本研究是將數學遊戲進行變形，其原本是在線段上分金幣，而我們改成在圓盤上分金幣，規則如下：在圓盤圓周上等距取𝑛個點，依序在點上放置金幣袋，每一袋的金幣數都比前一袋多一枚，每枚金幣皆相等(等值)，金幣總數為1+2+3+⋯+𝑛。兩人各丟一隻飛鏢在圓盤的相 異點上(不可丟在圓周上)，離袋子最近的飛鏢拿到它所有的金幣，若金幣袋距離兩支飛鏢等 距，則平分此袋內的金幣；我們想要觀察要如何丟飛鏢能讓分得的金幣數量最接近？並找出 一般化的平分手法。我們證明了在兩支飛鏢的情況下任意𝑛袋金幣都可被平分、第一支飛鏢落在圓盤上的任意點皆能找到對應點來使圓盤上的金幣被平分、飛鏢的數量進行變動後依舊能找到平分法及規律。

研究想法來自於三中線將三角形平分為6個面積相等的小三角形，試想如果分割線不是中線的話，分割結果會是如何？ 先研究三角形三頂點與其對邊上的三等分點連線，將三角形分成19個區域，我們運用孟氏定理計算出這些區域的面積比及一些延伸性質。 運用上述計算技巧，研究三角形三頂點與其對邊上的任意分割點連線，當三條分割線不共點 (非西瓦) 時得分割三角形，證得此分割三角形面積與原三角形面積比公式。 推廣至當分割點在邊上或其延長線上時，研究分割三角形存在條件及圖形分類。依分割點是否在邊的延長線上，分為八種類型圖形，以數學軟體模擬找出所有圖形有73種，證明這八種類型之分割三角形存在的條件及面積比，並歸納以一個公式表示面積比。

本研究以回收目前於電動汽機車及儲能設備中使用量最大的 Panasonic 18650 三元鋰離子電池為主軸，開發以三混深共熔溶劑(TDESs)將電池中的鈷、鎳回收之方法。 TDESs的合成，四級銨鹽選擇文獻中常用的氯化膽鹼，配對各種氫鍵予體(HBD)後，使 用針對鋰鎳鈷鋁氧化物(LiNi 0.8Co0.15Al 0.05 O2 ,LNCA)溶解度最高的 TDESs 組成作為探討主軸。 接著以循環伏安法(CV)分別量測 TDESs與LNCA及電池電解質溶於TDESs之電位窗及還原峰電位。並採用二極式電鍍還原鈷、鎳後，以掃描式電子顯微鏡(SEM)及能量分散光譜儀(EDS)分析鍍層表面的形貌及成分。最後以無電電鍍法還原出貴金屬。 結果顯示，溶入電池電解質之 TDESs溶液，在溫度373.15K，外加電壓4V、5V、6V的 條件下可單獨還原出鈷金屬，且在無電電鍍的實驗中觀察到，在室溫下靜置 2 小時後，可將 鈷、鎳還原。

Washing is one of the things that must be done by every household. Rural and urban communities have to wash clothes every day, to get clean clothes so they can be reused. But it turns out that with many households doing this activity, it will cause side effects that are not good. The impact will worsen the quality of the surrounding water because this activity is not equipped with a waste treatment process, but instead is dumped directly into the nearest ditch or river. As a result, this waste causes water pollution. The chemical compositions contained in detergents are grouped into 3, namely surface active substances ranging from 20-30%, reinforcing agents are the largest detergent components ranging from 70-80% and other ingredients around 2-8%, where surfactants are the main ingredients. cleaning agent in detergent. If not managed properly, it will cause environmental problems in the future. This research was carried out for 4 months at MAN Sidoarjo and Brawijaya University. The research method used was research and development and experiment methods, and data collection techniques using the observation method. From these problems, we offer a solution by making an internet of things-based device which we call HOPE WASTE (House Processor Waste) with IoT (Internet of Things) as the processing of household laundry liquid waste. HOPE Waste is a house-shaped device that functions to treat Laundry Liquid Waste which combines electrocoagulation methods and utilizes Biosorbents, namely Barringtonia Asiatica and Activated Charcoal which are made into powder. Where the Biosorbent content can bind chemicals in laundry liquid waste so that we can combine them using environmentally friendly IoT-based electrocoagulation methods.

模擬高風速對模型遙控車產生之Double D (Downforce下壓的力與Drag阻力)比值切入空氣力學套件角度研究。下壓的力增輪胎抓地力，轉彎速度增快，縮短單圈時間 (lap time)贏得比賽。我們選取Nissan GTR與F1 Ferrari SF21遙控車，以巴沙木自製單層、雙層(主副翼不同角度組合)、三層共17組尾翼，自製風洞模型、掃葉機風力、2個電子秤同測前後輪下壓的力、拉力計測阻力，發煙機及LED燈拍攝氣流。結果發現尾翼寬度增寬與尾翼攻角越大，可增加下壓的力。阻力與風速平方成正比，相關係數0.94。對雙層尾翼，增加副翼角度比主翼角度更可增車子下壓的力。主翼0∘-副翼75∘造成「總下壓的力變化量/阻力變化量」比值0.78為最大，乃增加穩定度之最佳尾翼選擇。再以3D列印技術製作出最佳主翼0∘-副翼75∘尾翼。

太陽能是永續乾淨的能源，但由於太陽能光電板的溫度每上升1℃會使發電功率下降約0.35~0.5%。在台灣夏天高溫炎熱，導致發電功率下降許多。我們開發了一組太陽能板散熱系統，透過適當的管路設計導引冷水，不僅有效地降低太陽能板的溫度，避免其光電轉換效率下降，更同時得到溫熱的用水。 經由本研究使用小型的太陽能板搭配金屬管製作散熱模組來評估，若以0.1L/min的流速，可將流過的水至少升溫10℃，若能放大到20 坪屋頂所能安裝的太陽能板面積，可產生約3528公升、40℃的溫熱水，足以提供標準家庭一日之用水，並且由實驗證明本研究設計的散熱模組，可實際將太陽能板進行降溫，改善輸出發電功率的下降百分比達20%。

Food safety was an important issue recently. Today sodium percarbonate was used to fake the vitality of shrimps to earn a good sell. However, it may cause harm to health because of the peroxides left over. To handle this problem, we set up two goals to achieve: detecting them and then removing them. In the past, the titration skill was an easy method for determining the concentration of H2O2. It not only spent too much time but also resulted in errors commonly. In this research, titanium sulfate and citric acid were used to prepare the colorimetric reagent. To measure the peroxides in water, several factors were controlled and the SOP for detecting and the calibration line for peroxides finally established. In practical, we turned the colorimetric reagent into the fast test paper which was easily for use. The other part of this research was to clear up the peroxides in water. We use titanium sulfate, hydrogen peroxide and citric acid as starting material via hot-bath method to prepare the nano-photocatalyst of titanium dioxide. Since the powder was inconvenient to deal with large amount of water. The powder-like TiO2 was further made into ball-shaped TiO2 in favor of water treatment and reuse. It was found that the photocatalytic performance of ball-shaped TiO2 was effective to be on duty for removal of the peroxides. In summary, this research provided two techniques to deal with the zombie shrimp. The novel method for synthesis of TiO2 catalyst and the preparation of colorimetric reagent for fast test paper were all in low cost. They had great potential to develop in marketing demand.

The emergence of antibacterial resistance has necessitated the development of alternative treatments, such as antimicrobial peptides (AMPs). AMPs are part of the innate immune systems of various organisms such as Momordica charantia L., a known medicinal plant in Southeast Asia. In this study, potential novel AMPs from M. charantia were derived in silico to provide prospective antibiotic alternatives using promising plant-based peptides. M. charantia protein sequences that were 500 amino acids long were digested using proteolytic enzymes, resulting in 3,621 peptides. Each resulting sequence was characterized as either AMP or Non-AMP using four statistical analysis tools, and those identified as AMPs were analyzed. This led to 102 AMPs, 53 of which were unregistered on the Data Repository for Antimicrobial Peptides, indicating that they have yet to be derived from other species. Six of the eight studied physicochemical properties show strong correlations with each other, suggesting that subsequent AMP design studies may focus on these six properties. As such, M. charantia may be a rich source of potential AMPs and, thereby, alternative antibiotics. The in vitro examination of these novel AMPs is also recommended to further understand their potential as alternative antibiotics sourced from locally available plants.

近年少子化使老年人口比例快速上升，政府對老年及失能人士的照護也愈發重視，而在輔助失能人士的輔具中，輪椅及便椅是日常生活不可或缺的存在，對行動不便的使用者而言，在輪椅與便椅兩者間的移動可能增加跌倒的風險，若能將輪椅與便椅結合，將大為降低移動的風險。本研究透過生活科技及資訊科技所學，設計將兩項輔具結合為主要目標，並試圖解決兩大問題：第一，輪椅如何提供座位中空來進行如廁，而中空的部分沒有支撐要如何來改善；第二，長期仰賴輪椅者臀部所產生的壓迫性壓瘡如何來防治。本研究將針對上述兩大問題，就現有照護文獻與輔具發明，進行探討、發想、實作與改良，期望打造一台能降低跌倒風險與壓瘡發生等多功能的『方便椅』。

海上漏油事故時有所聞，而漏油更會對海洋生物及環境造成危害。依專家研究顯示，此類事件洩漏出來的石油能被成功清理的，往往不到10％。而使用油分散劑固然可以在一定程度上解決岸邊油污回收不完善的問題，但同時仍會讓分散後的油持續在海中⻑時間存在，對環境的衝擊很大。有鑑於此，我們嘗試運用天然幾丁聚醣（Chitosan）具吸附力的特性，來探討其對柴油的吸附效果。透過實驗，我們將5%幾丁聚醣溶液製作成晶球，在不同環境條件下加入柴油並浸泡後再以真空抽濾法過濾出剩餘的油，結果證實幾丁聚醣確實具有吸附柴油的功用。幾丁聚醣可以吸附柴油及海洋中的重金屬又是生物可分解的物質，未來也許可以進一步做成濾材，用來保育海洋環境。

臺灣已進入高齡化社會，基於老人在面臨行動力與反應力逐漸退化過程中，造成心理壓力及自信心的喪失，本研究探討及建構一部樂齡勇腳椅，透過健腿檢測、輔助起身及久坐提醒等三個主要功能，配合麥克納姆輪設計多向式椅盤，讓高齡者能於狹小空間便捷行動，讓高齡者可以達成活動更自主(Confidence)、能力更提升(Capability)、移動更便捷(Convenient)、身心更健康 (Healthy)的 3C1H 生活支持策略。透過積木及3D列印技術建構勇腳椅的本體，以槓桿輔助起身，運用Micro:bit搭配按鈕、蜂鳴器、LCD、SG90 伺服馬達等元件，建構可以讓高齡者生活自主行動及監測健康，最後運用ESP8266的wifi晶片，建構可透過雲端搭配Line通知提醒周邊的親人或照護者。樂齡勇腳椅不僅是健身器材，更是支持高齡者生活品質與尊嚴的最佳解決方案。

阿拉伯芥的長期後天耐熱性（LAT）有如人類的「學習」，如何延長其「記憶」為本研究探討的主要目標。首先以改變熱處理間期之光週期來確立 hsp101、hsa32突變株在光照期變短下，LAT 處理後的存活率有提高之趨勢，而西方墨點法也發現 HSP101 之表現量與存活率有相同的趨勢，LAT 耐熱記憶的延續與否和 HSP101 的量息息相關。低溫降低代謝與光照期變短在存活率、西方墨點法的實驗結果相似，這顯示光照期變短可能也是透過代謝減緩，進而減少 HSP101的降解，使突變株的存活率提高。最後，花椰菜HV-427、HV-178的光週期實驗中，在進行LAT處理後，低光照下的受傷率有降低的趨勢，顯示降低光照能夠提升其耐熱性。我們期望此結果未來可應用在農業生物科技，透過更具經濟價值的方式來降低代謝進而延續LAT耐熱記憶，提升其對抗熱逆境的能力。