全國中小學科展

四等獎

『亮』出色彩-PLED 的製作

利用化學合成法合成出聚苯胺及MEH-PPV,經過一連串的製程作出高分子\r 發光二極體(PLED),再用I-V 儀量測。實驗中以聚苯胺及MEH-PPV 的薄膜厚\r 度為變因,進行實驗。設定I-V 的電壓值為10V,量測樣品通路上的電流。一開\r 始電壓在跑時,量到的電流都為0A,所得到的圖形為一水平直線;當電壓到達\r 一個值時會向上爬升,但爬到一個階段後圖形呈現鉛直掉落至電流為0A,圖形\r 又恢復成水平直線。過程中看到了薄膜厚度對樣品確實有影響,又鋁電極的厚度\r 不能承受過大的電壓,電壓一大,樣品馬上就燒壞了。\r Abstract:\r Using Chemiccal polymerize PANI and MEH-PPV make through a series\r Polymer light emitting diode(PLED)Produce.then using I-V meter surveies. PANI\r and MEH-PPV change of thick proces.Experiment design I-V volt for meter\r conduction of current of sample .The voltage moving.First meter current is obtaining\r the figure is horizontal when voltage increase to a special value , but increase a while ,\r the current will fall down to zero volt. Figure will go to horizontal that sample will\r change .Thick is different,and aluminum cathode can not suffer too much\r voltage .otherwise will burn.

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) ≦

日光燈下的二道彩虹

某次於學校的科學表演中,見到黑白陀螺在旋轉後會產生顏色的\r 變化,使人印象深刻。文獻上記載此類陀螺稱為“Prevost”圓盤,\r 其色彩產生的原因一般被認為是人眼產生之錯覺。不過究竟為何會有\r 這種錯覺,總令人相當納悶。於是我們請教了老師,不僅做了實驗,\r 也用像機拍攝下來分析,不過令我們感到奇怪的是:如果是眼睛產生\r 的錯覺,又為何能拍出顏色?甚至,在研究的過程中我們意外的觀察到鏤空圓盤內的色塊裡,\r 尚有像水波「波紋」般的條紋出現。這個現象十分奇特,於是我們設\r 計了一系列的實驗去探討這些現象,開始了這次的研究。在研究過程中我們遇到相當大的困難,所幸同伴的程式設計技術\r 卓越。為了實驗也撰寫了許多套色彩分析程式,使得實驗更能得心應\r 手。而我是負責實驗儀器的架設及實驗操作,希望能以分工合作的方\r 式,來完成這次的研究。

最小積包絡現象

思考公車車門開關時在地面上掃過的區域形狀與面積時,發現其中變動的直線為過定點與座標軸圍成三角形面積最小的直線,我們很好奇,這類圍成最小面積的直線更進一步的包絡現象,所以就動手去嘗試做研究。\r \r The research is done out of the curiosity we had when we pondered over the area and the shape a bus door sweeps on the floor when it opens or closes, and thus to discover the graph of the varying line which forms the smallest area so that we attempt to do research on such envelopment phenomena.

3D立體建構模擬之研究

現在的市面上,四處充斥著各式各樣的電玩或是3D立體動畫,但是在呈現動畫的\r 時候,依然存在著很多地方的不足,與狀況表現上的矛盾情形!於是令我興起:一個普\r 通的高中學生,是否也有機會運用所學的知識,創造出自己的虛擬實境?\r 我嘗試地寫出各種物體架構的函數,再對這函數圖形所呈現出的立體加工處理,使\r 它能自由的運動,甚至使它能多采多姿就有如我們在現實生活中所看見的一般,有著自\r 己的花紋與圖案!\r 期望在架構完整之後,有一天,我們這些學生可以不再被那些軟體公司牽著走,花\r 大把的錢買電腦動畫中種種的不合理,而可以自己擁有自己的3D 世界!!

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.

取代基替換之異構物數量計算

本研究以數學上的Burnside’s Lemma思維,利用排列組合結合化學領域中的群論概念,應用在計算取代基可被替換的化學結構,所具有的異構物數量。 研究中討論了環狀共振(例如苯環)、環烷、直烷、醇、醚、醛、酮、羧酸、酯、胺、醯胺等分子結構,推導出任意取代基種類與數量不同時,所對應的化學異構物數量公式與計算方法。 整理出公式與計算方法後,將CnHx中x個H的位置改成給定的取代基種類與數量時,然後系統化異構物數量的處理流程。最後再針對典型分子的化學點群,給出其對稱的數學排列群樣貌,作為各式計算的背景資料。

車輛滑動預防系統研究

近年來,未拉上手煞車所造成的傷害事故層出不窮,主要有兩個導因,一、車主已離車但未拉上手煞車;二、看見自己的車已經開始滑動,想用徒手力量阻擋。因為車輛的質量很大,往往沒有辦法阻止,反而造成了車主自身或周遭行人的傷亡。本設計主要功能是用於車輛滑動的預防。我們運用了加速規來感測地面的坡度,當車輛停放在斜坡,駕駛座上無人,且沒有拉起手煞車,本系統將會自動偵測,我們使用了OPA比較電路來判斷坡度是否達到我們預設的值,如果是,系統將會啟動警報器警告周圍的人,而且會自動將手煞車拉起,以防止車輛繼續下滑,這就是我們所發明的智慧手煞車的作動原理及基本的構想。我們希望藉由此設計,達到減少因未拉上手煞車而造成的事故,並且能藉由警報聲改正駕駛人習慣,減少傷亡提升車輛安全。

「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.

明察秋毫-動態測微器

The purpose of this research is to create a device that is able to precisely measure small dynamic changes which cannot be recognized by the human eyes. The Vernier Caliper and the screw micrometer are common tools used to precisely measure lengths of objects. However, things which are measured by the Vernier Caliper or the screw micrometer have to be in a solid state, and the shape cannot be changed. By applying the light lever principle on Lego bricks, this research uses the LabVIEW graphical programming system to design a device which is able to automatically measure small dynamic changes. The precision of this device is higher than that of the Vernier Caliper and the screw micrometer. Moreover, this device is able to precisely detect the small dynamic changes of solids and liquids as well. Through numerous tests, the least count of the device can reach the level of 10-3cm. Also, this device has successfully measured small changes, such as the height of the liquid surface by one drop of water, the evaporation of water in one minute, and the growth of a plant in one hour. By popularizing this device, people will be able to precisely measure small dynamic changes which are difficult to be measured in a short time.