尿酸氧化酶參與嘌呤代謝機制，然人類尿酸氧化酶基因已退化，易使過量尿酸沉積於關節造成痛風，因此微生物源尿酸氧化酶具極高研發價值。 本研究針對微生物源酵素進行基因體探勘，篩選出抗輻射奇異球菌(Deinococcus radiodurans)及耐熱雙球桿菌(Thermobispora bispora)源尿酸氧化酶基因，取得尿酸氧化酶重組蛋白質進行酵素活性測定、熱穩定分析、蛋白質結構解析、酵素對金屬離子耐受性分析與尿酸檢測應用。抗輻射奇異球菌源酵素於30℃催化速率較過去報導之酵素佳，而耐熱雙球桿菌源酵素於70℃催化效率與熱穩定性仍佳。解析耐熱雙球桿菌源酵素結構發現羧基端具特異性構型，推測與熱穩定性有關。本研究的兩種尿酸氧化酶，可分別作為降解尿酸的速效及緩解型藥物，並開發成快速檢測尿酸的簡易方法。

根據密克定理的陳述，於一個三角形的三邊上各任取一點，則三個外接圓會交於一點，且逆定理也存在。我在確認完定理和逆定理的正確性之後，以原本定理的敘述為基礎，推廣並探討了根據該定理所能做出的相似形和圓心的軌跡，並將軌跡視為三角形的基本性質，棄續探討軌跡的交點的軌跡，最後再將密克定理和密克逆定理推廣到多邊形。

Membrane bioreactors (MBR) are important components in the production of effluent in wastewater treatment systems. However, MBR are susceptible to biofouling, a process by which bacteria colonize the surface of the membrane in contact with water. Graphene could be a solution to biofilm formation. In this study, the graphene polymer nanocomposite’s antimicrobial and heavy metal removal properties and the mechanisms behind the properties were investigated. Five different films of nanocomposites with a form of graphene and a polymer were synthesized: Graphene, Graphene Oxide, PVK-GO, PVK-G, PVK. A Büchner funnel and a vacuum pump were used to coat membrane filters with solutions of each nanomaterial. Using the Büchner funnel, E. coli and B. subtilis bacteria were filtered through the filter and both the filtrate and the filter were examined for bacterial content. Similarly, a Pb2+ solution was filtered through the coated filters and percentage removal of the ion was calculated using Atomic Absorbtion Spectrometry. Further analysis from SEM data, ATR-IR, and an Oxidative Stress test revealed that the PVK-GO nanocomposite inactivates bacteria by causing oxidative stress and the carboxyl group binds to lead ions. PVK-GO was most effective at removing the highest percentage of heavy metal and inactivated the most bacteria and displayed the most antimicrobial properties. PVK-GO coatings provide an efficient and economical alternative to the current wastewater industry standard and can save millions of dollars and reduce environmental waste. Also, the coatings have applications in indwelling medical devices and can reduce the risks associated with biofilm formational and bacterial infections.

We present a study using microlensing event data from the Optical Gravitational Lensing Experiment (OGLE), recorded in the period 2002-2016 from the Galactic bulge. Our two algorithms are based on the standard point-source-point-lens (PSPL) model, and on the less conventional parallax model respectively. The optimal fit was found for each sample event in the chi-square optimization algorithm, along with the best fit parameters. Out of the 7 best fits, 4 show strong parallax effect. The microlensing fit parameters were then cross-matched with proper motion data from the Naval Observatory Merged Astrometric Dataset (NOMAD), to obtain lens mass estimation for four events. These were estimated to 0.447 solar masses, 0.269 solar masses, 0.269 solar masses and 17.075 solar masses respectively. All masses were within the microlensing mass interval for lenses found in similar studies. In this study, we conclude that the parallax model often better describe long events and demonstrate the importance of utilizing both PSPL fits and parallax fits, instead of only the PSPL model. By varying only 2 of the 7 parallax microlensing parameters instead of all simultaneously, we obtain plausible values for lens direction and lens transverse velocity: a method to investigate microlensing lens properties with no regard to its luminosity. In addition, we also present spectral classes of the NOMAD objects associated with each event, which is vital for future investigations to further confirm mass estimations. We present strategies to further enhance the algorithm to analyze the microlensing event light curve to better find deviations. We also conclude that our double model can potentially unveil the presence of dim lens objects (MACHOs) such as brown dwarfs, exoplanets or black holes.

By saving water you are saving lives including yours. All of us know that water is an invaluable and priceless gift. We can’t dispense it. The consumption of water differentiate from one country to another, we may use over quantities of water, in other countries people are thirsty living under the limits of poverty .It’s very important for agriculture, industry even human animals and plants can’t live without water. But people are careless, they consume a huge quantities of water in shower, washing car, gardening…. So that we thought to make this brilliant project F.W.S (frugal water system). This system is connected with you mobile phone by an application that shows you your water consuming and makes you control it. It record in every minute your consumption. This control system helps us to preserve water for the future generation. Besides, it tells you the price that you will pay and warns you if you pass the quantity of water that you should consume in a defined period. So you can also save your water bill. So we have to make this project works to let every person know that he is doing squandering water. With this system we can save planet resources of water. Finally, the water is as precious as our lives and with frugal water system, we will be able to monitor and control our water consumption. Also be alerted in the event of a leak or flooding. This project helps us to preserve water, reduce and avoid over-consumption. So we have to stand together against water squandering by making this project works.

Figs have become an expanding industry here in New Zealand and are a current export fruit which could potentially provide a large amount of profit to both growers and the New Zealand market as a whole. Nicola’s family has about 10 acres of fig trees. They sell the figs locally and as an export. They generally sell for about $13 per kilogram here in New Zealand and $26 in the USA. However, figs only have a shelf life of about 7 days. This is because at present there is no proven pre or post-harvest treatment or method of storage that helps to decrease the rate of decay of the fig fruit. After researching post-harvest treatments for figs, Nicola found a report which claimed to have developed treatments that increased the shelf life of figs by about 5 weeks. With this kind of increase, it would be possible to transport, store and export figs over longer periods of time without running the risk of losing large amounts of produce, or delivering unsatisfactory fruit to customers. Nicola developed 7 different post-harvest treatments based on the ones that had shown promise in earlier research. These were hot-water baths of different temperatures, both with and without different bleach concentrations. To test these on the fruit she set up four experiments – a dry matter test, a firmness test (using a penetrometer), a colour test and observation of detrimental features of the fig. She tested these treatments at 0, 7, 14, 21 and 28 days from harvest. Nicola found that after 7 days, the firmness of all of the figs that had been treated had decreased to a large degree. The only figs that did not have a massive decrease were the untreated fruit. However after about 14 days, the firmness of all of the fruit became about the same and after this 14 day mark, she would not have considered any of the figs to be edible. However, in the appearance tests, it seemed that the treated figs that had the least amount of mould and rot were the ones that had been treated with higher levels of bleach such as the 55 degree Celsius water bath with 0.003L of bleach to every litre of water, and the 35 degree Celsius water bath with the same concentration of bleach. Overall, Nicola’s results showed that the hot water bath, and hot water bath and bleach post-harvest treatments did not slow the decay of the fruit in the earlier weeks after picking. In effect, Nicola’s research showed that the information she had relied on to help plan her study had claimed too much and that the treatments were less effective than had been stated. More research will be needed to find a more reliable way to improve the shelf life of figs.

NO.62-01 2023 FEB | 科學研習期刊目錄 本期專題 大家的數學 漫談無限 | 李源順 值得再三玩味的黃金比例 | 賴以威 用數學論公平 | 陳宏賓 藝數摺學－一個可以從小玩到大的活動：哥倫布方塊 | 李政憲、李慧玲 貓是液體！鑲嵌與解剖的幾何魔數 | 張惟淳 教學現場 六年級學生數學詩學習之分析 | 孫國光 學生的課程反思初探 | 陳玉珊 跑馬拉松算數學！ | 李祐宗 科學新知 退火（Annealing）是什麼？ | 舒宇宸 特約專欄 不斷追問的問號：以問題為創作之始的作家梅麗莎‧史都華（Melissa Stewart） | 劉淑雯、林吟霙 森棚教官數學題──換汽水 | 游森棚 總召集人的話 過完很長的農曆年假，要如何讓自己收心？回顧自己二十多年來的研究歷程，都離不開數學；我們高中物理藉由運動中物體質量集中在質心的假設來學習運動學，我們在大學時得以透過常微分方程的建模，來重新認識運動方程式；真實的世界中又有更多複雜的問題需要描述，偏微分方程就可以貢獻更多，從彈性力學、流體力學、電磁學…到電子學的擴散理論都離不開偏微分方程。數學一直是生活的日常，從水龍頭的一滴水滴下、眨眼鋪上淚液、隱形鏡片跟淚液的力學、蓮葉上的露珠、下雨是打不中蚊子的、滴下的露水困住螞蟻、關節軟骨的潤滑液體流動、硬碟機跟水幫浦中的軸承、滾珠軸承中鋼珠的變形與隔開咬牙切齒間的口水、電動車馬達電磁鋼片的製程與電磁爐、煮溫泉蛋跟糖心蛋、煎肉餅到生魚片的解凍等等，都離不開數學。 數學是科學之母，數學的結構是很嚴謹的，能把嚴謹的數學寫的生動有味道的，必須在如何弱化嚴謹的程度以及維持應有的邏輯之間有所拿捏；因此本期的每一篇都值得大家列印出來細細品味。 〈漫談無限〉一文從生活中的無限談起、接續著數學上的無限、循環小數的演示與極限的概念、希爾伯特的旅館悖論跟Zeno的二分法悖論、直觀的檢查無理數是有理數數量還多的、可數的無限跟不可數的無限、幾何學上的無限、到物理學和天文學上的無限，最後以莫比烏斯環作為比喻宇宙之無限的概念。閱讀本文會開拓您對字面上意義的認知，李源順老師讓大家認識數學就是無限的科學。 熟悉代數運算的大人們遇見算術問題的解釋，就突然間發現需要回到童年時期的思考。國小的數學教育是很具挑戰性的，如何在先備知識不多的情境之下逐步建構學生的知識體系?半條蛋糕平分給四個人，要如何表達有感的分數教學?如何透過生活情境、學習需求及操作有感的學習啟動小學三年級的小數啟蒙教學?還有高年級的分數除法，結合數感理論的讓學生說、讓學生畫圖、讓學生舉例等教學策略，引導學生有感的數學學習。 課堂上要吸引學生的目光需要好的任務設計，如何透過活動及遊戲在競爭中增加挑戰性，還要從玩樂中增強學生數學的準備度?看見格子點---高中數學的探究與實作是思考與探究的很好例子，很值得讀者拿起鉛筆，跟著做一遍，動腦歸納動手畫。切割及拼布問題--朝三暮四，是講縫紉商透過適當切割正三角形拼布，再重新拼組為正方形的問題；透過討論四種不盡相同的正方形切割重拚為正三角的組法，並比較不同切割方式的差異性，非常有趣，看了好想跟著動手裁切拼裝。 〈值得再三玩味的黃金比例〉賴以威老師透過追本溯源從黃金比例的來源及定義開始整個有趣的故事，從五邊形到五星角的神祕角色、自然界中的費氏數列-兔子、松果與鳳梨，費氏數列前後項比值的極限就是黃金比例，盧卡斯數列、黃金矩形及黃金螺旋氏如何畫出來的？等角螺旋跟等速螺旋的差異又在哪裡？黃金比率是否無所不在？藝術作品的黃金比例說是否穿鑿附會？透過數學的考驗可以說明。 曾有人針對流行歌曲副歌總秒數對的一段落總秒數的比值來說有著黃金比例，您相信我們的感覺記憶可以這麼長嗎？我們很有機會在量測上讓分子分母的各自微調，使得比值接近黃金比例。 〈用數學論公平〉陳宏賓老師從疫苗供給的優先順序、快篩試劑如何分配引出公平性的問題。如何針對不同種類的公平：同樣滿足的公平、比例公平、無羨慕公平、共識公平 進行切蛋糕的程序？ 公平切蛋糕是很有學問的且在數學、計算機科學、經濟學和政治學領域是重要研究範籌。 〈藝數摺學──一個可以從小玩到大的活動：哥倫布方塊〉摺紙不僅僅是藝術，其間有很深厚的數學含量，李慧玲老師透過哥倫布方塊、哥倫布方塊球的摺製及堆疊，解構及說明其間的藝數摺學，可以邊玩邊學的文章，值得欣賞。 〈貓是液體！鑲嵌與解剖的幾何魔數〉張惟淳老師從貓咪的柔軟身段如液體般的可以填滿各式樣容器的比喻，講到真正的填滿-鑲嵌；如何讓平面上已知外型的貓咪變身為正方形？又已知外型的貓咪是如何給出的？看完本文，可以偷學幾招，還有延伸閱讀，讓你可以如裁縫師巧手般的裁切與組合，做出平面級的變形金剛。 〈六年級學生數學詩學習之分析〉教學現場中孫國光老師以林良翻譯Best Franco的〈數學詩〉書中的內容教學，讓同學透過數學詩創作的內容去感受、理解、比對、思考，理解四則運算符號在施裡面扮演的角色，再自由的找尋適當符號進行創作。透過本文的教學內容及經驗分享，我們將會有更多想像的教學應用。 〈學生的課程反思初探〉「學而不思則罔，思而不學則殆」在教學現場除了教學生會算，也要能具備思考的能力，也就是要在數學學習的認知層面及情意層面的反思能力要同時提升。陳玉珊老師第一線數學教學的經驗分享，讓大家理解知識層面的學習之外如何提升學生自我反思及統整的能力。 〈跑馬拉松算數學！〉跑馬拉松是近年來的熱門運動之一，長跑的許多行話，如「賽道全長42.195公里」是怎麼訂出來的？「6分速或5分速」、「全馬破4」、「配速員(或列車長)」、「吃甜甜圈」；如何估算操場各線道的的長度？起跑位置的不同標線位置是如何計算出的？ 李祐宗老師在文中都有揭密以及簡單易懂的計算說明。 〈數位退火技術介紹〉鑄造的過程有淬火、回火也有退火，如何鑄出削鐵如泥的寶劍也有許多秘方；如何維持某些高溫相？如何讓高溫相重新到達某種期待的穩定狀態？退火顧名思義也就是要讓這鑄件中的各原子晶格間的總體能量達到最小。舒宇宸老師以倉庫空間擺設為例、以數獨的填法為例說明如何透過計算機，以最小能量的目標規劃演算法進行「數位退火」快速且正確的填完數獨。數位退火技術還有更多的應用可以在延伸閱讀中找到。 〈不斷追問的問號：以問題為創作之始的作家梅麗莎．史都華〉學會問好問題很重要，跟ChatGPT聊天機器人問好問題才會有更有挑戰性的互動，透過不斷追問的問號有沒有可能會讓聊天機器人有更好的創作？「能夠通過學習有關自然世界的一切知識，並且與其他人分享，甚至能藉此獲得報酬，天底下沒有比這更好的事了」除了作家，老師這個行業也是。梅麗莎在自然科學及非小說類書籍的創作上成就非凡，仍不餘遺力透過教學現場參訪計畫去推廣非小說類書籍。雯子老師與林吟霙老師從新英格蘭農村的小女孩談起，讓您可以領略梅麗莎成長過程，也介紹她的許多作品。 〈森棚教官數學題〉「過年大優待！『七個瓶蓋加上三個空瓶』或『三個瓶蓋加上五個空瓶』都可以再換一瓶汽水」怎麼換汽水最划算？大家動動腦！ 黃金比例=1.618033988749895，這麼多位小數有必要嗎？ 總召編輯委員 - 李旺龍 關於本刊 出版單位：國立臺灣科學教育館 發行人：劉火欽 總召集人：李旺龍 編輯委員： 物理科吳仲卿/余進忠/戴明鳳/朱慶琪 | 化學科古建國/王伯昌/林如章/周金城/黃琴扉 | 生物科王美芬/蕭世輝/張育傑/辛懷梓/郭淑妙 | 地球科學許民陽/王郁軒/謝隆欽/盧孟明 科技科張玉山/汪殿杰/林育沖/徐新逸 | 數學科李源順/游森棚/嚴志弘/高欣欣 | 跨領域學科李名揚/劉淑雯/吳 嫻/李芝瑜/王淑音 | 特約專欄李名揚/劉淑雯/吳 嫻/李芝瑜/王淑音 策劃：李耕雲 主編：吳中益 本月專題特約主編：李源順 編輯：佟冠誼、林博雅 網頁設計編輯：施曉恬 投稿規範請來信詢問：article@mail.ntsec.gov.tw

1. Introduction In Japan the energy self-efficiency is very low: only 6%. Hydrogen (H2) has been expected as a new and alternative energy source to imported one, such as petroleum resources. Now hydrogen energy comes into the practical use in the field of the fuel cell. Hydrogen must be extracted from other sources, for example, water, fossil fuel, and so on. Hydrogen is obtained from water by using electronic or thermal or photo energy in most cases, whereas it is well-known that hydrogen is given by the oxidation reaction of silicon in alkaline aqueous solution: Si + 2OH- + H2O → SiO32- + 2H2 Free silicon (Si) is not only used in the steel refining, aluminum-casting in the field of fine chemical industries but also is used as a material in semiconductor electronics. However, a lot of used silicon is thrown away as a waste, being not reused and recycled. In this study we try to apply a waste silicon to obtain hydrogen based on the above reaction. The purpose of the study is to develop a safe and convenient manufacturing method to generate hydrogen for an energy source of the fuel cell.

Current medical intervention in cancer therapeutic methods has shown risks and side effects with normal tissues. This includes incomplete cancer eradication. In reference to numerous studies and literature reviews, a stimuli-responsive drug delivery system is selected as an innovative, safe and more assured treatment due to its site-specific release ability. This allows specific intervention upon the given stimulus which response to the presenting disease symptoms. Hence, we designed a ROS(Reactive Oxygen Species)-responsive BA-ADA(4-Hydroxyphenylboronic acid pinacol ester and 1-Adamantanecarboxylic acid bonded molecule) nanoparticle delivery system. In our study, ROS-responsive nanoparticle was designed and prepared based on a synthetic molecule from BA and ADA. A therapeutic payload, Doxorubicin, can be loaded into the nanoparticles and it can be selectively released within cancerous tissues whereby ROS level is over-expressed. This will enhance both therapeutic efficiency and reduce side effects. The stability and ROS-responsiveness of the particle were proven in a series of evidence-based experiments. The results showed a significant difference in cell viability during the experiments with healthy and cancerous cell samples. Further research will be required to extend the experiment in vivo.

Dronedarone is an anti-arrhythmic drug approved in 2009 for paroxysmal and persistent atrial fibrillation. It is less toxic than its predecessor Amiodarone as it does not cause systemic toxicity but has the same pharmacological activity. However the administration of dronedarone to permanent AF and heart failure patients leads to increased risk of stroke and cardiac death. The exact mechanism of the toxicity is currently unknown. Extrahepatic Cytochrome P450 enzymes play a dominant role in organ-specific drug metabolism and toxicity. Cytochrome P450 2J2 (CYP2J2) enzyme, a predominant enzyme found in human cardiac myocytes, metabolizes endogenous arachidonic acid (AA) into epoxyeicosatrienoic acids (EETs) which play an important role in maintaining normal cardiac physiology. Inhibition of CYP2J2 and perturbation of AA metabolic pathway could result in exacerbation of cardiac failure. This research aims to find out whether dronedarone inhibits CYP2J2 in a suitable cell model (H9C2) using astemizole as a probe substrate. Our in-house studies using recombinant CYP2J2 enzyme have shown that dronedarone potently inhibits CYP2J2. Rat myoblast cells (H9C2) will be seeded in 12-well plate and differentiated for 4 days. The cells will be then treated with different concentrations of astemizole and incubated for 24 h. The cells will then be harvested, lysed, and the cell lysate will be analyzed using liquid chromatography-mass spectrometry (LCMS). Using multi-reaction monitoring (MRM) on the LCMS, astemizole concentration as well as its CYP2J2-specific metabolite O-desmethylastemizole concentrations will be measured. The presence of O-desmethylastemizole confirms the metabolism of astemizole by CYP2J2 in H9C2 cells. By plotting a Michaelis-Menten kinetics curve, we will be able to determine the Michaelis constant (KM) and maximum rate of reaction (Vmax). H9C2 cells will be then treated with fixed concentration of astemizole while varying the dronedarone concentration. A decrease in metabolite O-desmethylastemizole conce ntration, indicates inhibition of CYP2J2 metabolism by dronedarone. Using this data, Lineweaver-Burke graph will be plotted, to determine the mode and potency of the inhibition. Our preliminary studies showed that the KM value was 2.7μM. This study will be useful in understanding if dronedarone inhibits CYP2J2 which may lead to clinically significant drug-drug interactions, one of the dangers of polypharmacy. Finally this study will shed a new light on the mechanisms for dronedarone mediated cardiac failure exacerbation.

在 1940 年代，Bouwkamp 提出一系列有關如何將矩形切割成若干個正方形的研究報告，但是如何找出正方形個數最少的方法仍是長久以來懸而未決的問題。在本研究報告中，首先引進「四角切割」的方法，並結合輾轉相除法的概念，來研究矩形的切割問題。我們的方法能大幅度降低正方形的個數，也適合做為此問題的上界函數。有關如何在長方體中切割出正立方體的組合，我們也將輾轉相除法的概念延伸到三維空間，進而建立所切割出最少個正立體數的一個上界模式。此外，藉由四角切割概念的延伸，我們也發現這個上界亦可再予修正。 In 1940’s, Bouwkamp proposed the study of dissecting squares from rectangles. Among the study, the problem of the least number of dissected squares has been open for decades. In this project, we first propose a corner dissection method, associated with the famous Euclidean algorithm. By reducing nearly three fourths of the number dissected by the primitive Euclidian algorithm, our method indeed establish a suitable upper bound of the minimal number of dissected squares from the given rectangles Meanwhile, the Euclidean algorithm has also been considered to dissect the cubes from cuboids. We analyze the fundamental properties of the method and establish a prototype of upper bound function for the minimal number of dissected cubes. Moreover, the method of corner dissection has also been implemented for some cuboids, which also exhibits the acceptable improvement being a suitable upper bound.

給定一個有n個頂點的簡單圖 G，將頂點標號為1,2,…n；考慮 任意相鄰的兩頂點標號和中最大值的最小值，稱此極值發生時的標號為圖G的擁擠標號。在這個研究中，我們得出方格表、m×n×l長方體、環狀圖、圓柱圖及樹圖的擁擠標號和其極值的通式，並討論相關的問題。 Given a simplicial graph G of n vertices, label the vertices with 1,2,…n. Consider the minimum of the maximum of the sum of any two close vertices’ labeling, and we call the labeling that has this extremum the “crowded labeling”. In this study, we found out the “crowded labeling” and the common equation of the grid, m×n×l cuboid, cycle, cylinder, and trees. And discuss the correlative questions.