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由兩個全等形構造的衍伸圖形之性質研究

本研究源於 2016 年數學雜誌 Crux Mathematicorum 的一個三角形定性問題[1],我們將這個問題進行推廣且創新探討其定量與定性性質。我們先討論任意三角形與任意凸四邊形、凹四邊形,分別針對不同連線情形下的兩個衍伸圖形的有向面積之和與有向面積之差進行完整討論,再巧妙利用平移不變性處理行列式級數和,最後給出一般化的不變量關係式與刻劃其幾何意義。此外,我們也特殊化探討其衍伸圖形恆為正三角形、正方形等有趣優美的定性性質。最後,系統性推廣到平面上任意封閉的凸四邊形、凹多邊形,先給出不同連線方式之間的重要輪換對稱性質,再分為奇多邊形與偶多邊形進行討論而得出任意連線構造的衍伸圖形之有向面積不變量的一般式。

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Bio-Circular-Green Superabsorber

As the world has become concerned about the global waste crisis and global warming, there has been a surge of research within materials science to find materials that would replace plastic, such as bioplastics or biodegradable materials, in order to reduce environmental pollution. Plastics generates the microplastics that allowed them to become cross contamination enter the ocean through land, sea and river. Science research found (Lusher et al. (2017)) over 220 species of marine animals ingested microplastic, half of them are considered relevant for commercial purpose and increasing the risk of human consumption as it can induce immune response, oxidative stress, cytotoxicity, alter membrane integrity and cause differential expression of genes. Thailand is also experiencing such a challenge, as seen by the overabundance of plastic waste that might take centuries to decompose. For example, around 1680 million personal hygiene products such as diapers, sanitary napkins, and tampons are used each year. This study highlights the use of naturally accessible absorbent fibers from malva nut (Scaphium scaphigerum) (G. Don) Guib & Planch.), which is widely available and biodegradable in nature and has a low carbon footprint. This study also aimed to develop natural absorbent pads using compostable spun, external layers, and biodegradable glue. A prototype sanitary napkin with biodegradable absorbent pads was developed and evaluated for absorption ability, absorption rate, pH, and biodegradability. The absorbent material absorbed up to 19 times its weight in 2 minutes and 33 times its weight in 2 hours, which is enough for an average of 80-150 mL of menstrual blood. The prototype napkin deteriorated within 99 days, based on naked eye observation. Some signs of degradation and microorganisms growing on the prototype were also observed from scanning electron microscopic images. According to the findings, natural absorbent pads made from malva nut have the potential to be converted into sanitary napkins. Furthermore, it is proposed that the components, which include superabsorbent renewable materials, spinning compostable layer, external compostable layer and biodegradable glue, may be used in a variety of goods, including adult diaper pants, incontinence pads, and laboratory bench mats.

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球面n邊形的孟氏共線與西瓦共點定理

本文主要在探討平面幾何學中的兩個重要結果—三角形中的『Menelaus定理』與『Ceva定理』推廣到任意的『球面n邊形』的相對應結果,對於任意的球面n邊形,我們分別找到了『球面n邊形的Menelaus共線定理』與『球面n邊形的Ceva共點定理』的一般化結果。

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Introduction of Omed-Omedan Tradition Through Augmented Reality-Based Card Games To Increase The Love of Local Culture

This research is motivated by the differences in the people's perceptions, mainly youth about the omed-omedan tradition. The difference is that many people think that the omed-omedan tradition violates the norms of decency and is also called the pornography tradition. The purpose of this study is to, 1) describe the mechanism of applying omed-omedan tradition recognition attitudes through augmented reality-based card games, 2) analyz the impact resulting from the application of omed-omedan tradition recognition attitudes through augmented reality-based card games, and 3) analyze about the feasibility of application resulting from the application of omed-omedan tradition recognition attitudes through augmented reality-based card games. This research is a type of R&D research conducted at Bali Mandara State High School from July 1-September 6, 2021. The subjects of this study were the teenagers of Kaja Sesetan Indigenous Village and the object of this study was the omed-omedan tradition through augmented reality-based card games. The data collection method used is the literature studies, questionnaires, interviews, and validation questionnaires. Data is processed based on qualitative descriptive approach and quantitative descriptive approach. The results showed that the mechanism of implementing the omed-omedan tradition originated from the download of assistive devices, namely android studios and applications from AR, the impact of augmented reality-based card games was seen as very helpful in the introduction of the omed-omedan tradition and was seen as able to help increase the love of local culture, besides that the media used was also very popular by players because it was seen as interesting and very helpful. Based on the feasibility tests that have been calculated, this game is considered very feasible to implement and researchers hope that the innovations that have been created can effectively provide understanding to help out the local community about omed-omedan tradition.

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兩組直線所構造的三角形外心軌跡性質

本研究源於 2022 年數學雜誌《Crux Mathematicorum》的一道四邊形動態幾何問題,我們先將此問題設定為三角形,利用綜合幾何方法給出了兩種構圖條件下的三角形外心軌跡皆為圓弧,並且發現兩種圓弧的變換關係,也給出豐富有趣的性質。值得一提的是,分別對三角形的三個頂點輪換進行第一種構圖得出三個圓弧,這些圓弧恰可組合成三角形的九點圓,這是有趣的發現!回到原始問題的四邊形,我們構造了兩個三角形,透過巧妙轉換頂角與直徑圓變換而給出外心軌跡所在圓弧的兩個定點而解決此問題。最後推廣至鄰邊連線時,我們用雙射對應觀點簡潔刻劃了軌跡圓弧。重要的是,本研究處理四邊形的手法與三角形的是一致的,意味著證明手法具有推廣性。

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過目不忘:Sans Forgetica字體的學習效果研究

閱讀、記憶與理解,對莘莘學子們乃至大眾來說,都是每天經歷著的重要日常。有鑑於此,本研究驗證了一款宣稱能藉由理想的閱讀難度來啟動深度認知歷程,進而提升記憶與理解的字體:Sans Forgetica的效果,以及其設計在中文的應用可能,結果發現無論在英文或中文材料中,Sans Forgetica字體都展現出提升記憶和理解的效果。另外,本研究又根據認知心理學的完形理論,提出Sans Forgetica字體效果成因的可能解釋,並以眼動追蹤技術驗證,結果雖不夠強烈,但仍具參考價值,開啟後續研究的方向。

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運用疾病軌跡搭配深度學習偵測胰臟癌風險

目的:在台灣,胰臟癌雖非癌症發生數最高,但85%為末期,五年存活率小於5%,有癌王之稱。如何早期偵測胰臟癌風險,一直是醫療上的重大議題。本研究運用時間矩陣搭配深度學習進行大量變數之胰臟癌風險偵測。 方法:健保資料庫收集國人疾病、用藥等結構化資料,可藉此反映每人健康狀態。將三年內診斷與藥物碼轉為時間矩陣,以卷積神經網路訓練,訓練組與測試組比例為9:1。 結果:共計案例組1095名及對照組10950名,訓練後測試組表現之AUROC(area under the receiver operating characteristiccurve)為0.937,六十歲以上及以下AUROC分別為0.846及0.897。 結論:結論:能將診斷、藥物、時間轉成矩陣,是以疾病軌跡預測胰臟癌風險,且能找到新特徵,未來搭配健康存摺,為低成本、快速、大量的胰臟癌數位快篩。

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聲聲不熄--熱聲效應之探討

本實驗以試管、鋼絲絨、酒精燈為主體,將鋼絲絨放入試管做為發聲裝置,並以酒精燈加熱試管,使鋼絲絨兩端產生溫差,而後產生音波,利用音訊分析軟體進行錄音、分析,搭配溫度感測器記錄、分析溫度,藉以探討 此裝置發聲的成因以及相關參數對其聲音的影響。 本研究分析了裝置發聲之過程,並製作五種變因,分別為鋼絲絨密度、試管口徑、試管長度、鋼絲絨位置以及 試管與火焰距離,並統整出四點通則1.溫差與分貝有直接關聯2.發聲與熱穿透深度、堆棧位置和空氣黏性有關 3.綜合熱穿透深度以及空氣黏性,發聲效果較佳者,會有上升速率快下降速率慢的特性4.堆棧所在位置之空氣塊移動及壓縮性,影響其音量、發聲時間與上升下降速率。

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「毒」善其身 ─ ─ 探討植物的毒他作用在 空心蓮子草與大花咸豐草的防治和農業上的應用

近年入侵外來種植物問題嚴重,造成農業損失,我們也在校園中發現某些樹木下方有雜草不易生長的現象,透過文獻探討得知許多常見植物皆有毒他作用。因此決定將其應用在雜草抑制層面,我們萃取常見植物(樟樹、榕樹、鳳凰木、金絲竹、血桐)的葉,施澆在作物(小白菜、九層塔及綠豆)和入侵外來種植物(空心蓮子草及大花咸豐草),觀察其萌發率和生長狀況。從實驗結果得知有些植物之毒他物質萃取液,能抑制入侵外來種植物而不影響作物生長,同時也利用土壤分析技術證明毒他物質不會影響土壤pH及電導率。本研究旨在找出種植不同作物的最佳雜草抑制方法,找出最適合之植物毒他物質萃取液種類與濃度,並發現毒他物質會影響植物根毛和維管束細胞的生長。

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「磁」「明」無雙 — 磁性碘氧化鉍可見光光觸媒對淨水效率之研究

本研究成功以不同化學方法自製磁性奈米粒子,並利用水熱法(Solvothermal)合成可見光光觸媒碘氧化鉍(Bi4O5I2),再以不同比例複合出具磁性的光觸媒,藉由光降解結晶紫(Crystal Violet)染料實驗探討分解染料效率最佳之複合樣本,其最佳樣本為Bi4O5I2 -Fe3O4-90 %,反應速率常數達0.1118 h-1,並運用一系列儀器檢測其特性並探討其與光催化效率之關聯性。此外,針對觸媒在生活中的應用性探討,在生活不同水質、極端pH值或是高濃度之有機汙染物均仍保持良好的降解效率,並以Arduino開發板搭配各項組件模擬小型淨水場,以達到自動化降解有機汙染物。另外,利用自製紫外光照光裝置模擬捕捉CO2之光催化反應,並使用Arduino開發板之氣體偵測器確認生成化石燃料作為未來展望目標。

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Stewart's Theorem的推廣及相關探討

本文主要探討:在頂角為∠A、腰長為 ̅(AB) =l的等腰三角形ABC中,給定t, 滿足(¯PA2-l2)/(¯PBׯPC)=±t的所有P點的軌跡方程式及圖形,我們得知: 一、t=1時,其圖形為直線¯(BC)與△ABC外接圓的聯集。 二、0

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