海格的爆尾釘蝦－鹼性電池的探討
鹼性電池使用的電解液均為強鹼，電池中的鋅極會與其發生腐蝕反應，使得電池放電壽命降低，並產生氫氣，而大量氫氣使得電池有爆裂的危險，為了改善上述問題，我們自行設計了氣體觀測儀器，用來檢測銀鋅電池充放電與靜置時之氣體產生量，更藉由探討影響變因的過程找出銀鋅電池較合適之使用條件，其中包含電解液種類及濃度之選擇、電極面積與充電電流對使用效果之影響，並改善電池腐蝕程度；我們將鋅極以浸鍍處理(Sn:Pb ＝1:1 )並搭配電解液添加物(KOH:Zn(OH)42 －＝ 2:1) 可效率地抑制氣體產生；更用氯化銀粉末取代傳統氧化銀極片為正極，發現氯化銀可代替氧化銀電極，且有不錯的放電效果。;As we know, the electrolyte solution used in an alkalinebattery is a concentrated alkaline solution, which corrodes the zinc electrode in a battery of this kind. The corrosive reaction not only reduces the lifespan of the battery but also produces hydrogen, causing the battery to explode. This study is intended to help us design a device to measure the quantity of hydrogen gas generated in the charging of a zinc-silver battery. We have studied several factors affecting zinc-silver battery, including the variety of electrolyte, the concentration of alkaline solution, the surface of electrode, and the density of charging current, etc. To reduce the corrosion of zinc electrode, we plate the zinc electrode by the immersion electroless plating method, using several kinds of low-polluting anti-corrosive additives (metallic compounds such as lead and tin). We also add zincate ion into electrolyte solution to further reduce the quantity of hydrogen produced. The experiments show a zinc-silver alkaline battery works most efficiently, if the powder of silver chloride is used instead of silver oxide.
灰色預測在雨量長期趨勢分析之應用
灰色理論近來廣泛應用於各行各業的管理資訊科學上，本研究乃應用灰色理論的一階微分中輸入變數為一項之 GM ( 1 , 1 ）模型，來預測台灣中部地區土石流主要因素雨量的月平均量值。本文運用三筆以上的歷史資料，作最近一年歷史性資料的預測，藉以驗證獲得其誤差（±△e）之校止參考依據值，比利用殘差檢驗所得的誤差校止數據，更能修止出精確的預測值，接著再做台灣中部雨量未來之預測，以作為未來雨水、土石流防治之參考 · 為了能迅速產生所要的灰色預測值，研究中並以 VB 程式語言及以Petri-net分析其動態處理行為，藉 GM ( 1 , 1 ）模型的專屬處理支援程式，以做為未來雨輦自動化處理警示與預測之支援機制。Recently Grey Theory has been widely applied to management information science in all kinds of areas. This research applies the first Level differential of the Grey Theory to put a variable in GM( 1,1) model to forecast the monthly average value of the most common precipitation, in the midland Taiwan earth-stone flood zone. This paper uses more than three historical data to forecast the most recent year’s historical data, which can be used to verify and acquire referential correction data of its errors ( ±△e). The aforementioned method can correct forecast data more precisely than the differential inspection. In addition, this method can then forecast future precipitation in midland Taiwan earth-stone flood zone and the results can serve as reference for future precipitation control. To rapidly receive the needed Grey forecast values, the research analyzes its dynamic process method by utilizing VB program and Petri-net to build a dedicated process-support program of GM( I , 1) model. This program will serve as a support mechanism for future automatic precipitation warning and forecast.
顛倒一族
一 Motivation and Purpose: In this study, we want to completely know about “The number abc…de, which times m/n, 1≦n≦m≦9?N can get ed… cba?”, and also expect to find out “The good rule within them”. 二 Procedure:Using method of enumeration, induction to collect sample of all and beginning from two digits to get information “good rule”. When get some useful idea, put them into the following research for the step easy go on, the method try and error is a very tiresome works, especially when we deal higher digits. till enough information is obtained, we solve problem and find new one, then likewise again research steps, just the basic science research ways, we are glad have the key of these problem. 三 Result and conclusion :Those number we named “converse No.” There are two groups: S=m+n=10 and 11 S=11, then Q=m/n=9/2,8/3,7/4,6/5=4.5,2.6,1.75,1.2 S=10, then Q=m/n=9/1,8/2,7/3,6/4=9,4,2.3,1.5 Each group have four type. When S=11,Q=7/4=1.75,if converse No.each digit is a multiple of 3, then can cancellation or extension of fraction to get another 3 or 4. Growth up rule: Converse No. = type factor x heritable factor x growth factor=rx hx g S=11,r=2~5,h=9, s=10, r=1~4, h=99 一 研究目的：盼能找出”顛倒一族”的族譜。二 研究過程：確定研究題目為ab…cde×m/n=edc...ba,0≦n≦m≦9?N 求ab… cde？以窮舉法收集觀察資料，歸納演繹尋求規律。1.先觀察兩位數，分析共有顛倒對36對。2.建立乘數Q=m/n一覽表，共有27個3.設計顛倒對大/小及其商一覽表，以利觀察、歸納獲得規律。4.接著觀察三位數，共有360對，綜合二、三位數規律，找出選擇式窮舉法：9之倍數法。5.再接著找出四位數，再綜合而知另有 全調法 重現法 半調法 GCD遺傳基因法等來繁衍高位數顛倒數。6.於是依諸法找得六位數資料，得知GCD遺傳基因法為繁衍通則，完成族譜建立模式。7.研究顛倒數位數與其個數間關係式，完成研究。研究結論：1.顛倒一族有兩大類：S=10與S=11 S=m+n。2.每一大類有四型： S=10中，Q =9/1,8/2,7/3,6/4(9,4,2.3,1.5)S=11中，Q =9/2,8/3,7/4,6/5(4.5,2.6,1.75,1.2)3.每一型均有一個顛倒數，除了S=11中，Q=7/4=1.75者可約、擴分而得3or4個。4.顛倒數原則上均為9之倍數，除了Q=7/4經約、擴分可能得非9倍數者。
再論巴斯卡三角形
本研究以b04課程中的巴斯卡三角形為研究對象，將原先巴斯卡以「1」為首、「+」為運算符號的規律三角形，改為以「-1」及「ω 」為首、「×」為運算符號，分別就其產生的新三角形作探討，發現其中似乎隱藏著原先三角形所沒有的規律性。為了更瞭解這種規律，藉由電腦軟體繪出其圖形，圖形顯示出如碎形般的複製關係，不論放大或縮小，其中的遞迴關係並未改變，頗令人好奇，因此著手研究。研究過程中對於圖形的規律性採用先臆測、接著歸納、最後給予證明的方式呈現。得到以下的結論：一、分別以數列呈現新三角形圖形的規律性。二、分別將新三角形中每一列中的某數字（如-1、ω 或ω 2 ）的個數予以通式表之。三、分別推算出新三角形第n 列第j 行的數是「1」或「?1」及「1」或「ω 」或「ω 2 」。四、相同的模式，在特定的圖形範圍中，不斷重複出現。許多研究將巴斯卡三角形中的所有數，以某數為模的餘數紀錄下，去探討其餘數在新產生的巴斯卡三角形中的分布情形；而在碎形的研究中，大部份著重如何畫出碎形。本研究著重圖形其規律性的探討，提供上述研究不同角度的詮釋與探討。 This research subject is based on Pascal’ s triangle in senior high school curriculum. The regular triangle begins with「1」and use「+」as operation. Let 「1」 be replaced with「-1」and「ω 」, the operation sign「+」be changed into「×」. I do research on the new triangle and discover the seemingly hidden regularity which doesn’t exist in the original one. To understand more about this regularity, I draw figures through the computer. The figures show the relationship of reproduction as fractal. Whether the figure is enlarged or minimized, it’s surprising curious the recursive relationship doesn’t change, so we begin to work on research. In the process of the research, we make careful observations, assumptions and deductions about the regularity of the figure. Finally, we come to some conclusions by means of giving proofs:（1）Present the regularity of the new triangle figure with progression.（2） Present such numbers as「-1」, 「ω 」, 「ω 2 」 in each row of the new triangle with formulas separately. （3）Figure out the number in the row n and in the column j of the new triangle is「1」or「-1」,and「1」or「ω 」or「ω 2 」. （4）The same model appears again and again in the specific range of figure. Many researches record Pascal’s triangle modulo certain number to explore the distribution of remainders in the new triangle. In the research of fractal, how to draw fractal is mostly focused on. The exploration of this research emphasizes the regularity of figure, offering the interpretation and exploration of researches above from different angles.
外接正多邊形法與對稱性
Motivated by Napoleon theorem, we study the properties of the triangles obtained by moving the midpoint of each side of a given trianle along the perpendicular bisector of corresponding sides, and extend the results to the case of quadrilaterals. On the other hand ,we consider the method of erecting a regular M-gon to each side of a given N-gon and joint the N centers of these M-gons to form a new N-gon. (abbreviated as CRG method),and get the following results. 1. We characterize some kinds of N-gons that can be transformed to regular N-gons via CRG method. 2. Of M,N are nature numbers with M|N, then it is possible to find a N-gon that can be transformed to a regular N-gon by CRG method. \r 3. If a polygon P is symmetric with respect to a fixed point or a fixed line, then P can be transformed by CRG to a polygon with similar symmetries. 4. If a polygon P is transformed by CRG to ′P,there exists a commonpoint G such that ΣGA=0 andΣGB=0, where A and B runs through vertices of and P′P, respectively. 本研究將拿破崙定理加以延伸。先探討由各邊中點沿中垂線延伸得出之三角形的性質並推廣至四邊形之情形條列式報告成果。另一個推廣是將給定的多邊形的每邊外接一個正多邊形，再以這些外接的正多邊形的中心為頂點造出一個新的多邊形。我們發現此幾何變換具有以下性質：（1） 「哪些多邊形能被變換成正多邊形呢?」，我們觀察出能被變換成正多邊形的多邊形其限制條件隨邊數增加而增多，並進一步區分了哪些多邊形可以被變換成正多邊形。 （2） 在將非正N邊形做變換時，不一定須外接正N邊形才能得到正N邊形，我們區分出可外接哪些正多邊形而得到正多邊形。 （3） 對給定的多邊形作此變換時，若原多邊形有點對稱或線對稱等性質，則新多邊形也將具有相同的性質。 （4） 此變換得到的新多邊形會與原多邊形共重心，亦即新舊兩多邊形內到各自的頂點向量和為0的點會是同一點。
南美蟛蜞菊相剋作用之探討
Few plants can grow in the place where Wedelia trilobata grows. In the following experiment, the leaves ans stalks(of the plants from Wedelia trilobata) are extracted for experimental purpose .The data and records of the experiment have shown that Wedelia trilo ata indeed refain the growth of plants such as mung bean, teeding seed, yeast’s respiration and the photosynthesis. We use the function of dieing the polyphenols to know that the Wedelia trilobata can produce Allelochemicals called as the polyphemols The mesophycell produce the polyphemols from chloroplast of cortex,the polyphemols transport to root and release from root exudation. The plant will absorb polyphemols of the soil, and will affect the growth of the plant. If we can separate and purify the Allelochemicals, we can make it as natural herbicideb. 南美蟛蜞菊所在之處，少有其他植物，本實驗採南美蟛蜞菊植栽區之土壤與南美蟛蜞菊莖或葉之萃取液進行相剋作用之研究，結果顯示南美蟛蜞菊確實會抑制小麥與綠豆種子萌發及幼苗生長，並抑制酵母菌的呼吸作用及植物光合作用中之光反應。 利用多酚類染色方法得知南美蟛蜞菊產生的相剋化合物為多酚類，且該多酚類由葉肉細胞與莖內皮層中具葉綠體之細胞產生，經韌皮部輸送至根，再由根經泌濾作用釋出。土壤中的多酚類會被植物吸收，進而影響植物的生長與發育。 若能將該相剋化合物---多酚類分離與純化，或可作為具選擇性之天然除草劑。