1.雙心n邊形中，過任一旁心作不相切邊的垂直線（旁心高）並與該旁切圓交於一點，再過此交點作旁心高的垂直線（旁高垂線）則 (1)過內心I作旁心高的垂直線，則該垂足與I、對應切點形成一角具有旁高垂線與圓I是否相交的判別性質。 (2)透過旁心高和旁徑、內切圓、外接圓半徑的關係，進而推導出雙心n邊形面積和三種半徑有關的一般式。 (3)只有雙心四邊形的四條旁高垂線相交形成的旁高垂四邊形和原雙心四邊形全等，且具有對偶性。 2.雙心n邊形中，過每個頂點作不相切邊的頂點高，會與對應外接圓圓心角之正弦函數值有漂亮的比值關係式。 3.推廣文獻1結果到雙心四邊形，可得內切圓半徑與四個旁徑間類似的關係式。

賽滅寧(Cypermethrin, CYP)是一種被廣泛使用的II型合成除蟲菊精類農藥，常利用於蔬果及驅蟲中。已知，攝入高劑量的CYP會影響人體健康，並殘留於毛髮、皮膚與脂肪組織之中難以代謝。本實驗藉由鹽酸模擬CYP進入體內後受胃酸分解的狀態，檢測其降解產物與方式，並由CYP與降解產物的實驗探討是否會對數種與體內疾病相關的酵素發生交互作用，從而對酵素的活性與功能產生抑制作用。實驗發現CYP經由強酸會水解為兩種化合物，並對造成阿茲海默症的酵素乙醯膽鹼酯酶(Acetylcholinesterase)產生抑制作用，當CYP濃度越高時，抑制性越強，且經由對人類神經母細胞瘤細胞(SH-SY5Y)的毒性實驗發現相對是安全的。希望能藉此研究進一步探討CYP對體內酵素作用的影響，並且探索CYP降解物對生物體是否帶來潛在的益處。

Over 30 million souls live in a world of darkness, a number greater than the populations of both Norway and Sweden combined. Every individual deserves the chance to embark on a journey across our magnificent blue planet. Yet, regrettably, little has been done to assist them. With this project, we’re lighting the way for the blind to explore our beautiful world independently, breaking free from dependence and embracing boundless horizons. In order to put our theory of the project into practice & explore the use of artificial intelligence & computer science, we started by collecting the required materials for our project such as micro-controllers, sensors, a pair of glasses, a laptop, and a miniature camera. Then we moved onto creating the project itself in which the digital software programmed onto the hardware plays the key-role, as the sensors and the camera will record the details and information from the surroundings and send it to the laptop for further processing. The camera would be the backbone of our project, as it will stream real-time footage to the laptop which will be analyzed by an open-source object detection model ‘YOLOv8’ for identifying objects. After finishing the base model of our project, we tested it in-front of objects such as toy cars, bikes, people, etc, and the results of the object-detection would be shown on the laptop. To observe this data, we created a device which has different modules and integrations for different functions. For example, we will use our camera and then stream it onto a laptop so the reading and the data can be processed on the laptop by AI using YOLOv8. As mentioned in the start, many people do not possess the ability to see, to assist them we have thought of this device which uses all readings and its analytical skills to analyze data and help them navigate, travel or simply, live a better life.

上高中後，我們將國中對閃電研究的興趣延續，國中的研究著重於閃電與降雨地形及溫溼度的關係，高中這幾年我們的目標是希望找出以容易取得的雷達迴波圖推估閃電得發生，高一及高二上學期間我們在研究過程中，對閃電的資料記錄方式、形成條件、現象等越理解，讓我們除漸漸得出穩定的研究結果，但也發現因為需不斷的調整以趨向大自然的真實狀況，我們方法有限制。本報告以我們初始研究為基礎，以調整後的方式進行深入分析，期望以其他的氣象資料輔助雷達迴波圖的可行性，並且以三維雷達回波資料分析降水粒子對閃電發生的影響，最終希望建立利用資料推估閃電發生的簡易閃電預報模式。

左手香是熱帶及亞熱帶地區常見的植物，文獻顯示左手香的廣泛應用如抗發炎、鎮痛及 抗菌等功效。本研究以抑菌功效為研究起點，探討主要抑菌成分(百里香酚、香芹酚)在何種環 境下可提升其含量；接著討論此兩種成分對於左手香及環境的影響。結果顯示斑葉左手香內 百里香酚與香芹酚含量較高；兩種抑菌成分對金黃色葡萄球菌、大腸桿菌及腸道沙門氏菌有 抑制效果；不同光照時數、光照強度的實驗中，6小時與9小時搭配高強度光照，百里香酚及 香芹酚含量最高；適度逆境可促進香芹酚合成。最後發現左手香葉片對土壤菌群亦具影響， 顯示其可能干擾微生物生態。本研究結果可為天然抗菌劑開發、醫療及永續農業提供參考， 並促進左手香在多領域的應用潛力。

昆蟲常藉由聲音或振動進行溝通，但等足目間的聲音研究相對稀少，正露丸鼠婦是少數能在受刺激時捲曲並發聲的陸生等足目，本研究探討其聲音特性及對其行為的影響。經頻譜分析後發現，叫聲的頻率多集中於2kHz、12kHz與16kHz，且波形可分為急促型與規律型，研究中透過卷積神經網路進行影像辨識，建立鼠婦聚集行為與聲音頻率的關聯，在T字迷宮及J字迷宮中，正露丸鼠婦受16kHz聲音吸引大於12kHz與2kHz，與對照組有顯著差異，我們提出正露丸鼠婦其聲音的頻率高低與刺激強度有關，且會導致鼠婦產生不同行為的假說，本研究期望可透過聲音進行生態監控或害蟲防治，本研究結果可以作為生物防治策略之參考。

本研究使用幾何繪圖軟體，利用五條直線繪製至少三個三角形，進而探討這些三角形的相似、全等、五心與內部結構，分析其中存在的數學規律或幾何性質，主要探討為三角形的五心共線和重疊問題。本研究發現，五條直線有一定規則才能繪製出三到五個三角形，且特定畫法的三個相似直角三角形的外心會共線、四個相似或全等三角形的垂心會重疊、三到五個相似或全等三角形的旁心皆會共線或重疊。

巴金森氏症是最常見的神經退化性疾病之一，目前尚無根治之法。研究已知，粒線體如果出現問題，會加速神經細胞退化。細胞自噬作用可協助清除功能不佳的粒線體，以維持神經細胞運作。電子傳遞鏈第三複合體核心中的UQCRC1 (Ubiquinol-Cytochrome C Reductase Core Protein 1) 基因點突變會導致巴金森氏症。然而，細胞自噬作用對於UQCRC1引起神經退化影響的仍不清楚。本研究中，在果蠅神經系統以RNA干擾方式降低UQCRC1表現量，建立巴金森氏症模式；而後利用不同藥物分別抑制或促進細胞自噬作用，觀察果蠅爬行能力；同時，利用MARCM遺傳工具，使果蠅組織細胞分為UQCRC1缺失和正常細胞兩群，觀察細胞自噬相關的蛋白表現量在兩群細胞間的差異。研究結果顯示細胞自噬對UQCRC1參與的粒線體功能缺損的神經退化有代償作用。

無線傳電是非常新穎的創舉，但卻沒有人用簡單且便宜的方法來改善傳輸效率不佳的問題。在主線圈加入軟鐵後，輸入和輸出的功率比從52%增加到70%，大大減少無線傳輸能量損耗，且若次線圈再加入諧振線圈，則功率比可從52%再增加到80%，這是一個重大發現。在主線圈加入軟鐵實際無線充電之效果是：充電到10mAh時間從9分32秒縮短到5分23秒，減少3分51秒，效率提升40%。在次線圈加入諧振電路對實際無線充電之效果是：大大提升次線圈原本輸出功率約3.8倍，且主線圈加入軟鐵後，充電時間又再縮短20%。由實驗最佳數據，本組設計了無電池風扇並結合3d列印及雷射切割技術，使研究結果商品化，只需插上電源就可以使用。

本研究從日本Subaru天文台 Hyper Suprime-Cam Subaru Strategic Program （HSC-SSP）及Hyper Suprime-Cam Legacy Archive （HSCLA）計畫網站下載公開的可見光觀測影像，撰寫程式進行彗星軌跡擬合（trail fitting）與孔徑測光（aperture photometry），分析已知彗星在遠日軌道時的光度並初步測量其彗核大小，進行後續討論。

Agro-guard aims to revolutionize disease identification and community-based projects in the field of agriculture. Integrating Machine learning, Computer vision, clustering, and community-based technology, this project helped farmers to detect their plant disease with their solution and for early warning of plant disease which was spreading in their community which helped in crop management. The research project is divided into three parts.First,Integrating Machine learning to detect and classify plant disease with their solutions.Second,Integrating Density-Based Spatial Clustering of Applications with Noise (DBSCAN),to identify disease and analyze the pattern within agricultural regions.Third,Establishing notification system to notify real-time alerts to farmers about disease spreading in particular region.The research is crucial because it solve one of the crucial problem of our community which is untimely detection of disease.The finding of the research highlight the effectiveness of Agro-Guard framework in early disease detection and community detection.The machine learning models achieved high accuracy in identifying common plant disease and clustering results the pattern in diseases that were very important for notifying the community.The significance of these findings is that it can build powerful system which will overall grow the production of crops and plants due to timely update of the disease prevailing in the community.It contributes in sustainability production of crops and plants which ultimately ensure the good livelihood of farmer.

Cardiac Arrhythmia is one of the conditions in the group of heart and blood vessel diseases that can lead to sudden cardiac arrest (sudden death) and other conditions if not diagnosed quickly and accurately. According to research, heart and blood vessel diseases are the most common diseases and have a mortality rate of one-half of all non-communicable diseases. According to WHO statistics in 2012, it was found that there were 7.4 million deaths from heart and blood vessel diseases, and in 2017, the number of deaths increased to 177 million people, or about 94,444 people per day. Diagnosis of heart and blood vessel diseases can be done by measuring the electrical activity of the heart, and after the examination, a specialized physician will read and analyze the graph to find abnormal patterns. Currently, the shortage of qualified heart specialists to read the graph and screen for heart disease is a medical position shortage, which requires transferring data to hospitals with specialists, resulting in delays in diagnosis and treatment and even death. The project "EIPCA: Electrocardiogram Interpretation Pattern for Cardiovascular Abnormalities prediction" is an application program that assists in screening for fatal diseases that arise from abnormal heart rhythm. It employs artificial intelligence to aid in the screening and analysis of the electrical waveforms generated by an ECG machine, thus reducing diagnosis time and addressing the shortage of cardiology experts. EIPCA is comprised of two systems: (1) a system for screening and analyzing ECG waveforms using artificial intelligence to solve the problem of a shortage of specialized cardiology physicians, and (2) a system for risk assessment of fatal diseases by analyzing the ECG waveform data. The target group of the project is Rural hospitals, as well as health-related agencies. The project team hopes that the development of this project will significantly improve the efficiency and speed of screening for heart-related diseases, ultimately reducing the mortality rate from these diseases in the future.