四等獎

罹患神經母細胞瘤的兒科病人，尤其是罹患stage IVs 神經母細胞瘤者，他們有些伴隨著非常嚴重的貧血，但卻檢測不出神經母細胞瘤已經侵犯骨髓；有時病情來勢洶洶，尤其是腫瘤細胞中已可偵測到N-myc 基因增幅者，診斷時腫瘤細胞可能已在腹腔四處擴散並已侵犯大部分的肝臟。但是，某些這種病患，特別是腫瘤細胞中N-myc 基因沒增幅者，即使在沒有治療的狀況下卻可能有自然恢復的現象，也就是腫瘤細胞會自動消退，但原因仍待進一步的證實與探討。可是，這些病人在其病情最嚴重的時候，骨髓內紅血球母細胞形態上的改變顯示可能與病毒感染有關。但是關於病毒來源的研究，現有的資訊仍然十分有限，其中最重要的是，病毒感染與引發其後天之免疫作用是否有關，更需要深層的研究。因此，為更進一步了解罹患神經母細胞瘤之兒科病人的病毒感染及病毒蛋白表現的作用，我們這次研究的目的在檢驗罹患神經母細胞瘤及貧血之兒科病人與微小病毒B19 (PVB19)、Epstein-Barr Virus (EBV)、腸病毒71 型(EV 71)和巨細胞病毒(CMV)的關係，以及病毒蛋白表現對這些病人的作用與臨床意義。In pediatric patients with neuroblastoma, in particular, those with stage IVs neuroblastoma, sometimes the disease was combined with severe anemia. However, no tumor involvement was detected in the bone marrow. Although some of these patients may have N-myc gene amplification, and the disease could have invaded many abdominal organs, especially liver, interestingly, the disease might regress spontaneously in some of these patients. The medical reason of the spontaneous regression, nonetheless, remains to be determined. It is worth noting that morphological changes of erythroid progenitor cells in the bone marrow have suggested virus infection in these pediatric patients. However, the available information of viral origin is limited. Furthermore, it is possible that the virus infection in these patients could be associated with the revocation of immune responses related to the spontaneous regression of the tumor. In this study we will investigate the relationship of parvovirus B19 (PVB19), Epstein-Barr virus (EBV), enterovirus 71 (EV71) and cytomegalovirus (CMV) with neuroblastoma by PCR in Taiwanese pediatric patients. Moreover, we will study the effect and the clinical significance of viral gene expression as well as N-myc gene amplification in these patients.

At the website “MathLinks EveryOne,” we found a problem “Snakes on a chessboard,” which was raised by Prof. Richard Stanley. The following is the problem. A snake on the m n chessboard is a nonempty subset S of the squares of the board with the following property: Start at one of the squares and continue walking one step up or to the right, stopping at any time. The squares visited are the squares of the snake. Prove that the total number of ways to cover an m × n chessboard with disjoint snakes is a product of Fibonacci numbers. We call the total number of ways to cover a chessboard with disjoint snakes “the snake-covering number.” This problem hasn’t been solved since it was posted on September 18, 2004, so it aroused our interest to study it. First, we used the way in which we added each block to the chessboard, and therefore we discovered some regulations about the snake-covering number of the1 × n , 2 × n and 3 × n chessboard. Through “recursive relation” and “mathematical induction”, we proved the general term of the snake-covering number of the1 × n , 2 × n and 3 × n chessboard. In the following study, we found a key method in which we added a group of blocks to the chessboard. Finally, we proved the general term of the snake-covering number of the m × n chessboard. Also, we discovered the way to figure out the snake-covering number of the nonrectangular chessboard.在網站“ MathLinks EveryOne ”中，我們找到了一個有趣的問題“棋然上的蛇” ( Snakes on a chessboard ) ，這個問題是由教授 Richard Stanley 所提出。問題如下：在m x n棋盤形格子上，蛇由任意一格出發，但蛇的走法只能往右 → ，往上↑，或停住 ‧ 若此蛇已停住，將由另一條蛇來走，且不同蛇走過的格子不可重疊”證明：將 m × n 棋盤形格子完全覆蓋的總方法數為費氐（ Fibonacci ）數列某些項的乘積。我們將把棋盤形格子完全覆蓋的所有方法數稱之為“蛇填充數” 由於這個問題自從 2004年 9 月 18 日被登在網站上後，還沒有人提出解答，於是引發了我們研究的興趣。首先，我們使用了將一個一個格子加到棋盤上的方法，並發現了 l × n 、 2 x n、 3 × n 棋盤形格子蛇填充數的一些規律。我們使用遞迴關係及數學歸納法來證明 l x n 、 2 x n ， 3 × n 棋盤形格子蛇填充數的一般項。在接下來的研究中我們發現一個特別的方法，一次增加數個方塊 ‧ 最後我們證明了，m x n, ，棋然形格子的蛇填充數的一般項 ‧ 而且，我們也找到如何求出不規則棋盤形格子的蛇填充數。

Two soldiers walk on a checkerboard. They can only walk one step once a time and two directions, front and left, are decided randomly. The gunshot is the column and row where a soldier is located, and one will die if he enters the gunshot area of the other. To treat the probability of winning, we first study the cases of 1×n, 2×n, 3×n, and 4×n rectangles iterately. Then we establish a general form of the probability of winning in a general n×k rectangle by using recurrence technique and generating function, respectively. Finally, we extend to the general n×m×k cuboid case to obtain the first soldier’s probability of winning.在一個長方形的棋盤中，兩士兵行走，每一次只走一步，而且上和左兩個方向是隨機的，射程範圍是所在的此行和此列，而進入他人射程範圍則死亡。探討其獲勝機率，從1×n 、2×n、3×n、4×n 矩形的情形逐步研究，並分別運用遞迴式的技巧及生成函數，導出 n×k 矩形中先走士兵獲勝機率的一般式。更進一步地，我們也獲得了n×m×k 立體空間先走士兵的獲勝機率。

本研究主要是探討翼端小翼對飛機飛行的影響，翼端小翼在現在不少的飛機上都有這種設計，假設小翼可以阻止飛機機翼末端的氣流上旋，進而增加升力與推力，讓飛機能提高飛行時的效率，為了驗證這個假設，因此製作了簡易風洞對小翼的升力與阻力進行定性和定量的探討。升力與阻力的定性定量探討是經由10 組主機翼與五個小翼組合，共有2000 次的測試記錄，再轉化成折線圖予以比較研究，而得到一個穩定性數值結果。這測試實驗的數值結果顯示：小翼可以增加升力，但是也會增加阻力，為了降低阻力，小翼的剖面最好是有弧度。The purpose of this research is to find out the effect resulted from the winglet of the plane to the flight. Many a winglet is nowadays designed for the airplane. Assumes the winglet can stop the air of the tail section of the airplane to revolve up, further increase the force of the raise and the push, and uplift the efficiency of the flight. In order to proof this assumption is correct, so makes an easy air hole to do the research of qualitative and quantitative analysis for the force of the raise and resistance. After about 2000 records tested through the combination of ten sets of the main wing and five tiny wings, and transference of curve diagram , we get a steadily value result. This test result appear the first the winglet can increase the force of the raise, and so do the resistance, and the second to have the force of the resistance decreased, it might be better the section of the winglet is not straight but circular.

本研究針對利吉惡地進行探討，研究此區之泥岩含水量、有機質含量、pH值、比重、可溶性陽離子含量、滲水特性和該區之植物種類，並探討坡度、水量對沖蝕率、山脊密度和溝痕形成之影響。 研究結果發現： 一、表層泥岩之含水率較高，深層泥岩最低。中層泥岩之有機質含量較高，表層與深層泥岩較低。各層泥岩pH值約8.1；無植被採樣點之 pH較高，有植被採樣點偏中性。有植被採樣點，其 Ca2+含量較高。 二、此區共發現十九種植物，其中銀合歡、相思樹屬優勢種。 三、坡度增加時，沖蝕率亦增加；水量增加時，沖蝕率、溝痕寬度也隨之增加，兩者呈高度正相關。第一區坡度較緩，山脊密度較大，第二區坡度較陡，山脊密度小，表面較平坦，溝痕較淺。Our research discusses with the contents of water in mudstone, the organic content, pH, the specific weight, the contents of dissoluble cation, dankness and the category of plants in Ligiligi Badland. Dissecting it`s slope, the abrasion of water, the density of mountain ridge and the formation of scuff mark. Outcome of our research： 1.Solum of mudstone is the dampest. Intermediate of mudstone has more organic content than others. Every bed of mudstone`s PH is 8.1. Having plants area is indifferent and having more Ca2+.2.We found nineteen categories of plants. For example Leucaena glauca and Taiwan acacia. 3.The more augmentation of gradient,the more increase of the abrasion of water and the breadth of the density and the abrasion of water too.

聚丙烯酸(PAA)是尿布中吸水成份，我們利用其結構上的羧基螯合Ag＋，並成功以甲醛將Ag＋還原成奈米銀。但我們意外發現螯合Ag＋的PAA白色粉末在沒有其他還原劑存在下也會漸漸變成黃色，與「利用甲醛還原製得的奈米銀」顏色十分相似。本實驗即揭開此粉末變色真相，希望能在不使用額外還原劑下，直接以PAA將螯合的Ag＋製成奈米銀，不僅具環保與實用價值，更能使奈米銀製程朝向綠色化學。我們透過水溶性聚丙烯酸鈉(SPA)在均相中進行變色機制探討及影響變因的研究，找出有利的反應條件，再應用於PAA。研究證實PAA能將螯合的Ag＋同步還原成奈米銀，反應機制與檸檬酸鈉作用模式相似，而提升濃度、溫度或照光有利於反應，酸性條件則不利，照各種色光也有所差異。

中文摘要 重金屬對人體傷害的無遠弗屆-人人皆知，根據流行病學的研究指出，長期處在 重金屬含量過高之地區，易造成生理病變。比方說，長期生活在砷含量高的環境中， 易導致肝臟、周邊血管及神經系的損害，各種癌症的發生機率也大為提高。 本實驗以中國倉鼠卵巢細胞（CHO-K1）為材料，利用微核偵測技術(Michronuclei, MN)及姐妹染色分體互換(Sister chromatid exchanges, SCE)之誘引來探討亞硒酸鈉 (Sodium selenite, NaSeO2) 及亞砷酸鈉(Sodium arsenite, NaAsO2) 的交互作用 (interaction)。實驗結果顯示亞硒酸鈉本身不會造成MN 的增加，但讓SCE 頻率增加； 亞砷酸鈉會誘引增加MN 和SCE。亞硒酸鈉前處理不會減少亞砷酸鈉誘引之SCE 和 MN，但可微微降低亞砷酸鈉抑制雙核細胞(Bunucleated cells, BN)的形成，但是不明 顯。本實驗結果未能看出亞硒酸鈉前處理與亞砷酸鈉有明顯的交互作用，但發現亞 硒酸鈉會增加SCE 頻率，因此亞硒酸鈉做為保健食品值得進一步的關切及探討。 英文摘要 It is well-documented that exposure to heavy metals could cause seriously adverse effects to humans. Epidemiological evidence has shown that illness is frequently observed in residents living long-term in heavy metal contaminated area. For example, arsenic exposure was associated with increased incidences of liver diseases, peripheral vascular and neurological diseases, as well as cancers. In this report we investigated the interaction of selenite and arsenite on micronuclei (MN) and sister chromatid exchange (SCE) induction in Chinese hamster ovary-K1 (CHO-K1) cells. The present results demonstrated that sodium selenite by itself did not induce MN, but it did cause the increase of SCE frequency. Sodium arsenite significantly induced MN and SCE in CHO-K1 cells. Pretreatment of CHO-K1 cells with selenite could not reduce MN and SCE frequency induced by arsenite, but slightly prevent the cells from arsenite-induced inhibition of binucleated cell formation. In the present study, no significant interaction between sodium selenite pretreatment and sodium arsenite was observed. However, sodium selenite was unexpectedly found to enhance SCE frequency in CHO-K1 cells. The application of selenite as health protection agent warrants our concerns and further investigation.

如果n-1 個正四面體在n 個面的多面體棋盤中翻轉(如：正八面體、正二十面體、五邊雙菱錐及三角錐台棋盤)，則正四面體相互之間會受到很多限制。本研究為探討n-1 個正四面體在n 個面的多面體棋盤中，利用其翻轉的特性，翻轉至相鄰空格，進而完成：1. 每個正四面體的底面及側面均能「同色共面」。2. 在滿足以上的兩個條件下做「數字排序」。3. 探討每個遊戲在各階段是否有解的情形。最後，將遊戲推廣至正八面體在多面體棋盤中的翻轉。If n-1 pyramids can turn in the chessboard of n planes pyramids (ex: 8 planes pyramid, 20 planes pyramid, 5 sides bi rhombus pyramid and triangular pyramid chessboard) there are lost of restrictions between these pyramids. This research is discussing about the n-1 pyramids in the chessboard of n planes multi pyramid, which have the peculiarity of turn that can turn to nearby space. We found that: 1. Each pyramid’s button plane and aide plane can be “same plane same color”. 2. Matching about 2 conditions then can do “order by numbers”. 3. Search for answers of each levels in each game. Finally, the game will be propagated to eight planes pyramid can turn on the chessboard of multi pyramid.

本研究以模擬實驗探討波浪在斜坡海灘上的行為。實驗在長1.8公尺、寬0.75公尺的透明水波槽中進行，以長0.90公尺、寬0.60公尺的木板在深水區產生單峰波向淺水區前進，同時以數位錄影機錄影後進行分析。結果發現單峰波由深水進入淺水，波速會變慢，但當波高對水深的比值增加到一定值時，波速隨水深變淺而變快，波高也變高。當比值繼續增加，波前方的水面形成垂直的水牆，接著波就碎了。如果坡度較緩，碎波點會離水岸線較遠，水牆維持的時間也較長。有趣的是，水波槽中的單峰波移動時，有蠕動現象，波寬會伸縮，波高會起伏，波速也會些微地忽快忽慢。 ;This study simulates the behavior of the wave on a sloping beach. Experiments are performed in a sloping wave tank. A paddle wave maker at the deeper end generates single crest waves. To analyze the wave height, speed and breaking point, a digital camera is used. The results show that when the wave moves toward the coast, the shallower the water is, the slower the wave moves. But when the ratio (wave-height/water-depth) exceeds a critical value, it turns out that when the water is shallower, the wave speed becomes faster and the wave height, higher. As the ratio keeps on increasing, the front part of wave becomes a vertical water-wall, and then breaks. If the slope is gentler, the breaking point will be farther from the coast and the water-wall will keep for a longer time. An interesting phenomenon is also found that a single crest wave squirms with slightly undulated changing of width, height, and speed while it propagates in the sloping wave tank.

The purpose of this paper is to study the roles of formic acid and formaldehyde playing in the Direct Methanol Fuel Cells(DMFCs).The assumption is now widely accepted that the Oxidation-reduction intermediate of cell like formic acid and formaldehyde will hinder the reaction of DMFCs. At first, we recorded data which measured the efficiency of DMFCs working under the different temperature of fuel, then we recorded data which measured the efficiency of DMFCs working under the different consistency. In the end, we compared the data we recorded before and chose the best reaction environment as standard environment for the future experiment. Then we discover intermediate has positive effect on DMFCs. we separately put formic acid and formaldehyde into fuel, and we discover the efficiency is better than\r before. For example, the volt stability and volt intensity of DMFCs are better. The above conclusion is mainly based on open current volt, equally volt and electric current density which is the standard of evaluation.本實驗主要探討甲酸、甲醛等雜質在直接甲醇燃料電池中扮演的角色，一般認為甲酸等是甲醇在電池中反應的中間產物，大多數人認為這些中間產物會阻礙燃料電池的反應。而我們先針對了甲醇在各種溫度下電池的效能先做出了圖表，並使用不同濃度的甲醇燃料來測量電池的效能並與之前溫度的圖表做比較，選出最合適的直接甲醇燃料電池反應環境作為添加雜質實驗的標準環境。接下來我們在研究過程中發現，其實中間產物可能對電池有正面的效果，我們發現甲酸、甲醛等對直接甲醇燃料電池的電源輸出有正面的影響，例如電壓穩定性與電壓強度的增強。在研究中，我們將甲酸等加入燃料電池的燃料(甲醇)內，模擬甲醇因不當保存而產生的雜質，針對添加物的濃度做些調整，以電池的開路電壓(OCV)、平均輸出電壓、以及單位面積的電流密度作為評比電池效能的標準，並找出甲酸等對燃料電池效能的影響，並進一步找出最適合的電池燃料配置。