At the 61st National High School Science Fair of Taiwan, the first-rank paper "The Study of the Largest Area of Inscribed Triangle within the Intersection of two circles" was presented. The authors discussed several properties of maximum area of inscribed triangles within intersection regions of two congruent circles. They only claim their results but without providing a rigorous proof. However, we give a proof by showing the convergence of the iteration of finding the largest height. Subsequently, we offer new methods to approach the problems such as the trigonometric identities, Jensen's Inequality to prove the maximum area of triangles and quadrangles within the intersection region of two congruent circles. Finally, we determined the maximum area for the case of n-gons. We conducted further research and discussion on this issue. In the future, we hope to prove why the maximum area of n-gons within the intersection region of two congruent circles occurs when there are two points on the intersection points of the two circles. We aim similar problems in the three-dimensional space, namely the maximum volume of tetrahedron within the intersection of two unit spheres.

The billiard table is a cuboid with integer side lengths. A point-wise ball moves with constant speed along segments making a 45◦ angle with the sides and bounces on these. We allow the ball to start from any of the 8 corners, resulting in a periodic trajectory known as a corner path. The geometry of the path depends on the artihmetic properties of the side lengths (for example if these are pairwise coprime). Points of contact between the ball and edges, known as edge points, are inves- tigated and their characteristics like distribution explicitly described. This generalizes a previous work by Perucca, Reguengo da Sousa and Tronto of University of Luxembourg.

蘭科植物的種⼦細微如沙塵然⽽胚發育不完全，亦無胚乳。在⾃然條件下，蘭科植物需仰賴菌根真菌⽅能順利完成其⽣活史。本研究欲探討綬草(Spiranthes sinensis)與根部共生真菌（root-originated mycorrhizal fungi）的關係，將實驗分為四個部分，一為觀察綬草根部、種⼦和共生真菌。二為探討綬草的根部共生菌種。三為測試共生菌絲與萌發所需物質的關係。四為探討共生真菌與綬草萌發的關係。結果發現綬草的根部共生菌種類會受環境影響，並且綬草根部的真菌種類不少，其中包含角擔菌Ceratobasidiaceae、膠膜菌Tulasnellaceae、傘菌科agaricomycetidae等，且能分解環境中的澱粉與蛋白質。

本研究旨在開發高效且符合綠色化學原則的Breitfussin B合成策略。Breitfussin B是一種極為稀少的天然產物，可自海洋苔蘚動物Thuiaria breitfussi中分離，分子結構包含吲哚(Indole)、噁唑(Oxazole)與吡咯(Pyrrole)骨架。儘管已有科學家完成其全合成，但現有方法步驟繁瑣，且涉及重金屬試劑，價格昂貴且難以回收利用。因此，本研究致力於開發更高效且環保的合成策略。 目前，我們透過一系列取代與還原反應和Sonogashira偶聯反應成功合成吲哚衍生物6-Bromo-4-methoxyindole，此產物可作為後續關鍵合成步驟的起始材料。此外，在疊氮酮(Azidoketone)至酮醯胺(Ketoamide)的轉化中，我們系統性研究了不同反應條件對產率及區位選擇性的影響。 本研究的成果不僅為Breitfussin B的合成提供關鍵技術支持，也對吲哚類化合物的全合成 具有重要的應用價值。

Our vision aims to raise the quality of life and we had planned smart cities from scratch but what about the current cities the residents of Riyadh suffer from extreme traffic and spend hours circling the block searching for a open park which wastes time money and is bad for the environment. 30-50% of traffic is causing by not being able to park and due to Riyadh lack of proper city planning and radid increase in inhabitants especially after allowing women to drive and as the car being the main way of transportation finding a open park could be a nightmare for some. We have approached this problem from the technological perspective by developing a free application for Riyadhs inhabitants that's main goal is to navigate each driver from their current location to the best open park possible in the shortest time possible but what dirstinguishes us from similar apps in the literature is that we provide the time of departure for each park as well as the ability to book suck parks even if it is ahead of time via a interactive live map. The technology's that we used are the cellar censor that will track the users location and the ultrasonic sensor to track the occupancy of the parking in case the driver doesn't have the app but in which case will case will not be able to provide booking features. We have struggled in the lack of expertise and experience and in motivating the drivers to input correct data about there time of departure we also didn't have enough time to validate our project For future work we will validate our project and we plan on making the detection of the time of departure automatic as well as vobering all kinds of parks. We plan on expanding the scope of target users to include institutes as well because with time the app will have collected enough data to help institutions provide better parking such as ruch hours parking scope percentage of booked parking etc we also plan on benefiting more from the cellular secsor to link data with the persons phone like certain access to private parks like disabled parking or home parking or private hotel offices parking etc

這項研究深入探討阿拉伯芥生理時鐘的轉錄調控機制，關注植物特有 GAGA 結合因子， BASIC PENTACYSTEINEs（BPCs）。通過監測 BPC 突變株和誘導株的葉片運動，及對 BPC 突變株生長缺陷的觀察，推測 BPC 於節律運動和葉形表徵扮演調控要角。藉數學建模和對突變與誘導株的 qRT-PCR 實驗，我揭示第一及第二類 BPC 在協調生物鐘節奏和葉片發育中的多種功能，更描述 BPC 內部調控網絡，了解這些蛋白質如何維持恆定。突變株實驗突顯 BPC 對關鍵時鐘成員 CCA1、ELF4、GI 和 PRR 家族的精確控制，而誘導株實驗則繞離 BPC 家族內部的補救途徑，從不同的尺度提供更直觀的檢驗方法。模擬進一步闡明 BPC 如何微調時鐘，確保振盪最佳化和晝夜間的無縫過渡。此外，我還發現 BPC1 和 BPC3 對第二類 TCP 基因的影響。他們抑制除 TCP5 外的多數 TCP 基因，透過不同下游途徑影響葉緣形態。概括而言，這項研究揭示了 BPC 家族是生理時鐘和葉片發育途徑的關鍵調控者。

Infections by the Dengue virus (DENV) cause a disease amonghumansreferred to as Dengue fever, which causes thousands of fatalities globally. There is no existing treatment as of yet that successfully targets DENV. Among the factors thatdeterminetheentry of the virus and severity of the disease is the envelope(E) protein of DENV. This study aimed to examine forty antiviral phytochemicals enumeratedinpaststudiesaspossibleinhibitorstotheEprotein of DENV to provide candidates to aid in drug discovery against DENV. The phytochemicals were screened for their likelihood of inhibition of the E protein using AutoDock Suite and LigPlot+. Seven phytochemicals produced favorable binding affinities to the E protein, which are based on the interactions between the phytochemicals and amino acidsintheactivesiteoftheEprotein.Lipinski’s rule of 5 was then used to screen the seven phytochemicals for oral bioavailability. Glabridin has a binding affinity of -7.6 kcal/mol and was predicted to be orally bioavailable. This phytochemical interacts with amino acids in the E protein active site through hydrogen bonds to Asn355, andPhe337, as well as ten hydrophobic interactions. These interactions ensure that glabridin is able to specifically target and fit intotheactivesiteoftheEprotein, preventing its binding to the host cell and activating its viral proliferation. Glabridin is known to be found in the roots of licorice plants, providing anatural source for a possible cure for Dengue fever.

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.

The DIVE&CLEAN project is an educational and innovative initiative aimed at addressing a significant environmental challenge: marine pollution. With oceans covering over 70% of the Earth’s surface and providing a home to 50–80% of life on the planet, their health is critical. However, marine ecosystems are under threat due to plastic pollution, which impacts wildlife, coastal communities, and global biodiversity. This project centers around the idea of introducing underwater trash bins, especially in areas frequented by recreational divers. While most divers explore the seas without specific tools to collect trash, they could contribute significantly with the right infrastructure. The vision of DIVE&CLEAN is to inspire behavioral change, encourage collaboration, and promote actionable solutions to reduce ocean pollution. Using interactive robotics and storytelling, the project tells the story of divers rescuing animals entangled in plastic and collecting trash from the ocean floor using underwater bins. Through creative performances, it seeks to educate and motivate individuals, resorts, and authorities to adopt sustainable practices.

自然界中，植物以NO₃⁻和NH4+作為主要氮源，在吸收後轉化為麩胺酸(Glu)和麩醯胺酸(Gln)作為第一產物進行基本生理反應，在我們實驗室先前的研究中，發現Gln會誘導阿拉伯芥側根生長、壓力反應和抗病性，所以提出了一種假說「細胞外的Gln是營養氮源，也是一種“危險訊號”」，藉由可能存在的Gln的受體表現。目前我進行了其中三組受體的測試，分別是wall-associated kinase2(WAK2)、wall-associated kinase3(WAK3)和EF-Tu受體(EFR)，WAK家族是穩定細胞壁果膠的受體激酶，然而我們實驗中發現WAK3在wak3 muntant的表現是不穩定的。EFR為接收EF-Tu(elongation factor thermal unstable)的模式辨識受體(PRR)，參與活化植物防禦及PAMP-triggered immunity (PTI)，efr muntant在Gln的誘導下表現了防禦相關基因與水楊酸生成之相關基因。本研究將有助於深入理解Gln在植物防禦和側根生長中的功能及其調控機制，並為未來的作物改良和病害防治提供理論基礎。

The DIVE&CLEAN project is an educational and innovative initiative aimed at addressing a significant environmental challenge: marine pollution. With oceans covering over 70% of the Earth’s surface and providing a home to 50–80% of life on the planet, their health is critical. However, marine ecosystems are under threat due to plastic pollution, which impacts wildlife, coastal communities, and global biodiversity. This project centers around the idea of introducing underwater trash bins, especially in areas frequented by recreational divers. While most divers explore the seas without specific tools to collect trash, they could contribute significantly with the right infrastructure. The vision of DIVE&CLEAN is to inspire behavioral change, encourage collaboration, and promote actionable solutions to reduce ocean pollution. Using interactive robotics and storytelling, the project tells the story of divers rescuing animals entangled in plastic and collecting trash from the ocean floor using underwater bins. Through creative performances, it seeks to educate and motivate individuals, resorts, and authorities to adopt sustainable practices.

表觀遺傳學(Epigenetics)是研究行為與環境因子如何對基因表現產生影響， 主要是藉由DNA甲基化、組蛋白修飾、非編碼核醣核酸來影響基因表現， Naa40p (N terminal-alpha-acetyltransferase 40 protein) 也稱為NatD、Patt1或Nat4 是一種組蛋白乙醯轉移酶，修飾組蛋白H2A及H4。在酵母菌的研究中，Naa40p 的缺失可以延長酵母菌的複製壽命(Molina-Serrano D., 2016)。在The Human Protein Altas資料中，可以看出人體中Naa40p在腦部有較高的表現。因此想了解Naa40p在小鼠海馬體神經細胞HT-22中具有什麼樣的功能。 藉由CRISPR基因編輯技術產生Naa40p剔除的突變株，進行細胞功能的檢測，在移動能力相關的傷口癒合測試中，Naa40p剔除的突變株癒合速度明顯快於野生型，期望能藉由更多細胞功能的檢測來更全面地了解Naa40p於神經細胞相關的功能與機制。