2024年

目前大部分電解產氫反應（HER）均使用貴金屬，如鉑和鈀，作為催化劑。而我們提出了更便宜的 FexNiyP 金屬磷化物用於經濟製氫。在催化劑的製備中採用不同的化學成分（x/y 比例）和合成條件（氧化溫度）。並將合成樣品通過掃描式電子顯微鏡（SEM）、能量色散 X射線光譜（EDS）和 X光繞射儀（XRD）進行了鑑定，以確認其形態、成分和晶體結構。再通過線性掃描伏安法（LSV）測試了它們的 HER催化效率。實驗結果發現，磷化程度強烈影響催化性能，且可以通過合成條件來適當調整，而 250° C是最佳氧化溫度。此外，電化學測試顯示，FeP 啟動反應所需之能量最低，具有最低的過電位(overpotential)；而 NiP 反應路徑最佳，具有最低的塔菲爾斜率(Tafel slope)。我們的結果解決了 HER的反應機構，並對氫燃料生產的發展提供了有用信息。

abcd–avoiding交替排列中的任⼀偶數項都要⼤於相鄰之奇數項，且其中任意四項皆不能有「abcd」的大小關係（「abcd」為 1 ~ 4 的⼀種排序），⽽偶數⾧度的 2341 和 3421–avoiding 交替排列皆為三維卡特蘭數的組合表徵。 本研究欲探討這兩種交替排列的組合關係以及可能的互相變換⽅法，我們發現兩種排列中「數字 1 在各項出現次數」有相同的分佈。我們推測可以透過移動數字 1 的位置在兩種排列中分別建⽴不同排列之間的對應的關係，並找到了兩種排列中部分的「數字 1 在第(2𝑘 − 1) 項」排列和全部的「數字 1 在第 (2𝑘 + 1) 項」排列互相變換的⽅法。利用這種排列關係，我們還證明了「數字 1 在第 (2𝑛 − 1) 項」的 2341 和 3421 – avoiding 交替排列具有一一對應的雙射變換法。

本研究源於 2022年數學雜誌《CruxMathematicorum》的一道四邊形動態幾何問題，我們先將此問題設定為三角形，利用綜合幾何方法給出了兩種構圖條件下的三角形外心軌跡皆為圓弧，並且發現兩種圓弧的變換關係以及豐富有趣的性質。值得一提的是，分別對三角形的三個頂點輪換進行第一種構圖得出三個圓弧，這些圓弧恰可組合成三角形的九點圓。回到原始問題的四邊形，我們構造了兩個三角形，透過巧妙轉換頂角與直徑圓變換而給出外心軌跡所在圓弧的兩個定點而解決此問題。 最後探討三角形的形心之軌跡為圓或橢圓的幾何結構是什麼？先考慮具有定角的形心切入，結果發現垂心的軌跡是橢圓，但內心與旁心的軌跡並非二次曲線。再從外心與垂心思考，我們進而給出了該軌跡的內在的幾何結構是歐拉線。值得注意的是，歐拉線上的任意點之軌跡恆為橢圓，並無拋物線或雙曲線。

本研究針對多人的跳躍數列在多顆球下的相關特例進行分析；多人跳躍數列規則為「同一個時間點任一人只會有一顆球回到手中」、「丟球期間需要連續、規律的接及丟出球並且無限持續下去」、「在多人丟球前可以有準備的時間」。 為了能呈現多人跳躍數列各個情況則用矩陣形式並採用有向圖進行討論，該圖的點元素代表當下每一顆球在幾秒中回到手中的狀態、邊元素則為每個狀態轉移時的丟球方式，接著將有向圖轉換為鄰接矩陣形式，並將點元素用類似 2進位的形式進行分類以便整理成規則一致的分塊矩陣，接著由 Cayley–Hamilton定理計算特徵方程式後，利用相關定理整理出各個特例分析的生成函數，如特定顆球同時回到手上的情況。

根據研究[1]指出：三角形磁磚邊之作用方式共有 5種，且共有 11種設計方法可在平面上密鋪。然而作者在解決問題的方法均是採用窮舉，方法不夠嚴謹。本研究運用不同的方法，透過代數計算證明了三角形磁磚共有 11種對稱密鋪圖結構；而 M.C.Escher在手作創作圖中只使用了其中 5種結構；在與前人的研究比較下，發現前人所歸納的 11種設計方法恰好對應到本研究中的 8種密鋪結構，而另外 3種結構是前人所未探討的磁磚內部變化方式。本研究也進一步推廣至相關立體圖形，如：正四面體、正八面體、正二十面體…等，並歸納出各種立體圖形可密鋪的種類數，透過適當軟體的支援下，可以快速且精確繪製出豐富有創意的圖樣。

Such as the plastic waste and industrial discharge that permeate our oceans, it is the insidious and infamous nature of oil spills that demands our immediate attention. These spills, with their far-reaching ecological ramifications, pose a profound danger to our marine ecosystems, demanding urgent action and a heightened awareness of the true menace that is caused by this oil

The Boycott Effect is a phenomenon where sedimentation rate can be increased by tilting the container which holds the suspension, making it a way to increase the efficiency of the process without additional energy input. This makes the Boycott Effect valuable in speeding up and optimising a multitude of industrial applications such as wastewater management and food processing, all of which employ sedimentation to separate particulate matter from the fluids in which they are suspended in. Thus, it is imperative to model the Boycott Effect accurately for a wide range of cases, including arbitrary shaped containers and suspensions of various concentrations without the need to run costly, computationally expensive numerical simulations. In this project I investigated the inclined sedimentation of suspensions both theoretically and experimentally. Experimentally, two image tracking programs were created and tested out on my own experimental videos. I demonstrated the use of a novel method for making use of the Beer-Lambert Law to optically keep track of local concentration of suspensions. This method allows more information to be gathered about the sedimentation process in a very low-cost, non-equipment intensive or invasive way. Theoretically, I expanded upon the well-known analytical 2D PNK theory by accounting for concentration-hindering and sediment build-up effects, as well as the geometrical theory for 3D cylindrical geometries. All parts of the theoretical model were verified with experimental data and shown to have good agreement. (233 words)

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.

As the world population grows, the demand of food products grows as well and there will be an expected food crisis in the coming years. To prevent those crises, alternative food farming methods must be used. This paper studied two farming systems in different conditions, to compare and find the best, natural and cost-effective system that will cover the current and future demand. The system which can also be used in those areas where soil is less cultivated with insufficient aeration. The first system is the soil-based system (traditional), and the other is hydroponic system. Hydroponic is a technique of growing plants in nutrient solutions with or without the use of an inert medium. Two types of seeds; peas and spinach were observed in both systems over a period of 25 days. In hydroponic plants coco peat was used in place of soil along with the Aegis nutrient. 8 plants were seeded for both types of plants in different systems, conditions, concentrations and pH to conclude the best condition. Growth parameters of all plants including root, shoot and leaf length were observed and recorded daily. On the uprooting, their weight (g), no. of root hairs and used nutrient’s volume(ml) were also recorded. Fungus and insects were seen in the soil plants. The results executed that the growth was maximum in spinach having normal manufacturer nutrient’s spray concentration(1.25ml/625ml) with pH 6 and in peas having normal supplier concentration (5ml/625ml) with pH 4. So, it can be concluded that hydroponic spinach, which is a green leafy plant, can ideally grow at the pH of 6 and peas in slightly acidic condition. Hydroponic planting system has a better growth effect than traditional soil system and this system don’t need any fertilizer, insecticide, pesticide, fungicide and herbicide. While soil plants’ growth was adversely affected by fungus and insects in the absence of these chemicals which can contaminate our food and make it less hygienic for our health. This result achieves the aim of this paper which is finding a planting system and its conditions that can increase the productivity to cover the food demand.