基於Anubhav Mishra提出的尚未被證明問題：由基準三角形OAB之兩邊OA與OB生成共頂點O兩正方形，在兩正方形中選取兩組對應點，並做交叉連線相交於N點，則AB之中點M與O、N具有三點共線之性質(此線稱為共軛對稱軸)。首先提出此原題的不同證明，再推廣至正n邊形，並找到一般化的必要條件及廣義共線性質。 研究結果發現並證明:在正n邊形共線蝴蝶對稱圖形中，存在兩稜線在共軛對稱軸鉛直方向投影長相等，及其成形的臨界角範圍；蝴蝶翅膀種類公式、衍生類別及總數量；面積與稜線長的幾何不變量；基準三角形三邊對應之共軛對稱軸共點於其重心；當n為偶數，共軛對稱軸垂直特定共軛對稱點連線段。當n趨近於∞時，共線蝴蝶對稱圖形收斂到圓內接等腰梯形。

在這個計畫中預計透過發酵作用，將過熟或剩餘的水果轉化為酒精，以實現資源回收與環境保護。我們選擇含糖量較高的水果（如鳳梨、火龍果、柑橘、葡萄等），壓碎後加入酵母菌，在適當溫度下發酵，促使糖分轉化為酒精與二氧化碳。發酵完成後，利用蒸餾法獲得初步的蒸餾酒精。 此外，測試不同水果的酒精產量、溫度對發酵效率的影響，並分析蒸餾後酒精的濃度與產率。我們最終將驗證所得酒精的殺菌效果，探討其應用於日常環境消毒的可行性。由於有效消毒的酒精濃度需達 75％~78％，我們將進行多次蒸餾，提高酒精濃度，並記錄細菌與微生物的活動情況，以確認其可用性。此結果不僅能減少食物浪費，還能運用科學方法將剩餘水果轉化為有價值的清潔資源。

本研究邀請60位國小學生參與猜拳比賽，採用嚴謹的統計方法進行母群體分層隨機抽樣與270場循環賽，以利誘激發勝負動機並加以錄影。本研究對資料進行重覆檢核的三角校正以獲得信度。之後利用ChatGPT進行統計分析和考驗全體學生、不同年段、性別的出拳偏好及致勝策略（含回應文獻），再徵詢統計專家分析之合宜性。 結果發現：1.小學生整體偏好出剪刀，尤其男生與低年段在第一拳特別明顯；2.無文獻中提及的「勝後堅持」及「首拳石頭」等偏誤；3.有非常明顯的「敗後改變」、「平手後中斷」與「社會性循環行為」（石頭→剪刀，剪刀→布，布→剪刀）；4.出拳策略可透過觀察對手上一拳，依循環模式反制。高年段勝場數最高，顯示經驗與觀察力有助策略制定。

特斯拉閥是一種神奇的發明，能利用管路的設計，達成流體在一個方向上流動時阻力最小，而在相反方向上流動時產生顯著的阻力的目的，我們想要運用在阻擋水流來降低災害上，我們的研究有以下的發現：(1)特斯拉閥的進水口角度為40度及出水口角度為30度時，減流的效果最佳；(2)特斯拉閥的支流愈寬，減流的效果愈佳；(3)交錯型主水道略優於對稱型主水道，但結構較複雜；(4)水流愈強，特斯拉閥減流的效果愈好；(5) 水的溫度與鹽度對於特斯拉閥減流效果沒有太大影響； (6)前後排列支流的特斯拉閥效果優於平行排列支流，且支流數量愈多，減流效果愈佳。

為因應氣候變遷造成的淡水資源短缺問題，本研究以可吸收廢水中營養與重金屬的小球藻，探討水資源再利用的可行性。實驗發現小球藻在6%畜牧廢水中為最佳生長濃度，且添加黃耆作為植物源生物刺激素，顯著提升小球藻葉綠素含量與耐鹽性。在海水環境下，小球藻經黃耆處理後，其細胞數與葉綠素含量分別為對照組的175%與173%。此外，利用培養過小球藻的廢水灌溉青江菜，種植第4天時，根長與莖長分別為對照組的129%與146%，且減少青江菜根部細胞受損。推測黃耆與小球藻皆可透過分泌次級代謝物，作為生物刺激素，促進植物生長與鹽逆境耐受力。期望本研究可解決農業汙染與淡水資源不足等問題，並拓展小球藻的利用價值。

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.

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.

Such as the plastic waste and industrial discharge that permeate our oceans, it is the insidious and infamous nature of oil spills that demands our immediate attention. These spills, with their far-reaching ecological ramifications, pose a profound danger to our marine ecosystems, demanding urgent action and a heightened awareness of the true menace that is caused by this oil

Understanding species abundance is critical to managing and conserving planetary biodiversity. Pacific salmon (Oncorhynchus spp.) are keystone species of cultural, economic, and ecological importance in Alaska and especially Southwest Alaska. Traditional methods of enumerating salmon such as weirs and visual surveys are often costly, time-intensive, and reliant on taxonomic expertise. Environmental DNA (eDNA), which identifies and quantifies species based on DNA they shed in their habitats, is a potential cost- and time- saving alternative. The relative ease of collecting eDNA samples also enables citizen scientist involvement, expanding research coverage. Currently, more research is required to define eDNA’s potential and limits. This project investigates whether quantitative eDNA metabarcoding can accurately quantify the abundances of six fish species: the five Pacific salmon species plus rainbow trout. Water samples were collected from eight creeks in the Wood River watershed of Southwest Alaska. eDNA metabarcoding and subsequent bioinformatics processing produced a read count for each species. These were compared to visual survey counts, taken to be the true counts for the purposes of this study. Data analyses showed a positive, linear relationship between visual survey count and eDNA count for sockeye salmon. The regressions were significant for both the early (p = 0.089) and late (p = 0.030) sampling dates when 𝛼 = 0.10. eDNA detections of non-sockeye species generally corresponded to visual survey observations of species presence or absence. Overall, the results of this study support eDNA’s potential to be an alternative or supplement to standard methods for the enumeration of fish species.

馬祖北竿鄉大坵島上的外來種植物－玉珊瑚（Solanum pseudocapsicum L.）在近年來大舉侵佔原生植物的棲地。玉珊瑚屬於茄科的觀賞植物，但含有辣茄鹼（一種毒素)，人類誤食會導致嘔吐和腸胃炎，梅花鹿(Cervus nippon)亦不會食用。因為在島上沒有天敵，近幾年快速蔓延，取代了原生植物的棲地，造成在島上以原生植物為食的梅花鹿漸漸無法找到足夠的食物，面臨餓死的困境。 本研究拔除有毒玉珊瑚製作成生物炭，以不同土壤組成及生物炭的比例種植小麥草(Triticum aestivum)，觀察生物炭對小麥草種子發芽率及生長高度是否具有幫助。研究結果顯示，土壤組成使用純培養土來種植，對小麥草的發芽率及生長高度最有幫助；而生物炭與培養土的比例以1:30為最佳，可提高小麥草發芽率約28%、生長高度約19%。

一般用硝酸溶解銅時會產生有毒氣體(NO、NO2)，本研究利用過氧化氫水溶液在適當的酸性條件下溶解銅，具有更環保、更有效率的特性，符合綠色化學的趨勢。研究中採用的酸有醋酸、檸檬酸、酒石酸、硫酸；鹼則有氫氧化鉀、氨水與二乙烯三胺。最後發現以過氧化氫配合硫酸的效果比同濃度的硝酸更好，可以有效的溶解銅金屬。

本研究的目的為使用回收處理後的農業廢棄物製成薄膜，並且以取代含塑化劑、需非常大量時間才能被環境分解的塑膠保鮮膜為目標。本實驗以蝦殼中的幾丁聚醣為原料，並在其摻入不同重量百分濃度的樹葡萄皮萃取液，製備薄膜後進一步對樣品進行特性的檢測。 我們採用ISO 22196方法測試薄膜的抗菌活性；DPPH自由基清除活性測試薄膜抗氧化能力，以及將其放入土壤進行降解能力的測試。實驗結果發現含20%萃取液之薄膜在各項特性測試中表現皆最佳，除卻顏色較深可能無法達到美觀需求外，其能達到的保鮮效果具有最大的潛力。