2025年

工業環境中揮發性有機化合物(VOCs)的洩漏不僅危害人體健康，更可能導致工安事故。現有氣體感測器常存在選擇性低、反應時間長等限制。本研究開發高選擇性與快速反應的奈米材料導電式氣體感測器，以實現即時監測。 研究中合成並測試六種銀奈米 (Ag-MPC)材料：Ag@C6、Ag@C12、Ag@C16、Ag@MCP、Ag@C12/MCP及Ag@C12/MBT複合材料。在500-5000 ppm濃度範圍內偵測1-丁醇、正辛烷及間二甲苯等目標氣體的電阻變化。實驗結果顯示，Ag@C12經官能基修飾後，對1-丁醇具有明顯的選擇性。我們開發基於Arduino微控制器的即時監測系統，透過運算放大器電路實現高精度的電阻變化檢測。可以在工業環境中持續監測VOCs濃度並即時示警。未來將著重於優化訊號放大電路、開發新型官能基修飾材料、實現複雜氣體混合物的組分分析。開發成本低、反應快、選擇性好的感測系統，為工業安全監測領域提供實際應用價值。

在這篇作品中，主要研究Repunit數列=在模n之下的餘數數列循環性質。我們探討了Repunit餘數數列在什麼條件下 為純循環週期數列、混循環週期數列和完全純循環週期數列，同時給出了循環週期的公式及上界。接著我們發現一階非齊次線性遞迴數列在模n之下的循環週期與c進制Repunit數列在模 n/gcd(n,c)之下的循環週期相同，並且進一步探討餘數數列在什麼條件下為純循環數列、混循環循環數列和完全純循環數列。

隨著網路技術不斷的進步，意見和情感分析逐漸成為人們日常生活中的一部分。儘管如此，目前人們缺乏一個方便且快速的情緒分析模型，供廣大大眾使用。 本研究旨在提供人們一個緩解憂鬱情緒的管道——當人們輸入一個需要被安慰的情境時，我們的系統將輸出安慰語句，以緩解該使用者之憂鬱情緒，達到安慰效果。為此，本研究訓練了BERT model以及 LLaMA model。BERT model能判斷使用者輸入的語句是否為需安慰語句。而LLaMA model則作為安慰語句之生成模型，以達到安慰之效果。

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.

本研究欲利用機器學習演算法，透過觀察重力波訊號來判斷黑洞融合訊號的時間。本研究 的數據來源於雷射干涉引力波天文台的開放資料庫，我從中獲取最被廣為認定的64筆原始數據，並生成具有不同黑洞質量與不同訊噪比的模擬信號。我將模擬信號與不同噪聲混合 後，進行強度調整、Q轉換和資料白化等數據處理，並提取資料的統計量，將其用於訓練三種決策樹演算法和兩種迴歸演算法中。最終研究結果顯示，決策樹演算法的判斷能力優於迴歸演算法，以及指出強度差值的標準差是最關鍵的特徵，重要性達全體特徵的27%。 我們的模型在重力波訊號判斷上表現出較高的效率，並成功降低了模型的複雜度，使其更適合實際應用。

本研究先觀察著名的密克定理（Miquel theorem）與密克點（Miquel point），我們創新給出了新的研究項目，關注密克點𝑃與密克三角形的頂點所構成直線和原三角形𝐴𝐵𝐶三邊直線的其餘六個交點，這是前人沒有觸及的研究項目，從而定義旁接三角形與衍伸三角形。 我們先針對特殊型（直角）的構圖，發現滿足兩個衍伸三角形的有向面積 [𝐴1𝐵1𝐶1]=±[𝐴2𝐵2𝐶2] 時，𝑃 點形成的軌跡為原三角形的 Kiepert hyperbola 與外接圓，這個是有趣且重要發現，我們也進一步給出其幾何必然性。進一步考慮 [𝐴1𝐵1𝐶1]=𝑟[𝐴2𝐵2𝐶2] 時，則刻劃出 𝑃 點軌跡為圓錐曲線系。在前面的基礎下，再針對一般型（任意角）的構圖，若 𝑃 點位於原三角形外接圓及Kiepert hyperbola 與 Steiner circumellipse 的線性組合曲線上，此時兩個衍伸三角形 𝐴1𝐵1𝐶1 與 𝐴2𝐵2𝐶2 的有向面積比值為定值，且兩者恆為相反數。

本研究中，我們對模型逆向攻擊在語音辨識系統中的影響及風險進行深入分析。隨著Siri、Google Home等智能助理設備在日常生活中的廣泛使用，其語者辨識系統的安全隱患引起了我們的注意。本研究目的在於深入理解模型逆向攻擊的運作機制，並探討其對語音辨識系統的攻擊效果。我們透過實施多樣化的攻擊策略，對不同的模型架構和數據處理方法進行了評估，並對人聲與非人聲的數據集進行了攻擊效果的比較。此外，我們亦實現了基於差分隱私的防禦算法，在多數模型架構下達到接近50%的防禦效果，顯著提高攻擊代價。研究整體揭示了語音辨識系統在面對模型逆向攻擊時的脆弱性，並藉由實驗分析推論出可能的防禦策略，期待能通過策略來增強模型的安全性。

我們是探討磁星的短X射線爆發(Short X-ray burst)。利用RXTE太空望遠鏡觀測磁星1E2259+586的數據，經由Bayesian block方法對光變曲線篩選找出爆發，並配合「波松分佈」與「虛無假設」找出50筆爆發事件(爆發的正確性有5σ的信心水準)。再利用HDBSCAN非監督式學習演算法來對短X射線爆發進行分群，找出此磁星有「短暫且高能爆發、中等持續與能量爆發、較長持續且溫和爆發、快速且低能爆發」現象，暗示了磁星爆發的多樣性並有不同的爆發機制。此外我們也發現磁星可能有「週期性」的現象，也許是自轉週期、地殼受的應力或磁場變化經過同樣時間累積(有週期性)而爆發。我們也比對有快速電波爆發 (Fast radio burst, FRB)的磁星SGR 1935+2154，看是否1E2259+586有FRB現象，結果暗示1E2259+586可能沒有FRB現象。

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.

「在格狀平面中用矩形以互不重疊的方式鋪滿(2D rectangle tiling problem)」為一NP-complete問題(Dani`ele Beauquier et al ,1995)，目前多項式時間只能求出盡可能覆蓋最大面積的近似解。本研究所創的階梯演算法 stair algorithm 透過改變動態規劃紀錄狀態的方式，使狀態數大幅減少，進而改善求準確解的時間複雜度，也成功證明此演算法的正確性。本研究的演算法可被應用於平行計算中的負載平衡、積體電路設計等方面。隨後，本研究寫了一個互動展示品清楚呈現此演算法的功能。且以階梯演算法成功檢驗並比較 RTILE PROBLEM 的 7/3-approximation algorithm (Krzysztof Lorys and Katarzyna E. Paluch,2000 [4]) 與 11/5-approximation algorithm (Piotr Berman et al,2001[7])進行比較與分析。