大部分的作品都是在研究五方連塊和它的特性，本研究特別以三角多連塊以及六邊多連塊為出發點來探討。一開始，我們針對連塊可以擴充的數量來分析，隨著圖形擴充，發現連塊數量、連接邊、Ｖ字角會影響總擴充數。接著，蒐集三角多連塊、六邊多連塊，研究它們的周長、角的數量、內角和等幾何性質，隨著圖形發展，發現平角、周角的數量會影響幾何性質的表現。 最後在n階三角形、n階六邊形中，拿走最少個數並找出規律拿法，讓指定三角多連塊、六邊多連塊無法放入n階圖形內。未來，我們希望在更多指定多連塊下，找出各種規律拿法，讓n階圖形呈現更多規律之美。

本研究旨在解決肢體障礙或單手使用者在操作電腦時所面臨的不便，設計一款融合鍵盤與滑鼠功能的單手操作裝置。透過自製PCB電路板、客製化鍵帽與鍵軸配置、3D列印人體工學外殼，以及整合滑鼠感測器與QMK韌體技術，實現單手即可同時完成鍵入與游標控制的操作方式。我們的實驗結果顯示，單手使用時相較於傳統鍵鼠組合，本裝置能大幅減少手腕移動的距離與次數，有效提升使用效率並降低疲勞感。產品設計不僅針對身障者，也適用於特定單手使用情境，具備良好的通用性與實用價值。未來將持續優化硬體與軟體，期望推廣至更廣泛的使用族群，實踐科技輔具的社會意義。

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。

鳳凰木的花朵擁有五片花瓣，上方花瓣與其他紅色花瓣不同，是白色底紅色斑點，根據文獻，這片花瓣稱為旗瓣，功能是作為蜜標來吸引傳粉者。研究觀察發現鳳凰花的旗瓣會先捲曲凋零，和蜜標存在的功能互相矛盾，本組推論與環境、授粉有關連。經研究發現，旗瓣凋零與生長環境、花粉及花蜜是否被採集無關，與授粉方式有關。異株授粉導致旗瓣凋零的時間提前；同株異花授粉旗瓣凋零的時間與自然狀態相近；自花授粉、無授粉則導致旗瓣凋零的時間延後。異株授粉對鳳凰花而言是有效且成功的授粉，會導致旗瓣提早凋零，蜜標隱藏，提高其他尚未有效授粉花朵成功授粉的機會，並且產生成熟的種莢。無效的授粉會導致旗瓣凋零時間延後，藉此等待有效的授粉機會。

本研究設計與合成一系列的電子供體分子，以研究分子單體的化學結構對於所形成的激發複合體光物理性質的影響。 五個所設計的供體分子已被成功的合成並確定均具有分子內電子轉移的性質 其躍遷偶級距變化分布範圍在17.6-28.6D之間。 將此五個供體分子分別與兩種電子受體分子在溶液聚集在一起，利用在長波長處所新生的螢光發光，推測激發複合體的形成。研究的成果並顯示，具有類似三角形結構的供體分子將更容易形成激發複合體，而具有棒狀結構的分子則較不易形成之。此成果有效的提供有關於單體分子結構的設計對於所需激發複合體光物理性質的影響，形成可快速地提供各式不同發光波長的材料，將可作為在發光二極體發光層材料、螢光感測器、生物成像等領域需求時的分子設計藍圖與指引。

本研究旨在優化鋅離子電池陰極材料的性能，選用沸石咪唑酯骨架材料（ZIFs）與釩氧化物（V6O13）進行複合材料的合成與應用。隨著鋰電池成本的上升，鋅離子電池因其安全性與成本效益逐漸受到重視。ZIFs 具有高比表面積及良好的離子導電性，而V6O13則因多價態和優良導電性而成為潛力材料。通過結合這兩種材料，我們開發了具有多孔結構和優異穩定性的複合陰極材料，再使用 PXRD、SEM 及 EDX 對材料進行結構表徵，並使用此新材料製作鋅離子電池進行電化學性能測試。結果顯示，熱裂解後的 PY-VxOy@ZIF-Zn/Co具有最佳的克容量及穩定性，且在500次循環後保持良好的穩定性。本研究展示了ZIFs和V6O13結合在鋅離子電池中的應用潛力，為低成本、高效能的儲能解決方案提供了新的方向。

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.

遺傳性表皮分解性水泡症（EB）是種罕見疾病，因突變使角蛋白異常，造成表皮組織脆弱易形成水泡，單純型水泡症（EBS）是最常見的類型。此計畫旨在：（一）建立果蠅EBS疾病模型；（二）探討溫度對病徵的影響；（三）以此果蠅EBS疾病模型發展藥物篩選平台。初步使用Diacerein測試，評估對EBS症狀的改善效果。 目前顯示突變角蛋白K5/K14R125C會形成積聚體，與正常K5/K14形成的角蛋白網絡不同；全程25℃培養，約32%果蠅翅膀有水泡，亦符合EBS病徵。篩藥平台建置已完成色素和溶劑DMSO劑量測試，初步顯示Diacerein有助病徵緩解。目前將擴大統計不同溫度對 EBS果蠅死亡率、水泡發生率和角蛋白積聚形成比例。希望以本研究建立的果蠅EBS疾病模型與篩藥平台，能為罕見遺傳疾病療程開發奠定基礎。

本研究透過專家訪談了解自行車訓練核心訓練要素，開發「我的AI自行車教練」系統，期能提升初學者騎乘穩定性，利用micro:bit三軸加速度感測器即時監控騎乘姿勢變化、霍爾感應器量測速度以及i20心率感測器偵測心跳。所有數據透過藍芽傳送至 Scratch (bDesigner)，進行即時騎乘姿勢與數據可視化呈現，並整合生成式人工智慧（GAI）分析結果，提供個人化的訓練建議與姿勢調整建議，最後讓訓練者進行實際測試。結果顯示，本系統能有效提升騎乘姿勢穩定性與騎乘效率，GAI能提供科學化的訓練報告及精準訓練建議，與專業自行車教練的意見一致，證明「我的AI自行車教練」具實用性與應用潛力。

Upcycling abandoned beehives to make new products can reuse the useful materials in old beehives and produce less trash. As known that bees leave their beehive in these following situations like insufficient replenishment, frequent unboxing and environmental issues. Then the beehive will be abandoned and will have no use left. In this project, a piece of honeycomb was collected from abandoned beehive and melted in order to extract beeswax. The potential of the extracted beeswax for replacing plastic to produce fillers of 3D pens was studied. Natural materials like seashell, rosin, soy bean and coffee ground were tested as ingredients of 3D printing materials. Finally, the potential of using extracted beeswax in 3D printing was confirmed. Beeswax has a low melting point at around 64°C and solidify quickly at room temperature. The high plasticity of this natural wax fulfills the criteria of 3D printing materials. Biodegradable wastes, like coffee grounds and soy bean grounds were tested as additives for reducing the beeswax content. Sea shell grounds were eliminated from the tested list as its filaments broke into small pieces of brittle fragments during the production process. 5% and 10% of these additives were the optimal formula for making long filaments. Yet, the thin filaments made by pure beeswax were not strong enough, filaments of selected beeswax-soy bean grounds were further strengthened by mixing with 5% or 10% rosin. Among the four different ratios of Beeswax: Soy bean grounds: Rosin (9:1:0.5 / 9:1:1 / 9.5:0.5:0.5 / 9.5:0.5:1), filaments in the ratio 9.5:0.5:0.5 demonstrated better flexibility, higher tensile strength and compressive strength, thus B9.5:S0.5:R0.5 was the final formula of biodegradable beeswax 3D filament.

In recent years, lower inter-limb asymmetries have become a topic of increasing interest in sports research. Numerous studies have investigated the occurrence of between-limb differences in a variety of physical tests, ranging from strength, sprinting, and change of direction speed to jumping tasks. The main focus has been the association of asymmetries to either enhanced injury risk or reduced physical performance. Sport specific aspects and differences of lower limb asymmetries have not often been analysed. Additionally, most studies have been performed with male athletes. Women, however, present higher prevalence of lower limb asymmetries in strength, coordination, and postural control than men. These two aspects were therefore addressed in the present study. Female youth soccer (n=18, age: 16.7 ± 0.8 years) and floorball (n=18, age: 17.6 ± 0.9 years) players completed a test battery consisting of six unilateral jumping tasks in horizontal and lateral direction to detect sport specificity in inter-limb asymmetries. The test comprised the following hops: (1) Single Leg Hop for Distance and (2) a newly created version of it, (3) Single Leg Triple Hop, (4) Single Leg Crossover Hop, (5) Side Hop and (6) Single Leg 6-meters Timed Hop. The scores of every jump were calculated into Limb Symmetry Indexes for each participant. A linear mixed effect (LME) model (using function lmer in program R) was applied to evaluate the effects of sport and jump type on asymmetries. In terms of the whole test battery, there was a significantly higher magnitude of asymmetries in soccer compared to floorball (p=0.0067) with a mean difference of 1.9%. Three significant differences between the effects of different jump types were detected (5>2: p=0.027; 5>3: p6: p=0.014). Moreover, the results showed no significant effect on leg dominance. According to the findings of this study, soccer appears to be more asymmetric than floorball, leading to the suggestion that inter-limb asymmetries may not only be task-specific, but also sportspecific. Since no significant correlations were detected, this study suggests that inter-limb asymmetries are independent of leg dominance. Considering the possible reduction in athletic performance and increasing injury risk, strength and conditioning coaches are advised to assess athletes' inter-limb asymmetries using a broad, sport specific test battery and decrease them.

The environmental implications of rapid industrialization, including rising pollution, depleted resources, the effects of climate change brought on by global warming, and unrestrained groundwater extraction, are contributing to a growing water scarcity crisis [1-3]. The improvements in quality of life are largely attributable to the innovations in manufacturing technology made possible by the Industrial Revolution, but these innovations also pose risks to the natural world and human health [1-3]. The textile business uses a wide variety of raw materials, including natural fibers like cotton as well as synthetic and woolen fibers, and the chemical components of dyes are just one example. The annual output of synthetic dyes is around 700,000 tons, and there are over 10,000 different varieties available. As much as 200,000 tons of synthetic dyes are released into the environment every year due to the inefficient dyeing technique commonly employed in the textile industry. According to the World Bank, the processing of textiles for dyeing and finishing accounts for between 17 and 20 percent of industrial wastewater [1-3]. Textile wastewaters contain a high biological oxygen demand (BOD), chemical oxygen demand (COD), nitrogen, color, acidity, high suspended particles, high dissolved solids, surfactants, dyestuffs, heavy metals, and other soluble chemicals [3] due to the variety of dyes used to color textile items. In particular, water-soluble reactive and azo dyes are employed to obtain the required color. Ten to twenty percent of the dyes used end up in the effluents, where they might harm wildlife and the ecosystem (carcinogenic or mutagenic). Headaches, nausea, skin irritation, respiratory difficulties, and congenital deformities are only some of the health problems linked to exposure to textile wastewater. There are repercussions for aquatic ecology, environmental biodiversity, and the quality of receiving water bodies. New, low-cost, and highly effective water treatment methods are needed to deal with polluted wastewater. Adsorption and coagulation, two common water purification methods, just concentrate pollutants by shifting them to other phases; they do not "eliminate" or "destroy" them. Sedimentation, filtration, chemical oxidation, and biotechnology are all examples of conventional water treatment methods, but they all have their drawbacks. These include insufficient removal, high chemical reagent consumption, high treatment costs, long treatment times, and the creation of toxic secondary pollutants. New water treatment procedures are needed to improve the quality of treated effluent [1-3]. The use of semiconductor particles in photocatalysis is gaining appeal as a solution to global pollution problems due to its shown efficiency in degrading a wide variety of contaminants. Photocatalyst-coated surfaces-based reactors have proven to be practical for long-term operation over photocatalytic powder-based reactors (i.e., slurry-based reactors) [4-5]. As a promising photo-electrode and photocatalyst, titanium dioxide (TiO2) has enjoyed wider applicability in photocatalytic hydrogen generation, solar cells, and remediation of organic contaminants among other photo-catalytic applications [4-6]. TiO2 has been recognized as one of the low-cost, most effective, and fascinating photo-catalyst as a result of its interesting thermal and chemical stability, desirable electronic features, others, and environmental benignity [6-8]. Pristine TiO2 semiconductor is characterized by a wide band gap that can only utilize the UV part of the light spectrum with a wavelength of less than 385 nm, which is just 5% of the sunlight energy capacity. Spectrum usability extension to visible regions warrants further and extensive research study [8-10]. Additionally, the quickness of the recombination of photo-generated holes and electrons further restricts the practical applicability of the semiconductor [10-12]. It is highly desirable to develop a cost-effective scalable strategy to over these drawbacks toward sustainable development and a clean environment using only natural sunlight irradiation [5-11]. In addition, it is preferred to fabricate them as films rather than powders as photocatalytic immobilized reactors are more practical than powder-based reactors [4-8]. Dye sensitization, supports, magnetic separation, and surface modification by doping with non-metals, metals, and transition metals and coupling with other semiconductors have all been used to enhance the photocatalytic activity of TiO2 photocatalyst. Higher photonic efficiency can be attained through the synergistic fine-tuning of features such as physical, chemical, and electronic, and these composites and hybrid materials based on TiO2 are creating a big trend. Doping has been widely studied as a means of altering the surface of TiO2. Rare earth metals, noble metals, and transition metals are all discussed in the existing literature on the surface modification of TiO2 doped with cations [4-12]. In this study, for the first time, Ag nanoparticles loaded mesoporous TiO2 coating was prepared and applied as an immobilized photocatalytic reactor for water decontamination and bacterial deactivation under natural sunlight irradiation.