There have been numerous studies exploring the applications of graph theory in traffic management, often finding ways to reduce traffic congestion and make traveling more efficient. Such studies will be beneficial when applied to heavily congested areas such as España Boulevard, one of the busiest thoroughfares in Manila. This paper aimed tooptimize the road map of España Boulevard using graph theory. The current road map of España Boulevard was represented as a directed graphand subjected to the mutation method of edge removal, wherein an edge isremoved in each mutation based on a computed fitness function, F(G),which depicts better efficiency at lower values. Edges were removed until the graph got disconnected, which was tested using the Floyd-Warshall algorithm. The 28th mutation resulted in a minimum F(G) value of 144.4; this is a 50.18% decrease from the F(G) of the original graph, which is 290. After the 28th mutation, the removals resulted in an increase in the F(G). As a result, the final mutation resulted in an F(G) of 311.89, which characterized a less efficient graph. This study was able to apply graph theory concepts to optimize the España Boulevard road map using the mutation method, minimizing its F(G) by at most 50.18%. For future studies, the practicality of the alternate road map may be tested in simulations to examine its efficiency when other factors, such as traffic volume, are introduced.

In order to recycle disposable diapers, we investigated the conditions where sodium sesquicarbonate (Chemical formula Na2CO3・ NaHCO3・ 2H2O hereinafter called sesqui) precipitates selectively from sodium carbonate and the conditions for high yield. For the selective precipitation of sesqui, we defined the time required for the reaction solution to pass through the sesqui precipitation area in the Na2CO3-NaHCO3-H2O phase diagram (45°C) as Δ t. As a result, we revealed that Δt is involved in the selective precipitation of sesqui, and that we can synthesize sesqui without the expensive addition of L-Arginine as used in a previous research. Also, we proposed the “Stay method”, in which the supply of CO2 is stopped for 30 minutes to the lengthen the Δ t, and found that we could synthesize sesqui selectively even under conditions in which sodium bicarbonate is likely to be precipitated as well. Regarding the high yield of sesqui, the yield was greatly improved by the common ion effect of Na by adding NaOH to the reaction solution, sesqui synthesis by repeated reactions with CO2, and sesqui recovery by adding the anti-solvent ethanol, reaching a sesqui conversion rate of 95%. This means 109 g of sesqui can be synthesized from 100 g of Na2CO3. Moreover, we confirmed that these synthesized samples have almost the same detergency as commercial sesqui. We did a test calculation to reveal the usefulness of this research. First, if diaper recycling technology is put into practical use and all used diaper waste in Saijo City can be recycled, a reduction of 534 t/year of used diaper waste can be expected. This corresponds to a 2.3% reduction in Saijo City's waste output. From the ash that would ultimately remain after being recycled, we expect up to 35.3 t/year of synthesized sesqui using our experimental method. In addition, a CO2 reduction of 8.2 t/year is possible in the process, which is about equivalent to the volume of one gymnasium.

流體力學與人類許多空中交通運輸工具的設計息息相關。本研究使用與空氣黏度相近的肥皂泡膜模擬空氣流場，利用泡膜因薄膜干涉產生色彩的「流場可視化」特性，統整、歸納鈍體撞擊流所產生渦流的變化。藉由設計實驗，將連續錄製的影像匯入軟體分析，發現渦流因泡膜在不穩定流場下受高、低壓差影響，導致次渦流的形成；渦流脫落鈍體後運動的加速度值恆定；主次渦流分離時，恰與渦流脫落木棒的時刻相同，並渦流形成的時間愈長，面積愈大，而渦流脫落後其面積變化趨於平緩；雙渦流與單渦流運動的加速度值比為根號2，推得能量差為2倍。

本研究於2021年8月至2022年5月進行，採砂地點北至宜蘭蘭陽溪口，南至台東太麻里，我們利用室內觀察以及野外考察等方式進行研究。 磯崎灣、鹽寮廟以及都歷砂灘明顯有發亮的砂石顆粒，鐵砂含量多，磁鐵砂量也多，經顯微鏡觀察，發亮的砂石應屬於磁鐵砂。加路蘭溪出海口砂石鐵砂含量近乎80％，且加路蘭溪山壁岩層標本含鐵量78.6％，對比地質圖後，此山壁屬於八里灣層中泰源段的岩層，此層屬砂頁互層的沉積岩層，磯崎灣的鐵砂可能來自泰源段；而研究區屬於火成岩區的都巒山層，含鐵量及磁鐵量高，尤以綠色火成岩及輝長岩為最，所以暫時推論磁鐵砂多來自火成岩。

非負整數的各位數字重新排列後，由大到小減去由小到大的運算稱為Kaprekar運算。若原數和結果相等，則此數為Kaprekar常數。在此條件下，Kaprekar變換最終定會進入循環(包含循環節為1的情形)。本研究探討Kaprekar常數與循環的結構。 結果如下: (1)二進位分為五類，得到二進位常數的形式和規律。 (2)我們定義了g(x)來討論三進位的變換形式，得到能判斷其結構和循環節及數量的規則。 (3)g(x)在任何有理數區間中必有任意的n-循環點，其中n是任意正整數。 (4)關於四進位，我們發現將任意非負整數運算四次後必符合一形式，且其結果可類比於部份三進位的情形，進一步可得到所有四進位數的結果。

化學工業廢液的排放在現今工業發展盛行的國家是不能忽視的問題，而廢液的回收也是近年來熱門的的研究課題，又因為有機溶液能使離子化合物析出，所以我們利用此特性來討論其析出的情形。 我們研究探討有機溶劑(乙醇及丙酮)在不同的劑量、不同溫度、不同酸鹼物、使用兩種溶劑、和濾液再次使用的情形下，加入到硫酸銅溶液中析出硫酸銅，並找出析出率最好的數據，再進行不同變因的改變，來找出析出效果最佳的實驗數據。 其中我們觀察到在使用的溶劑中，乙醇在低溫下析出硫酸銅的量會最多，較丙酮佳，且乙醇對環境造成的傷害也較低。 我們期望能找出環保、快速且有效的回收方法，回收有機廢液中的離子化合物，來有效改善化學工業排放廢液的環境問題。

The development of rapid and efficient synthetic approaches to the bioactive cyclic and polycyclic azaheterocycles is one of the most important challenges in organic synthesis. In this work effective and simple synthetic approaches to polysubstituted pyrrolidin-2-ones 2 and isoindolines 3 from donor-acceptor cyclopropanes 1, bearing the ester group as the one of acceptor substituents, and amines were developed. The γ- pyrrolidone based skeletons and isoindoline ring system is a constituent of many biologically active molecules, both natural and synthetic, and a key component of clinically relevant entities (Fig.1,2) [1,2]. The synthesis of pyrrolidin-2-ones 2 includes Lewis acid-catalyzed opening of the donor-acceptor cyclopropane with primary amines (anilines, benzylamines, etc.) to γ-amino esters, followed by in situ lactamization and dealkoxycarbonylation. The reaction has a broad scope of applicability; a variety of substituted anilines, benzylamines, and other primary amines as well as a wide diversity of donor-acceptor cyclopropanes bearing (hetero)aromatic or alkenyl donor groups and various acceptor substituents, can be involved in this transformation. In this process, donor-acceptor cyclopropanes react as 1,4-C,C-dielectrophiles, and amines as 1,1- dinucleophiles. The resulting di- and trisubstituted pyrrolidin-2-ones can be also used in subsequent chemistry to obtain various nitrogen-containing polycyclic compounds of interest to medicinal chemistry and pharmacology, such as benz[g]indolizidine derivatives. The synthesis of the substituted isoindolines 3 is based on the domino-reaction between donor-acceptor cyclopropanes, bearing in ortho-position of aromatic substituent a bromomethyl group, and different primary amines (e.g., anilines, benzylamines, cycloalkylamines) was developed. The reaction involves the generation of secondary amine followed by nucleophilic ring opening of cyclopropane with amino group. Moreover, this process provided a new practical method for the rapid synthesis of benzo[b]pyrrolizidinone 4 from readily available starting materials.

減塑是必行的工作， 由2021年消耗28億杯咖啡紙杯資料中，我們計算出每年消耗約2000公噸的PE，我們以愛 玉子：水 =1g：80ml的比例，以20℃的水用果汁機攪打90秒萃取愛玉凍，透過蔬果烘乾機以50℃烘乾8小時製成愛玉薄膜，以自製的測量薄膜的張力，找出較堅固的薄膜，薄膜厚度經測量為0.004cm。愛玉薄膜具有防水、在100℃熱水煮1小時也不溶化，在烤箱140℃烘烤20分鐘不被破壞、不溶於99%酒精、丙酮、飽和檸檬酸、99%醋酸、飽和小蘇打溶液中，化學性質穩定等特性。透過將高熔點起司煮成起司糊當黏著劑，成功將愛玉薄膜鍍於塔模餅乾上， 在裝熱水的測試中，成功的在1小時後都不滲水，並透過咖啡測試，發現對於熱飲味道的影響頗低，可以成為取代PE膜的環保替代方案。

本研究旨在透過DCT-SVD演算法，即時對動態影像，嵌入人眼幾乎不可見的浮水印。經過測試，該演算法具有一定的抗攻擊性，可以保障影像受到他人壓縮、裁剪等操作後，能還原嵌入的浮水印資料。 嵌入的浮水印有多種用途。舉例來說，版權方可以在動態影像中，嵌入可辨識被授權者資訊的資料。當被授權者私自將影像給予未授權者，版權方可以透過還原浮水印的方式，追蹤違反授權的被授權者，並採取必要的法律行動，以保障版權方的權益。或者反過來思考，對於監視器畫面之類需要做為證物的影像，當偵測到浮水印遭到破壞時，就代表該影像經過人為修改，可能不具有法律效力。

本篇研究是比較釀酒酵母在象草汁、紅甘蔗汁和白甘蔗汁酒精發酵時產製酒精的效率。結果顯示，植物汁液的成分和特性會影響酵母菌的發酵效率和產物。紅甘蔗汁和白甘蔗汁中的其他微生物對酵母菌的影響會隨時間增加而增強，pH值也會影響酵母菌的活性。不論是否在無氧環境，象草汁中的酵母菌產製酒精的效率最好，並且在象草汁中的酒精被氧化的情形比在紅白甘蔗汁中來的小。因此，將釀酒酵母放入象草汁中進行酒精發酵是取得酒精的最佳方法。本篇研究的禾本科植物中，象草是相當適合作為生質能源的材料。

在小正三角形拼成的三角形和菱形棋盤中填入數字，使得棋盤邊長－1的三個(三角形)或四個(菱形)角落區塊總和皆相同。隨著棋盤邊長增加、填入數字越多、角落重疊部分擴大，使用了順時針接力和順逆迴轉等方式，有規律的填入數字。研究內容包括： 1.找出重疊區的圖形與小三角形的數量，並觀察圖形與小三角形增加的規律。 2.在求角落總和最大值和最小值的目標之下，如何有規律的填入數字。 3.推論角落總和最大值和最小值的公式。 接著用小正三角形設計出六邊形棋盤，依循之前的實驗過程，修正六邊形棋盤會遇到的困難，發展出星星對稱、右逆跳格和對角跳格等方法，雖然過程複雜，但都能夠找到共通性，也有了肯定的結論。

此研究利用複數、向量及三角形的重心公式，去找出多邊形的重心性質與計算公式，並探討以任意三角形三邊作出之各種相似多邊形，連接對應頂點或重心後，所構成之三角形的重心與原三角形重心的關係；再討論以此任意三角形三邊作出之正 邊形，連接相近的頂點（異於原三角形）與兩正 邊形的邊構成之三角形，其邊上依固定比例作出的點相連後的三角形之重心以及其重心相連三角形之重心，兩者與原三角形重心的關係；最後再用不同的切三塊方式，處理連接各區塊重心所得的三角形，其重心相連三角形之重心與原三角形重心的關係。