「膠」流電-黏度及外加電壓對電解質溶液離子暫穩態通道之影響
在本次實驗中，我發現膠狀電解質溶液中的帶電離子，會因為離子團的熱運動，和電偶極的庫倫吸引力 (electric dipole) 的交互作用下，使溶液的I-V curve (電流-電壓曲線)，具有類似磁滯曲線(Hysteresis curve) 的效果；而膠狀溶液之濃度越高，電解起始點的對應I-V 值也越大。此外，白金電極與銅箔電極的距離若改變，也會使溶液的I-V curve 變的不一樣。另一方面，我也發現，在給予膠狀電解質溶液一緩慢外加的電壓或衝擊電壓並持續維持此一定額外加電壓時，會因為該溶液的黏度持續增高、帶電離子濃度增高且反應不斷變化下，而使該溶液的對應電壓，形成一重複出現「先降-後升-再降」的震盪現象，且電壓值節節升高。最後，我利用掃描式電子顯微鏡（SEM）及能量分散光譜儀（EDS）觀察銅箔電極之表面變化並分析其上之化學組成，藉此嘗試解釋上述這些有趣的現象。In this experiment, with the interaction of the heating action of ionic atmosphere and electric dipole, I find that ions in the gel make the I-V curve in the colloid electrolyte liquor show up with the effect similar to Hysteresis curve. The higher concentration of the colloidal solution, the bigger value of I-V at the initial electrolysis reaction was found. Furthermore, the shape of I-V curve is dependent on the distance between platinum electrode and cupper electrode. On the other hand, I find that when I apply a gradual extra-voltage or a fast extra-voltage to the colloidal electrolyte solutions and then maintain to a fixed value, this will make a unique ‘two peaks’ state oscillation of corresponding voltage. The reason is owing to the climbing viscosity and ion concentration in the solution. With the methods of scanning electron microscope (SEM) and energy dispersive spectrometer (EDS), I observe the change and analyze the components of chemicals on the surface of the cupper electrodes. Finally, I present the interesting results and try to interpret these phenomena.
完全圖立方乘積之最小控制
完全圖Kn是指一個圖中有n個點，且任意一個點都跟其它的點有邊相連。兩個圖G和H的卡氏乘積G□H的點集V(G□H)＝{(g,h)| g∈V(G),h∈V(H)}，兩個點(g1,h1)和(g2,h2)有邊相連若且為若g1=g2 且h1~h2，或g1~g2且h1=h2。
三個完全圖Ka、Kb、Kc 的立方乘積是指Ka□Kb□Kc。一個圖G中的一點v所連的其它點稱為這個點v的鄰居，也就是N(v)={x | x~v}。一個點集S中的所有點的鄰居的聯集稱為這個點集的鄰居，也就是N(S)=∪v∈S N(v)。如果一個點集S和它的鄰居N(S)包含了一個圖G的所有的點，也就是S∪N(S)＝V(G)稱這個點集S是這個圖G的一個控制集。我們把圖G的所有控制集中點數最少的稱為最小控制集，並定最小控制集的點數為最小控制數γ(G)，也就是γ(G)＝min { | S |, S是G的控制}。
本文的目的在於研究完全圖立方乘積的最小控制，也就是要給γ(Ka□Kb□Kc)一個上界。特別當 a = b = c = n時，γ(Ka□Kb□Kc) = 。
A complete graph Kn is a graph with n vertices, which any vertex is adjacency to every other vertices. The Cartesian product of two graph G and H which is denoted G□H is define as follow: the vertex set V(G□H)＝{(g,h)| g∈V(G),h∈V(H)}，and two vertices (g1,h1) and (g2,h2) is adjacent if and only if g1=g2 and h1~h2 or g1~g2 and h1=h2. The Cartesian product of three complete graph Ka,Kb,Kc is Ka□Kb□Kc,which is the same with (Ka□Kb)□Kc.
In a graph G, the neighbor of a vertex v N(v) is the set of the vertices adjacent to the vertex v, that is N(v)={x | x~v}。 The neighbor of a vertex set S is N(S), which is the union of the neighbors of vertex v over S, that is N(S)=∪v∈SN(v). For a graph G, if a vertex set S unions its neighbor N(S) equal to the vertex set of G, that is S∪N(S)＝V(G), we say that S is a dominating set of G. The domination number of a graph G will be denoted as γ(G), which is the minimum size of all dominating set of G..
We give an upper bound to γ(Ka□Kb□Kc). And when a=b=c, γ(Ka□Kb□Kc) ≦
Comfortable Equipment for Pedestrians
The phenomenon of pedestrians nowadays is still found. Due to frequent walking, sometimes our legs feel tired and hard to move. This is become the basis for developing tools that are convenient for pedestrians. An easy tool for humans is needed for our activities, especially walking. The Synergy between our hands and feet provides a big and significant contribution to the appliance. Normally, the movement of our hand gets along with its motion with a different side of the foot. When the right foot step, then the left hand is swung forward, and vice versa. The tools can be developed by utilizing a variety of systems. The system includes the tools concentric wheel and axles system, spring system, and pulley system. The concentric wheel and axles system is useful in controlling the rope. Movement on the rope could activate the entire system on the appliance. Wheel that related with the hand is three times bigger than wheel that related with pulley that is applied on foot. Spring system is able to lighten the pressure of the foot with a given upward force, and able to provide downward force when the spring returned to its original position. While the pulley system on the tool used to provide mechanical advantage two times is also useful to lighten the pressure of the foot when walking. The tools can be designed with simple, and able to provide benefits to users. By trial and error, it shows that the tool is able to lighten human’s activity when they walk. The tool can be able to lighten the leg’s load by utilizing arm muscles work. Utilization of the arm muscles which helps to ease the pressure of the foot can provide more benefits. One of them is that it can strengthen the arm strength, so the tool can be used as sport equipment. Utilization of the tool can also be reserved for special people who have difficulty in walking due to an accident or birth with leg defect.
重複圖形
「重複圖形」是本篇報告研究的問題，我們利用「方程式」建立一個尋找重複圖形，並証明其個數的方法。利用此方法得出下面的結論：1.會形成lap 2 的凸多邊形只有2 種，即三角形和四邊形。(1)「lap 2 三角形」只有1 種，即等腰直角三角形。(2)「lap 2 四邊形」只有1 種，即二邊之比為1： 且內角是45°、135°的平行四邊形。2.會形成lap 3 的凸多邊形只有2 種，即三角形和四邊形。(1)「lap 3 三角形」只有1 種，即內角為30°–60°–90°的直角三角形。3.其他的lap k 三角形：(1)任意內角為30°–60°–90°的直角三角形都是lap 3k²，其中k是正整數。(2)邊長比為1：m： 的直角三角形是lap (m²+1)k²三角形，其中m、k是正整數。
To find repeated figures, we construct a method to search them with the help of algebraic equations. Here we arrive at：1. There are only two kinds of lap 2 convex polygons, triangles and quadrilaterals. (1) The only lap 2 triangle is isogonal right-angled. (2) The only lap 2 quadrilateral is the one that contains angles 45°, 90° and two neighboring sides with the ratio 1: . 2. There are also two kinds of lap 3 convex polygons, triangles and quadrilaterals. (1) The only lap 3 triangle is the one with angles 30°, 60° and 90°. 3. Other kinds of lap k triangles are listed as following: (1) A triangle with angles 30o, 60°, 90° is a lap 3k², the k is a natural number. (2) A right-angled triangle whose ratio is 1 : m : is a lap (m2+1)k², the m and the k are natural numbers.
流體碰撞物體所產生的波形之研究及應用
當流體由圓管流下，在碰撞到物體後水流會產生類似駐波的形狀。為瞭解此現象的產生機制，及影響此現象的變因，我們改變流體的表面張力、流速及與碰撞物體間的距離，以探討各變因對波形所產生的影響，進而研究此現象的成因。由實驗結果發現波形會因流速加快、擋板距離增加、表面張力減少而有波長變短的趨勢，且可以用表面張力波的理論解釋。由理論推導的結果，可測量液體表面張力。由於圓球狀的外型使表面積增大，可增加液體之散熱的面積，因此可應用在水冷系統方面。A phenomenon similar to the standing wave, which occurs when a slow-velocity fluid jet collides with an obstacle, was observed. Because the free surface profile was observed to be stable, the phenomenon was not considered as standing wave. To understand the mechanism of this phenomenon and the factors that can affect the free surface profile, the surface tension of the fluid, jet velocity and the distance between the exit of the tube and the obstacle are varied to study their influences on the free surface profile. According to our experiment, the wave length is shortened when the jet velocity or the distance between the tube and the obstacle increases or when the surface tension decreases. The tendency of the investigated phenomenon can be explained by the capillary wave theory. Based on Bernoulli’s principle, continuity principle and surface tension\r equation, an ODE (ordinary differential equation) could be formulated. By using numerical method to solve this ODE, we predict the free surface profile which could match the experimental photo well. The tendency of the phenomenon can also be explained by the ODE. In order to measure the surface tension of the fluid, we wish to minimize the experiment apparatus. To enhance our assumption we use laser to locate the individual particle that we add in the fluid and calculate the velocity field of the flow jet.
利用雙雷射精密測定準靜物的極微小變位
To-be static objects, such as bridges, volcanoes, seldom move ordinarily but have mini displacement only under special conditions, like flood or earthquakes. Therefore, how to measure their mini displacement has never become fully popular with scientists’ research. Then, beginning with “ Optical Lever Theorem”, through a series of speculation and discussion, I decide to use laser ray as light source to perform an experiment ------- trying to find objects with mini displacement in our daily lives, such as revolving electric fans, engine-opening motorcycles, shaken trees, testing their magnifying effect first. Next, I try to use the control-experiment method to find out the magnifying relation and formula of the rotation angle of the plane mirror and the displacement quantity of light focus. As to the measure of mini displacement on objects, I utilize the pillar mirror as a reflection plane to research the magnifying relation of reflection light focus and original displacement quantity. The image made from the light focus of pillar mirror’s reflection, however, isn’t so perfect that I have to use a special plastic-made light-concentrating mirror, which is also called “ Fresnel Lens ”, to focalize the light for easy observation. Besides, I find out the “ function graph ” of the mini displacement quantity on to-be static objects and the displacement quantity of reflection light focus. At last, I try to build up a “ Bridge Alarm System ” of Optical Lever Theorem. 準靜物如橋樑、火山，由於平常不輕易移動，只有在特殊情況下（如洪水、地震）時，才會發生位移的現象。因此，其微小變位如何測量，一向是科學界較少探討的題目。於是，先由光學槓桿原理著手，經過一番思考、探討，決定採用雷射光作為光源，並作了第一個實驗－－找生活中具極微小變位的東西，如轉動中的電扇、引擎發動的摩托車、被搖動的樹木等，先測試其放大效果。接著就試圖用控制變因的方法，找出平面鏡旋轉角度和光點平移量的放大關係和公式。至於物體微小的平移量之測量，則是利用柱面鏡作為反射面，來探討反射光點的位移與本來的平移量之放大關係。然而，柱面鏡的反射光點成像並不理想，於是用一種特製的塑膠集光鏡，又稱Fresnel Lens，將光點集中以利觀測，並且找出準靜物之微小平移量及反射光點的位移量的函數圖形。最後，嘗試建立一套光學槓桿式的「橋樑預警系統」。
On Course Line Management
The Online Course Management system was developed in 2012 by George Moon to address the issue of creating course books at Burnside High School in Christchurch, New Zealand. The course books are designed to inform students, staff and parents of the many courses that are available for students to choose for their next year of study. In the past, the system that the school used consisted of large amounts of paperwork and duplication. Not only did this system require a lot of effort from staff, but the course book cost the school thousands of dollars to produce, as it had to be sent off to be published into a large book that would be read by students for a week, then likely thrown out. This year the school decided to digitise the course book, so that students would look at their courses online. Earlier this year, the school believed that the new School Management System (SMS) ‘KAMAR’ would be able to handle all of the necessary information, however this was not the case. Because of this, they needed a simple solution that would collate all of the course data, and then output it as a course book. I developed my project to do this. It is a web based program that is accessible by staff on their computers which enables them to enter in all of the course and assessment data for their departments. As it is all securely stored on a central database, it reduces duplication and staff workload, as well as the added environmental bonus of less paper being used. The program also outputs data in a number of ways including as a coursebook PDF (digital document which can be uploaded or printed), an Excel spreadsheet and a webpage for easy viewing. It can be sorted or printed by different categories (such as level, faculty, department), which proved to be a very useful feature. Following some research on areas such as design principles, browser compatibility and screen resolution (computer screen size), the program was designed to make best use of this this information. For example, most of the computers that staff would access the website on were of a similar size screen, so I made sure that my website worked well for them. I also used my research on design principles to try and create a simple, clean interface that users with limited computer skills would easily be able to navigate around. The outcome was real, as it was used by the school to generate their coursebook this year. Following a 95% student completion rate of course selection many months earlier than previous years, the system (although it had some issues) was pronounced a success, and the school is looking to use it in the years to come. There are a number of steps I am looking to take in the future with this program including the potential sale to other schools, so they can take advantage of the features it has to offer.
高分子複合材料的性質、製作與分解
Synthesis of Polymer Material and its Decomposing Processes Because plastic cannot be decomposed naturally by itself, therefore, additives needed to be added to facile the decomposing process. Let us choose one common material: thermoformed Nylon 66. During the formation process, addition of glucose powder and monosaccharide polymerized will result in yielding the products of methyl cellulose, soluble starch and agar powder. Observe whether adding additives would allow changes to occur structurally, or would the elasticity be improved when exist in a linear state, or even it would form a better pH resistance property. According to the experiments, when Nylon 66 contains methyl cellulose, it can sustain the highest tension. Its coefficient of elasticity is 2 times as large as the original one. In terms of the data, we can also observe that when Nylon66 contains soluble starch, it has the lowest ability to sustain tension. Besides, it has the lowest coefficient of elasticity. And when Nylon 66 contains cellulose, it has the highest rate in the process of decomposing.As we look at the surface of polymers under 400 diameters, we can observe that the Nylon 66 with agar powder has some filiferous substance. But we have not confirmed what the matter is. 由於塑膠不能在自然情況下順利分解，所以我們在塑膠中添加其他成分使塑膠可以較易 分解。我們選定常見的塑膠—熱塑性的耐綸-66。在聚合物的製作過程中添加葡萄糖、澱粉、 洋菜粉末以及甲基纖維素，並觀察加入添加物的塑膠在結構上是否有變化？其塑膠在線型時 之張力是否有增強？耐酸鹼性是否有變化？由實驗結果我們可以得知含有甲基纖維素之耐綸 -66 所能承受之張力強度最高，且其彈性係數也比無添加物之耐綸-66 高出近2 倍；而含可溶 性澱粉之耐綸-66 所能承受之張力最小，且彈性係數也最低。此外，進行生物分解的實驗可發 現，含葡萄糖的耐綸-66 分解的速率最快。使用400 倍的光學顯微鏡可發現含有洋菜粉末的耐 綸-66 表面與其他耐綸-66 複合材料差異較大，值得進一步研究。