Video compression is indispensable to web streaming and memory storage.Most video\r compression technology has difficulty to achieve high quality video at lower bit\r rates.Apparently,limited transmission bandwidth and network resources often degrade\r video signals.Thus the goal of my research was to enhance video degrade video\r signals.Thus the goal of my research was to enhance video compression performance and\r to improve visual quality.It is hypothesized that the reduction in neighboring pixels\r coding,and humans perceptual mechanisms(psychovisual)redundancy could produce a\r low-complexity geometry streams for animated visual objects.A set of algorithms is\r developed to parse bidirectional interpolation pixels into their characteristic cells,which\r vary in spectral energy and wavelength.The bits contained in these cells are vectorized and\r transformed recursively to identify lower correlations among vector arrarys for blocks\r filtering.DCT function calculates energy ratios between high spatial frequency and low\r spatial frequency,to devote most of the highest spatial frequency bits with the calculated\r energy ratios.A variable quantization method is used to measure the sensitivity of colors\r and its intensity ratios to restore any missing high spatial frequency pixels.presnted in\r mathematical intrinsic.This approach leads to the ability to compress video data that\r normally require a large amount of memory to store and high bandwidth to\r transmit,Results form the enhanced video compression experiment have attained\r 0.1bpp(256kbps,25fps)without noticeable effects comparable to the video compression\r technique that achieved 0.5bpp(1.5Mbps,25fps)in use today.

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。

此研究的目的是要設計出一套完整編輯顯現數學式、加以計算，並求出解的一套方法與成品。而這項工作的執行者，在此稱之Equatetor 。一般的數學式子，若要計算的話，普通的計算機是不足夠的。原因是它們沒有辦法表現出數學式的「原貌」，例如分號、指數、函數、根號等數學符號混在一起時的情況。於是，我便擬定了一個研究，希望設計出一套更方便且實用的方法。換句話說，我要設計出一個功能強大的工程計算機程式。其中，自然牽扯到數學式子的顯現方式（以MathML 實現），以及計算機科學的演算法及資料結構。我主要的目的有四：(1) 顯示數學式(2) 方便編輯數學式(3) 計算數學式(4) 處理可以以不同形式輸出解答的計算（如輸出分數、根號、函數解等）。研究結果中，成功地運用XML 中的MathML 與二分逼近分數等演算法及若干資料結構，達到了以下實用的幾點：(1) 結構化的數學式編輯(2) 完整地顯示數學式(3) 正確運算並輸出運算式的答案(4) 提供一般數學形式之解（非小數之解）;The object of this study is to design a method and processor which is able to edit, display a mathematical expression representing a number, calculate and output the answer. The executor of this task is called Equatetor. Normal calculators are not adequate for this kind of task. The main reason is that they can’t reveal the original expression, such as fractions, radicals, exponents or mathematic functions. Therefore, a simple and convenient method is needed. To perform the possible way of handling those tasks, a computer program has been written. Several techniques were used, such as MathML, computing algorithms, data structures, and so on. Following are main purposes: (1) Displaying mathematical expressions. (2) Editing mathematical expressions simply. (3) Calculating mathematical expressions. (4) Outputting the answers(in different expressions). And the achievements:(1) Structured methods of editing of mathematical expressions. (2) Displaying mathematical expressions completely. (3) Calculating mathematical expressions precisely. (4) Offering answers in different expressions.

以隨手可得拍攝影像的工具（如智慧型手機、個人數位助理、網路攝影機等）及網際網路的便利性，讓使用者能隨時透過書籍條碼影像向遠端資料庫查詢書籍的相關訊息。本研究以「ISBN書籍條碼」為例，經過條碼影像的擷取、偵測並分割出影像中的條碼、歪斜校正以及辨識後，透過網際網路，從ISBN書籍資料庫中查詢出該書籍的相關資訊，讓我們體驗行動通訊科技所帶來的便利。在程式的實作上，除了使用現有影像處理技術中的霍夫轉換與邊緣偵測外，也搭配上自行設計的變化量分配圖，使得ISBN條碼的辨識能力大為提升。此外，為了將使用者查詢時等待回應的時間降至最低，採用了記憶體直接存取的方法來處理影像外，也針對程式執行時的瓶頸部分，以平行處理的機制來加速，經過在Intel i5 M560四核心處理器上的實際測試，一幅900×675像素的影像，平均只要花費1.08秒即可辨識出ISBN條碼，相當的迅速。

A program based on the simulated annealing (SA) algorithm was developed to allow for a longer-term prediction of the occurrence of solar flares, thus reducing the risks they may pose to astronauts, satellites, and ultimately the planet Earth. Sunspot data such as the solar cycle, the appearance of sunspots, the sun's magnetic field, the occurrence of solar flares and other factors that concern the sun were considered in the development of the algorithm. The program, coded in C++, included providing for an initial random state that pertained to the sun's state at a specified time. A neighborhood function was designed based on how sunspots are formed and how they disappear, and the probability function was designed using previous solar cycles to show relationships between the number of sunspots and the time it takes for the sun to reach solar maxima. Finally, the cooling function was designed as a representation of the time. Recorded sunspot counts obtained from the US National Geophysical Data Center (NGDC) during the solar cycle 22 from 1986 to 1996 was used as test data. The output was compared to the actual recorded solar events or the period. The program was found to be 66.7% accurate in predicting solar flares when compared on a smoothed trendline, while it exhibited a 50.5% accuracy when comparing day-to-day data. Since solar flare acitivty is predicted in terms of the trend of activity and intensity, improving daily data accuracy is superfluous. Smoothed trendline prediction accuracy may however be improved by altering the importance of each factor in predicting solar flare activity and by devising a different sunspot classification scheme for intensity and activity.

金瓜石為什麼產金？ 地殼中的黃金含量稀少，但是在特殊的地質條件下，地層中的黃金卻能夠聚集在一起，具有開採價值，這就是所謂的金礦。 許多金礦的形成，都與古代的岩漿活動有關。如金瓜石地區金礦的形成，就與百萬年前基隆火山群的岩漿活動關係密切。 在金瓜石地區，地下水被岩漿加熱成溫度極高的溫泉，而且岩漿物質也溶入溫泉裡頭，使得這類溫泉大多呈現酸性，能夠溶解許多地層中的礦物質(包括黃金)，稱之為熱水礦液。 熱水礦液沿著地層中的破碎帶向上流動，壓力和溫度降低，黃金等各類礦物在岩石裂隙中沉澱，逐漸聚集成為金礦。這就是「點石成金」的熱水礦化作用。 含有黃金成份的熱水礦液沿著斷層向上滲流，一點一點沉澱累積，終於形成黃金礦體。 金瓜石的金礦，最初深埋在地下，在板塊運動的作用下，逐漸被抬升到現在的高度。隨著覆蓋在上頭的厚重地層漸漸被侵蝕消失，地下的金礦也就離地面愈來愈近，部分金礦甚至還會露出地表呢！ 如何區分黃金與愚人金？ 在九份、金瓜石地區販賣礦石的攤位上，經常可以見到一顆顆黃澄澄的立方體結晶，這就是似金非金的愚人金~黃鐵礦。 黃金的產狀通常都不規則，可是在野外卻常有機會找到晶形漂亮的黃鐵礦。 其次，雖然看起來都是黃澄澄的，可是黃鐵礦的顏色偏白，不像黃金是金黃色的。 把黃鐵礦在白色瓷板上刮刮看，會留下一條黑色的條痕，可是用同樣的方法，黃金的條痕卻是金黃色的。 而且，兩者比重明顯不同，黃金比重高達19.3，可是黃鐵礦只有5.0，將差不多大小的黃金和黃鐵礦分別放在雙手一秤，就可以明顯感受的黃金沉甸甸的份量。 黃金為什麼珍貴？ 金是一種稀有的元素，在自然界分佈相當廣泛，但是含量卻極少。在自然狀態產出的金，常含有銀，偶而也含有少量的銅、鉛、錫、鋅等類的金屬。 自古以來，黃金就是財富的象徵，不單只是它閃亮的金黃色，更因為它的稀有珍貴，所以人們總是把黃金製成錢幣、條塊或各種飾品，既具有保值功用，又有藝術價值。 黃金的導電性佳，不容易受日曬雨淋而發生化學變化，穩定性很高，而且還能敲成非常薄的金箔和金絲，所以許多電器產品的零件都少不了它，像電腦裡的電路板就有這種材料。

二元根樹是資訊科學上最重要的結構之一，因此其結構的探討就很有價值。在這個研究中，我們探討二元根樹上反鏈(Antichain)，鏈(Chain),獨立集(Independent set)計數。在每一個子題之下，我們求出計算反鏈，鏈，獨立集的方法。之後我們求出極值(包括最大跟最小值)，並且討論該極值之下所有可能的樹形。此外，我們並討論要列出二元根樹上這些資料(反鏈，鏈，獨立集)所需的演算法。In this paper we enumerate the number of antichains, chains, and independent sets of a binary tree of size n. After that we focus on the extreme values (maximal/minimal). we calculate the extreme values and discuss the possible graphs of trees when achieving these extreme values. Moreover, we offer algorithms for listing all the objects in each extreme case.

When you draw a wet finger around the edge of a half filled wine glass, a sweet musical sound comes forth. The pitch of this sound is directly correlated to the amount of liquid in the glass- the higher the height of the liquid is, the lower the frequency is. It means that the shorter the air column in the glass is, the lower the frequency is. This phenomenon differs from the variance in pitch in a wind instrument. In a wind instrument such as a flute, the shorter the air column in its chamber is, the higher the resulting pitches are. In order to study the wine glass phenomenon, we used a piezoelectric crystal loudspeaker connected to an oscilloscope. We recorded the resulting data by using a digital video recorder to capture the images of the waveform of sound, and than analyzed the waveform by using the computer. Our conclusions are as follows: 1. The frequency of sound thus produced was the same whether we draw our finger around the rim, or we strike the glass rim. The higher the height of the liquid is, the lower the frequency is. But the frequencies vary when we strike the glass and when we blow on the edge. 2. When we used a glass without liquid in it, the frequency emitted when we drew our finger around the edge, this frequency varied inversely as the cube root of their weights. 3. In a glass with liquid, the emitted frequency did not have any correlation to the weight of the contents. By taking two identically filled glasses and placing in each a solid object of the same size but different weight, we were able to see that there was no change in the frequency emitted between the two glasses as long as the height of the liquid remained constant. 4. According to “The Flying Circus of Physics”, if we tap the side of a glass of beer, because of the air bubbles in the beer, the frequency emitted will be lower than that from a glass of pure water. This is according to the book, because the speed of sound is lower in air than in water, therefore the speed of sound in an air-water mixture would be lower than in pure water. The resonant frequencies of the mixture will also be lower. However, in our experiment, we discovered that\r when the glass contained air bubbles, the frequency emitted higher. Our explanation is that the sound emitted since the rim of the glass oscillated transversely, the frequency depends only on the retard of the rim and that the frequency is independent of the speed of sound. The intention of this research is to clarify the many misconceptions of this interesting phenomenon.以溼的手指在玻璃酒杯邊緣摩擦，會有悅耳的聲音，而且頻率會隨著內裝液體減少（空氣柱變長）而變高，這種變化與管樂器隨空氣柱的變長而音調變低不同，為了研究它的原因，我們利用壓電晶片喇叭連接到示波器上，並且利用數位錄影機錄下示波器上的訊號，再以電腦分析出瞬間的頻率，結果發現：一、摩玻璃杯與敲玻璃杯，杯所發出之頻率相同，都是所裝液體愈多發出之頻率愈低。但敲玻璃管與吹玻璃管所發出之頻率不同。二、不裝液體之高腳杯，摩擦時所發出之頻率與重量之立方根成反比。（與鐘相同）\r 三、裝液體之高腳杯發出之頻率，不再與總重量有關，而是與液體之高度有關，保持液體高度不變，即使在杯子中央加入不同重量之固體，杯子振動頻率還是不變。若改裝不同密度之液體，則密度愈大頻率愈低。四、在“The Flying Circus of Physics”書中提到輕敲裝有啤酒之杯時，會因杯中含有氣泡而聽到較低之音調，書中解釋是”空氣中之音速低於水中之音速，混有空氣之水中音速變低，其共振頻率也會降低。”但我們的實驗結果是有氣泡時頻率反而高。我們的解釋是杯子所發出之聲音是由於杯面之振動也就是杯壁的橫向振盪，振盪頻率與液體對杯壁之阻尼有關，但與液中聲速無關，密度愈大之液體阻尼愈大。有氣泡時接觸杯壁之液體變少，阻尼較少所以頻率高。希望本研究能使大多數人對這有趣之現象不再有誤解。

掃描式穿隧顯微鏡(Scanning Tunneling Microscope)，是在奈米尺度下觀察物體表面的一大利器。但一台精密的STM，造價動輒數百萬元新台幣，本研究嘗試利用簡單、便宜的材料，製作一台簡易的掃描式穿隧顯微鏡。眾所皆知：掃描式穿隧顯微鏡的關鍵，就是量子力學中的穿隧效應原理，及壓電材料的應用，所以這些主題都是本實驗涉及的內容。除此之外，我們也運用簡單的物理原理，取代價格高昂的儀器，例如：利用彈簧代替昂貴的避震系統等。此研究利用穿隧效應的原理，並進而利用電腦得知樣品表面的結構，以達顯微鏡觀察分析物體之功用。 ;The major purpose of our project is to assemble a simple scanning tunneling microscopy with cheap and available materials for ordinary senior high school students. For example, we use springs for damping instead of electromotive force device. Weweld all the electronic circuit boards for ourselves in order to not only lower the cost but also inspect the inner structure more clearly and precisely. After the microscopy is assembled, we will use it as an appliance to observe the samples of nano-particles. We must repeat this procedure several times so as to make sure that the images we’ve gained is true, not just some disturbances produced by the environment. Finally, the microscopy can be applied to research fields as well as academic courses.

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。

In our daily life, objects and the contacts between objects they will have mutually affect each other, some initially chaotic systems after a sufficient amount of time will mutually correct each other, and finally achieve synchronization (example: the speed of bird and fish migration, market prices, infantry…), although some are unable to achieve this. We will illustrate and explain the synchronization system, its process and discover the conditions for synchronization. Using linking concepts, we will integrate the coupled map lattices with global coupling and coupled map lattices with intermediate-range models into a synchronization mode in order to simulate a synchronization system. We first used a small system of n≦50 to obtain results that will demonstrate the linking concepts: 1. The more chaotic a system, a longer period of time is required for synchronization. 2. An increase in the number of individual objects requires an increase in the range of concepts and the amount of time in order to achieve an in depth synchronization. 3. Initial concept values which randomly effect synchronization critical point conditions are not obvious in a mathematically incorrect graph. In a closer look, when we increased the synchronization to n≦400 and the number of times to t-->100,000 we discovered:1. Using the function G(x) we hoped the results from the graph after apply the function and correction able to overlap and test with “Scaling and Universality in Transition to Synchronous Chaos with Local-Global Interactions”, but the part which overlapped the measurements was not identical: 2. We can use the significance of the critical point and the Interactive Process to find the approximate value of the critical value up to 4 digits following the decimal point. 3. We can also use the approximate value to find out the range for the simultaneous conditions and the various points on the system itself, as well as obtain a negative correlation between them, and then it can be similarly expressed with using a curve. A computer can calculate values with this kind of enumerating method, even without any special resolution capabilities to quickly obtain large amounts of approximate values of simultaneous conditions, this is especially true when calculating unfamiliar systems. 日常生活中，物件與物件的接觸，彼此會互相影響，有些原本雜亂的系統再經過充裕時間的互相修正後，最後竟能達成同步(例如：鳥群、魚群遷徙的速度、市場價格、行軍步伐…)，有些則不能。因此，我們試著利用描述同步系統的模型，觀察系統同步的過程，並且找出同步的條件。由連結的觀點，我們將Coupled map lattices with global coupling 和Coupled map lattices with intermediate-range 模型的優點整合成Synchronization mode 去模擬同步系統。我們先用小系統(n≦50)得到能印證連結觀點的結果：(一)、系統越雜亂，就需要稍長的時間同步；(二)、個體數越多時，各點需要更大範圍的點數去影響於每單位時間內以及更深的影響才能同步；(三)、起始值隨機影響同步臨界條件並不明顯，在誤差範圍內。更進一步，我們將系統推向n≦400 點,t→100,000 次，我們發現：(一)、在”G(x)”我們希望能將圖形經過函數修正之後能疊和，驗證”Scaling and Universality In Transition to Synchronous Chaos with Local-Global Interactions ”中的結果，但只有部分疊和，尺度不相同；(二)、可以直接利用臨界點的意義用十分逼近法求出臨界值的近似值到小數後四位；(三)、我們用近似值也能發現同步條件與系統各點本身可跳躍的數值範圍是負相關，可用曲線去近似。這種窮舉方式，交由電腦運算，不需要特別的解析能力就能夠快速且大量求得同步條件的近似值，尤其在運算不熟悉的系統時。

本研究以b04課程中的巴斯卡三角形為研究對象，將原先巴斯卡以「1」為首、「+」為運算符號的規律三角形，改為以「-1」及「ω 」為首、「×」為運算符號，分別就其產生的新三角形作探討，發現其中似乎隱藏著原先三角形所沒有的規律性。為了更瞭解這種規律，藉由電腦軟體繪出其圖形，圖形顯示出如碎形般的複製關係，不論放大或縮小，其中的遞迴關係並未改變，頗令人好奇，因此著手研究。研究過程中對於圖形的規律性採用先臆測、接著歸納、最後給予證明的方式呈現。得到以下的結論：一、分別以數列呈現新三角形圖形的規律性。二、分別將新三角形中每一列中的某數字（如-1、ω 或ω 2 ）的個數予以通式表之。三、分別推算出新三角形第n 列第j 行的數是「1」或「?1」及「1」或「ω 」或「ω 2 」。四、相同的模式，在特定的圖形範圍中，不斷重複出現。許多研究將巴斯卡三角形中的所有數，以某數為模的餘數紀錄下，去探討其餘數在新產生的巴斯卡三角形中的分布情形；而在碎形的研究中，大部份著重如何畫出碎形。本研究著重圖形其規律性的探討，提供上述研究不同角度的詮釋與探討。 This research subject is based on Pascal’ s triangle in senior high school curriculum. The regular triangle begins with「1」and use「+」as operation. Let 「1」 be replaced with「-1」and「ω 」, the operation sign「+」be changed into「×」. I do research on the new triangle and discover the seemingly hidden regularity which doesn’t exist in the original one. To understand more about this regularity, I draw figures through the computer. The figures show the relationship of reproduction as fractal. Whether the figure is enlarged or minimized, it’s surprising curious the recursive relationship doesn’t change, so we begin to work on research. In the process of the research, we make careful observations, assumptions and deductions about the regularity of the figure. Finally, we come to some conclusions by means of giving proofs:（1）Present the regularity of the new triangle figure with progression.（2） Present such numbers as「-1」, 「ω 」, 「ω 2 」 in each row of the new triangle with formulas separately. （3）Figure out the number in the row n and in the column j of the new triangle is「1」or「-1」,and「1」or「ω 」or「ω 2 」. （4）The same model appears again and again in the specific range of figure. Many researches record Pascal’s triangle modulo certain number to explore the distribution of remainders in the new triangle. In the research of fractal, how to draw fractal is mostly focused on. The exploration of this research emphasizes the regularity of figure, offering the interpretation and exploration of researches above from different angles.