2025年

Due to widespread water shortages, there is an increasing need for innovative water conservation strategies, such as reusing greywater from laundry. The World Health Organization (WHO) recognizes greywater as suitable for plant irrigation, but commercial laundry detergents contain synthetic chemicals that can harm both the environment and plant health. Soap nuts, derived from the Sapindus mukorossi tree, offer a natural alternative. Their pericarp is rich in triterpenoid saponins, amphiphilic compounds, composed of hydrophilic sugar group and hydrophobic triterpenoid sapogenins. These saponins mimic the chemical structure of surfactants in detergents, allowing soap nuts to act as natural foaming and surface-active agents in water. As a result, soap nuts have long been used as a sustainable option for shampoo and laundry detergent in many Asian countries (Sochacki & Vogt, 2022). Greywater, an often overlooked resource, is generated from household activities like laundry, showers, and basins. Unlike blackwater, it contains lower levels of pathogens and bacteria. However, due to a lack of awareness, greywater is frequently mixed with blackwater and directed to the same sewage treatment systems (Greywater Systems: From Recycling to Filtration, n.d.). Greywater accounts for 50-80% of a household’s daily wastewater (Wong, 2011). Repurposing greywater offers a promising and sustainable solution to address water conservation challenges.

Energy has had an enormous impact on the development of technology and is a main factor in humans’ advancement towards an evolved society. Nevertheless, nonrenewable energy resources – which are the most effective in everyday application - have led to changes in the climate, environment, human health, and the world in general [1], which has encouraged researchers to switch to the use of renewable energy sources. Solar Cells are one of the most effective resources that rely on renewable energy. They come in a variety of types, operation methods, and efficiency as shown in Figure 1, including Dye-Sensitized Solar Cells (DSSC), which, inspired by photosynthesis in plants, uses photo-sensitive dye to capture sunlight and generate electricity. DSSCs were proved to have generated a great deal of interest and are one of the most promising solar cells among third-generation PV technologies, due to their low cost, simple preparation, good performance, and environmental friendliness compared to conventional photovoltaic devices [3]. However, their efficiency is quite insufficient for everyday use. Previous studies proved that Tandem DSSCs – which are two dye-sensitized cells stacked on top of each other – are able to enhance cell performance. The light absorption range of a tandem cell is increased because the bottom cell behind the top one absorbs and uses the incident light that was not absorbed by it [4]. It operates as shown in Figure 2, where the light photons excite the electrons of the dye molecules. The electrons are then transported to the FTO (conductive glass) by the semiconductor, which is used in the figure as TiO2 nanoparticles. The electrons pass through the circuit to perform the work, then move to the counter electrode (shown as Platinum). They are then transported by the electrolyte (I-/I3-) back to the dye molecules, and the process is repeated.

本研究從2022年APMO第五題的代數題目出發，題目為a1,a2,a3,a4∈ℝ，(4∑k=1)ak2=1，試求出(a4-a1)(3∏k=1)(ak-ak+1)的最小值。我們希望將原問題的四個未知數，希望推廣到n個未知數的通解。我們首先用算幾不等式及其他幾何性質算出了n=2~4的解，其中包括了偏微分求切平面的方法。在研究n的未知數的通解時，我們利用實數的完備性說明最小值一定存在，接著我們利用舉例以及反證法，發現到n個未知數時其最小值會小於0，以及最小值成立時各項相加會等於0，我們運用這些特別的性質，並且使用了各種不等式得出n=2(mod4)的通解。最後我們用拉格朗日乘數可以求出n=k(mod2k)的局部最小值，還有部分相加與相減的關聯性，未來希望能求出絕對的最小值和最大值。

本研究開發一種新穎孔洞性吸附材料：金屬有機骨架 (MOF)。MOF 在反應溶液中自組裝形成孔洞結構，透過物理吸附有效捕捉氣相乙酸分子。研發出綠色、快速可在常溫常壓下大量合成三種MOF（HKUST-1(Cu)、UTSA-280(Ca) 及 A520(Al)）方法。此外，為提升材料機械強度和應用價值，採用 PVA 聚合技術製備 MOF 複合物，使其造粒型化更易處理，提升商業和環境應用價值。吸附實驗結果顯示，HKUST-1(Cu) 粉末對乙酸移除率高達98%，而HKUST-1(Cu) PVA 複合物達93%，對比活性碳及其PVA複合物（移除率分別為85%和78%）表現更優異。MOF憑藉優異吸附性能和可大量生產低成本優勢，成為極具潛力有機無機氣體吸附劑，可為半導體產業提供一種維持高標準製程環境精密且簡便解決方案。

本研究從濕地篩選出可能為新種的耐鹽菌Oceanobacillus sp.，暫命名為OC2，其在無植物相伴狀態下不會降低土壤含鹽量，但卻在與植物共存後誘發特殊機轉，促使土壤含鹽量降低約，並提升植物耐鹽能力，顯示 OC2與植物存在特殊交互作用。深入研究發現，OC2能產生IAA，並吸引植物根部向其生長以利其進入根部，並在鹽逆境下分泌代謝物以刺激植物合成脯胺酸 (增加達98.5%)提升根部滲透壓、增加葉片類胡蘿蔔素及類黃酮含量以提升植物抗氧化力。植物方面，鹽逆境下植物分泌的化學物質會觸發OC2產生更多的IAA(約17%)，藉以刺激植物根系發展以利水分吸收，而OC2的存在會促進根部澱粉酶活性上升達88%，以分解澱粉產生可溶性醣類供OC2使用，推測兩者存在共生關係。本研究展示新種耐鹽菌與植物的交互作用，期待透過此菌改善鹽化農地並能提升作物產量。

氣候變遷加劇了蚊媒疾病對全球公共衛生的威脅，迫切需要創新的解決方案。在台灣，登革熱的傳播主要由蚊蟲滋生所致。為了解決此問題，我們設計了一款三層結構的3D 列印誘蚊器，包括吸引懷孕雌蚊產卵的誘餌層、捕捉蚊蟲的黏膠層，以及防止異物進入的保護層。該裝置成本低、易製作且不需要外部電力，特別適合在資源有限的地區部署。 我們結合校園監測站每日捕捉的蚊蟲數據與氣象站提供的溫度、濕度和降雨等環境數據，運用SARIMA 與隨機森林混合模型進行分析與預測。SARIMA模型負責捕捉蚊蟲數量的季節性與長期趨勢，而隨機森林模型則處理環境變數與蚊蟲密度之間的非線性關係。此混合模型不僅提高了預測精度，還能解析蚊蟲的生態模式，進一步指導誘蚊器的最佳配置。此外，我們還開發了紅外線感測系統，即時偵測蚊蟲活動，為監測提供精準數據。 為評估氣候變遷的影響，我們模擬了不同全球暖化情境下的蚊蟲密度變化趨勢。結果顯示，隨著溫度上升，蚊蟲密度呈現非線性收斂趨勢，但正相關性依然存在，強調了氣候變遷可能帶來的潛在危害。我們還開發了一個網站，用於即時呈現蚊蟲密度預測，幫助政策制定者和公共衛生機構有效應對疾病防控挑戰。 本研究與聯合國永續發展目標（SDGs）中的SDG3（良好健康與福祉）及SDG13（氣候行動）高度契合，展示了結合3D列印、機器學習、即時感測和網路技術應對蚊媒疾病的創新潛力。此系統提供了一個可持續的全球蚊蟲控制模型，為公共衛生、疾病預防及流行病學的未來創新奠定了堅實基礎。

Impostor Syndrome, a psychological phenomenon where individuals doubt their abilities despite evident achievements, can hinder personal and academic development. This study aims to evaluate the effectiveness of the interactive journal “I am Great Because of Me”, integrated with artificial intelligence (AI), in addressing Impostor Syndrome among high-performing students. The journal features innovative tools such as the Clance Impostor Phenomenon Scale (CIPS) test accessible via QR code, self-acknowledgement pages, and virtual consultations powered by AI chatbots. These elements aim to support self-reflection, provide real-time diagnostics, and deliver actionable recommendations for users. The ADDIE model was employed for the journal's development, incorporating feedback from experts and users. Likert scales and Cohen’s D analysis were used to evaluate satisfaction, usability, and impact. Results showed that 90.1% of students expressed high satisfaction with the journal’s accessibility, interactivity, and capacity to enhance self-awareness and motivation. A pre-test and post-test conducted on the intervention group revealed a significant reduction in Impostor Syndrome by 42.5%, with an effect size of 2.84, categorized as "very large." Features such as the self-acknowledgement worksheets helped students recognize their strengths, while AI consultations offered additional psychological support. Expert validation emphasized the journal’s clarity, relevance, and objectivity, noting the absence of bias in AI-driven suggestions. The journal was praised for its accurate content, ease of use, interactivity, and the protection of user data, ensuring a safe and private environment for self-development. Students found the journal beneficial not only for addressing Impostor Syndrome but also for fostering personal growth and self-confidence. This research demonstrates the potential of combining psychological theories with AI-driven tools in education. The journal “I am Great Because of Me” effectively aids students in overcoming Impostor Syndrome and improving self-perception. It serves as a scalable solution for schools and individuals aiming to tackle similar psychological challenges. Future studies are encouraged to explore its application in broader contexts to maximize its impact.

本研究運用綠藻、螺旋藻、卡拉膠（k,i,λ）進行製備碳點並應用高效超級電容。本實驗已完成綠藻、螺旋藻、卡拉膠（ k,i,λ）在不同的pH值中的溶解度測試，並找出綠藻、螺旋藻、卡拉膠（k,i,λ）各自適合溶解的溫度及溶液。此外，中途也已透過文獻中的實驗證實我們實驗中所運用的電化學實驗設計及裝置可以成功製備出碳點。而在電化學製備碳點的部分目前完成單獨藻類、藻類加histidne的電擊實驗以及測其吸收光譜，也運用先前製備出較穩定的碳點加入MXene進行電化學分析，透過碳點擴大MXene分層，以達到增加MXene電化學效能的效果。最後，預計之後將進行更多的電化學分析，進一步地確認碳點結合MXene能在超級電容的應用。

This research presents a novel approach to understanding the curling and uncurling behavior of tracing paper when exposed to water, identifying limitations in traditional diffusion-based models like Fick’s second law. While Fick's model adequately represents the uncurling phase, where water content is stable, it falls short during the curling phase due to its inability to account for dynamic changes in diffusivity. Our study identifies capillary action, modeled through Richards' equation, as the primary mechanism in the curling phase, where diffusivity varies with water content due to capillary-driven water movement through the paper's porous structure. Experimental data align well with the Richards' equation model, highlighting a saturation point where curvature peaks, governed by evaporation's impact on moisture balance. To simulate this phenomenon, we developed a finite difference approximation scheme based on Richards' equation, discretizing the spatial domain for detailed control over moisture dynamics and incorporating the Robin boundary condition with virtual points. This approach, combined with evaporation considerations, produces simulation results consistent with observed data, emphasizing evaporation’s role in steady-state moisture gradients and the subsequent deformation mechanics. Our findings further reveal that factors like paper thickness, temperature, and salt concentration significantly influence curling behavior. We established linear correlations between peak time and thickness reciprocal, as well as between peak curvature and thickness squared, supporting theoretical models. Temperature affects both peak curvature and curling rate due to changes in viscosity and surface tension, and higher temperatures prevent full uncurling due to sustained evaporation effects. Increased salt concentration heightens peak curvature without altering expansion ratio, suggesting additional variables in play.

本研究以空氣為催化劑，降低KOH在水中解離成K+及OH- 的解離能，大幅提升KOH在水中解離的效率，配合以鋁板為電極，還原H2O及OH-，釋出氫氣H2。這還原反應過程同時輸出K+及H2為電力能源。利用解離出的K+組裝成鉀離子電池，同時以解離出的氫氣運作燃料電池，組成雙輸出埠電力裝置。本雙輸出埠電力裝置，可以分別利用KOH濃度及或空氣輸入量，來調控輸出功率。KOH濃度增加或空氣輸入量增加，均可提高兩輸出埠的功率。測試時採用KOH濃度為5M，輸出電壓達0.19 mV，電流達0.166 mA。採用摻雜0.3%鉍的鋁為電極板，提升輸出電壓達0.67 mV，電流達0.199 mA。在鉀離子電池2MKOH水溶液中串聯4組電極板，電壓提升至2.9 V，電流達5A，並能成功點亮LED燈及驅動市售燃料電池。再經電路板穩壓後，電壓從2.9 V提升至5 V，適合USB充電，顯示出其作為無碳排放電力能源。