無紫外光下的抑菌－可見光奈米光觸媒研發
In this experiment, we hope to produce appropriate-sized nano particles of by using the chitin. By mixing the particles with the metal of Ti, Fe and Zn of proper proportions and therefore narrow their band gaps. Thus, the Bacteriostasis of LightPhotocatalysts could appear under the environment where the energy is lower than ultraviolet ray. We use de-acetylated chitin in three ways -- chelating agent, surfactant and protecter. Then we put a thin layer of the mixture of chitin and metal nano particles on a piece of glass, and afterwards, sintering the mixture on the glass. Next, we scan the surface of the glass with AFM(Atomic Force Microscopy) to measure its particle size. The result we got showed that the surface-roughness of the Ti-Fe nano particles was 30.642nm, the best solution of all the samples. Yet, in this experiment, Fe was not suitable. Therefore we should choose the sample of Ti-Zn mixture, which is slightly smaller in roughness. According to the result we got from the experiment, we found that, under the yellow light, the survivable strain-number ratio of the sintered Ti-Fe-Zn mixture on the glass and empty glass was 0.09±0.06. This was much better than the survivable strain-number ratio of 0.17±0.06, the result we got out from the glass of pure Ti and empty glass. From the measurement, we found that the proportion of mixture could lower the excitation energy Ti needs. Through this experiment, we hope to create a layer of film containing nano particles, and by applying it to daily-use products, we could prevent harmful bacteria. 本實驗的目的，就是希望可以利用幾丁質製作出適當粒徑大小的金屬奈米顆粒，混合適當比例的鈦、鐵、鋅金屬，使其能隙變窄，讓我們能在低於紫外光能量的光譜下，產生奈米光觸媒的抑菌效果。筆者在實驗中利用去乙醯化之幾丁質在本實驗中扮演三種角色:螯合劑、介面活性劑及保護劑，以將幾丁質與金屬奈米顆粒均勻塗抹於玻璃上，並以燒結玻璃的方式進行實驗。並且利用AFM掃描玻璃表面，確認其表面尺度，驗證的結果Ti-Fe混合比例的奈米顆粒之表面粗糙度為30.642nm，為最佳狀態，但在本實驗中Fe並不適用，故應以粗糙度僅次於Ti-Fe的Ti-Zn混合比例為主。根據實驗的結果，在綠光下，混合比例的Ti-Fe-Zn玻璃與空白玻璃的菌落數比，菌落存活率為0.09±0.06，相較於純Ti的0.17±0.06來的低，代表混合比例可降低Ti所需之激發能量。經過此實驗未來筆者希望可以以幾丁質製作出一層含奈米顆粒的薄膜，應用到各種生活用品防止細菌的危害。
心手相連的正方形
正方形兩條對角線的交點（即中心點）距四頂點等長，也與四邊等距。如果將正方形的頂點比擬成它的「手」，兩對角線的交點當成它的「心」，則兩個正方形頂點間、中心點間、或頂點與中心點間的線段相連（或重合），就如同「手」或「心」彼此相連。本文即探索當多個正方形間「心手相連」時，衍生圖形間的面積關係。而四個正方形中某幾個頂點相接（邊未重疊），恰圍出兩個三角形的圖形則是本內容討論圖形的主體架構，我們以此架構向外作出「層出不窮」的正方形，再配合中心點連接成四邊形，將推導出這些四邊形與基準正方形（Reference Square）間的面積關係。In a square, the lengths from the intersection point （center point） of two diagonal lines to the four apexes are the same, and so are they from that point to the four sides. If the apexes are “hands” and the intersection point of two diagonal lines is the “heart” of a square, the connection or overlap of two squares’ apexes and apexes, center point and center point, or apexes and center points is just like the connection of hands with hearts. In this article, hence, we are to explore the relation in area of derivative graphs formed by several squares connected “heart in hand.” When some apexes of four squares are overlain without sides overlapped, two triangles are created. And that’s the theme we are going to discuss. Furthermore, we extend the operation to infinitely overlain squares and frame out quadrangles referring to the center points of some squares. Then, the relation in areas of these overlapped squares and the Reference Square would be deduced.
巨型小翼效應—未來長程客機經濟省油妙方
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.
在浪碎之前
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.
步步為營
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。
死亡巧克力—切切割割好計謀
三角形的邊上取任意多個點，我們可以把這塊大三角形沿著切割線切割成較小塊的三角形，但切割線必須是點（或頂點）和點的連線，而且必須切割三角形，同時可以切任意大小的三角形，如圖（1）與圖（2）。但不可以一開始就取走整個三角形。定義拿到最後一塊三角形的人獲勝，而在多邊型中的玩法與在三角形中相同。 我們分A、B、C三種規則來討論，其中A規則即是上面提到的玩法，B規則大部分的玩法和A規則都相同，唯一不同的地方在於：A規則中，只要有一方取到剩下的圖形為三角形，另一方就可以直接取走剩下的三角形，而B規則規定即使剩下的圖形已經是三角形，也必須取到剩下的圖形邊上都沒有分點為止。C規則是限制玩家一次所能取的三角形數來進行遊戲。 我們完成了A、B、C規則中三角形與多邊形的必勝策略，並找出必勝策略之間的關聯。 ;Given any numbers of points on the sides of a triangle, the players can cut this triangle into pieces. Each cutting line has to be one, linked between two points given from two different sides. And the player can’t have to cut smaller triangles out of the original triangle. The out-cut triangles can be chosen randomly without any restriction in size, just like what’s shown in picture（1）and（2）. Meanwhile the first player can’t cut the original triangle exactly all out in the very beginning process. We define the player as the winner, who gets the last triangle. And the above way we play can be applies to any multi-side shapes. We discussed the question respectively in three rules, A, B, and C. Rule A is what we mention above. Rule B is generally the same as rule A, except for the only difference：The rule A , if there is any triangle left , the next player can get it directly, but while in rule B, the every next player has to cut out smaller triangles until no point is left on sides. Rule C proceeds on conditions that there is a limitation to a certain number of triangles cut out at a time. We has finished the winning tactic respectively in rule A, B, and C in the games with a triangle and multi-side shapes. Furthermore, we find the connection between the winning tactives.
共點圓、共圓點
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.