (Radford et al., 2019; Zellers et al., 2019; Keskar et al., 2019). Although TGMs have many potential positive uses in writing, entertainment and software development (Solaiman et al., 2019), there is also a significant threat of these models being misused by malicious actors to generate fake news (Uchendu et al., 2020; Zellers et al., 2019), fake product reviews (Adelani et al., 2020), or extremist content (McGuffie & Newhouse, 2020). TGMs like GPT-2 generate text based on a given prompt, which limits the degree of control over the topic and sentiment of the neural text (Radford et al., 2019). However, other TGMs like GROVER and CTRL allow for greater control of the content and style of generated text, which increases its potential for misuse by malicious actors (Zellers et al., 2019; Keskar et al., 2019). Additionally, many state-of-the-art pre-trained TGMs are available freely online and can be deployed by low-skilled individuals with minimal resources (Solaiman et al., 2019). There is therefore an immediate and substantial need to develop methods that can detect misuse of TGMs on vulnerable platforms like social media or e-commerce websites. Several methods have been explored in detecting neural text. Gehrmann et al. (2019) developed the GLTR tool which highlights distributional differences in GPT-2 generated text and human text, and assists humans in identifying a piece of neural text. The other approach is to formulate the problem as a classification task to distinguish between neural text and human text and train a classifier model (henceforth a ‘detector’). Simple linear classifiers on TF-IDF vectors or topology of attention maps have also achieved moderate performance (Solaiman et al., 2019; Kushnareva et al., 2021). Zellers et al. (2019) propose a detector of GROVER generated text based on a linear classifier on top of the GROVER model and argue that the best TGMs are also the best detectors. However, later results by Uchendu et al. (2020) and Solaiman et al. (2019) show that this claim does not hold true for all TGMs. Consistent through most research thus far is that fine-tuning the BERT or RoBERTa language model for the detection task achieves state-of-the-art performance (Radford et al., 2019; Uchendu et al., 2020; Adelani et al., 2020; Fagni et al., 2021). I will therefore be focussing on attacks against a fine-tuned RoBERTa model. Although extensive research has been conducted on detecting generated text, there is a significant lack of research in adversarial attacks against such detectors (Jawahar et al., 2020). However, the present research that does exist preliminarily suggests that neural text detectors are not robust, meaning that the output can change drastically even for small changes in the text input and thus that these detectors are vulnerable to adversarial attacks (Wolff, 2020). In this paper, I extend on Wolff’s (2020) work on adversarial attacks on neural text detectors by proposing a series of attacks designed to counter detectors as well as an algorithm to optimally select for these attacks without compromising on the fluency of generated text. I do this with reference to a fine-tuned RoBERTa detector and on two datasets: (1) the GPT-2 WebText dataset (Radford et al., 2019) and (2) the Tweepfake dataset (Fagni et al., 2021). Additionally, I experiment with possible defences against these attacks, including (1) using count-based features, (2) stylometric features and (3) adversarial training.

Aspirin is one of the most used and well-known medicines world-wide. It can be synthesized by reacting acetic anhydride and salicylic acid in a warm temperature of around 60-80°C. This reaction is usually catalyzed by sulfuric or phosphoric acid. This paper will investigate alternative catalysts, safer and more environmentally friendly, as well as compare different synthesis methods with different heat mediums, one using a water bath and the other amicrowave. By doing so, the effects of the catalyst and the method of synthesis on the yield, purity and environmental consequence of crude aspirin synthesis will be deduced. The targeted utcome is to find the alternative method as more energy efficient, and to find a greener safer catalyst to sulfuric and phosphoric acid. Further background information, exploration, and explanation is in the appendix. The targeted outcome will be to find a viable alternative catalyst that is safer and more environmentally friendly, and to find that the microwave synthesis method consumes less energy.