我們使用C++撰寫了一個音準練習程式：使用者輸入聲音後，經由音頻辨識方法求出其頻譜中最高能量之頻率，以之為基頻，再將其與目標音高相較，得到誤差率及走音程度。此外程式還可秀出所唱的樂譜，和發出對應的鋼琴或正弦波的聲音，方便使用者校音。而為了做音高辨識，我們也收集了許多聲音檔案，觀察其特色，研究不同音色的頻譜或是波形特性，並利用其特徵完成一個音色自動辨識程式。\r 首先我們測試了各種演算法，並且選用了快速傅利葉轉換作為主要製作的演算方法；接著我們利用Microsoft Visual C++撰寫我們的程式。這個程式主要可分為錄音、辨識以及樂譜繪製三大部分，皆會在此份報告中詳細說明。\r 文中將說明音頻及音色辨識的方法，一些關於音樂的基本知識，微軟公司的wave檔格式，此系統之應用，以及音色的波形頻譜分析。我們使用FFT 求得聲音的頻譜，且將針對此部分演算法做簡單的說明，並探討如何達到所需之頻率準確度，如何以較高效率辨識，及如何找出不同音色的特性。

本篇研究利用網路攝影機、DVD-R光碟片、木製暗箱、比色管、筆記型電腦、各式燈泡等器材，搭配上自行撰寫的程式，製作出一簡易的光譜儀系統。先經由實驗測試，找到最佳光柵角及觀測角的組合，再將DVD光柵及網路攝影機封裝在木製暗箱中，完成硬體製作。軟體使用VB.Net搭配EmguCV函式庫當作平台，發展出來的程式可以利用螢光燈光譜中的特徵線條進行頻譜校正，校正完成後可以精準且即時地顯示各種光源頻譜曲線。此外，我們也以自製的光譜儀系統進行不同濃度之硫酸銅溶液的吸收光譜檢測，與專業的光譜儀的吸光度做比對，數據非常的接近，代表以本研究方法自製出來的光譜儀確實可用。

本研究利用雷射光、光感測計、偏振片、齒輪及馬達組裝成一個簡易、精確且可接於電腦的數位旋光度計。我們先藉由Arnao研究的ABTS/ H2O2/HRP分析系統，以不同濃度的維生素C與延遲時間畫圖作為標準曲線來測量總抗氧化活性，並比較奇異果、火龍果、聖女蕃茄、加州李四種水果，以微波、水煮及油浴三種方式測得熱處理後抗氧化活性的變化趨勢。之後，我們再利用自製旋光度計來求得水果經過熱處理後的旋光度與熱處理時間之關係。研究顯示，經熱處理後，此兩種方法有一致的趨勢，所以證明了我們成功地開發出一種可以利用旋光度來測定抗氧化的新方法。最後，我們進一步將此裝置應用於真假蜂蜜的檢驗，同時利用物質旋光度具有加成性，建立一套方法來計算蜂蜜中蔗糖、葡萄糖、果糖的含量。

滿足之M 點，我們稱之為Pi(i=1…n)的均值點。當n=3，M 恰為△P1P2P3 的重心 (G); n=4 時，M 亦為三角錐P1P2P3P4 的重心！因此不免引人遐思：滿足之M 點是否皆為其重心？ 我們藉由電腦幾何作圖軟體GSP 協助觀察，掌握了圖形變化間之不變性，再配合向量解析及推理，得以發現均值點、多邊形的重心、以至多面體的重心、及平行多邊形的一般性作法。附帶又發現：任意相鄰三頂點即可決定一平行n 邊形。並進而證實：平行四邊形為四邊形M＝G 的充要條件。但當n≧5 時，平行n 邊形只是n 邊形M＝G 的充分非必要條件！一般而言，具有對稱中心O 的n 個點所構成的圖形必可使M 與G 重合於O 點上。 The point M satisfying is called “the mean point of Pi(i=1…n)”. As n=3, M is the center of gravity (G) of the △P1P2P3. If n=4, then M is also the center of gravity of the triangular pyramid P1P2P3P4. Therefore, I began to wonder if the following assumption stands: The point M that satisfies is always a center of gravity. By using the computer software GSP (The Geometer’s Sketchpad) to observe figures. It is found that when a figure is changing there is still constancy. Furthermore, supported by the analysis based on vectors, general constructions can be established concerning the mean point, the center of gravity of polygon, the center of gravity of polyhedron, and the parallel polygon. Also, I find that any three neighboring vertexes decide a parallel polygon. And thus it is verified that the parallelogram is the sufficient and necessary condition for quadrilateral M=G. As n≧5, the parallel n-sides shape is the sufficient, not necessary condition, for n-sides shape M=G. In general, a central figure of n points having the center of symmetry O can make M and G meet on O.

本實驗利用喇叭、薄膜電極、波型產生器、鎖相放大器、及750 介面卡組合一套系統,此系統可使偵測精密度大幅提升(±4*10-5cm),使得水槽及地表模型尺度變小(40*22*35cm),因此可節省實驗的成本與時間我們在坡度實驗中,發現坡度在3 度左右,淺化係數都超過3. 對照台灣沿岸發生海嘯的歷史記載,確實在台灣東北角及西南沿岸等坡度為三度之地區都發生較明顯的海嘯危害. 反之,坡度在四度以上的東岸其海嘯波高都非常低.最後再藉著硬體系統及電腦2D 動畫模擬的整合,使我們可方便掌握波浪在不同坡度及位置,其波長及波高變化比,如此有助於預估及說明海嘯隨地形變化的狀況.By using the horn, membranous electrodes, function generator, phase-locked amplifier, and Science Workshop 750, we plan to assemble a tsunami simulation system in which the precision can be getting increased (±4*10-5cm) .Because of the improvement of its precision, the size of the tank and of the surface models will become smaller .As a result, the money and time spent on the experiment will be spare. When experimenting on the influence of inclination of the landforms, we observed that when the inclination reaches about 3 degrees, the shoaling coefficient exceeded 3 .The result of our experiment can provide an explanation to the tsunami on the northeast and southwest coast of Taiwan .According to the historical records, the disastrous tsunami happens frequently on the northeast and southwest coast of Taiwan where its inclination is also about 3 degrees as well .On the other hand, on the eastern coast, the wave height is lower and its inclination exceeds 4 degrees .Apparently, our experimenting result is correspond to the natural phenomena in Taiwan’s coast . Besides, with the help of hardware system and computer 2D animation simulation, we can easily measure the wavelength and wave height scale of the wave in different inclinations and positions. Therefore, this tsunami simulation system can provide a great help to estimate and explain the phenomena of tsunami which may change its condition in different landforms.

中文摘要：\r 本研究旨在探討，在TCP/IP 協定之下，最大網路傳輸效率之MTU\r （Maximum Transmission Unit,最大傳輸單位）值。根據IEEE 所公\r 佈Ethernet 之標準，經實地模擬實驗，本研究之結論如下：（1）在\r 單純兩台電腦直接串接時，由於幾乎無任何干擾與封包的碰撞，可設\r 定之MTU 最大值以1500bytes 為最佳；（2）但在模擬真實的大型廣域\r 網路時，由於碰撞增加及雜訊增多，經模擬實驗顯示，MTU 值為\r 1500bytes 時無法在資料傳送、接收及重組時取得平衡，最佳之MTU\r 值落於500 到600bytes 之間，進一步研究顯示MTU 值設在500 到\r 600bytes 時可提升傳輸效率約50%。同時，本研究亦討論將此機制應\r 用於未來新網路標準之可行性及其必要性。Abstract：\r The main purpose of this research is to explore the best network\r transmission efficiency's Maximum Transmission Unit under TCP/IP\r protocol. According to the Ethernet's standard of IEEE and simulated\r experiments, the outcome of this research are :( 1) When connecting two\r computers serially, there is almost no interference and impact of packets,\r the best MTU that we can set up is 1500bytes ;( 2)When simulating the\r truly wide area network, interference and impact are rising. The result of\r this simulates experiment shows that when MTU is at 1500bytes, it's\r unable to keep balance when sending, receiving and re-composing. The\r best new MTU is between 500bytes and 600bytes. And when MTU is\r between 500bytes and 600bytes, the network transmission efficiency can\r be promoted about 50% higher. At the same time, the research is also\r discussing the feasibility and necessity of applying it to the standard of\r the future network.

Drought and inundation are two unusual natural disasters in Taiwan. The two natural disasters\r have some relation of abnormal rainfall become more and more in Taiwan. So it let me think about\r can climate vicissitudes make the chance of abnormal rainfall become more?\r The study have researched the chance of abnormal rainfall by "rainfall duration" and "total\r rainfall". It collect the day by day total rainfall from 1960 to July 2002, collect locals are Taipei,\r Taichung, Kaohsiung and Hualien. Than enter the data into the computer, let computer calculation\r total rainfall, rainfall days, heavy rain days, pouring rain days and torrential rain days. Then\r analysis the tendency of long-term change.\r According to the analysis, the chance of abnormal rainfall happened become more in Taipei,\r Taichung, Kaohsiung and Hualien. The ratio of Hualien and Kaohsiung is the most obviously. It's\r also find that there temperature and total evaporate became higher, the total sunshine duration\r became lower. Then El Nino have some influence in abnormal rainfal. In El Nino year, total rainfall\r will become lower. When La Nina year, the total rainfall will become more in Taipei and Hualien.\r Then the long influence is clearly in Taipei.\r 乾旱與水災是台灣地區相當常見的二項天災，這二項災害的發生都與異常降水有直接的\r 關係。近年來台灣地區因異常降水造成的天然災害，似乎有逐年增加的趨勢。因此讓人聯想\r 到氣候變遷是否會導致異常降水頻率增加。\r 本研究主要由「降雨時數」與「降雨量」二方面探討異常降水發生頻率。先收集台北、\r 台中、高雄、花蓮四地自1960 年至2002 年七月三十一日之逐日雨量資料，將資料輸入電腦\r 後，統計各站歷年降雨量、降雨日數、大雨、豪雨、暴雨日數，並分析長期變化趨勢。\r 分析結果，台北、台中、高雄、花蓮四地異常降水發生機率，有增加的情形；其中以花\r 蓮及高雄變化的比例最高。再與其他各地氣象要素比較可發現，可能與氣溫及蒸發量數上升，\r 以及日照時數縮短有關。另外聖嬰現象也可能對異常降水有長期性的影響。一般而言聖嬰年\r 雨量減少，反聖嬰年台北、花蓮地區雨量反而會增加。而長期性的影響，以台北地區最顯著。

本研究以攝影紀錄的方式，透過電腦進行影像分析，記錄不同刺激下美洲蜚蠊(Periplaneta americana)的觸角擺動模式，計算出各項觸角運動的參數，以瞭解光線(光刺激或光適應)、震動刺激、喝水與進食對其觸角行為的影響。我們發現在不同因子的刺激下，觸角擺動的模式具有差異，若兩種不同的刺激同時發生，蜚蠊觸角的行為亦具整合性的反應。蜚蠊於不同狀態下(如喝水或進食)，對相同的刺激有不同的反應，證明蜚蠊觸角的行為模式，受環境因子與個體狀態調節。透過掃瞄式電子顯微鏡的觀察，也發現觸角具多種感覺毛，且雌雄的感覺毛的分佈與數量具有差異。綜合以上發現，證明觸角除了為敏感的受器，亦為能反映出生理與環境狀態的動器，同時也適合進行發展檢測器的仿生學應用，用來檢測環境中物理及化學因子。The aim of this study is to investigate the different swing motion modes of antennae of American cockroach (Periplaneta americana) by computer-aided Imaging Analysis. The parameters of each swing movement were calculated in order to analyze how light (including light stimulation or light adaptation), vibration, food and drinking water may affect the antennae behavior of American cockroach. It was found that the antennae swing motion modes were significantly different under different types of stimulus. If two different types of stimulus occurred at the same time, the reactions of antennae motion may become conformable. Under different environmental conditions (such as food or water), same stimulus may result in different reactions. The antennae behavior has shown to be significantly affected by environmental conditions and individual physiological status. Through the observation with scanning electron microscope (SEM), it was found that the antennae has many types of sensilla; and the distribution and quantity of these sensilla are significant different between sexes. In conclusion, not only the antennae are considered as the sensitive receptors, but also they are the important effectors to reflect physiological status and environmental conditions. The current model is suitable for the development of specific detectors in the applications of Bionics to detect the physical and chemical factors in certain environments.

本研究利用麥克風與相關電腦設備，結合成自製頻譜儀用以觀測多種情況下蜜蜂的聲音頻率。若將蜜蜂的翅膀加以修剪，可測得有不同的頻率，解析頻率發現「翅膀為主要發聲點，但去除翅膀仍有高頻的發聲，且有三種不同的頻率。」將蜜蜂置於不同溫度下，解析頻率得知「一定溫度範圍內，溫度越高蜜蜂發聲頻率越高，反之亦然。」幼期在胸部塗顏料使絨毛無法生長，去除雙翅後，仍有頻率相近的發聲，得知「胸部絨毛不是造成高頻的原因。」靜置５分鐘，待蜜蜂停止發聲後，剪去腳、挑弄蜜蜂會發出高頻，得知「情緒是引起高頻的原因。」將蜜蜂的翅膀加以修剪，分別放回蜂窩口，發現「同一族群蜜蜂可用發聲頻率來辨別同伴。」比較義大利蜂及中華蜜蜂，得知「在多種情況下中華蜜蜂發聲頻率皆較義大利蜂高約７０Hz。」因此本實驗之結論並不受蜂種影響。The study, capitalizing on a hand-made frequency divider, the microphone and computerized equipment, observes a variety of frequency of sound given off by bees. We read different frequencies from the apparatus when the bee’s wings were trimmed. Analyzing it, we discover that the bee’s winds are major source of its sound, but it still gives out high-frequency sound when the wings were completely cut off.” After analyzing the frequency, we discover that within a certain temperature range the higher the temperature is, the higher the frequency is, and vice versa. In one experiment, we painted the thorax at its pupal stage to stop the bee from growing fine hairs. Even though the wings had been removed, it still gave out high-frequency sound. We, therefore, conclude that fine hairs on the thorax have nothing to do with the making of the sound. In another experiment, bees were placed in an undisturbed environment until they are completely silent. Then, some of the bee’s legs were cut off, while others were provoked. And all the bees make high-frequency sound in the process. We make a hypothesis that emotion could be the cause of bees’ sound-making. The bees with different trimmed wings were put back to the beehive; the bees can still recognize one another by the different sound frequencies. If we compare A. m. ligustica with A. c. cerana under different conditions, we find that the frequency from the latter is about 70 Hz higher than that form the former.

國中數學第三冊1-4 的主題是「商高定理」，或稱「畢氏定理」。三百多年前法國數學家費馬在研究「畢氏定理」的方程式(x1)^2+(x2)^2=y^2後，把它的「次數」（原是二次）提高到三次、四次??直到(x1)^n + (x2)^n = y^n （ n ? 3），並且猜想說這個方程式在任何情況下都無自然數解。他的猜想在1994 年被證明正確。我聯想到：如果不是把「畢氏定理」的方程式的「次數」提高，而是把它的「元數」增加到三元、四元??直到(x1)^2 + (x2)^2+…+(xt)^2 = y^2 （ t ? 3）。就如同把費馬的方程式放在哈哈鏡前一樣，我把一個「高次」的方程轉變為一個「多元」的、較「長」的方程式。在這種情形下，我想研究下列的不定方程：(x1)^2 + (x2)^2+…+(xt)^2 = ny^2 在 t 和n 設任意自然數(但t ? 3)時，有無自然數解(x1,x2,…xt,y)以及若有解，解的形式會是什麼。我研究的過程分五階段。第一階段－進入題目：先探討一下n =1，t = 3、t = 4的情形，先熟悉問題。第二階段－證明一般化：嘗試將第一階段的結果推廣一般化到任意t ? 3的情形。第三階段－主題推展：嘗試將第二階段的結果再推展到n 是完全平方數k^2，以及n = 2、n = 3的情形。第四階段－推展一般化：嘗試將第三階段的結果接著推展到任意n 和t ? 3的情形。我所設計的證明方法只能涵蓋t ? 4，或是t = 3，但n 可以分為不超過三個數的平方和的情況。第五階段－解決特例：當t = 3，且n 無法分為不超過三個自然數的平方和的情形（是4p(8q + 7)( p?Z0 、q?N) 的形式）。因為我的研究是屬於建設性證明，所以我還研究了求解的方法，並撰寫電腦程式求解，驗證我的研究結果。研究結果大致如下：(1) t ? 4時，或是t=3，但n不為4p(8q + 7)( p?Z0 、q?N) 的形式時，原方程式有無限多組自然數解，且可依遞迴公式求解。(2)t=3時，且n為4p(8q + 7) 的形式時，原方程式無自然數解。這篇研究的應用主要是在立體及高次的抽象幾何。原方程式在n=1、t=3的時候，(x1)^2 + (x2)^2+(x3)^2 = y^2其x1,x2,x3,y依序正好為一長方體的三邊長及對角邊長。根據這篇研究的結果，可知：只要找一個不小於 3 的自然數，便可找出一個以此為邊長，其他邊長和對角線長也為自然數的長方體。如果再將此結果推展至更高次的話，則在t 次空間中，只要找一個不小於3 的自然數，便可找出一個以此為邊長，其他邊長和其對角線長也為自然數的t 次長方體。至於這篇研究的未來推展，則可將原方程式的各指數提高。

為探索蝴蝶為何在太陽光的高溫持續照射下仍可以快速散熱,且優美自在的飛翔, 所以本研究想進一步瞭解蝴蝶翅膀的構造, 及其散熱機制之後，仿照此一機制其中的蝴蝶鱗片的材質- 細微幾丁質, 達到材料仿生的目的。本研究將蝴蝶鱗片, 100%幾丁質, 細末甲殼素(92%幾丁質), 奈米碳,石墨烯,及散熱膏,在燈泡上加熱, 以尋求散熱最佳組合; 也將之應用在熱水加入玻璃杯, 鋼杯, 鋁合金等容器之外殼, 更將甲殼素與散熱膏混合物, 填補在電腦CPU與熱管縫隙中, 實驗結果得證, 果然細末幾丁質(本實驗稱甲殼素), 果然有良好的散熱傳導效果。

在這篇報告中，我們探索了「將錯就錯的Knuth 河內塔問題」。傳統河內塔問題在電腦科學上佔有重要的地位，是一個極具內涵的模型。由於這個模型的深厚數學內涵，使其和巴斯卡三角形建立了緊密的連結，且利用這個緊密的數學連結，設計出復原任意起始狀態的良好演算法。Knuth 河內塔起因於數學家Knuth 在論文[3]中，描述傳統的河內塔問題時所發生的一次筆誤。在這個新的規則之下，我們意外發現Knuth 河內塔存在著一個和傳統河內塔平行的模型，此模型在電腦科學及數學上有著完全不同於傳統河內塔的內涵。我們的研究主要如下：(分別為內文中的四大段)(一) 結構分析。移動環所需要的次數，如何移動環並分析每一次動作所動的環，及每個環何時被動到並給出演算法。(二) 正整數的分割。所有的移動步驟將正整數做了一個新的分割(Partition)；此分割模k之後有良好的循環性質。(三) 費波那契真分數的排序。這個正整數的分割形成一張表，這張表恰好就是分子分母皆為費波那契真分數之排序。(四) 隨意亂排的Knuth 河內塔復原演算法。在Knuth 河內塔的規定下將起始狀態改變，找出良好的復原演算法，並分析。 In this project we study the "Knuth Hanoi Tower", which is motivated by a typo in a paper of Knuth. This inadvertently typo leads to a new rule of moving the discs on the Hanoi Tower (see introduction below for definition). Although seemingly similar to the traditional Hanoi-Tower problem, it turns out that under this rule the "Knuth Hanoi Tower" problem consists of amazing properties, and is totally different from the traditional one. Our study focuses on the following directions: (1) Structure analyzing: We analysis the sequences recording the disc moving and offer enumeration results and recurrsive/non-recurrsive algorithms. (2) Partition of N: The moving sequence forms a partition (a table) of N, which has an amazing congruence property. (3) The order of Fibonacci proper fraction: The row/column of the partition table is, even more amazing, exactly the order when sorting the Fibonacci proper fraction with fixed denominator/numerator. (4) The Restoration of an arbitrary initial state: We offer an efficient algorithm for restoring any initial state of discs. We hope that our study on the "Knuth Hanoi Tower" offers a simple, neat, and new example on the theory of Algorithm, Number theory and Combinatorics.