臺灣

關於平面上若干點的集中度之定義，一直很少有人予以仔細的探討，因為判別的方法有很多種。本研究是以平面上三點所構成的三角形之三頂點作討論，分別以三角形的面積、周長，內心、外心和重心至三頂點距離，三點的標準差及平均差的概念，作為不同的判別方式，並以動態幾何化版ＧＳＰ模擬不同的判斷方法做為研究，在利用統計學上的方法，找出哪一種定義方式最為適合、誤差最少的判斷方法。There are many ways to determine the centralness of three dots on a plane; however, no definition study has been applied. In this study, we focus our interests on the entralness of three vertices of a triangle formed from three dots on a plane. Various methods such as the relationship of area, and the distance of the triangle to the centralness of three dots, the distance from the interior point, exterior point, the barycenter to the vertices of triangle, and the standard error and differences average obtained from three dots were determined with a dynamic geometry software GSP, and a statistic method was used to find a least error way to determine the centralness of three dots on a plane.

細胞脂肪分化是造成肥胖、骨質疏鬆、和糖尿病的重要前置因素。我們若要維持良好身材又想省去減肥藥的問題，那麼我們必須了解造成脂肪化的原因，才可能擁有好的預防之道。利用人類骨髓間質細胞可以分化成骨質與脂肪等細胞的特性，我們研究氧化壓力對間質細胞\r Ras基因轉換表現後骨質與脂肪分化的影響。結果發現以添加超氧根 (O2-，l5nM)形成氧化壓力，可促進正常Ras基因表現的間質細胞朝骨質分化;相反地，超氧根會促進\r Ras基因突變而不表現的細胞，朝向脂肪分化的現象。進一步研究其作可原理，發現氧化壓力可促進 RaS蛋白質啟動細胞外訊息活化酵素(ERK)，接著驅動骨質轉錄因子(CBFA1)表現，再到骨鈣蛋白質與骨結節形成。而抗氧化酵素(超氧根轉化酵素;SOD,5OOU/ml)的作用，可以抑制正常Ras基因細胞氧化壓力下骨質分化的進行;但不能防止氧化壓力促進Ras基因突變細胞，朝向脂肪分化的作用。總結而言:Ras基因的表現與否，是決定脂肪分化的關鍵切換點;也是影響氧化壓力對間質細胞朝骨質分化的樞紐。這種基因與氧化壓力互動影響骨質與脂肪分化的剖析，將有助於提醒人們:使用抗氧化劑來調節抗衰老、肥胖、和美容時，必須是在不同情況和不同基因體質的人，有所不同。 \r Human\r mesenchymal stem cells are able to differentiate into bone, muscle, cartilage or\r fat tissues. Our preliminary study with human mesenchymal cell line (HS-5) showed\r that HS-5 cells could differentiate to bone, cartilage and muscle but not fat cells\r as determined by histochemical staining of phenotypes. We have further studied the\r influence of oxidative stress on the switch between bone and fat cell differentiation.\r Results showed that oxidative stress started with exogenous superoxide, produced\r by the interaction of xanthine oxidase and hypoxanthine, promoted the differentiation\r of osteogenic lineage showing expression of osteocalcin and bone nodule formations.\r The mechanism was investigated and superoxide was found to induce ERK (extracellular\r regulated signal kinase) activation; and then the expression of osteogenic specific\r transcriptional factor (CBFA1). A plasmid containing ras-mutant (Ser 17 Asn) which\r can inactivate the expression of ERK was transfected into the HS-5 cells for studying\r the influence of oxidative stress on ras-mutated mesenchymal cells. Surprisingly,\r it was found that oxidative stress did not promote osteogenesis but it enhanced\r adipogenesis from the ras-mutated HS-5 cells. Further studies indicated that superoxide\r neither induced ERK activation nor CBFA1 expression, but it did enhance expression\r of adipogenic specific transcriptional factor (C/EBPα) and lipoprotein lipase in\r the ras-mutated mesenchvmal cells. Taken together, the study model to induce the\r bone cell differentiation from human mesenchymal stem cells may be employed to make\r bone cells for tissue engineering.

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 鹽酸溶液中之腐蝕狀況，以鹼式中問氧化態聚苯胺（ Emeraldine base 。）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 ·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 Erneraldine-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.

In the previous year study, we assumed that the fish basin as a column-shape model in order to exam and explain how the water spouting. This year, we established a reality-like situation of the fish basin to construct our theory base. At this point, round-waves and up-down waves are found as the beginning point of the water spouting. The sound from the basin is the frequency of the vibrations. Meanwhile, this process enables us to understand the causes of four, six, and eight waves. In addition, we tried to change the basin's positions, the capacities of water, the densities of liquids, and the sizes of the containers to demonstrate the theory. Furthermore, we used similar containers, such as high-heel cup and big magnetic bowl to experiment. The results are also corresponded with the theory. These results can also be used to explain the Chinese aeolian bell, clock, shaking bell, etc. That is a major innovation for us. Finally, we obtain better understanding of the abstractive theory though the simulation of the computerized photographs. 魚洗，也稱龍洗，傳說是中國唐宋時代皇帝洗臉的臉盆，內底四條魚紋，麟尾畢具。洗內盛水後，用手摩擦其兩個雙耳，立即發出響亮的嗡鳴聲，並出現美麗了漣漪，水珠四濺，摩擦越快，聲音越響，波浪翻騰，水珠越烈。對此在上一年度的研究中，是將洗盆視為圓柱狀，然後由圓柱狀所建立的模型去解釋水跳的原因，初步瞭解了水跳的原因。今年我們以洗盆真實的情況建立理論模型，在殼體產生共振的圓形駐波及上下駐波，此為水跳產生點，此時殼體發出的聲音就是共振的頻率。也瞭解了有四個、六個、八個、十個波腹的原因。並以改變殼體不同位置、水量、液體密度及洗盆大小等變因應證模型，結果與理論相符合。繼而以高腳杯、大磁碗等類似魚洗盆構造的容器，加以實驗應證，也能符合此理論。甚可推到中國古時候的編鐘、搖鈴、風鈴等器材。對於我們總認為碰撞就產生聲音的觀念實是一大突破。最後經由電腦動畫的模擬，讓此抽象的理論更容易瞭解。

塑膠一向被認為絕緣體。但Heeger，MacDiarmid，以及Shirakawa證實，塑膠可以被改製成電的良導體。這須在高分子合成的過程中，使碳鏈呈現單、雙鍵交錯排列情形。此外，高分子也須加以摻雜(doped)，換言之，電子必須在氧化過程中被移除或在還原過程中被加進聚合物。電子移除所留下的電洞，或新加進的電子則可自由在分子鏈上移動，形成導電性。我們所要製備的導電高分子二次電池就是由這個原理完成的。所謂的二次電池(Secondary Cell)簡單的定義就是「可反覆充電、放電，循環使用的電池」，我們將會將其與市售電池比較，並改良出合適商品化的高分子二次電池。我們將以聚苯胺做為我們電池的正極，並用鋅片(原本我們要用鋰金屬的，但其再空氣中即易氧化，因此改採鋅)做為負極，製成一聚苯胺二次電池。The plastics is thought to be a insulator, but Heeger, MacDiarmid, and Shirakawa had proved that conductivity of plastics can be improved by doping other media. The conjugated polymers such as polyacetylene、polyaniline have the interlaced single-double bonds that electrons can move from one side to another side caused the production of electric currents. The purpose of this study is try to study the application of the conjugated polymer polyaniline to make a secondary battery. First, we use the chemical and electrochemical method to compose the polyaniline. Then we test the conductivity of the produced polyaniline and test the current and electrical potential of the polymer battery. The battery that we made from our laboratory has the electric potential about 0.5 volts and the electric current is greater than 50 microamperes. Finally, we also try to use the lithium as cathode to improve the performance of the polyaniline battery.

蜜蜂(Apis mellifera) 可以透過視覺經驗的累積與學習，增加辨識影像的正確率，這種透過先前學習過的經驗而增進視覺辨識的能力，與一般所熟知在視覺上是由眼睛將影像訊號傳至大腦進行辨識的過程恰好相反，因此被稱為top-down process。 \r 我們以Y型迷宮進行蜜蜂的行為實驗，制約訓練蜜蜂辨識文字影像。蜜蜂能在訓練後成功地辨識文字，並建立所謂top-down process的現象：無法直接辨識複雜的文字影像→經過提出的簡單影像特徵進行訓練後→能顯著地辨識原來的複雜影像。可見蜜蜂能夠藉由經驗中的提示訊息辨識影像。 \r 若以「提示形狀」、「提示位置」、「提示正確端」及「提示錯誤端」等不同影像特徵進行實驗，則發現蜜蜂會擷取形狀或正確影像的訊息，在記憶中形成較深刻的經驗，增強辨識能力。 \r 蜜蜂能夠辨識文字，且能在短時間內擷取重要的影像特徵，做為執行top-down process的經驗。蜜蜂只用不到1 mm3的腦部處理複雜的視覺訊息，牠們的行為與神經機制值得我們繼續深入探討。

本研究探討在給定範圍的面積下，以最省錢的方式用籬笆圍出最大的矩形土地，其中矩形的邊長為正整數，且矩形對邊使用相同單價之材質的籬笆，但相鄰邊使用不同單價之材質的籬笆。我們希望透過轉換，將單價不同的情況回歸到單價相同的情況，以便完整的解決這個問題。\r 藉由改變邊長，將 轉換成 ，使問題轉換成相鄰邊之單價相同的情況；但是經過運算找出的最佳解 轉換回 後卻不一定符合「整數邊長」的要求(即 和 不一定是整數)。為了解決這點，我們重新以不同的角度探討單價相同的情形，以找出整數的最佳解。\r 最後我們發現，若 和 切線斜率的差值大於或等於1，則 坐標愈近 的解愈佳，而在差值小於1的範圍內，我們提出一個檢驗法，可以找到整個問題的最佳解，同時讓此最佳解 轉換回 後仍符合「整數邊長」的要求，進而解決問題。

George Sicherman discovered that it is possible to take a couple of 6-sided dice re-labeling them with different positive integers (1,2,2,3,3,4) and (1,3,4,5,6,8) having the same probability distribution as rolling a standard pair of 6-sided dice. Such unique pair of dice is calling Sicherman dice. The secret behind the Sicherman dice can be studied by combining the powerful mathematical tool “Generating functions” with the symbolic manipulation software “Derive 6”, The same procedure may be applied to studying the possibility of the generalized Sicherman dice along the consideration of :\r (1) Adding more dice. (2) Changing the number of faces. To this end, we introduce the concept of the Sicherman Bound. For a given integer n, the number of n-sided Sicherman dice is finite. We computed manually such numbers for n?50 based on the method of “Elimination of negative terms”. Sicherman Dice 就是一對點數配置與正常骰子(6 面正立方體，點數為1到6)不同的骰子，它所拋擲出的每一種不同點數和(2,3,4...,12) 的機率恰好與一對正常的骰子相同。這種骰子是美國的Col. George Sicherman 所發現的。 Sicherman 更進一步指出：在不使用Sicherman Dice 的情形下，不可能找到一組大於或等於三顆的非正常骰子，它們拋擲出的每一種不同點數和的機率恰好與一組同數量的正常骰子相同。本研究的目標在於1. 尋求計算「Sicherman Dice 的組合和正常的骰子有相同的出現機率」的方法2. 證明Sicherman 結論的真偽及是否適用於其他正多面體(4 面/ 8 面/12 面/ 20面) 的標準骰子3. 修正Sicherman 的結論，並定義Sicherman 極限(Sicherman Limit)。在假設n面正多面體(n 為自然數， n ? 50 )存在的情形下，探討每一個正多面體的Sicherman 極限4. Sicherman Dice (Crazy Dice) 的延伸探討(1) 不同面數骰子的組合，是否可以找到面數組合相同，但點數配置不同的Crazy Dice( 如4 面與6 面的標準骰子組合，找到4 面與6 面的Crazy Dice)(2) 多個面數相同或不同骰子的組合，是否可以找到面數、個數及點數配置皆不同的Crazy Dice ( 如3 個4 面標準骰子組合， 找到2 個8 面的Crazy Dice)在研究的過程中，我發現以下的現象：(1) Sicherman Dice 的產生，是生成函數因式重新組合的結果(2) Sicherman Dice 是否存在，則視上述重新組合的結果是否有負項產生由於上述的觀察，我使用自行發展的「負項消去」法來檢驗Sicherman 結論的正確性及求得n 面正多面體其對應的Sicherman 極限。同時我也和Col. George Sicherman 取得聯繫， 討論當年他發現Sicherman Dice 的經過及其結論的限制條件，作為本研究未來發展的參考。

有毒重金屬是一個全球矚目的環境污染問題，為了解決這問題，人們常使用沈澱法和螯合劑兩種主要化學手段來吸附重金屬物質，這些方法的缺點是在某些情況下(如:酸雨)，重金屬可能會再溶出污染環境。本研究旨在提出一個低成本且環境友善，能整治重金屬污染的新方法，使用牛糞來吸附重金屬離子，再將此已經吸附重金屬的牛糞回收製成觸媒。研究發現摘要如下: (1).磷酸鹽適合作為吸附劑，以穩定重金屬離子。 (2).發酵處理的牛糞由於微生物分解有機質，使成分中磷酸鹽含量變高，牛糞磷酸鹽愈高吸附重金屬離子的效果愈好。 (3).牛糞置於Cu2+、Ni2+水溶液，能有效吸附Cu2+、Ni2+離子，在應用上可預防重金屬污染地下水源。 (4).模擬土壤淋融的實驗中，超過99%的金屬離子可被牛糞固定於土壤中。 (5).回收吸附的重金屬離子牛糞，製作成活性碳觸媒，可進行脫色實驗，達到回收利用的目的。

全球暖化造成水災頻繁，嚴重威脅植物生存。看似耐淹水的水稻，在完全淹水下亦有其生存危機。水稻FR13A 因耐水性極佳而常用於分子育種，IR64 產量高卻不耐水。是那些特質使稻種間有不同耐水機制？我們觀察其幼苗淹水24 小時後生長情形、通氣組織 (aerenchyma) 變化及應用即時反轉錄聚合?鏈反應 (real time RT-PCR)，研究酒精醱酵的主要蛋白質：乙醇脫氫? (alcohol dehydrogenase, ADH1, 2) 及丙酮酸脫羧? (pyruvate decarboxylase, PDC2) 基因之表現量。兩種水稻的胚鞘及根都因淹水減緩生長，以FR13A 減緩最明顯。通氣組織在淹水期間都有增加，FR13A 中的形成近似於對照組，IR64 則明顯較差。FR13A 中ADH1 及ADH2 在淹水一小時後迅速增加60 至100 倍，IR64 僅增加10 至20 倍。PDC2 在IR64 中表現量的增加幅度較大，但最大值仍小於FR13A 之基礎表現量。由此可知，FR13A 在完全淹水時成長減緩而原有通氣組織則持續生長，且酒精醱酵中的基因有獨特誘導反應，因此耐水性較佳。藉由此研究揭開水稻細胞及分子生物學上的耐水反應策略，將可更精準地改良稻作使其對抗淹水逆境，解決未來因環境造成的糧食危機。Global warming increases the frequency of flooding, which drastically reduces the growth and survival of plants. Although rice (Oryza sativa) appears well-adapted to flooding of roots as it is often farmed in paddies, problems arise when the whole plant is submerged in water. I am interested in the structural and molecular responses that result in different submergence tolerances in rice cultivars. Indica rice FR13A is submergence-tolerant and frequently used in molecular breeding for this trait, while IR64 is a high-yield but submergence-intolerant cultivar. In this study, I monitored the growth rate, aerenchyma formation, and gene expressions of the carbohydrate metabolism in FR13A and IR64 seedlings subjected to submergence for 24 hours, by means of real time RT-PCR and microarray. FR13A had prominently inhibited coleoptile growth and sustained levels of aerenchyma formation whereas IR64 did not. The mRNA levels of alcohol dehydrogenase 1 (ADH1) in FR13A was induced prominently, while ADH2 was induced in IR64 during early hours of submergence. The induction of pyruvate decarboxylase 2 in FR13A was stronger than IR64. The expression of sucrose synthase was similar in both strains. Expressions of the genes involved in anaerobic carbohydrate metabolism were also studied by analyses of microarray data. My findings demonstrate that elongation quiescence, persistent aerenchyma formation and shifts in anaerobic carbohydrate metabolism gene expressions are beneficial strategies of FR13A towards submergence. Through elucidating the molecular basis of coordinating submergence tolerance genes as this study provided, it will be possible to discover multiple traits associated; hence crop improvement for flooding tolerance could be achieved.