花了不少時間了解聲音的波動現象後，我們由已知音叉自組「Ｕ行長管空氣柱測量法」去推測實際聲速大小，結果與標準聲速誤差在10﹪以下，同時也比較出未知音叉的頻率。為了了解聲波與其他介質波動傳遞數率的快慢差異，我們由自製的「自動振動機」已成功的比較出粗繩波、細繩波及緊繩波的波速大小；以自動振動機控制單擺的規律擺動去撞擊自組煙霧箱，感受撞擊時產生的聲音及能量的傳遞，讓煙以不同的速率方式擴散，也從這個實驗比較出：空氣的聲速(20℃下)34300cm/s＞＞單擺擺動的速率10~20cm/s＞煙圈自煙箱出口的速率3~9cm/s。為了讓聲音以更有活力、更有趣的方式具形化，我們以聲音三要素的方式設計了音波功的實驗。以錄影、電腦播放或現場感受的方式，就算聽不見也能看得到聲音的威力！為了讓聲音以另一種型式光來展現，我們以視覺暫留的現象定出音符定點展開的上、下、左、右的光點，再畫出音符的完整畫面；再企圖從跳動的反射光路徑中帶出舞動的Do Re Mi音符及曼妙的音樂。為了留住聲音的軌跡，我們將聲音以色彩的方式舞動出來、以不同紙材吸附對照，以感受古典音樂、搖滾音樂…等節奏下形成的色彩畫面。

我們藉由電腦模擬來研究宇宙微波背景輻射中之Sunyaev-Zel’dovich 效應，以探討星系團及宇宙的一些根本性質。重要的發現有： 以上的結果，將可在短期的未來直接應用在許多期待中的觀測結果上，以揭開星團的總質量、質量密度、以及宇宙中的黑暗能量等神祕面紗。 We study the important properties of the galaxy clusters and our universe by using numerical simulations for the Sunyaev-Zel’dovich effect in the Cosmic Microwave Background. We found that: These results can be applied to the observations in the near future, in order to reveal the total mass of clusters, their mass density profile, and the dark energy of our universe.

本研究主要在了解興達港地區的天氣變化，透過學校百葉箱，乾溼球溫度計、雨量筒、風向風速器、記錄表、電腦、記錄板等儀器，每天固定在上午9 時20 分觀測記錄百葉箱內儀下，測算水汽凝成水珠的速度的實驗，藉著校園氣象站累計的資料並經過Excel 軟體分析，研究本區2008 年10 月至2009 年2 月的天氣，我們發現從氣溫、氣壓及相對溼度間的變化和天氣關係發現：該天最高、最低溫差越大，相對溼度通常較低，氣壓較高，天氣多為晴天。當天最高、最低溫差越小、氣壓就小，相對溼度就較大天狀況多陰天或有霧。但願我們的研究能拋磚引玉，提供大家進一步研究小區域氣象的風氣及培養關心氣象與地方生活環境的態度。

We study the effect of dark energy on the evolution of cosmic structure in a scenario where the dark energy is treated as free particles and thus can be localized. By theoretical derivation and numerical simulations, we found that: 1. The dark energy particles gain kinetic energy from a moving dark matter particle through gravitational interaction. Due to energy conservation, the dark matter particle will slow down with time Ek(t) = Ek0 - 9 × 10-5[|1+3w|ρDE]1.92t where Ek(t) is the kinetic energy of the dark matter particle,Ek0 is its initial kinetic energy, w is the coefficient of equation of state for dark energy, ρDE is the mean energy density of dark energy, and t is the time. 2. The formation history and structure of galaxy clusters are different in the presence of localized dark energy. The more the localized dark energy, the earlier the formation of the cluster core. In addition, the kinetic energy Ek(R) as a function of R will be different if the ρDE is different. Thus we can compare the observed Ek(R) of clusters with our results to deduce the ρDE in our universe. The results here can be applied to the observations in the near future. 我們探討宇宙結構演化受到可局部叢集之黑暗能量粒子的影響。藉由理論推導及電腦模擬，我們發現： 一、黑暗能量粒子會透過重力交互作而從運動中的黑暗物質粒子獲得力學能。因力學能守恆，黑暗物質粒子的速率會減慢，滿足 Ek(t) = Ek0 - 9 × 10-5[|1+3w|ρDE]1.92t 其中Ek(t) 為黑暗物質粒子的動能，Ek0 為其初始動能，w 為狀態方程式係數，ρDE 為黑暗能量的平均密度，t 為時間。 二、星系團的形成過程及結構，會因可局部叢集之黑暗能量的存在而改變。黑暗能量越多時，星系團的核心會越早形成。而且動能 Ek(R) 隨著至星系中心距離R 的變化，會因 ρDE 的不同而不同，因此可以將量測到的 Ek(R) 和這裡的結果比對，推導出宇宙中的 ρDE 。 這些研究成果將可直接應用在未來的觀測結果上。

本研究在不改變傳統汽車電動後視鏡機械結構下，設計出一可自動調整後視鏡視角的智慧型汽車後視鏡。本研究首先以真值表研究電動後視鏡的機電特性，並藉以設計出一可以與原先人工控制後視鏡並存之驅動電路。微電腦單晶片被使用來控制後視鏡之轉向時間及轉向條件。後視鏡之轉角偵測乃利用方向盤帶動齒輪，藉由齒輪間的傳動並利用位置編碼器將轉角資訊轉換成為電訊號，並將訊號傳送至單晶片來控制後視鏡之轉向時間。研究結果顯示，一可隨方向盤轉動而自動改變後視鏡視角之汽車後視鏡確能減少開車時視角的因轉向而減少的問題。

我們以電腦程式控制喇叭的聲音頻率，並利用保利龍球的跳動來觀測音叉及金屬片的共振(鳴)現象：、實驗發現音叉、金屬片都有多個共振頻率的情形，而共振頻率彼此之間呈簡單的數學比例關係。、我們利用操縱變因的方式，研究了長度、寬度、厚度、溫度等因素對共振(鳴)頻率的影響。發現隨著長度、寬度減少，共振頻率反而增高;隨著溫度上升，共振頻率反而下降。、移動保利龍球和金屬片的接觸位置，可以測得各點的振動強度，進而繪成振動的駐波波形。縱向(y)上的駐波波形是由多個振動模式的混合組成，這實驗結果可由混波的理論數值作圖印証。研究振動波形，可以得到平面波速的資訊。研究顯示，不同材料有不同的波速。

放洗澡水時，偶然間見到旋轉中的液面呈現下凹現象，做化學實驗調配藥品攪拌溶液時，亦可看到液面下凹的現象，十分有趣。而數學正學到拋物線的我們，靈機一動，心想：「這下凹的液面，會不會是「拋物面」呢？ 因此我們將整個容器旋轉，觀察其中之液體所形成之凹面，並設計實驗及利用電腦計算、繪圖，二者配合，加以比較、證明。若我們能在實驗室中以簡易的方式將拋物面製造成功，並設法產生鏡面，即可利用此結果，自製各式的光學儀器。

本文由‘‘分數7/17是否能表示成兩個相異的埃及分數之和’’這個問題出發，藉由簡單數論的性質以及反證法，得到一個真分數可表示成兩個相異埃及分數之和的定理檢驗法(定理1)。有了這個基礎，我們進ㄧ步推廣定理1 的結果，做出了嶄新的結果(定理2、定理3) 。此定理分別可以用來檢驗真分數表示成三個、四個相異埃及分數之和的存在性; 至於將真分數表示為5 項、6 項….k 項相異埃及分數之和的部分尚在嘗試。利用定理1、2，我們寫了兩個Matlab 軟體工具的電腦程式，使得我們可以檢驗任意真分數是否可以表示成兩項及三項的和，並可把所有的解列出來; 最後我們研究的是一個有關埃及分數的猜想(Erdos-Strauss Conjecture)問題，當分子為4，且分母為4k、4k+2、4k+3 時，猜想皆成立。對於分母為4k+1 而言，當k 為3r+1、3r+2 猜想亦成立，k=3r 且r 為奇數時也是成立的，因此目前需解決的問題只剩分母為24t+1 的情況了。值得一提的是，我們用Matlab 的程式檢驗出當分母為1014 至1014 +240000 之內的正整數時，猜想都是成立的，這已經超越了已知文獻的結果。This paper begins with the question: ‘‘Is 7/17 able to be the sum of two different Egyptian fractions?’’ to discuss the problem of Egyptian fractions. According to the complete division properties and the counter-evidence method, we get a back-check theorem which is about a true fraction can be the sum of two different Egyptian fractions (see theorem 1). Using the same method we obtain a new back-check theorem that is a fraction can be the sum of three or four different Egyptian fractions (thereom2, thereom3). Similarly, we can follow the same procedure to get the rule that a fraction can be the sum of five or six …or even more different Egyptian fractions. By the theorem1 and 2, we propose two programs written vie the Matlab software to examine that any true fraction can be the sum of two items and three items or not. Finally we focus on the Erdos-Straus Conjecture, which related about true fractions can be divided by three different Egyptian fractions. The conjecture is when the denominator is 4k, 4k+2, or 4k+3, the problem mentioned above can be solved. As for the denominator is 4k+1, then the conjecture also can be solved, as k equals to 3r+1 or 3r+2. Also, k being 3r and r is an odd number, the conjecture is satisfied. As for the case of r equals to even number, the problem has not been solved. But it is worth to mention here that we use Matlab software to examine the conjecture is agreeable as the denominator is between 1014to 1014+ 240000. This is beyond the results from the literatures.

This study was to explore the nature of two basic constitutes of the regular pentagon,With these two constitutes, the regular pentagon could be multiplied into any times. We used four multiplication methods (m2 = 2m1 + n1 、n2 = m1 + n1 、m2= k2m1 、n2= k2n1、a2 = a1 + 1、a2 = a1 + ) to show how the regular pentagon could enlarge and to verify that the enlarged regular pentagons derived from computer did exist. By integrating these four multiplication methods, we were able to arrange regular pentagon of any length of side, and evidenced the equation was ( If the side length of a regular pentagon is a form of m,n is the number of A,B respectively ) We further proved that the first multiplication method could be developed into a new modified method, which could divide a regular pentagon with a given side length into a combination of A and B. But only when the x and y of side length of a regular pentagon could be divided by a natural number, k, and made x/k into an item of the Fibonacci Sequence and y/k a successive item. When we tried to verify if any regular pentagon could be constituted by other smaller regular pentagons, we also found that it was un-dividable only if the length of pentagon side were ( the number of A, B were the 2n and 2n-1 item of Lucas Sequence). Otherwise, any regular pentagon might be able to be constituted by other smaller regular pentagons. 本研究是以正五邊形的兩個基本組成元素(B)作為討論對象，利用此二元素可以將正五邊形做任意倍數的放大。我們共使用4種繁殖法則(m2 = 2m1 + n1 、n2 = m1 + n1 、m2= k2m1 、n2= k2n1、a2 = a1 + 1、a2 = a1 + ) 來說明正五邊形的放大情形，並利用此4 種繁殖法驗證電腦運算出的放大圖形確實存在。利用這4 種繁殖法則的改良與整合，已達到能排出任意邊長之正五邊形的目標，並能計算並證明出其通式為。 (若正五邊形的邊長為形式,m、n代表、的個數) 更特別的是，我們能用第一繁殖法反推出一種方法，將給定邊長的正五邊形利用簡單的切割方式分成由A、B 組合成的形式，但只有正五邊形邊長之x、y 值可同除以任一自然數k 而使 x/k 為費波那契數列之一項且 y/k 為其後一項者才可以使用。 將此想法推廣至一個正五邊形能否由比他小的其他五邊形組合而成時，我們也發現當正五邊形之邊長為時（其A、B 個數為盧卡斯數列之第2n,2n-1 項），不可分解，否則應該皆可將一個正五邊形分解成比它小的其他五邊形組合（我們也可以利用這些質形檢驗出其他正五邊形是否也為質形）。但其分解形式，不只一種，而我們推測只用兩種較小的正五邊形就能達成，我們期待能找出一或多種分解方法，能將正五邊形分解成標準的分解形式。

為了瞭解黃斑黑蟋蟀叫聲和溫度之間的關係，我應用物理熱平衡原理，自製水浴槽控制環境溫度，以電腦錄音程式分別錄製15℃、20℃、25℃、30℃、35℃時的蟋蟀叫聲，利用Sound Forge軟體分析並比較不同溫度下的各種特性。結果發現所分析的chirp、chirp period、syllable period、pause均和溫度呈負相關，而單位時間內的叫聲次數則與溫度成正相關，並推導出15~35℃範圍內蟋蟀叫聲次數與溫度成正相關的公式。最佳直線為：﹙15秒內叫聲次數＋19.385﹚÷2.483=當時溫度﹙℃﹚，呈高度正相關﹙相關係數：0.9398﹚。本實驗也比較母蟋蟀對不同溫度下雄蟋蟀叫聲的偏好程度，發現母蟋蟀較偏愛25℃時的雄蟋蟀叫聲，此結果可能與雄蟋蟀在25℃時叫聲的波形最為穩定有關。為探測蟋蟀觸角上的溫度感受器位置，我們曾將不同部位的觸角加以剪除，結果顯示觸角剪除面積越大的雄蟋蟀越不傾向鳴叫，但無法證實是否為溫度偵測異常所導致。本實驗除供學術研究外，因黃斑黑蟋蟀在世界各地均有分布，所以希望能藉由分析溫度與蟋蟀叫聲的相關性實驗，未來嘗試能探討其在不同環境的適應行為亦或種化的可能性。另外，全球暖化問題日益嚴重，也希望能藉由相關實驗探討暖化對蟋蟀生態上的影響。最後，我們的實驗證明了蟋蟀叫聲和環境溫度確實有極大的關聯性，未來或許能參考蟋蟀感覺溫度的機制，製作出一個天然零污染的溫度計。 To find out the relationship of cricket’s calling and temperature, we use a hand-made water-bath tank to control the temperature and record the callings with microphone and software, Sound Forge. After analyzing the collected data, we’ve found that cricket’s chirp, chirp period, syllable period, and pause are indeed affected by temperature (15 degrees - 35 degrees C). Moreover, we also compare female cricket’s preference to the callings, and the result indicates that female cricket’s preference is changing with temperature. In the last, we tried to find out where the thermoreceptors are by cutting out the antennae. After cutting, crickets tend to not to make any calls at all, so we conclude the antennae might play an important role in sensing and calling. The experiment proves that this communication system is temperature coupled. Because the cricket, Gryllus bimaculatus, is a worldwide species, we may learn the accommodation or the possibility of performing a new species by researching the relationship of temperature and cricket’s callings. By the way, the Green House Effect is getting more and more serious, so we want to search for the influences on crickets that are caused by Green House Effect. The last but not the least, according to the report, maybe we can investigate the mechanism of sensing temperature and then make a natural thermometer that is no pollution in the future.

從小習染之餘，對篆刻藝術的濃厚興趣及對電腦程式之熱愛，萌生將篆刻藝術與電腦 科技結合，於是應用PHP（Professional Home Page）的文字圖形（Text Image）處理功能 將中華文化之篆刻藝術透過網際網路推廣到世界各角落。本研究規劃建置了一個 FreeBSD Server 可完善處理PHP 功能的作業平台、應用PHP 的文字圖形處理功能，編 寫可在線上DIY 設計印章的程式，以及藉由Java Script 的技術在Client 端建立一個人 性化且相容性高之使用者界面網頁，達到提供多語系、多功能、依使用者偏好作調整 印章及輸出分享的功能。為使非漢語系國家能深刻體驗中華篆刻藝術，本研究同時建 立一個超過三萬筆之由英文名音譯中文名的資料庫，提供給使用者切身的服務。 Inspired by the interest of the art of seal engraving and the love for the computer programming beginning from my childhood, I combine the art of seal engraving and computer technology, and apply the Text-Image's function of PHP to promote the seal-engraving art of Chinese culture via the Internet to everywhere around the world. This project constructs a FreeBSD Server to process PHP platform perfectly, applies the Text-Image's function of PHP to write a program for online DIY pattern design, and uses Java Script to establish a human and compatible user-interface web page for clients to provide multi-language, multi-function, and being able to adjust pattern according to the user's preference and output sharing functions. This project also sets up a database of English-Chinese translation of over thirty thousand English terms to help people who are not Chinese to experience the art of seal engraving.

The larceny is always annoys our family and our society. They usually steal on the day when people working in the office or studding in the school. They always wait for people leave the house, and try the bell until them confirm the owner of the house leaved and nobody at home. Then they will open the door or break the lock of door. So we can find that if any body home or the lock is very hoard to open or to break. Then the thief is always choice to give up. That prove if we con let the thief think the house is some body home. Then it can to avoid larceny. This project is about how to design a system which is used AI technology to be a robot that is like a human. That robot can talk to the thief and can be a special lock when the thieves try to break the lock of door. The goal of this project is to design a robot that will be a door angel. It will let thief thinks that is some people always in the house. So they can not to steal in this house. We use the AI speech recognition & house environment control I/O system to be a robot which is setup in the door. It is like an angel to protect our home and family. And can stop the larceny. 「住宅竊盜犯罪」一直持續困擾著人類社會，住宅竊案最常發生於大白天，小偷常趁著家中成員上班、上學等時機，稍加觀察，再加以測試（按門鈴） ，確定家中無人，下手破壞鎖具侵入搜括；小偷只要遇到非常難開的鎖或認為有人在家就不會進一步的行竊。所以這證明只要讓小偷認為家裡有人，就能防止竊案的發生，而我們的研究目的就是如何在小偷還在徘徊尋找目標時，就要讓他感到這一家不能偷，如何讓他感覺家裡有人，進而打消入侵行竊的意念。我們希望能設計一套系統，利用AI人工智慧語音辨識及家庭環境控制，來建立一個充滿智慧的門神機器人，來事先嚇阻小偷的行動，就像門神一樣，可以預防竊案的發生，並整合大門門鎖內鎖與家電，形成智慧型的門神機器人，來保佑我們的家庭，也讓竊盜率降低，作為竊盜犯罪防治的利器。