Cultivating plants from seeds or cuttings is a fundamental aspect of gardening and agriculture. While traditional methods have been practiced for centuries, there is a persistent need for innovative and efficient approaches to enhance plant growth and development. This section explores the challenges associated with traditional propagation methods and examines potential solutions offered by emerging technologies and materials. Plant propagation is necessary to allow efficient multiplication and distribution of desirable plant varieties (Sorensen & Garland, 2024). Plant propagation is the process of creating new plants. There are two primary methods of propagation: sexual and asexual. ．Sexual propagation involves the union of pollen and egg, drawing genetic material from two parent plants to create a new, genetically diverse offspring. This process utilizes the floral parts of a plant. ．Asexual propagation, on the other hand, involves taking a part of a single parent plant and inducing it to regenerate into a new plant. The resulting offspring is genetically identical to its parent. This method utilises the vegetative parts of a plant, such as stems, roots, or leaves. One emerging technology that has garnered attention in this field is the use of cocopeat, a sustainable growing medium derived from coconut husks (Pane et al. 2021). Cocopeat has been extensively studied as a potential alternative to peat moss in plant propagation (Gericke, 1940). It offers a favourable balance between air porosity and water holding capacity, promoting root development and nutrient uptake (Kalaivani and Jawaharlal, 2019). Furthermore, cocopeat is a renewable and environmentally-friendly resource, making it an attractive option for sustainable seedling cultivation. Research has shown that the use of cocopeat as a growing medium can enhance the growth of both vegetables and various ornamental plants, such as Impatiens. The biostimulant effect of the Trichoderma atroviride fungus, which can readily colonize coir, has been observed to increase aboveground biomass, flower production, pigments, and nutrient concentration in these plants (Traversari et al., 2024).

本研究探討傳統廟宇彩繪用之「豬血灰」膠黏劑之性能，透過調製不同配比的豬血、石灰/蚵灰、熟桐油，分析其力學、黏度、透水性與老化色差等性能。創新之處為加入豆腐、蚵灰、立德粉與石膏粉製成可保存之粉狀豬血灰，並應用於實地廟宇壁畫修復。結果顯示，豬血與石灰體積比1:1、豬血灰與熟桐油比3:1最具黏著力與抗龜裂性，且環保配方具實用性與儲存性，可作為文化修復之綠色材料。

本研究探討隨機生成數列的長度期望值。一個籤筒中有n支籤，編號分別為1,2,3,…,n，每抽出一支籤，就將抽取的編號寫在紙上，形成一個數列。數列只能向左右兩端添加項，不能從中插入。抽出的籤若大於目前數列的最大項，則將抽出的數寫在目前數列右邊；抽出的籤若小於目前數列的最小項，則將抽出的數寫在目前數列左邊；抽出的籤若介於目前數列的最小與最大項之間，則操作結束。基於此想法，研究者將數列依照添加項的方向分為「單向數列」與「雙向數列」兩類。顧名思義，單向數列只能向一端延伸（本研究不失一般性討論往右延伸），雙向數列代表可以向左右兩端延伸。此外，研究者又將數列分為「嚴格遞增減」和「非嚴格遞增減」兩類。在生成原理上，嚴格遞增減等價於「抽後不放回」；非嚴格遞增減等價於「抽後放回」。在這樣的規則下，本研究探討了n支籤抽完放回與不放回時，單雙向隨機生成數列的長度期望值之通解，並成功證明了一些恆等式及性質。

When doing an experiment to produce colloidal ferric hydroxide, the bottom of the beaker used was colored in yellow-brown with thin film interference. This phenomenon is well-known, but the cause has not been clearly studied. As a result of the research, the coloration on the bottom of the beaker is caused by β-FeOOH forming a thin film which is chemically bonded with Si-OH on the glass surface. Also, the amount of β-FeOOH depends on the number of experiments, the area of the bottom of the beaker, and the concentration of FeCl3 aq. We found that it can be possible to determine the amount of β-FeOOH from the formula m=knsc and the adhesion constant was found to be 6.8✕10-3 (L/m2). In addition, from machine learning we predicted that the thin film thickness becomes thicker as it moves away from the center.

本研究以錄影方式紀錄BR反應並透過自研程式分析色相值變化以探討澱粉濃度、溫度、硫酸錳(Ⅱ) (𝑀𝑛𝑆𝑂4) 濃度與金屬配位對 Briggs-Rauscher 震盪反應的影響。查閱文獻發現反應系統中澱粉的存在影響三碘離子 (𝐼3−)與澱粉的吸附與反應 (Csepei & Bolla, 2015)；而本研究發現，平均週期與澱粉濃度呈非線性關係。實驗過程發現反應時週期先抑後揚，有頻率飄移發生，推測為錳(Ⅱ)與自身放熱所致並進行實驗；將結果與文獻相比顯示，本研究觀察到的震盪模式應屬諧波成分震盪 (harmonic oscillation) (Vukojevic, Soerensen, & Hynne, 1993) 或更複雜的震盪型態。 而在分析過程中，使用FFT頻譜分析與CWT時頻分析結合VMD與HHT嘗試以時域、頻域方法找尋與量化差異；並發現使用延遲時間遷入的相空間重構可以產生顯著的圖樣做非線性化學指紋應用。

1. Research Motivation Have you ever seen news stating that spring is gradually disappearing from the Korean Peninsula? The characteristics of the four seasons are disappearing due to the impact of global warming. As supporting evidence, droughts and heatwaves continue during the rainy season, and unexpected heavy rainfall occurs during autumn. These abnormal temperature phenomena are greatly affecting agriculture. Crops wither due to untimely cold spells or summer droughts, and the proliferation of bacteria and pests worsens. We need to conduct a thorough investigation and response to such weather phenomena. Carbon is known to be the main culprit behind these abnormal temperature phenomena. We want to explore how carbon affects climate change and understand the implications it has. 2. Research Objectives The consequences of climate change, such as deforestation and rising sea levels, will cause significant damage to society as a whole. This will also have a profound impact on the survival of all living organisms on Earth. Unless industrialization is halted, global warming will continue, making it crucial to gain a proper understanding and find accurate alternatives. The damages caused by global warming are expanding the habitats of mosquitoes, which is expected to have an impact on the spread of mosquito-borne diseases. This can also influence the emergence of novel viruses similar to COVID-19. By examining past outbreaks of diseases transmitted by mosquitoes, we aim to predict and understand such occurrences, as well as explore ways to minimize global warming. 3. Expected Benefits Based on this research, a focused exploration of the ecological impacts of global warming can provide essential data to understand the effects of climate anomalies on us and prepare for them. As these phenomena are expected to worsen over time, it will be possible to develop measures to minimize the damage caused by bacterial infections and agricultural losses.

本研究探討給定三角形經由其三中線、三中垂線、三高、三內角平分線、兩外角平分線及一內角平分線，將線段延伸為直線，分別以其與邊或邊的延長線的交點為旋轉中心同時旋轉，作為新三角形的三個邊，圍出新的三角形時(簡稱為變換)的性質，並關注重心、外心、垂心、內心、旁心的位置。 本研究分析變換一次，尋找新三角形隨旋轉角度變化的性質；及固定某個旋轉角度，進行n次變換時，形成的點列所在的曲線方程式。 結果顯示，變換一次時，根據三線選擇的不同，各自出現陪位重心、心的重疊、Kosnita 點、多心共圓、共圓錐曲線…等性質；而當固定某個旋轉角度，進行n次變換時，則分別有等角螺線或收斂到特定形狀的性質。

本研究從著名的歐拉三角形公式出發，我們將圓內接同內心三角形，推廣至圓內接同重心三角形和圓內接同垂心三角形。有關同重心與同垂心三角形的存在性與作圖範圍，我們巧妙利用原三角形的九點圓來進行刻劃！再將研究項目放在同心三角形的邊的包絡線，我們先給出其焦點，再用純幾何方式來證明銳角三角形時，其包絡線為橢圓；鈍角三角形時，包絡線為雙曲線；直角三角形時，則是退化為垂心與外心。值得一提的是，本研究進一步整合同內心、同垂心、同重心三角形，發現面積成等比之關聯性。最後考慮將圓內接改成圓外切的同心三角形，這個難度提升很多，我們成功利用奈格爾線來處理這個研究項目，它顯著不同於圓內接同重心三角形。

本研究探討仿生集水表面應用於台灣山區霧氣捕捉，並聚焦如何為需水性高的植物提升種植水源。近年來氣候變遷導致水氣減少，農作需仰賴額外技術補充水源。藉由模擬沙漠甲蟲圓弧凸起與蜂巢六角形凹槽仿生結構能顯著提升霧水蒐集效率；3D列印不同表面結構的捕霧杯，於實驗室內模擬霧氣環境。進而走入台灣不同海拔地區，驗證各環境條件對捕霧效率的影響。研究發現，陽明山濕度99%風速5.7 m/s環境中，集水效果最佳（32.7g）；大雪山高海拔，但濕度低風速變化較大，捕霧量幾近為零，風速及海拔影響顯著；特別在高濕度環境下表現最佳。提出具潛力之補霧杯模型，應用於水資源不足地區，提高需水性植物水源供給，以維護生態多樣性環境。

為深入了解家鄉的地質歷史與古生物遺跡，本研究聚焦於新北市外挖子山（位於安坑與南勢角交界處）之大寮層沉積岩。參考南勢角地質圖幅，確認該區屬中新世（約2,000萬年前）地層，並自露頭處收集岩石樣本進行實地觀察與手工磨製岩石薄片、自製洗選設備洗選岩石進行分析。研究結果發現包括有孔蟲與角管蟲（Ditrupa）在內的多種典型海洋實體化石及生痕化石。此一發現證實該區在地質過去為海洋環境，甚至可能為高生產力的淺海海域。透過化石組成與分佈之觀察，可進一步探討該地層之年代特徵與沉積環境，對了解本地區的古環境變遷具有重要參考價值。

本研究探討乘法賓果雙人對戰遊戲的設計原理與對戰策略。 探討問題與獲致結果如下： 一、正整數1～c兩兩相乘所得乘積總個數，找出計算公式。≤500只有7個c恰可組成正方形棋盤。重複的乘積，其最大質因數≤𝑐/2。 二、由棋盤邊長n和m數連線，可計算出棋盤各位置的賓果組合數量、及可與之賓果的位置數量，且可判斷合適的m值。 三、按照數字大小排列邊長≤6的完美棋盤，都是先手較占優勢的不公平棋盤。對戰策略包括：取得棋盤中央位置、選擇平方數、賓果係數較高，考慮可連跳乘積數的相關性質、倍數位置分布等。 四、設計公平棋盤並用不同方法驗證。 五、編寫程式，找出可排成較大正方形棋盤的數，且模擬隨機對戰，找出雙方勝率，以驗證棋盤的公平性。

Problem • Rice is the primary cereal crop consumed by nearly half the population worldwide • By 2050, there will be a 50% increase in demand for rice • The world’s poor populations depend more on rice, both for income and consumption, than any other food. Rice is the single-largest source of employment and income for rural people • Worldwide, 51–82% of agricultural crop yield is lost annually due to abiotic stress due to climate change • Climate change causes extreme temperatures, erratic rainfall, dangerous droughts, and increased salinity from rising sea levels Solution • To adapt to abiotic stress, rice has intricate signaling pathways, particularly those mediated by the phytohormone abscisic acid (ABA), that cause an increase in stress tolerance • Clade A genes of the Protein Phosphatase 2C (PP2C) gene family are known to be negative regulators of the ABA signaling pathway. • “Deleting” these genes activates the ABA pathway and increases stress tolerance in rice without inducing stress CRISPR gene editing technology is the ideal solution Research Goal • While the role of PP2C genes in stress response is recognized, there is a gap in understanding the specific genes within this family that contribute significantly to stress signaling. Furthermore, there is a need for a detailed investigation into the effects of targeted CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) genome editing on rice stress response pathways.