2025年

本文研究了一個信息完全公開的組合遊戲，探討當一群人被完全隨機的分配到模型裡時，其初始位置與特定位置所形成的包圍關係，並探討最佳的人力分配。本研究通過座標解析與不等關係的代數運算等方法，成功找出獲勝條件對於遊戲雙方的限制，並進一步解決問題。在研究的過程中，也將結論擴展到不同模型，探討不同模型對於遊戲造成的影響，並比較其結論有何區別。

本研究探討在一場圓桌會議中，n人逐一亂序入場找尋各自對應的名牌編號(1~n號)入座，其中1號第一個入場並坐到了k號位，此後入場的人們若發現與自己編號相同的位置是空的，就直接入座；若與自己編號相同的位置被占走了，就以逆時針方向尋找空位入座。在上述的規則下，若共有n 人，且 1 號坐到 k號位的情況，給予與問題相關統計量的組合證明。後續本研究將規則改為1 ~ p號 按照順序進場且皆想坐到 k 號位的前提下，探討了坐錯的人們是怎麼樣的循環和坐錯人數的次數分佈。並多數的研究結果皆與 stirling numbers of the first kind 有相關。 本研究還 探討了共有 n 人，且 1 號坐到 k號位的情況下， 坐錯人數的標準差函數的遞增情況 與對數函數完全曲線相關。

MAGALH˜AES, Eduardo De Mˆonaco. PiezoPioggia: Energy Harvesting with Raindrops. 2024. 24 p. Research report – Scientific Apprentice Program, Col´egio Dante Alighieri, S˜ao Paulo, 2024. This project wishes to study and analyze the possibility of generating clean and accessible energy with the plain impact of droplets in the ground. Therefore, it was necessary to use piezoelectric devices in order to convert the kinetic energy of each droplet into electric energy throughout piezoelectric energy harvesting processes, (PEH). Piezoelectricity is a method of clean and sustainable energy generation, developed and explored by several scientists worldwide. Thus, while studying the proprieties of those devices, the project evaluates the present situation of electricity harvesting in Brazil, the benefits of piezoelectric technology and the possibilities it presents to economy and society. Throughout the development the project builds itself upon mathematical equations and experimental results, analyzing the deformation and generated tensions of piezos. Brand new data on the behavior of rain, as well as about the potential it presents for PEH are highlighted throughout the research, reinforcing the value of such process as a sustainable energy generation method alongside with its investment potential, both from governmental and private institutions. The project also deeply characterizes the piezoelectric device studied, diving deeply in its characteristics and evaluating the deformation of the device and treating the data sets with statistical analysis methods, in order to improve the precision of the data presented. All in all, the opportunities of piezoelectric energy harvesting in the rain, nella pioggia, shall be discussed profoundly throughout the project.

This study dives into the benefits of a heart rate (HR) monitoring application to aid families in identifying mood changes in children diagnosed with neurodivergence. Children with neurodivergence often struggle with communicating their emotions, which often results in tantrums or emotional outbursts, and this study plans to address this by creating an app that detects users’ HR to calculate heart rate variability (HRV) and detect when the user’s heart rate variability (HRV) levels become higher than usual. Heart-rate variability is defined as a small variation of the interval between every heartbeat, it’s calculated with the formula of . By looking at the developments of these small variations, it will be 60/𝐵𝑃𝑀 × 1000 easier to notice then the interval for heartbeats are shorter, meaning the body is in need of more blood pumped quickly for support. The app is connected to a heart rate sensor that is worn by the user. The heart-rate sensor frequently uploads data to the app which the app processes and carefully observes while looking for any sudden, dramatic change. The sensor and app was tested and proved to meet the expected requirements of functionality. Four participants with neurodivergence were asked to equip the heart-rate sensor and results showed that different developments of heart-rate variability were able to be detected by the app, these participants varied in their type of neurodivergence as well as their age. As an example, the third participant showed the purpose of the app most visibly, having a resting heart-rate of 86 BPM (697.67 ms) turning into a high 107 BPM (561.68ms) after changing activities. When the user’s sensor detects a sudden spike in heart-rate variability, the app notified the parent account about this change in emotion. This study has supported the relevance of using heart-rate variability to observe changes in mood.

On average, the agricultural sector uses 70% of water withdrawals worldwide to produce crops1 and contributes to the eutrophication of lakes by using nutrients that are leached from the soils into lakes and reservoirs2. Vertical farming has great potential to remedy some of these issues. By growing plants vertically in controlled environments with artificial light and reusing the water, vertical farms use op to 99% less water3 and can produce up to 10 times the yield per square meter4 compared to traditional greenhouses. This improved efficiency comes at a cost; on average, vertical farms use more than 600% more energy per kilogramme of crop compared to traditional greenhouses5. 55% of this energy use is due to the use of artificial lighting6. Even though a lot of research is conducted on yield optimisation of crops in vertical farming, few research articles focus on the growth efficiency of crops to reduce the energy use in vertical farms. Only a few previous studies have tested photoperiods under 10 h·d-1. This study focuses on reducing the energy costs of light use in vertical farms by finding the photoperiod with highest energy use efficiency for the leafy vegetable arugula (eruca sativa). Energy use efficiency is defined as fresh mass per unit of electricity input (measured in kWh). In this study, arugula plants were exposed to LED growth light, with photoperiods ranging from 0 h·d-1 to 24 h·d-1 (0 h·d-1, 4 h·d-1, 7 h·d-1, 9 h·d-1, 12 h·d-1, 14 h·d-1, 16 h·d-1 and 24 h·d-1) and a PPFD of 800 μmol·m-2·s-1. The photoperiod 7 h·d-1 had the highest energy use efficiency of all photoperiods and, if used in vertical farms, this could account for approximately a 10 percent decrease in energy per kilogramme used in vertical farms (a 4 kWh decrease), with the planting density of 1400 plants per m2. This could amount to a yearly energy saving of 4,000,000 kWh per vertical farm (based on the yearly harvest of the vertical farm Nordic Harvest). This could help make vertical farming a more sustainable plant production for the future and in turn, help farming protect our water resources instead of consuming and polluting.

海洋中有許多重金屬汙染，其中汞元素因為濃度低很容易被忽略，但卻容易經由飲食進入人體，造成嚴重傷害。也因其濃度低不易被測量，現今也少有海洋中汞汙染的完整資料。然而，在生物體中汞濃度會因生物累積及放大作用而較海水的濃度來得高，故本研究利用魚體汞累積速率（MAR）當作追蹤海洋污染之生物指摽，此方法將魚體總汞濃度除以年齡得到的汞累積速率，以去除生長時間的影響因素。 本研究利用習性不常移動之底棲魚種之MAR，分析與生物放大作用相關的掠食階級（Trophic Levels）之相關趨勢，經過篩選，研究分析了31篇過去於大西洋、太平洋及地中海採樣的文獻，將其中資料整理成趨勢圖，比較各區域汙染程度，發現各區的汙染程度呈現差異，同時提供觀測區域海汞汙染的新方法。

本研究利用Slow Earthquake Database長微震資料探討日本南海海槽長微震事件發生的特性、嘗試找出造成此區長微震發生的原因。我們將日本西南部的四國島、紀伊半島、愛知縣依空間細分為八個小區，分區將長微震的資料繪製成圖表，並利用快速傅立葉轉換Fast Fourier Transform進行頻譜分析，尋找該區長微震的活躍程度及復發週期，復發週期為一季至一年不等。另外，我們也將環境參數與長微震的月平均發震時長做比較，發現兩地皆與風速呈負相關、和累積雨量推遲1～2個月後兩者間成正相關、和地下水位高度呈負相關。潮汐與長微震的相關性上，潮位高度的影響較漲退潮狀態顯著， 但兩者均對長微震的發生有著正相關。

臺灣北部海岸富貴角地區的風稜石母岩為兩輝安山岩，經過風化、風蝕及海蝕而形成目前獨特之外觀。這些岩石源自火山噴發形成的熔岩流，岩漿冷卻形成熔岩塔，裂解後受外營力作用逐漸成形。不同地理位置的風稜石受侵蝕的影響差異顯著：海岸邊的風稜石同時受到海浪和風的影響，外型較圓鈍；陸地部分則因受到海蝕影響較小，外型較為尖銳。另外，本研究利用噴砂實驗進一步驗證不同風速和風向對風稜石生成過程的影響，並分析其形態差異及地質學意義。

團隊透過分析臺灣台灣周遭八個處海洋浮標測站資料，自2021年1月到2024年10月為止之示性波高、平均週期、平均風速、海溫等資料間之相關性，並試從不同位置測站之海洋條件與大氣因素，來綜合探討影響臺灣周遭海域波浪能蘊藏量的關鍵因素。並透過分析海溫與波浪能變化的關係，試圖瞭解全球暖化平均海溫上升，對臺灣周遭波浪能蘊藏的變化趨勢。 團隊發現影響臺灣周遭海域波浪能蘊藏的因素，除了季節性季風的影響，黑潮主流以及澎湖水道的黑潮支流湧升流，也都 可能 是影響臺灣周遭海域波浪能蘊藏的重要因素。團隊也發現，在臺灣周遭海域波浪能蘊藏與海溫變化有負相關的趨勢，此現象與臺灣中央研究院針對過去70年，全球波浪能的變化趨勢並不一致。其原因可能是臺灣所屬地理位置環境的關係，也可能是分析的數據資料僅有4年無法準確看出趨勢變化。

全球約有9千萬的兒童是視障者，他們的學習依賴著點字器材。點字書難以傳達3D (三維)圖形的概念，讓他們在理解3D圖形有許多挑戰，而點字書過長的文字描述加大了他們與正常同儕之間的差距。本研究旨在開發一個學習輔助平臺，同時強化視障者的觸覺認知和文字圖形理解能力。 在強化觸覺認知方面，開發之系統能將傳統的圖片，利用影像轉3D之人工智慧建模(Image-to-3D AI model)技術，轉換圖片轉為3D，呈現在開發的擴增實境顯示器上，讓視障者能夠親身透過觸摸立體顯示器之3D模型，瞭解圖片表達的空間結構。在文字優化方面，利用微調大型語言模型與搜索式強化生成等方法，優化視障者閱讀之內容。系統開發過程中，二位視障者進行體驗，持續以修正系統設計的便利性、友善性與有效性。 本研究成果為視障者帶來新式個人化的學習輔助工具，增強視障者對立體圖形學習能力與文字理解。