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。

此研究是以實驗方式，驗證理論模擬中指出水漂在不同入水模式下，入水攻角為 20 度時皆可產生最佳的彈跳效果。因此我以壓克力板作為模擬水漂的模型，設計了以下四組操作變因，分別是入水攻角、水的流速、水漂邊界形狀以及接觸面的粗糙程度，接著透過Tracker 分析壓克力板的質心彈跳高度及運動軌跡，再利用 Excel 分析數據，找出其中的運動相關性。最後透過座標轉換，可以利用此實驗來分析打水漂的運動行為，成功發現入水攻角在 20 度時的確有最佳的彈跳效果，並以此實驗結果來優化打水漂的運動行為。

本研究主要目的為改變風力渦輪機的結構，將原始的單層葉片設計改為雙層葉片，當風流過第一層葉片時將產生尾流效應，使葉片後氣流產生偏轉，若將第二層葉片更具此氣流偏轉區域調整，將能有效的提升發電效率。根據實驗結果顯示，葉片後的尾流造成氣流偏轉的角度約為 15 度，因此當渦輪機的兩層葉片位於理論最高的相位夾角時，應再減去 15 度的尾流偏轉角，該夾角才為最大的發電效率配置，基於此結果所設計的渦輪機，儘管與單層葉片渦輪機具有相同的葉片數量，卻能提升發電效率約 40%，同時相關文獻指出，葉片的成本約佔整體發電機總成本之 14%，因此透過使用本研究之作法，預估可降低約 18%的成本，整體而言，本研究之設計不僅能提高風能發電效率，同時將有效的減少成本，未來具高度前瞻性。

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。

Within the scope of sustainable cities and responsible consumption, which are among the goals of sustainable development, it is aimed to contribute to life safety, defense industry, protection from disasters and economy with the new generation environmental building technologies and materials to be developed in the field of construction. It is a critical issue to protect reinforced concrete structures, piers, bridge piers, overpasses against impacts, and to reduce the damages and economic losses in disaster situations. Reinforced concrete scaffolding is the load-bearing component of the structure and its impact resistance is crucial to the overall safety of the concrete structure. Therefore, there is a need to develop technologies that can protect structures against explosion and impact loads. Within the scope of the project, environmentally friendly and low-cost concrete materials with industrial waste glass, aluminum, plastic material additives, which can be used in columns, which are the most important part in the strength of reinforced concrete structures to prevent explosion and impact damage, were produced and their strengths were analyzed. The use and design of these materials in the strength of concrete creates the originality of the project. When the results obtained in the project were examined, it was observed that the steel fiber concretes with the addition of waste glass, aluminum ring, disc, beverage can and plastic bottle were resistant to high pressure when compared with the control groups without additives, and the change in surface height after the impact test, visual analysis and load-time graphics showed this. It is seen that the additives have a cushioning effect against the impact, absorbing the energy against the force by 87.6% and increasing the strength significantly. In this project, where it is aimed to increase the strength of concrete structures by using the impact energy absorption feature of waste glass, plastic and aluminum, products with high added value are developed, contributing to the literature and the construction sector. With the large-scale use of the project, the costs spent on the disposal of waste materials will be reduced, the upcycling based on re-using the waste products will be contributed, and the loss of life and property due to impacts and explosions will be prevented.

「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。

一價銠金屬催化反應已經被廣泛應用於有機化學合成領域中。而本研究以具保護基之肉桂胺衍生物1與四芳基硼鈉試劑2a作為起始物進行銠金屬不對稱氫芳基化催化反應，得到具有保護基的掌性2,3-雙芳基丙胺衍生物3，並探討此反應的掌性雙烯配基對於反應的影響。本研究已完成使用Ts（對甲苯磺醯基）保護基之肉桂胺衍生物1a作為起始物進行反應，並改變與銠金屬錯合的配基，發現當配基使用2,5號位為芳基取代之配基L（掌性雙環[2,2,1]雙烯配基）時，反應有較好的位置選擇性，其中最佳的是芳基取代為苯基之配基L1，其位置選擇性比例為1:0:0.09。目前將進行改變起始物1之氮上的保護基，以L1作為配基進行反應，並與1a比較，優化反應性及產率。

細胞核是真核細胞內最大且至關重要的細胞結構之一。其具體位置在各種細胞中可能有所不同。為了深入了解細胞核位置對於細胞功能的影響，我們選擇以果蠅幼蟲眼疊為研究對象，探究細胞核在神經系統發育過程中所扮演的角色。神經系統在生物體中扮演著極為關鍵的角色，包括神經元和神經膠細胞。如果失去神經膠細胞，將導致神經退化或死亡。在我們的研究中發現，神經膠細胞核在其發育過程中會發生大規模的內部移動。為了限制神經膠細胞核的移動，我們利用了果蠅作為研究動物，並應用了果蠅常用的 GAL4-UAS系統和GrabFP技術，這使得我們能夠限制神經膠細胞內細胞核的移動。我們的實驗成功證明，限制神經膠細胞核的移動會影響神經細胞的軸突發育，但不會影響神經細胞 R1-R8 聚叢的發育。未來，我們計劃將 GrabFP 技術應用於研究不同胞器在細胞內相對位置對其功能的影響。

肺癌是世界上死亡率第一的癌症。根據近期研究發現，環形RNA (circular RNA；circRNA)比一般的線狀 mRNA穩定，並且會調控癌細胞。但circRNA於肺癌中的調控機制仍不清楚，因此我們決定挑選一個circRNA作為研究對象。首先，我們從 GEO 公開資料庫中篩選肺癌病人中差異表現的 circRNA，經 qPCR在肺癌細胞株驗證後，最終找到circACTN4 進行後續的研究。實驗結果顯示 circACTN4 在肺癌細胞株中確實為環狀結構，內生性表現量上升，且大都分布在細胞質。使用siRNA降低 circACTN4 表現量後，會增加細胞停留在細胞週期之G1期的數量，且 CDK4 和 CCND1 蛋白量也會降低。因此我們推測 circACTN4 可以促進肺癌細胞增殖的效果。更進一步的研究揭示，circACTN4能與LRPPRC蛋白結合，這種相互作用可能是circACTN4在肺癌中發揮調控作用的關鍵機制。總上所述，circACTN4 會促進肺癌細胞的生長，盼未來能作為預後的指標，並發展為治療肺癌的新標的。

In photodynamic therapy (PDT), reactive oxygen species are generated within the cytoplasm to destroy cancer cells selectively. Using porphyrinic structures (PS) as photosensitizers holds promise for targeting cancer cells. However, direct incorporation of the porphyrins into cancer cells remains elusive. Hence, Dr. Martina Vermathen’s research introduced specific membranous phospholipid nanocarriers for topical porphyrin applications. However, since a sufficiently high enough concentration of PS in cancer cells has not yet been achieved, this study aimed to improve skin uptake of the nanocarriers. Two approaches were examined: (1) comparing polar and nonpolar porphyrins and (2) assessing the effect of a penetration enhancer, DMSO, through a neat and diluted application. The polarity of the porphyrins was first quantified with a log P test. The nanocarriers were assembled by incorporating two different PS compounds, either the mono- or tetra-4-carboxy substituted phenyl porphyrin. They were then characterized by 1D and 2D-NMR analysis. The porphyrin permeation was tested by Franz diffusion tests on pig ear skin. For the second approach, DMSO was added in the Franz diffusion test, either directly applied on the skin (“neat“) or diluted in the nanocarriers (“diluted”). The log P test for the mono- and the tetra-carboxyphenyl porphyrin resulted in values of 4.5 and -1.1, respectively. The more polar tetra-carboxyphenyl porphyrin exhibited 2.8 times better skin uptake compared to the mono-carboxyphenyl porphyrin. The neat DMSO application increased uptake by a factor of 5.5. The diluted DMSO application worsened skin uptake slightly. Analytical techniques revealed differences in porphyrin encapsulation: The mono-carboxyphenyl porphyrins were encapsulated in the centre, whereas tetra-carboxyphenyl porphyrins were localised around the nanocarriers. Results indicated potential instability of the nanocarriers. The more polar tetra-substituted porphyrins showed superior skin diffusion than the mono-substituted derivative. The neat DMSO application facilitated enhanced skin uptake by inducing membrane destabilization and pore formation but may have limited applicability. Further research is suggested to explore porphyrinic PS with alternative polar substitution patterns and tailored penetration enhancers for lipid-based delivery systems. Overall, the study underscores the importance of molecular properties of the PS system and demonstrates the potential of penetration enhancers in optimizing PDT for skin cancer treatment.