令Sn 為{1,2,…,n}任意排列所成的集合，π ? Sn 為其中的一個元素，我們記π = (π(1), π(2),…, π(n))。今給定π ? Sn ，若對所有i,1? i ? n，都有π (π (i)) = i 時，我們稱π 為involution。假設π ? Sn ，並給定σ ? Sm (m ? n)，當π 中任取m 項，其大小關係的順序都和σ 不同，我們稱π 避開σ，或稱π 是一個σ-avoiding 排列。在這篇報告中，我們主要分析了2143-avoiding involution，1234-avoiding involution，和3412-avoiding involution 中的一些統計量，給出了十數個結果與幾個猜想。Let Sn be the set of permutations on {1,2,…,n} and π ? Sn be an element in Sn. Denote π as π = (π(1), π(2),…, π(n)). We say that π is an involution if π(π(i)) = i for every i, 1? i ? n. Given π ? Sn and σ ? Sm (m ? n) , we say that π avoids σ (or π is an σ-avoiding permutation) if π does not contain any m-term subsequence in the order of σ. In this paper, we discuss some classic statistics on 2143-avoiding involutions, 1234-avoiding involutions and 3412-avoiding involutions. We get many new results in this field and give some interesting conjectures.

The aim of the work is inventing the way in which the power of the ICE is the same and consuming of the fuel decreases. The following methods of investigation were used: analysis of the experience of the improvement of ICE, modeling, the brainstorming, methods of Decition Theory of Invention’s Tasks (DTIT). In this work Ivan Semyonov based on a hypothesis that if the non-supporting combustion exhausts will be drawn with the vacuum from cylinder fuel for the same power it needed less. The practical meaning of this work is in the attempt of studying the question of improving the ICE for getting and making the more perfect ICE.

The applications of digital image are rapidly growing with the developments in computer technology. This enforces digital image industry to produce devices with better quality. Despite the today’s advanced level of technology, it is known that input and output devices somewhat cause color distortions. International Color Consortium suggests that we can use ICC profile to overcome the problem mentioned above. But the related hardwares and softwares are too expensive for the general users. In this study, we base on the ICC profile’s mechanism to develop a color calibration method for low cost image acquisitions. From the theoretical and experimental results, it can be demonstrated that our method appears satisfactory.數位影像的應用隨著電腦資訊科技的快速成長而蓬勃發展，這也促使著數位影像工業的相關產品漸漸地普及與廣泛地使用，時至今日，雖然有著很好的製造技術，但是任何數位影像設備均無法完美無失真地將原有的色彩呈現出來或紀錄下來，或多或少都有色彩偏差的存在，尤其在價格越低廉的設備上更為明顯。雖然可以依據國際色彩協會的建議，使用每項設備的專屬色彩描述檔來克服色差的缺點，但是用來產生色彩描述檔的相關軟硬體均價格昂貴，實非一般使用者所能承受的負擔，本篇研究以色彩描述檔的色彩轉換機制為基礎，發展出針對廉價取像設備的色彩校正程序，無論從理論數據上的探討以及實際影像上的測試看來，我們的校正方法確實有效，讓原有的色彩能精準地重現。

It is used by practically everyone that has vehicle. The device checks your spare wheel and wams you when it is going flat.

Early physicists such as Newton thought that all objects have definite positions. For example, they thought that an apple is either inside a fruit bowl, or outside of it. The advent of quantum physics in the early 20th century proved this viewpoint wrong. There is an uncertainty in the position of any object; we can find a set of possible locations where the object might be. This concept was termed superposition. Quantum tic-tac-toe (QT3) elegantly extends the popular game of tic-tac-toe by adding this quantum physics concept of superposition. Each turn, 1 piece is simultaneously played into 2 distinct squares of a 3-by-3 grid. Eventually, however, every piece will occupy exactly one square, like in tic-tac-toe. Yet, despite this intriguing addition, not much research has been done on the game. Hence in this paper we explore the game in terms of extension, analysis and solution. Firstly, we note that the quantum extension proposed by Alan Goff in QT3 is incomplete. In reality, there can be more than 2 possible locations for any object. Unfortunately, the QT3 game rules do not allow for this extension. Thus we non-trivially generalize the game (GQT3) by proposing a new set of rules. We show that the original QT3 is a subset of GQT3 and prove that our generalized game can always be successfully played from start to finish in a finite number of moves. Then, we begin our analysis of GQT3. Firstly, we investigate the game tree complexity, state space complexity and computational complexity of the game; indicators of how complicated the game is. Notably, we find here that QT3 has a total of about 18 trillion possible games, which is substantially higher than tic-tac-toe’s 400 thousand. Then we examine the Nash Equilibrium of the game; the result if two ‘Gods’ play the game against each other. We find that in this scenario, the first player will win by 0.5 points. To make the game fairer, we suggest minor variations on the scoring, which make the Nash Equilibrium a draw. Note that standard methods to analyze all of these would take at least a year, but we bring down the time to about a minute using symmetry considerations and other optimizations. Finally, we extend our programs into an artificial intelligence that is a perfect solution to the game. We then supplement this with a utility function to make the run-time performance pragmatic for more time-consuming versions of GQT3. Ultimately, GQT3 is a challenging and unique game with myriads of exploration possibilities; we have only scratched the surface here.

My project is about investigation on traditional medicines in\r Namibia. This is all about plants and different herbs that different\r people in Namibia use for medicinal purposes. The objective of this\r project is to inform the world of how valuable nature is and how we can\r try to conserve nature’s treasure so that valuable knowledge cannot pass\r away with olden experienced herbalists. Understandably the enquiry\r into indigenous medicinal herbs arose from the need to expand the\r possibilities of ones own medical practice. It was very important for me\r to satisfy our farmer’s thirst for knowledge, which is what I want to do\r with the rest of the world.\r In this project I have included most but not all of the plants that we\r use in Namibia for medicinal purposes. Seeing that some of these plants\r do not grow in certain parts of the country, I have also tried to clone it in\r other parts of the country. I have also made a powder from one of the\r plant’s leaves and tested it on several people within the country.\r To conclude my findings and experiments I would like to say, let us\r try to take these precious knowledge left for us from our ancestors and\r maybe one day in the future we might need it in some ways.

本實驗是以實際探勘的地質及泉水資料和文獻為基礎，對於幾個可能造成冷泉降溫的原因(岩石種類、泉水pH值、流通氣體之壓力、流速)進行實驗。我們製作了一個模擬地下泉水流動的實驗管路，此管路並可同時觀察紀錄氣壓、氣體流速，以及實驗前後模擬管路的溫度變化。透過對實驗管路的熱容量校正，我們可以找出各變因對泉水降溫的關係，以建立出一個模型，期望可套用於實際冷泉的狀況，進而推論出更多冷泉的性質。This experiment uses data and bibliography from real exploration as bases to find the possibilities of why the cool spring drops in temperature. (Mineral types, spring water's pH value, air flow pressure, and movement flow.) We created a model of underground spring water for the simulation. From this model, we could observe the air pressure, movement, and the spring's change of temperature before and after the tests. By adjusting the thermal capacity in the model, we could find the direct cause of the spring's temperature drop. And hopefully be able to adopt this model to the realistic problem, increase the effort of analyzing the natural cool spring's properties.

The objectives of this investigation were to evaluate the growth conditions and the antioxidant activities of fermented black bean soy milk(BBSM) with Bifidobacterium longum B6 and 15708 cultured in four media, namely, ( BBSM ( 100%)+ 1% glucose ), ( BBSM (100%)), ( BBSM (50%) + milk (50%)), (milk (100%)) . These results indicated that; (1) both strains attained viable cell numbers about 7.19~9.53 log CFU/ml after 18 hrs of incubation and were in the order of ( milk (100%))＞( BBSM (50%) + milk (50%))＞ ( BBSM (100%) + 1% glucose)＞( BBSM (100%)), (2) both strains in ( BBSM (100%)) exhibited higher pH value ranging from 4.79 to 5.50 , but lower titratable acidity(%) ranging from 0.27% to 0.61% than the three other media after 48h of fermentation, (3) both strains displayed an even smaller tolerance to simulated gastric juice at pH = 2.0 for 3h, especially in ( BBSM(100%)), while in simulated gastric juice at pH =3.0 for 3h had higher tolerance , (4) both strains had high resistance ranging from 72.51% to 92.62% to 0.3% bile solution for 12h, (5) the reducing power of ( BBSM (100%)) was more excellent than that of ( milk (100%)), (6) the scavenging effect of yogurt (BBSM ( 100%) + 1% glucose) on DPPH radicals was significantly higher than that of ( milk (100%)), (7) In general, at ten- fold dilution the chelating effect on copper ions of these four un-fermented media except ( milk (100%)) was significantly higher than that of fermented media with B.longum B6 or 15708. 本研究是探討雙叉桿菌(Bifidobacterium longum B6及15708)在四種發酵基質(【黑豆奶(100%)+1%葡萄糖】、【黑豆奶(100%)】、【黑豆奶(50%)+牛奶(50%)】、【牛奶(100%)】)中的生長情形及抗氧化活性。結果顯示： (一) 兩株菌在四種培養基中的生長菌數大小順序如下：【牛奶(100%)】＞【黑豆奶(50%)+牛奶(50%)】＞【黑豆奶(100%)+1%葡萄糖】＞【黑豆奶(100%)】。 (二) 兩株菌在【黑豆奶(100%)】的pH值比較高於其他三種優酪乳，而最終發酵可滴定酸度比較低於其他三種優酪乳。(三) 兩株菌於pH2.0環境下，在【黑豆奶(100%)】優酪乳中耐酸性很低，而於pH3.0環境下卻有很高的耐酸性。(四) 兩株菌對0.3%膽鹽之耐受性均很高為72.52%~92.62%。(五) 在稀釋10倍的四種基質中，不論發酵前或發酵後的還原力皆以【黑豆奶(100%)】為最高，【牛奶(100%)】為最低。(六) 在濃度稀釋10倍時，【黑豆奶(100%)+1%葡萄糖】對DPPH‧自由基清除率明顯比【牛奶(100%)】高。(七) 在濃度稀釋10倍的四種優酪乳中，除【牛奶(100%)】外，發酵後比未發酵的銅離子螯合率明顯降低。

安非他命的濫用在台灣是非常嚴重的公眾健康及社會問題。安非他命會導致一連串的行為異常，包括在中腦紋狀體內釋放多巴胺及阻止多巴胺回收來增加使用者的活動力。由於安非他命會對腦細胞造成傷害，本研究的目的為探討低劑量、無立即毒性之安非他命(類似於人類使用習慣)長期施打下，是否會對C57BL6 小鼠大腦紋狀體內的蛋白質表現有影響。因此利用西方點墨法分析施打低劑量安非他命(2 到6 mg/kg) 約一星期之後，C57BL6 小鼠的大腦紋狀體中一些重要蛋白質(包括腺.酸受體A2A-R、第五亞型腺.酸環化.AC5、caspase-8 及PARP) 的表現是否有改變。實驗結果顯示，低劑量安非他命處理對這些蛋白質的表現並沒有明顯的差異。但利用二維電泳法可看到有少許蛋白質，在經過安非他命處理下有顯著的差別，如KIAA0193 homolog 、GOS-28、gammacrystallin A、malate dehydrogenase 和phosphoglycerate mutase isozyme B (PGAM-B)。這些蛋白質中，malate dehydrogenase 和PGAM-B 與代謝和產生ATP 有關，但前者是增加的，而後者減少，推測安非他命會影響神經細胞的能量代謝，因此長期施打安非他命對紋狀體造成的影響值得進一步探討。;The wide spreading use of amphetamine (AMPH) in Taiwan has become a serious public health and social problem. AMPH evokes a series of behavior abnormality including enhanced locomotor behavior by releasing dopamine and inhibiting dopamine-uptake in the striatum. Since AMPH is known to cause brain damage, the purpose of this study is to investigate the expression of several important proteins in the striatum of C57BL6 mice after chronic treatment with low and non-toxic dosages of AMPH (mimicking the common usage pattern of AMPH addict). C57BL6 mice were daily IP-injected with various dosages of AMPH (0 to 6 mg/kg) for one week. Expression levels of A2A adenosine receptor (A2A-R), adenylyl cyclase type V (AC5), caspase-8 and PARP in the striatum were analyzed by Western blotting analysis. Most proteins examined were not affected by this 1-week AMPH treatment. By the aid of two-dimensional gel electrophoresis, expressions of a few striatal proteins (such as KIAA0193 homolog, GOS-28, gammacrystallin A, malate dehydrogenase and phosphoglycerate mutase isozyme B (PGAM-B) in AMPH-treated mice were altered. Note that malate dehydrogenase and PGAM-B are two enzymes involved in energy metabolism and ATP generation. Interestingly, the former was increased and while the latter was decreased in AMPH-treated mice. Collectively AMPH may affect the energy metabolism in neuronal cells. These results suggest that the injury induced by long-term AMPH exposure warrants our further concerns and investigation.

NO.59-06 2020 DEC | 科學研習期刊目錄 本期專題 透過STEM、STEAM提升科技素養與AI素養 工程設計與跨領域教學的課程分享 | 汪殿杰 從科技發展到Maker教育該如何實踐 | 黃信惠 影像AI在自駕車上的模型訓練實作 | 連宏城 教學現場 簡易ROV設計製作於108課綱 | 郭銘哲 從創意到實作-「跨領域的STEAM教育」點亮孩子的學習 | 詹羽菩 結合POE教學法與跨領域美感之小學科技教學活動設計與實施-旋轉舞者_螺旋斜面應用 | 何仁偉 特約專欄 從兒童文學的作品中探索「穩定與改變」的概念 | 劉淑雯 融合STEAM理念，創發「自製扭蛋機」課程 | 黃琴扉 極端天氣下的加州大火 | 吳育雅 森棚教官數學題 - 巧拼 | 游森棚 科普活動報導 2020高中生太空酬載研習營 | 趙吉光 深耕女力科學－「傑出女科學家」桌遊推廣成效初探 | 陳萱、黃真瑱、呂玉環、蘇萬生 能源教育議題課程的發展與實踐－科普素養的向下紮根 | 黃真瑱、陳世文、蘇萬生 總召集人的話 摩爾定律(Moore's law)說，積體電路上可容納的電晶體數目，約每隔兩年便會增加一倍。簡單地說，晶片效能約每18個月，就會成長一倍，接近指數型的成長。例如最近引起注意的「量子電腦」，以不同的邏輯運算，則可能更以雙指數(指數的指數)的倍數成長。屆時，量子電腦應用在各生活層面時，人工智慧(AI)將造就更不同以往的生活形式。跟上科學科技的腳步，發展AI時代的關鍵能力與跨域能力，便成為重要的課題。在尖端科技發展下，STEAM跨域的科學科技教學，成為國際矚目的教育趨勢。就如Georgette Yakman和史丹佛大學所強調，透過STEAM設計思考來引發探究和創新，在設計創新中應用知識，也在設計創新的需求下，探究新的知識，又應用回到設計任務中，STEAM知識在探究求知和設計應用中，相生相長，如同太極一般，如下圖。 圖一.STEAM知識的太極理念 因應科技發展的趨勢，本期聚焦在科技普及、科學探根的核心。本期從專題到教學現場，一脈相承，從AI影像辨識的技術與自駕車上面的應用，深入淺出地介紹AI影像模型的建立與演算法的發展。再把科技發展與科技實作(Maker)，進行教學觀點的解析，告訴科學與科技教師，如何將科技實體引介到課堂中，讓科學與科技教師掌握住科技，並且介紹給學生。然後是以高中的「高壓空氣競速車專題製作的STEAM融入教學」，介紹跨領域的STEAM科技教學實例。在教學現場，「遙控水下載具設計與製作」的教學實務整合工程設計與跨領域的知識，為新課綱科技領綱的工程設計教學提供很具體的實例。接下來在小學階段的結合POE教學與跨領域美感教育，以及跨領域STEAM創意實作的教學現場，透過教學實例的分享，呈現科學探究、科技創新設計、以及人文與美感的整合教學，讓有助於學生建立核心素養。 特約專欄中的繪本跨科以及扭蛋機兩篇文章，延伸STEAM跨科教學的推動經驗，讓科學科技更具人文的關懷。極端天氣的加州大火與森棚教官數學題，提醒我們對環境的關注，也動動數學腦。最後的太空人營隊、科學女力、和能源教育的科普素養扎根，讓我們看到了卓越的未來科學菁英與幼苗。 代理總召編輯委員 - 張玉山 關於本刊 出版單位：國立臺灣科學教育館 發行人：劉火欽 代理總召集人：張玉山 編輯委員： 物理科吳仲卿/陳耀榮/李柏翰/盧玉玲 | 化學科古建國/許良榮/王伯昌/林如章/周金城 | 生物科王美芬/蕭世輝/陳建志/郭淑妙 | 地球科學許民陽/王郁軒/李文禮/謝隆欽 科技科張玉山/汪殿杰/林育沖/趙珩宇 | 數學科李源順/鄧家駿/溫世展/張宮明 | 跨領域學科李名揚/連信仲 | 特約專欄 游森棚/黃琴扉/陳正改/劉淑雯 策劃：曾聰邦 主編：吳中益 本月專題特約主編：張玉山 編輯：佟冠誼 網頁設計編輯：施曉恬 投稿規範請來信詢問：article@mail.ntsec.gov.tw

我的研究是利用一些特殊的手法來探討所有情況皆會產生共點圓或共圓點。在一個由四條直線(無平行線組、無共點)所構成的圖形中，可以找到四個三角形及它們的外接圓。我知道它會共點，在此稱其為限制點。且若再添加一條直線，則可以任意的取出四條直線，分別找出它的限制點，而這些限制點又會共圓，吾稱其為限制圓。我欲證明此種情況會不斷延續下去。即是六條線時又會有限制點，七條線時又會有限制圓…。在本研究中，我利用了數學歸納法、特殊的編號方法以及「方向角」來做出此證明。由於固定的線組對應至固定的限制點或限制圓，希望能向找出其性質的方向發展。In my study, I use some skills to discuss all the situations which satisfy following conditions. The result is that concurrent circles or concyclic points will be found in every situation. In a graph consisting of four lines, conforming to conditions that any three lines won’t be parallel or intersect at one point, I can find out four triangles and their circumscribed circles. I know these circumscribed circles will be concurrent and I call the point at which all the circles meet “restricted point”. If another line is additionally added in the graph, I can discover that restricted points determined by any four lines in the graph will be concyclic. I call the circle “restricted circle”. What I want to prove is that the above situation will go on. In other words, restricted points will exist when I have six lines, and restricted circles will exist when I have seven lines and so on. In my study, I used Principal of Mathematical Induction, special ways of numbering points and circles, and “orientated angle” to prove my hypothesis. Because of particular line groups corresponding with particular restricted points or restricted circles, the further work I want to attain is to find the relation of them.

此研究著重於機器瓢蟲在不同的操控變因下所走出之路徑是否存在著某些性質。對於轉向次數k→∞且轉向角θ為任意角時，我們計算各收斂點P於坐標平面上恰形成圓C：(x- 1/(1-r2)2+y2=(r/(1-r2))2。將瓢蟲的轉向點P1、P2連線，圓心C與收斂點P連線，則P1P2與CP之交點S的軌跡形成長軸長為圓C半徑(r/(1-r2))的橢圓，且此橢圓的焦點為P1(1, 0)與C(1/(1-r2), 0) 。各轉向點Pn(n∈□)位於一個方程式為R=mrθ-π/α，m=OP=√1/(1-2rcosα+r2)定角為cot-1(㏑r/α)之等角螺線上；同時繪出轉向次數k在不同值時，瓢蟲行進終點之軌跡，以驗證當k愈來愈大時，各終點形成的軌跡會趨近於一個圓。當k=2時，圖形為蚶線並證明其經平移後之極坐標方程式為 R=r+2r2cosθ。最後我們展示行進公比r→1- ，r=1，r→1+時所呈現的終點軌跡，並對此軌跡所呈現出的意象與自然界連結，而其實質關聯性則有待未來研究。