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.

台灣現行的「毀農式種電」政策犧牲農地以增進太陽能發電，導致農業用地縮減、農民收入減少，能源需求與農業發展間產生衝突。我們參考日本成功的農電共生模式，提出一種可滑動的太陽能發電系統，利用Arduino控制太陽能板的開合，兼顧農地種植與發電效能。此系統結合植物光合作用原理，特別適合種植半日照作物或具有光合午休特性的植物。當植物進行光合午休時，太陽能板滑動展開以提高發電量；在強光高溫時段，太陽能板則可遮蔽陽光，避免植物葉片受損。此方案不僅能恢復「毀農式種電」土地的種植功能，也讓農民獲得穩定收入，實現農業與綠能發展的平衡。這套模型提供具體且可行的解決方案，期望在提升台灣總發電量的同時，達成淨零減碳目標，並促進農業的永續發展。

光柵作為常見的分光元件，應用於許多光學儀器中。然而，傳統光柵彈性較差且硬度較高，限制了其應用範圍。本研究利用具有高彈性和易形變特性的 PDMS 作為柔性光柵的材料，對不同厚度和彎曲程度的光柵進行一系列測試。為了探討厚度和彎曲曲率對繞射效果的影響，進行了不同厚度柔性光柵的繞射點分析實驗。實驗結果顯示，增加柔性光柵的厚度會提升其彎曲時第一亮紋的變化率；相反，減少厚度則會降低該變化率。隨後的研究進一步探討不同施力方式是否會影響柔性光柵的分光效果。通過拉伸和壓縮光柵，發現拉伸會使光柵的軌距變大，而壓縮則會使軌距變小。此外，研究還探討了利用 PDMS 複製類似光柵的結構是否具有分光效果。實驗結果顯示，複製的指紋確實展現了類似特性，期望未來能夠將這些特性實際應用於相關領域。

This thesis presents the design and construction of a small-scale humanoid robot, covering all aspects from 3D modeling to electronics design and programming. The robot is built entirely from custom 3D-printed components, with a new servomotor developed specifically to meet the project’s requirements. During the robot’s development, custom electronics were also designed, leading to a modular platform that enables easy interaction with diverse modules like servomotors and inertial measurement unit (IMU) modules. This modular approach allows these components to be programmed and controlled with minimal adjustments, as well as making development of potential future modules straightforward. The robot is operated via a computer application that includes a graphical user interface for displaying real-time data from the robot.

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.

本研究採用創新設計的「水代法」處理養殖鰻魚加工後廢棄魚骨，成功解決過往鰻魚骨含油量高，無法利用而丟棄的環保問題，使生物資源得到充分利用。透過「低溫烘乾前處理」製成的鰻魚骨粉香氣與口感俱佳，適合作為食品添加物。 水代法是將鰻魚骨在90℃水溫、粉水比1：3狀態，藉由攪拌、壓榨去油，不僅保留營養成分（蛋白質、鈣質、磷質），同時降低高達90%的脂肪含量。水代產生的處理液可進一步開發為胺基酸萃取物和鰻魚油，創造多元的商業價值。「食鹽水浸泡處理」取代較不環保的「強鹼處理」製作鰻骨鈣粉，可有效減少環境負擔。本研究製程簡便且低耗能、低耗水，可降低成本，顯著提升產業競爭力和環境效益。

本研究以 Minecraft 為例，探討沙盒類遊戲式學習平台系統伺服器架設的節能效率，旨在透過動態調整伺服器數量降低總CPU使用率，提升伺服器的管理效能和能源使用效率。隨著線上遊戲的普及，伺服器的營運管理變得越來越複雜，如何在滿足玩家需求並同時降低能源消耗成為一個重要議題。本研究將分析伺服器資源使用狀況，特別是在玩家活動量高低波動的情境下，透過管理策略的調整，探討其對節能效率的影響。 研究透過實證數據的收集與回歸分析，建立一套可應用於 Minecraft 伺服器的節能動態調整系統，並探討動態調整的具體效率。研究結果發現隨著玩家人數增加，越接近系統負載上限，節能效果會越來越不明顯，以本次研究的伺服器來講玩家人數到達35人以後就無法再減少伺服器數量。

Increasing energy needs alongside the urgent issues of chemical pollution has prompted the need for developing novel green energy sources. Nitrogen-based fertilizers are of fundamental importance for the ecosystem as their usage has increased eight times in the last fifty years [1]. On the other hand , increased use of nitrogenous fertilizers is followed by higher ammonia emissions, which are dangerous pollutants responsible for deterioration in biodiversity by means of eutrophication, acidification of soil and water, and climate change [2]. Ammonia has the2apacityy to bond with other pollutants including sulfur oxides and nitrogen oxides to create particles that cause smog, which is associated with lung disease. Ammonia also increases frost sensitivities and causes necrosis of many plant species [3.] Therefore, there is a need to properly manage the ammonia-rich nitrogen waste to decrease the environmental threat factors. Of the possible approaches suggested for ammonia waste treatment, the ammonia electro-oxidation reaction (eAOR) has various promising features for application in the energy sector. It is economically appealing because Ammonia can serve as an excellent hydrogen carrier due to its storage capabilities and existing transport infrastructure alongside having no net carbon emissions. Apart from this, it requires 95% less of the theoretical energy [4] to perform the process. But the reaction is kinetically slow [5], which has been a research obstacle during the development of (eAOR), due to factors ofmslow reaction rate and large catalytic overpotential that this process consumes an unnecessary amount of power [6]. Nickel-based catalysts are a promising solution to these problems, they are cheaper , more stable and easier to produce than electrocatalysts for water electrolysis which makes it highly energy efficient for widespread use on the industrial scale. N films deposited on the anodic side also allow the creation of N-containing products such as (NH42SO3) and nitrates, which can be converted into fertilizers or renewed into the nitrogen cycle to make the process more environmentally friendly while enhancing the (eAOR) process [7,8]. Compared to Pt and Ir which are the most used noble metals, they are less poisoned on the potentials less than 0.65V and are more stable [9,10]. However , noble metals are scarce, and their cost is high for industrial applications as well as the energy they waste during (eAOR) [11].

Climate changes that include ocean acidification and global warming are serious problems in the ecosystem, affecting marine phytoplankton, including Nannochloropsis oceanica. In the effort to further explore the impact of rising temperature and carbon dioxide (CO₂) concentrations on oceanic ecosystems, the phytoplankton Nannochloropsis oceanica was used as a model organism. This study explored the effect of temperature change and CO₂ concentration on the growth of Nannochloropsis oceanica, achieving 243 samples that were tested with three different temperatures (24 degrees Celsius (°C), 28°C, 32°C) and CO₂ concentrations (0 milliliter (ml)/min, 0.4 ml/min, 0.6 ml/min), utilizing a hemocytometer counting method. Results indicate that the CO₂ concentration has a significant effect on the population of Nannochloropsis oceanica. But the temperature doesn't affect a lot. The Nannochloropsis oceanica in the lowest temperature and highest concentration of CO₂ in its environment had the highest population growth, and in the highest temperature and lowest concentration of CO₂, it had the lowest population growth. Results show the serious negative effect of climate change on the cosystem and the importance of environmental protection. Population blooms due to excess CO₂ taking up ocean resources causing dangerous ecological imbalances.

禽畜糞堆肥常伴隨氨氣排放而有異味問題。目前成本低、培養易的木黴菌已廣泛用在堆肥中來加速發酵。此外，部分業者會將含氨臭的氣體蒐集再以稀硫酸水洗，產物硫酸銨可作為氮肥，但多被排棄。本研究結合木黴菌添加與排氣稀硫酸水洗，可縮短堆肥期程，更將氨氣肥料化，以 (1)木黴菌合適添加劑量、(2)稀硫酸水洗參數等二項為試驗主軸。結果顯示：(1)添加2/100木黴菌可使堆肥成品中總氮增加13%，減少氨排放；(2)含氨排氣經pH6-7稀硫酸水洗，98%的氨氣轉化成含約1,400mg/L之硫酸銨溶液，氮含量為300mg/L，相當於沼渣沼液農地施灌水準。

色彩偏好影響生活的許多決策，對於背景對色彩偏好的影響，現行兩個色覺理論(對比理論與生態價理論)有不同的解釋，本研究以高中生為對象，旨在探討背景對色彩偏好影響與支持理論，並提出運用方向。 之前色彩定量方式缺乏對敏感度與視錐細胞的考量，本研究發展以中性灰為基礎對不同色彩的定量方法，並以此進行色彩偏好測試。實驗結果發現：顏色偏好會受到背景影響(支持對比理論)，背景對各色彩具不同影響力，偏黃偏綠顏色受背景影響較大；綠色與藍色背景提升偏黃與偏綠之顏色偏好而紅色背景則會下降(支持生態價理論)，背景亮度不影響顏色偏好。期望研究結果有助於青少年環境與產品設計配色參考，並對未來背景影響顏色的神經機制研究提供基礎。

本研究專題利用混沌電路所產生的信號來實現混沌雷達偵測物體的距離，在實作上面，使用運算放大器、電阻、電感及電容來實現蔡氏電路，並證明可用其混沌狀態發生的紊亂振盪來產生混沌雷達所需的信號，其產生的電壓信號，經由數位儲存示波器取出資料再加上軟體MATLAB的資料處理及信號分析，並使用了類神經網路中的循環神經網路，嘗試回復電路的設計參數，可證實蔡氏電路所產生的混沌信號，用於雷達信號的偵測不容易被破解、干擾且具有高度的安全性，未來極具發展潛力。