Refer to Figure 1. Suppose ABCD is a trapezoid and . Passing the intersection M of and we construct a parallel line intersecting and at E and F, respectively. We obtain that , and then we can generalize the result. 如(圖一)，若ABCD為梯形且，過 和交點M 分別作平行線交、 於E 、F ，可得 的關係，再加以推廣。

槐葉蘋(Salvinia natnas)生長於台灣低海拔淡水濕地，目前已列為嚴重瀕臨滅絕的台灣原生物種，為不具有根的植物，是世界珍稀的漂浮型水生蕨類。本研究是探討槐葉蘋形態、生活史及生存環境因子，實驗發現可藉由成熟浮水葉外部形態特徵來區別槐葉蘋與外來種之人厭槐葉蘋(Salvinia molesta)；槐葉蘋成熟浮水葉呈橢圓形，葉上毛被物是叢生且分岔，人厭槐葉蘋成熟浮水葉呈雙耳形，葉上毛被物則像打蛋器。當兩物種共存於同一個環境空間時，人厭槐葉蘋以平均11.6 cm2/week 的生長率將槐葉蘋完全取而代之，顯示人厭槐葉蘋之入侵對槐葉蘋生存影響之深遠。經由兩年的槐葉蘋物候觀察，發現3~11 月為抽芽成長期、3~12 月為成熟繁殖期、12 月~隔年2 月為冬枯期及孢子囊果出現期，12 月~隔年5 月為孢子囊果成熟開裂期。其繁衍策略可分為無性繁殖（頂芽及側芽生長）及有性生殖（異配子體交配）。探討環境因子（光照度、氣溫、濕度、水質、水溫、pH 值）分析結果，適合槐葉蘋生存環境的條件為(1)陽光間接照射（半遮蔭，遮蔭度58.33%）、(2)乾淨未受污染的水質(pH 6.5~8)、(3)通風性良好。生長環境符合以上條件即可達到移地保育的目的。Salvinia natans, a floating fern without roots, grows in low elevation fresh water wetlands of Taiwan, and is a critically endangered precious Taiwanese native species. This research investigates the life form, life history, and living environment of Salvinia natans. Our experiments show that we can differentiate Salvinia natans and Salvinia molesta, two easily mixed up species. The shape of matured floating leaves of Salvinia natans is elliptical and smaller, while it is twin-ear shape and larger for Salvinia molesta. Also, they can be distinguished by their leaf hairs. The hairs of Salvinia natans are tufted and separated at the tips, while the hairs of Salvinia molesta form an ‘eggbeater’ shape at the tip. When these two species lived together, Salvinia molesta grew in a rate of 11.6 cm2/week and will replace all Salvinia natans eventually. This shows the profound impact of invasion of Salvinia molesta. From the data of 2-year phenology observation, we concluded that budding took place from Mar. to Nov., growing and reproducing from Mar. to Dec., decaying from Dec. to Feb. (sporocarps were born in this period), and sporocarps matured from Dec. to May. There are two reproduction strategies: sexual reproduction (intergametophytic mating), and asexual propagation (by terminal and axillary growth). After investigating the environment factors (illuminance, air temperature, water temperature, humidity, pH), we found that ex situ conservation for Salvinia natans requires 1) indirect sunshine, 2) unpolluted water (pH 6.5 ~8), and 3) good ventilation.

由於台灣山區溪流短小陡急，土石流災害嚴重，透過式防砂壩攔阻工法為現\r 今之趨勢，而帄面透水柵具有一般透過式壩的優點，不但能將土石流轉化為水砂\r 流，還可以減低土石流衝擊力造成的損壞及改善上游儲砂空間不足的問題。本研\r 究採用改良式帄面柵，在下游處增設分流河道，可改善分離出之細顆粒土砂水與\r 大礫石再度結合之危險。此工法於2003 年引進台灣後，尚未廣泛應用，主要原因\r 為缺乏設計之經驗式，因此本研究針對透水柵的柵棒長度（L/ Dmax）、棒淨間距\r （b/ Dmax）、柵面架設方式、柵面篩分角度（θ）等多項重要因子進行室內渠槽\r 試驗，最後提出土砂篩分比與攔阻率的趨勢方程式，設計時以總攔阻率（R）高為\r 原則，輔以篩分比（S）與貯砂率（R1）高，即可有良好之成效，期望能作為國內\r 外現場工程施做時之參考，結果如下所示。

可聽聲有向四周擴散繞射特性，而超聲波具有指向性，改以超聲波載送可聽音訊號後，其載波與旁頻帶均在超聲波範圍，實驗中人耳卻可聽到高度指向性聲音，且調幅解調後的可聽聲衰減率比純超聲波來的低。那為什麼超聲波會解調可聽音？我們以非線性的數學轉換概念，成功以數學推導解釋實驗中所聽到的可聽聲，是由旁頻經由非線性轉換而來的。為了證實空氣中的超聲波有非線性現象，以發射40KHz單頻訊號，除了接收到40KHz訊號外還可接收80KHz訊號，而80KHz訊號振幅，會隨著發射強度而遞增，也會隨著傳輸距離增加至穩定狀態，這所我們從文獻中的非線性理論所吻合。接下來進行調幅超聲波實驗，我們經理論計算旁頻帶強度為頻率響應與調變率乘積的一半，而解調可聽聲的強度為調變率、頻率響應與非線性係數三者乘積，我們也由實驗數據證實理論計算結果，在實驗中，換能器在40KHz有最佳的頻率響應，其非線性係數與所載送可聽聲頻率高低約略成正相關，並且與換能器距離遞增而越遠而增加。此外在提高高指向可聽音輸出功率方面，除製作專屬的放大器、運用方波取代正弦波來載波、配合陣列換能器輸出；在改善音質方面，利用等化器調整訊源頻譜分佈，降低低頻振幅，增強高頻振幅，讓各頻率的原始訊號都能有適當的調變，達到最佳音質。The audible sound has the characteristics of spreading and diffracting. And ultrasonic is directive. We modulate sound into ultrasonic signal. The carrier and sideband are ultrasonic frequency bands. But in the experiment, human can hear highly directive sound. In terms of attenuation rate, AM demodulation sound is lower than pure ultrasonic wave. Why can human hear the directive sound? By using the nonlinear mathematical transform, we managed to explain the audible sound which is transformed from sideband with nonlinear effect in the experiment. In order to confirm that nonlinear phenomena in the air ultrasonic, we launch 40KHz single tone ultrasonic signal. Besides the 40KHz signal, we also received 80KHz signal. The amplitude of 80KHz signal will increase with the emission intensity, and also with the transmission distance to increase its stability. These are consistent with nonlinear theory in the literature. Next we began AM ultrasonic experiment. We calculated the sideband intensity that is the product of frequency response and modulation index. The demodulation sound intensity is the product of modulation index, frequency response, and nonlinear coefficient. We also proved the calculated consequence through the experiment. In the experiment, the ultrasonic transducer has a best frequency response in 40KHz. The nonlinear coefficient has positive correlation with the modulation frequency, and increases transmission distance. To boost the power of directive audible sound, we made an amplifier, using square wave to replace sine wave of carrier, and in conjunction with array transducer output. To improve the sound quality, We use the spectrum-Equalizer to adjust the frequency distribution of the origin signal. The EQ reduces the low-frequency amplitude, and boost high-frequency amplitude, which enables every frequency of the original signal to be properly modulated, achieving the best sound quality.

NO.58-01 2019 FEB | 科學研習期刊目錄 本期專題 運用科技的物理教學 智慧型科技與行動學習： 以手機APP為例 | 賈至達 綠能數位與實作教材 之發展與運用 | 盧玉玲 蠟燭燃燒實驗的IoT 之旅 | 李柏翰 、江政龍、蘇萬生 智慧型手機立體影像STEAM實作教材 | 洪連輝、張益嘉 運用Arduino探究視覺暫留 | 陸健榮、鄭依佩 科學探究隨手做：手機感應器的物理原理與教學上的應用 | 盧政良 教學現場 動手玩科技：射箭Robot自己做 | 施皇羽、許弘叡 量子力學之美：電腦叢集計算在附中 | 李柏翰 科學新知 淺談「智慧電網」 | 蔡振明 特約專欄 變色龍 | 游森棚 帶得走的STEAM課程設計：古機械鐘創意課程 | 黃琴扉 趣讀科普，昇華閱讀，活化STEM腦 | 劉淑雯 科普活動報導 看得獎影片 學有趣科學 | 李名揚 科教館GO好玩 電漿球演示融入科學劇的情節歷程--以｢電漿球｣演示為例 | 陳香微 總召集人的話 本刊自本期起改為雙月刊，於「臺灣網路科教館」網址刊登，文章方向將更緊扣STEAM教育與國中小物理、化學、生物、地科、科技、數學六大領域或分科。除將於「本期專題」和「教學現場」單元刊登和12年國教課程與教學相關文章外，亦結合科教館「科普傳播中心」做更多元化的分享與傳播。物理科召集人是國立彰化師範大學物理學系吳仲卿教授，「本期專題」推出「運用科技的物理教學」專題。 「本期專題」共有六篇文章：〈智慧型科技與行動學習：以手機APP為例〉一文以智慧型手機的APP為主軸，論述智慧型科技在「行動學習」的應用，以及在科學學習的幾個面向。〈綠能數位與實作教材之發展與運用〉一文分享作者研究室所研發的「綠色能源」數位教材，教材係整合情境式數位學習與實作探究而成，以風力發電為主題。〈蠟燭燃燒實驗的IoT之旅〉一文帶領讀者利用國中理化課程單元--密閉容器蠟燭燃燒實驗，結合國家晶片系統設計中心開發的MorSensor測定晶片，設計一套創新的實驗流程。〈智慧型手機立體影像STEAM實作教材〉一文作者分享其整合STEAM教育精神，所開發出主題為「立體視覺與虛擬實境」的一套光學領域課程與教材。〈運用Arduino探究視覺暫留〉一文分享如何運用新科技--開源微控制器，針對視覺暫留現象進行定量的探究與實作，同時訓練學生測量與分析以及程式與電路等跨領域的基本素養。〈科學探究隨手做：手機感應器的物理原理與教學上的應用〉一文分享利用手機進行數位量測教學的的經驗與建議。 「教學現場」刊登兩篇文章：〈動手玩科技：射箭Robot自己做〉一文分享在國小利用木工課程搭配microbit的程式設計，進行「射箭Robot」的設計經驗。〈量子力學之美：電腦叢集計算在附中〉一文分享在高中開授多元選修課程「量子力學之美，電腦叢集計算」的經驗與成果。 「科學新知」刊登〈淺談「智慧電網」〉一文，介紹智慧電網的三大要件：智慧電表，資訊、通信與自動化系統，和儲能系統。 「特約專欄」刊登三篇文章：〈變色龍〉拋出兩隻不同顏色的變色龍相遇會同時變成第三種顏色的問題。〈帶得走的STEAM課程設計：古機械鐘創意課程〉一文分享跨校、跨領域、跨單位整合，創建一系列古機械教具與教材教法的經驗。〈趣讀科普，昇華閱讀，活化STEM腦〉一文從STEM教育觀點介紹四種類型的科普書籍。 「科普活動報導」刊登〈看得獎影片 學有趣科學〉一文，報導已有公播版的「永不妥協－實驗室的挑戰故事」系列影片。 「科教館GO好玩」刊登《電漿球演示融入科學劇情節歷程探討—以｢電漿球｣的演示為例》一文，分享科教館科學劇「今天我們去哪兒」，將展品｢電漿球｣的演示融入劇情中，彰顯科學與藝術跨領域整合的效果與心得。 總召編輯委員 - 李隆盛 關於本刊 出版單位：國立臺灣科學教育館 發行人：陳雪玉 總召集人：李隆盛 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 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/劉淑雯 策劃：曾聰邦 主編：錢康偉 本月專題特約主編：吳仲卿 編輯：吳郡怡 網頁設計編輯：施曉恬/陳璽君 投稿規範請來信詢問：article@mail.ntsec.gov.tw

自由基會產生在神經系統、免疫系統、血液循環系統等等，進而影響到人體各器官的運作,甚至於近年來許多醫生學者提出自由基病理:自由基是百病之源。本次實驗筆者挑選葡萄子、維生素C、綠茶來抑制清氧自由基(OH.)所採用的方法是將10%雙氧水製入注射筒並加亞鐵離子催化,,使其與抗氧化物反應,由於雙氧水分解會產生氫氣自由基與氧氣,因此筆者用倍率放大器(OPA)放大生成氧氣造成的電壓,並用Data Studio測量記錄,最後可由氧氣體積對電壓的趨勢圖看出抑制氫氣自由基的效果;Free radicals will be produced in our nerves system blood circulation immunization system etc. and they able to influene the operaion for our organs many medical scholars have even come up with "free radical pathology"-free radicals are sourse of all he diseases in recent years.In this study, I chose rape stone vitaminC and green tea to restrain hydroxide radicals(OH.) Here is summary of the experimental process. First,I put 10%hydrogen peroxide into an injector and then added ferrous ion to hydrogen peroxide to catalyze it. Second I let it reaact with the sample. Because hydrogen peroxide can produce hydroxide radicals and oxygen, I used the mutiplier(OPA) to amplify the pressure caused with the prducion of oxygen, measuring and recording resuls by the software"Data Studio"Finally, we can tell which antioxidant is more effective in restraining hydrode radicals from volume-voltage gragh.

磁粉探傷過程包含兩個重要的物理現象，其一是磁力線於工作瑕疵處的漏磁現象而形成邊緣磁場，其二是鐵粉顆粒受邊緣磁場的影響而向工作瑕疵處附近聚集現象分別反應出磁場在通過不同介質時所遵循的折射原哩，以及磁場分佈對鐵粉顆粒產生的磁力原理。本研究以電磁通電產生靜磁場，並利用兩電磁鐵間的氣隙來模擬工件瑕疵，因電磁鐵的磁導係數遠大於空氣之磁導係數而造成漏磁場方向機與漏磁面垂直，形成一單純的邊界條件使得邊緣磁通密度的解析解可直接利用馬克斯威爾方程式求得。我們亦導出空氣中的磁通分佈對微小的鐵粉顆粒所產生的磁力公式，發現鐵粉顆粒受靜磁力的大小與該顆粒的體積、磁通密度與磁通密度之梯度成正比，而其方向則與磁通密度之梯度一致，此結論與磁粉探傷過程中，鐵粉向工件瑕疵處聚集的現象吻合。實驗設計採用螢光粉混合鐵粉以獲致明顯的鐵粉顆粒運動軌跡，用數位錄影機紀錄後再擷取影像圖檔判讀其位置與時間之關係，進而反算鐵粉顆粒之位置與所受之靜磁力的關係，以定量的方式證實所推導的邊緣磁場分佈公式以及磁力公式。Two important physical phenomena are observed in the practice of magnetic particle inspection (MPI). The first one is that leakage flux is present in the defect area of the work-piece under inspection. The second one is that magnetic particles aggregate in the vicinity of the defect. These phenomena manifest the theory of flux refraction, which occurs in the intersection area of two different magnetic materials, and the theory of magneto-static force, which is experienced by the iron powder in a magnetic field distribution. Two electromagnets, made of cast steel, are aligned together such that the leakage flux in the air gap forms a fringing field distribution. It is this magnetic field distribution that simulates a defect area in a magnetized magnetic work-piece. Since the permeability of cast steel is far larger than that of air, the direction of the fringing field at the surface of the electromagnets is almost perpendicular to the surface. Such a simple geometry renders an analytical solution to the Maxwell’s equations. The magnetic force of the magneto-static field exerting on the magnetic particle, an iron powder in this case, can be derived by using the principle of virtual displacement. We obtain a formula of magnetic force, whose direction coincides with the gradient of the magnetic flux density and whose magnitude is proportional to the magnitude of the particle volume, the magnetic flux density and its gradient. This formula also agrees with the observation in MPI that the magnetic particles aggregate in the vicinity of the defect.

本研究利用蛋白質的環保、生物活性，金奈米粒子的低毒性，及蛋白質金奈米粒子的螢光特性，合成可應用於生物體內之螢光蛋白質金奈米粒子，從而利於標靶藥物研究。本研究選擇與眾多疾病相關的胰島素，以最佳方式合成紅色螢光胰島素金奈米粒子，有助於探討糖尿病相關機制。並嘗試以養晶得到結晶狀的胰島素金奈米粒子；經由離子測試發現胰島素金奈米粒子十分穩定，更可應用於細胞內微量氰離子檢測；根據CD光譜，確認胰島素金奈米粒子與胰島素的蛋白質二級結構相似。之後利用MTT測試細胞毒性，並將胰島素金奈米粒子餵入細胞，並取得細胞螢光影像，證明胰島素金奈米粒子可經由細胞表面之胰島素受體進入細胞內，且呈現紅色螢光，證明胰島素金奈米粒子可用於生物體內顯影追蹤。利用老鼠實驗證明胰島素金奈米粒子具有胰島素降血糖之功用。

在本實驗中，我們合成了三個新的鋅的幾何異構物：trans-facial-[Zn(dipica)₂]Cl2.CH3OH(dipica=dipicolylamine，C12H13N3，雙(2吡啶甲基)胺)trans-facial-[Zn(dien)2]Cl2(dien=diethylenetriamine，C4H14N3，二乙基三胺)及反式-[Zn(demn)2Cl2](demn=N,N’-dimethylethylenediamineC4H12N2，N,N'-二甲基乙二胺)。本實驗的特色皆在室溫下反應，採用擴散法培養晶體。trans-facial-[Zn(dipica)22]Cl2.CH3OH晶體為三斜晶系，晶格常數a=8.8269(6)Å, b=8.9908(6)Å, c=10.0292(6)Å,α=76.715(1)。,β=81.232(1)。,γ=67.753(1)。;其空間群為P1，可信度R=0.025,Rw=0.0697。六配位的陽離子，其結構為扭曲八面體，兩個含氮三牙基(dipica)trans-facial配位，赤道面(ZnN(1)N(2)N(1A)N(2A))由兩個含吡啶環之氮(N(1)、N(1A))及兩個飽和胺之氮(N(2)、N(2A))所組成。主軸為兩個吡啶環之氮所組成。兩個含氮三牙基(dipica)與鋅的咬合角皆為84.5。。trans-facial-[Zn(dien)2]Cl2晶體為單斜晶系，晶格常數為a=11.3050(3)Å,b=10.9264(3)Å, c=12.6147(3)Å,β=92.884(1)。;其空間群為P21/c，可信度R=0.0191，Rw=0.0484。六配位的離子，其結構為扭曲八面體，兩個含氮三牙基(dien)與鋅的咬合角為156°、157°。反式-[Zn(dmen)2Cl2]晶體為單斜晶系，晶格常數 a=10.3397(4)Å,b=8.5916(4)Å,c=7.9774(3)Å,β=100.520(1)°;其空間群為C2/m，可信度R=0.0266，Rw=0.0686。其結構為八面體，鋅原子四個氮原子組成赤道面(ZnN(1)N(1A)N(1B)N(1C))，兩個氯原子位於此平面的兩側。兩個含氮雙牙基(dmen)與鋅的咬合角皆為83.0(1)Å。 In this study, we have synthesized three new geometrical isomers of zinc(II)complexes: trans-facial-bis(dipicolylamine)zinc(II)chloride-mathanol(1/2)(trans-fac-[Zn(dipica)2]Cl2.2CH3OH), trans-facial-bis(ethylenetriamine)zinc(II)chloride(trans-fac[Zn(dien)2]Cl2)and trans-bis(N, N'-dimethylethylenetriamine)zinc(II)chloride(trans-[Zn(dmen)2]Cl2). The crystals suitable for X-ray diffraction were obtained by slow diffusion of ether to solution of the products. There molecular strctures determined by X-ray diffraction. The complex trans-fac-[Zn(dipica)2]Cl2.2CH3OH crystallizes in the triclinic space group P 1 with a=8.8269(6)Å, b=8.9908(6)Å, c=10.0292(6)Å,α=76.715(1)。,β=81.232(1)。,γ= 67.753(1)。, for Z=1. The R value is 0.0259 for 3286 significant reflections. In the hexacoordinate cation, the two tridentate dipicolylamine ligands are trans-facially coordinated with two pyridine nitrogens and two secondary amine nitrogens situated on four positions in a basal plane(ZnN(1)N(2)N(1A)N(2A)). The remaining two pyridine nitrogens constitute the axis in a distorted octahedra structure. Colorless trans-fac-[Zn(dien)2]Cl2 crystallizes the monoclinic space group P21/c with a=11.3050(3)Å, b=10.9264(3)Å, c =12.6147(3)Å,β=92.884(1)。,and Z=1. The R value is 0.0191 for 3285 significant reflections. The zinc(II) atom has distorted octahedra coordination, in which the ligands are bound in a trans-facial configuration. Colorless trans-[Zn(dmen)2Cl2] crystallizes the monoclinic space group C2/m with a=10.3397(4)Å, b= 8.5916(4)Å, c=7.9774(3)Å,β=100.520(1)。, and Z=2. The R value is 0.0266 for 856 significant reflections. The zinc(II)atom of trans-[Zn(dmen)2Cl2]is six coordinate with 4 nitrogens of bidentate dmen forming a basal plane(ZnN(1)N(1B)N(1A)N(1C)),and two chlorines on the axial sites completing an octahedra structure.

氫氣在燃燒後只會產生水而不產生溫室氣體之二氧化碳，可謂一種潔淨能源。 生質能源是屬於碳中性(Carbon neutral)型之利用方式，因此本研究著眼於如何建構一個操作簡便的共代謝系統，將生質料源從微生物之發酵反應中釋放氫氣出來。 實驗的主要方法是利用好氧性的Bacillus thermoamylovorans 與厭氧性的Clostridium butyricum 共培養分解廢紙漿以生產氫氣。廢紙漿是混合的基質，內富含纖維素、並含一些油墨及少許雜質。利用Bacillus thermoamylovorans 是好氧菌，同時也能將廢紙漿中的纖維素轉換成還原醣的特性，將原本有氧的環境轉換成絕對厭氧的環境，並將廢紙漿中的纖維素轉化成Clostridium butyricum 可以利用的還原醣。如此一來，原本不利於Clostridium butyricum 生長的環境，卻能透過簡單的共培養方式創造出有利於Clostridium butyricum 生長的環境並產生氫氣。除此之外，我們也對不同碳源、不同的植菌量、不同的氧氣量，比較其產氫能力差異，發現增加氧氣量可以提升最後的產氫量大約2.7 倍。 ;Our major goal is to develop a cost-effective biohydrogen production system by the co-culturing of Bacillus thermoamylovorans and Clostridium butyricum. The aerobic Bacillus thermoamylovorans will consume oxygen and converse waste paper pulp into reductant-sugar and the anaerobic Clostridium butyricum will generate hydrogen after oxygen is consumed. With the increase of aeration, the aerobic Bacillus thermoamylovorans growsappropriately leading to more biohydrogen production. However, in enhanced aeration condition, the Bacillus thermoamylovorans will consume sugars that can offer for the Clostridium butyricum. So we can conclude that the control of oxygen is the key point for the system to operate.

We consider a game played with chips on a strip of squares. The squares are labeled, left to right, with 1, 2, 3, . . ., and there are k chips initially placed on distinct squares. Two players take turns to move one of these chips to the next empty square to its left. In this project, we study four different games according to the following \r rules: Game A: the player who places a chip on square 1 wins;Game B: the player who places a chip on square 1 loses;Game C: the player who finishes up with chips on 12 . . . k wins;Game D: the player who finishes up with chips on 12 . . . k loses. After studying the cases k = 3, 4,5 and 6 for Game A and the relation among these four games, we are led to discover the winning strategy of each game for any positive integer k. The strategies of Games A, B and C are closely related through a forward or backward shifting in position. We also found that such strategies are similar to the type of Nim game that awards the player taking the last chip. Game D is totally different from the rest. To solve this game, we investigate the Nim game that declares the player taking the last chips loser. Amazingly, the strategies of two Nim games can be concisely linked by two equations. Through these two Nim games, we not only find the winning strategy of Game D but also the precise relation between Game D and all others.\r 去年我研究一個遊戲：有一列n個的方格中，從左至右依序編號為1,2,3,....n。在X1個、第X2個、第X3個格子中各放置一個棋子。甲乙二個人按照下列規則輪流移動棋子：\r 一、甲乙兩個人每次只能動一個棋子(三個棋子中任選一個)。遊戲開始由甲先移動動棋子。二、甲乙兩個人每次移動某一個棋子時，只能將這個棋子移至左邊最近的空格(若前面連續有P個棋時可以跳過前面的P個棋子而且只能跳一次)，而且每個方格中最多只能放一個棋子。\r 研究這個遊戲問題時，我討論四種不同"輸贏結果"的規定：甲乙兩個人中，A誰先將三個棋子中任意一個棋子移到第一個方格，誰就是贏家。B誰先將三個棋子中任意一個棋子移到第一個方格，誰就是輸家。C誰先不能再移動任何棋子，誰就是輸家。D誰先不能再移動任何棋子，誰就是贏家。\r 當"輸贏結果"的規定採用ABCD時─我們稱為遊戲ABCD。今年我將把這個遊戲問題中棋子的個數由三個推廣到一般K個情形之後，再繼續研究遊戲的致勝策略，同時也將研究遊戲ABCD之間的關係。

Lotus effect（蓮花效應）是蓮葉表面化學組成（wax）與物理組成（微纖維結構）兩者所造成。本研究是以模擬Lotus effect，採用Sol-Gel 製成，將氟化矽聚合為奈米膠體。實驗結果發現，以異丙醇為溶劑，再依序加入氟化矽、硝酸以製成的Sol-Gel，將其塗覆於玻璃表面，可得到最高的接觸角（114.71°），且少量的氟化矽可製成大量的成品，已具有實用價值又兼顧成本的優點，最重要的是，本研究克服了目前Sol-Gel 製程與應用的四大難題（機械強度、與基材接著問題、透明度、溶膠凝固問題），可說是一大創舉。利用所研發出來的奈米溶膠，我們能成功地將Sol-Gel 附著於布料、玻璃、釉表面、粉體，也能成功地研發出具有自潔透氣的布料、救生衣、雪衣、棉被及自潔功能的玻璃、磁磚與市面上尚未研發出的防水粉體（接觸角＞140°），因此我們研發出的Sol-Gel 應用甚廣，有無限的發展潛力。Chemical composition (wax) and physical characteristics (microstructure) of lotus leaves are both responsible of the so call Lotus Effect. In this study we intend to demonstrate louts effect by applying Sol-Gel method to polymerize fluorosilane into nano-scale colloid. Our experimental results shown that the sol-gel made based on isopropanol solvent with fluorosilane and nitric acid added in order, when coated on glass plate, can achieve highest (liquid-surface) contact angle of 114.7 degrees. In addition, only small quantity of fluorosilane is sufficient to produce large amount of product, making this method feasible and cost-effective. More importantly, this procedure overcome the four major difficulty of sol-gel processing and application, namely mechanical toughness, adhesion with substrate, transparency, and consolidation. Using the nano-sol-gel developed in this study, we have successfully coated the sol-gel onto fabric, glass, ceramic grazing surface, and powder, which allow one to make self-cleaning breathable clothes, life jacket, snow cloth, futon and self-cleaning glass and tiles, as well as water-proof powder (contact angle > 140 degrees) which is brand new on market. We therefore believe that there is a great potential for the application of sol-gel developed in this study.