在此文中我們研究： 一個 n×4 的長方形網格中，所有從(1, 1)或(1, 4)出發，在不重複且經過每個格子點的情況下，走到(n, 1)結束的所有路徑總數分別為 Tn 、Un。 In our research, we study a n× 4 rectangular network lattice, of which all the routes are starting from (1, 1) (resp.(1, 4)), and ending at (n, 1) (situations are considered only on the conditions of passing every spot and not being repeated ). And we set the sum of all the different routes as Tn (resp. Un).

Characterization of telescope lenses using physical optics and selection of the optimal physical parameters of a reflecting telescope’s optical units were done to improve the design, cost-efficiency, and quality of the 64-cm telescope (named Oof) housed at the National Institute of Physics. Characterization has been done through numerical modeling of the point spread function (PSF) in Python. The PSF code was based on the method of getting wave vectors by Richards and Wolf. The optimal PSF was established to be the PSF of a large monolithic mirror. The PSF of a single optical lens was compared to its counterpart segmented lenses. Through the comparison of maximum intensity, the normalized mean square error (NMSE) and the Linfoot’s criteria of correlation quality, fidelity, and relative structural content, the study has produced results which proved that highly segmented optical components produce results with less quality compared to less-segmented optical components. It was found that as the segmentation increases, the maximum intensity decreases. Higher values of maximum intensity denote higher light gathering power. The normalized mean square error of the set-ups having one to seven layers had values greater than zero but less than one. This denotes that the PSF of those set-ups are near the PSF of the optimal set-up. Higher values of correlation quality, fidelity, and relative structural content denote higher correlation, higher signal to noise ratio, higher closeness of correspondence between the optimal set-up and the segmented set-up. The number and the size of the optical components of the segmented mirror were manipulated in order to achieve a negligible difference between that of the optimal PSF and the PSF of a segmented mirror. The equivalent single lens radius in terms of maximum intensity of the current set-up of the telescope was determined to be 234.25 mm. If the optimal PSF is achieved, the physical parameters of the optical components generated may be applied to the optical components of the 64-cm telescope. The design that resulted from the study could be used in the future construction of a wide-aperture telescope, which could aid in the acquisition of knowledge about heavenly bodies.

本次科展由一個高中關於柯西不等式的題目『設0

圖(一)中，在半徑r的圓形披薩上選一個任意點P，過此點畫四條線將披薩切成八份，要求這四條線中，任兩相鄰的線必須夾45?，圖中四塊黃色披薩與四塊白色披薩的面積相等，這就是有名的披薩定理。 這是台灣師大數學系教授許志農在「龍騰數亦優」中所撰寫的，但其處理的手法涉及微積分，本文將以更初等的數學方法加以證明，並推廣出下列結果： 一、 在圖(二)中，半徑r的圓形披薩內任一點P，過此點畫四條直線，四塊黃色披薩的夾角皆為θ，四塊白色披薩的夾角皆為90?-θ，則四塊黃色披薩的面積為r2(2θ) 二、 在橢圓形披薩，正2n邊形的披薩及球體，我們亦有相似的結果 另一部份，我們將用組合的手法，證明並推廣一個古典問題：「一個西瓜切n刀最多可以切多少塊，其中有幾塊不含西瓜皮」。

Research Question: To what extent does totarol show antibiotic potency against significant strains of Staphylococcus aureus causing skin and soft tissue infections in New Zealand, compared with commonly prescribed drugs used to treat the specific strain of Staphylococcus aureus being tested? Purpose of research: This essay will investigate the antibacterial potency of totarol against significant strains of Staphylococcus aureus (S.aureus) causing skin and soft tissue infections (SSTIs) in New Zealand. Only a small amount of research on totarol has been conducted. They all suggest totarol possesses antibiotic potency against various species of bacteria. The mode of action of totarol is currently unknown. Procedure 1: The totarol I ordered from Mende Biotech Ltd arrived in two forms; a powder called Totarol™ and a viscous brown liquid called Liquid K7 (LK7) in which the Totarol™ powder was dissolved in mostly sunflower oil. The investigation took place in two stages. In the first stage, the MIC value of the LK7 against reference strain S.aureus 29213 was determined by following the CLSI methodology for MIC testing (M07-A9 Clinical and Laboratory Standards institute). The MIC test was also conducted to identify whether any major ingredients in the LK7 possessed significant antibacterial potency. MIC values where compared with that of flucloxacillin. Data from stage 1 testing: LK7 had an MIC value of 1µg/mL, which was very similar to flucloxacillin’s MIC value of 0.5µg/mL. No other major ingredients in LK7 showed antibacterial potency. Totarol™’s antibacterial activity could not be accurately measured, due to the powder resisting even mixing. Procedure 2: In the second stage, disc diffusion tests were conducted against various S.aureus clinical isolates obtained from SSTIs in the Waikato community. The discs that were placed for each clinical isolate included LK7, cefoxitin, fusidic acid, mupirocin and erythromycin discs. Data from stage 2: 75% of LK7 discs produced double zones of inhibition. I hypothesized that this was due to two active ingredients found in the LK7. I predicted the one that produced larger zones of inhibition to be Totarol™. The other more stable ingredient producing the inner zones of inhibition is unknown. Conclusion: I proposed a breakpoint of outer zone sizes that were ≥ 15 mm in diameter to signify that that particular clinical isolate was ‘susceptible’ to LK7. From this breakpoint, LK7 and fusidic acid both had the same number of clinical isolates that were classified as ‘susceptible’. LK7 was the median of the number of susceptible clinical isolates. This data answered my research question; totarol in the LK7 form specifically, would be just as effective in treating SSTIs caused by S.aureus, as even the most commonly prescribed antistaphylococcal drugs currently being used.

Most football managers are not aware of the need for analysis of soccer data, which is one of the dynamic sports. In this study, we developed a statistical model with performance indicators and score indicators of individual soccer player based on various event data including dynamic features such as goal, assist, pass, etc. In this study, the correlation between the dependent variables and the explanatory variables, and each explanatory variable was confirmed through the correlation analysis to solve the problem of multiple communicability from the regression model and to analyze the statistically significant preliminary model. In addition, we analyzed the correlation between individual rating of the players and the data recorded in the soccer games, and found that there has been a problem with the rating of the soccer players evaluated by the reporters and the soccer statistics site. To solve this problem, we developed a model that best fit the performance indicators of individual soccer player using the linear regression model and the beta regression model. The performance index model of the athletes was developed by comparing the R-squared value and the mean absolute percentage error of two models, the linear regression model and the beta regression model, and found out the beta regression model is better model to use. By using the estimated regression coefficients of the regression model we made new PI model. Score Index, which is the attractive point of soccer, was developed by comparing Poisson regression model and negative binomial regression model based on AIC value, and the one using negative binomial regression model was found to be better. Through the model developed by this study, it is possible to collect the event data recorded by individual athletes for each soccer game, and obtain the PI & SI index which are the athlete performance index models. This allows us to evaluate each team's players objectively, analyze the team's deficiencies, and provide tools to find players, who can fill in the missing positions of the teams. This study can also be utilized to grasp the performance of athlete in real time by simulating the resultative model.

The research is based on the production of biodegradable plastic-like material by only using household materials. Also, it can be made at home and it causes no harm to the environment. The biodegradable plastic-like materials made by different ratio of amylose, amylopectin, glycerol and water has different use. The finished product has smooth surface, highly transparency and well flexibility. Also, it can support strong load and be able to be deformed under stress. Ratios of components are tested on: 1. Easy to injection mold 2. Flexibility 3. Tensile strength and ductility & 4. Water resistance. It is found that the ratio of tapioca starch: glycerol: water = 1.5: 0.5: 9 can withstand 13N of force and 1.5: 0.93: 9 with high ductility. To improve water resistance, more amylopectin should be added to amylose. The best water resistance ratio is glutinous rice flour: tapioca starch: glycerol: water = 0.6:0.91:0.5:9 can withstand 16N force, while 0.6:0.91: 0.93:9 and 1.35:0.16: 0.5:9 with high ductility. All materials are available in supermarkets. Higher ratio of tapioca starch can produce bookmark, with laminate effect. More tough, higher ratio of glutinous rice flour can make cups, spoons and dishes.

Monte Carlo methods are non-parametric algorithms that use random numbers and theorems of probability theory to approximate values that are not random. The purpose of my research was to approximate the surface of different geographical areas that can be easily approximated to polygons (e.g. lakes, glaciers, deserts) with Monte Carlo simulations starting from either Cartesian coordinates or pictures. Computer science would not exist without math, and this research project showed me the importance of a deep understanding of probability theory in the world of simulations and, more generally, the importance of developing new theorems and algorithms. The results of my research could be developed in different ways: it would be interesting to produce software that allows one to approximate areas from pictures taken from a smartphone; as well, the theorem I found has to be proven, and also Monte Carlo methods as a means of random number generation can always be improved. There are still many possibilities.

This science project is designed to answer a question of whether or not a chemical reaction is needed to produce industrial quantities of carbon nanostructures by exposing dry ice to a high temperature that is at least 3100°C. A small carbon arc furnace powered by an electric welder is used to produce the high temperature. During control runs, the carbon arc furnace is energized for a predetermined time, after which the carbon arc furnace is de-energized and any carbon particles within the furnace are collected. During carbon nanostructures synthesis runs, dry ice is placed within the carbon arc furnace. The carbon arc furnace is energized and the dry ice is consumed for the predetermined time. Carbon nanostructures synthesized during the synthesis runs are collected once the carbon arc furnace is de-energized and allowed to cool. The volume of the carbon particles collected during the control runs is compared to the volume of the carbon nanostructures produced by the synthesis runs. This science project has discovered that on average at least 16 times more carbon nanostructures are produced during synthesis runs consuming dry ice as opposed to the control runs. Moreover, the synthesis runs did not rely on chemical reactions. Further still, samples of the synthesized carbon nanostructures were imaged using a transmission electron microscope (TEM). The TEM images clearly show high-quality carbon nanostructures that include carbon nanotubes, faceted carbon nanospheres, and the super-material graphene.

本研究在觀測前根據GCVS（GeneralCatalogueofVariableStars、俄羅斯大學變星資料庫）找尋適合的目標，我們考量星體的光度變化、週期及適合觀測的時間、方位，經篩選後，再從可能之目標中選定此次觀測目標：VZCnc，並且擬定計畫，以利於觀測及拍攝的進行。使用TheSky6軟體找尋VZCnc附近星體分佈的情況，以供分析使用。我們使用CCD(ChargeCoupleDevice、電荷耦合裝置)拍攝，以V濾鏡拍攝三天共一千零七十八張影像，加以整理及刪除不適合者，再進行疊圖使繪出的圖有較高的準確性，並根據光變曲線圖加以分析其變化範圍、週期，和手邊擁有他人的觀測資料對照，充分了解其亮度變化的情形。

聚苯胺導電高分子的發展蓬勃迅速， 其應用也愈趨廣泛， 金屬防蝕為其可能應用之一。台灣四面環海， 工業發達， 造成金屬腐蝕損害嚴重。本文為探討聚苯胺導電高分子在鐵系金屬防蝕上之應用， 針對以下各點進行研究：（ 1.） 探討導電高分子聚苯胺性質與合成方法（ 2.） 探討聚苯胺導電原理（ 3.）測試不同腐蝕條件下聚苯胺的防蝕效果（ 4.）探討聚苯胺防蝕原理（ 5.）各種氧化還原態聚苯胺防蝕效果之比較。實驗結果顯示塗布聚苯胺與未塗布聚苯胺之鐵系金屬（ 生鐵、不鏽鋼、鍍鋅鐵）在3﹪ 氯化鈉、0.5M鹽酸、1M 鹽酸鹽酸溶液中之腐蝕狀況， 以鹼式中間氧化態聚苯胺（ Emeraldinebase）最具防蝕效果。聚苯胺防蝕機構包含阻隔防護、腐蝕抑制劑、陽極保護、惰性化、形成保護性氧化物薄膜、阻礙離子擴散速率、電化學介面遷移等機構。\r 英文摘要：\r The development and application of the conducting polymer polyaniline is getting prosperous and popular. One of the applications is corrosion protection. Because Taiwan is surrounded by sea and the pollution of industry is more and more serious than before, the damage of corrosion is greater and should be properly controlled. In this paper, the authors attempted to study the effect of the corrosion protection of polyaniline in ferrous metal. This study could be divided into four parts: (1) the study of the property and synthesis methods for the conducting polymer polyaniline, (2) the conduction theory of the polymer polyaniline, (3) The corrosion protection effects of the polymer polyaniline under different corrosion situations, (4) the corrosion protection theory of the polymer polyaniline, and (5) the comparison of the corrosion protection effects of various polymer polyanilines. According to the experimental results, the Emeraldine-based polyaniline gets the best corrosion protection effect. The mechanism of corrosion protection may be the result of the following ones: barrier protection, corrosion inhibitor, anode protection, innobeling, chemical active layer, inhibition of diffusion rate, and the shift of electrochemical interface.

NO.61-03 2022 JUN | 科學研習期刊目錄 本期專題 海洋環境的變遷 臺灣的海洋環境與海岸地形的演育──東部海岸與西部海岸的比較 | 許民陽 臺灣海洋環境問題──臺灣海岸後退變遷舉例 | 許民陽 全球暖化正影響著各種尺度的洋流系統——黑潮、大西洋經向翻轉環流、與全球海流 | 鄭志文、葉庭光 探索內太空：從郵票看深海潛航的百年演進 | 李孟陽 教學現場 等鱟到來 | 盧家豪、張錦霞、蓋玉軒、陳麗淑 鱟來遇見你～鱟的海洋教育課程 | 張雅菱、管郡潔、蓋玉軒、陳麗淑 「鱟」事知多少 | 曹瑞芸、許芳瑾、鄭淑菁、蓋玉軒、陳麗淑 科學新知 集眾人之力的氣象研究 | 王嘉琪 上天下地——淺談龜山島地形與地質 | 梁勝雄 特約專欄 繪本科學閱讀的跨領域教與學：爸爸的機械魚 | 劉淑雯、蕭 敏 我國氣象觀測站網的建置和演進（三）臺灣東部地區 | 陳正改 森棚教官數學題——星球的另一面 | 游森棚 科普活動報導 海洋科普教育與化石巡迴展——讓海洋生物化石重新找回生命 | 張詠斌 2022第一屆量子科技科普線上推廣壁報展 | 林昱廷、余進忠、蘇萬生 科教館GO好玩 他山之石——加拿大全國科展評審制度探討 | 陳香微 總召集人的話 最近重讀了《這個不科學的年代～費曼談科學精神的價值》一書，也回顧了一些學倫的事件，有些歪樓的感慨。在這個年代，我們有自駕車、AI、IoT、護國神山…許多科技的進步，改善我們的生活；但同時有空氣及海洋河川的污染、極端氣候、疫情、戰爭、能源等生存問題；同時也有許多假議題、偽科學、假新聞積極影響我們的生活；國家與國家之間的衝突也透過許多人工製造的訊息來追求正當性；如果要說這是個科學的年代，倒不如說這是個自媒體的時代。當有人說我們接受教育是為了能知道誰在胡說八道時，「明辨是非」就是一件重要的事情。知道自己沒做而要求掛名是不對的、知道找人捉刀是不對的、知道幫人捉刀是違反學術倫理的、知道有科學依據的討論是對的、知道不製作假消息是對的…。掛名文化是不可取的，是不誠實的，當大人汲汲營營為著小孩的學習履歷積點時，就要知道自己的行為是不是在幼小的心靈中建立了不良的「典範」？沒有做的可以找槍手？貢獻比率不高還是掛名了？十年後這些小朋友長大了，造假的行為會不會習以為常且蓬勃發展？為達目的可以不擇手段嗎？我們要從小灌輸學術倫理的觀念，才不會「細漢偷挽匏，大漢偷牽牛」。 臺灣島為什麼長得像番薯？凸出的部位是沖積造成？凹陷的部位是沖蝕造成？事情沒這麼簡單，有許多複雜的因子，如：海洋環境、海岸地形地貌地質、河川位置、流體的沖蝕作用…許多影響因子複雜的交互作用才變成現在這個身形？ 地球上占比71%的海洋在地球生物演化、生態平衡、能量平衡、氣候調節及海岸地景演育上扮演重要的角色；海洋透過季節風、波浪、 潮汐與海流，不斷塑造多樣性的海岸地景。受到全球氣候暖化的影響，海平面不斷上升，海岸線會如何變化？這些都是陸上岩石圈、海洋的水圈及大氣圈三者交互作用的結果？ 還是沒這麼簡單，更精準的說法在許民陽老師的兩篇文章中〈臺灣的海洋環境與海岸地形的演育–東部海岸與西部海岸的比較〉及〈臺灣海洋環境問題-海岸後退舉例〉有很清晰的基礎說明。 流體力學是很重要的學科，含括質量、動量、能量守恆，也是計算量大到需要超級電腦的學科；我們的日常生活離不開流體力學，從早上起床的一杯熱茶、洗臉、尿尿、沖馬桶、滴眼藥水、香檳酒杯中的泡泡…到火力電廠的排煙、PM2.5的淤積、洋流、颱風及氣象預報等等，都是流體力學的範疇。當你煮著開水時，可以觀察到許多的小小躁動、之後的大大翻滾以及沸騰時的水蒸氣讓人不敢面對，煮開水的熱量傳遞以及產生的能量重新分配到以不同能量形式呈現，都是很值得深究的熱力學。如果把觀察的尺度從煮開水到整個地球上的天氣與氣候、海洋、生態、地形與地貌，這些因子間環環相扣的交互作用，不但導致相當規模的物種滅絕、甚至對經濟、政治產生重大的影響。全球暖化就是個大尺度的問題，從北極冰層的融解造成淡水釋出，從而些微的海水溫度、鹽度、與密度的改變，竟然會開啟大規模海水水體運動的變異，進一步影響海域環流的變化；這些交互作用，成為現在極端氣候的成因之一，是亟需許多跨學科的研究。〈全球暖化正影響著各種尺度的洋流系統——黑潮、大西洋經向翻轉環流、與全球海流〉文章中有著多尺度的觀點，為您局部的以及宏觀的解釋洋流系統。 〈探索內太空：從郵票看深海潛航的百年演進〉一文從方寸之間來看科學技術歷史發展，從科幻小說〈海底兩萬里格〉講起，小說的「鸚鵡螺號」潛艇也成為率先潛航抵達北極的美國核子潛艇命名的原由。要潛入深海會面臨哪些需要解決的技術問題？本文透過深潛技術的國際競爭以及合作的歷史，來說明如何一一透過科技發展以及跨國合作來克服。「從早年列強爭相競逐深潛紀錄，到近年深海熱泉調查、海底地形測繪，乃至水下工程及水下救援，各類型的深海載具不時成為郵票發行的主題。這一枚枚設計精美的郵票，展現歷來深海探險家的冒險事蹟、深海探勘的傑出成就，深海技術的創新突破以及海洋科學的重大發現，承載著人類探索這顆藍色星球的共同記憶。」 海水海風沖蝕腐蝕的能力很強，一台新的腳踏車，在沿海鄉鎮使用，很快就會生鏽；七美的電腦要隨時維持開機狀態，才不會因為鹹水煙（台語，瀰漫在空氣中，帶著鹹鹹海味的水霧）而無法開機；疫情只要配給平板給偏鄉，線上教學即可解決？我們在冷氣房中做的許多決策都需要與第一線教師有密切的互動連結調整才能更接地氣。 鱟本身就是個充滿議題的生物，海科館的海洋公民科學家實踐行動計劃以鱟為主角，海科館團隊透過應用BEST學習模組-Building（建構學習）、Experiencing（體驗探索）、Solving（解決問題）、Teaming Working（團隊行動）- 結合海洋環境學習的體驗探索，讓學生浸潤在有感的自主學習環境，深化學習的內涵與價值；分享開發〈等鱟到來〉課程的歷程，讓讀者有感學習。安康高中及中正國中及社區與海科館合作，規劃及參與〈鱟來遇見你~鱟的海洋教育〉〈「鱟」事知多少〉課程，靠山區的社區型中學，於校內生物實驗室進行鱟卵孵化飼養至今，讓學生在engage過程中對海洋有感，從鱟卵孵化與幼鱟的飼養開始來引起學生學習動機，藉由課程的引導，讓學生設計以鱟為主題之探究與實作題目，探索鱟的生物學…，讀者深入閱讀必有收穫。 科學新知 科學研究中常有需要大量人力處理但是難度不高的基礎步驟，透過集結眾多民眾或學生的力量參與，通稱為「公民科學」。最有名的例子就是20世紀末利用民眾家裡閒置的電腦尋找外星人的「SETI@Home」計畫。〈集眾人之力的氣象研究〉一文，王嘉琪教授讓您清楚公民科學在氣象上的應用及中央氣象局推動相關研究計畫-歷史氣象紀錄的數位化或數值化；民眾在參與的過程中，除了對科學研究有直接貢獻，也可獲得一些相關知識與成就感，可說是個互惠的過程，透過互動也大幅拉近科學與一般人之間的距離。 踏上401高地，這名列國際間12座地貌特殊的島嶼之一的龜山島，地貌特殊。龜山島是如何生成？龜山島會再噴發嗎？龜山島的自然環境又是如何？龜山島又有哪些特殊的地質景觀？您知道氣象局、中研院地科所及中央地調所合力於龜山島上設置那些觀測站嗎？〈上天下地-淺談龜山島地形與地質〉為您揭開神秘面紗，一睹她美麗婀娜的型態。 特約專欄 接續前兩期陳正改老師的歷史回顧，〈我國氣象觀測站網的建置和演進（三）臺灣東部地區〉本期來到東部地區。「花蓮的地形屬狹長型，北迴歸線正好通過瑞穗鄉，致使瑞穗以北屬副熱帶氣候區，瑞穗以南則為熱帶氣候區。另因受到黑潮洋流的調節以及中央山脈阻隔影響，氣候相對溫和，雨量亦充沛；夏季常遭受颱風的侵襲，冬季因盛行東北風，風力較強勁。」看著不同氣象站的變化及消長，除了設備更新帶來的新氣象之外，也該重視那歷史建築、設備及資料。〈繪本科學閱讀的跨領域教與學：爸爸的機械魚〉文章中，透過繪本〈Papa’s Mechanical Fish 爸爸的機械魚〉融入閱讀、數學和科學教育，蚊子老師與第一線教師合作，擔任協同教學人員在數學、生活、英語繪本、美勞、童軍四門課程中融入多方面領域知識搭配設計，並分享教案規劃以及從共讀繪本、動手操作到回饋互動解決問題的課程經驗。千呼萬喚始出來，猶抱琵琶半遮面，〈星球的另一面〉挑戰您的投影、遮掩的觀點。 物理教育學會理事長余進忠分享舉辦〈2022第一屆量子科技科普線上推廣壁報展〉的經驗及原由，除了有大學教授也有許多熱血的高中教師參加，也提供壁報展的經營策略。我國的科展制度如何訂定的？我們總是一成不變嗎？在改變調整時是不是有一些功課要做？ 〈他山之石——加拿大全國科展評審制度探討〉一文分享國外經驗，有比較是好事，國內制度多重防弊，國外制度多重科學思考。 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 | 特約專欄 游森棚/黃琴扉/陳正改/劉淑雯 策劃：李耕雲 主編：吳中益 本月專題特約主編：許民陽 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