一些Moire patterns 的數學性質研究
Moire 為法文，其英譯為watered， 是古代織布技術的一種應用；將印有規律條?的透明薄片重疊時，稍微移動或轉動其中的一片，會形成極大的圖形變化，稱為moire pattern本作品針對三個moire pattern 的數學式加以推導：(一)、兩張透明片各印有等間隔平行線，轉動其中一片使兩線的夾角θ，亮紋垂直距離和暗?垂直距離的比值為tanθ/2tanθ 。(二)、兩張透明片各印有輻射線，重疊後行成圓系，可由代數或幾何加以證明，利用三角函數可推導出此圓系方程式為：x2+{y-rtan[π/2-(θ-?)]}2)]}={rsec[π/2-(θ-?)]}2)]}\r \r (三)、透明片A 印有等間隔平行線，B 印有符合高斯曲線的平行線，AB 重疊時，形成一系列的高斯曲線，AB 的夾角減少時，會增大曲線的曲率，我們進一步討論曲線的曲率和平行線斜率的關係。Moire is the French word “watered” and refers to an ancient technique employed in cloth making. The moire occurs whenever two or more transparent sheets with periodic strips on them are superposed. The characteristic of moire patterns is the fact that a slight shift of sheets will create dramatic alternations in the observed patterns. In the present report, We derive the equations of three different moire patterns. First of all, take a sheet with equal spaced straight lines and placed it on top of another identical sheet. They are made to intersect and form an angle of θ. As the angle changes slightly, it produces huge changes in the spacing of moire fringes. We can derive a formula related to the interfringe distance. The ratio of bright fringes and dark fringes is tanθ/2tanθ.Secondly, two transparent sheets with radial lines on them are overlapped, forming a pattern similar to the lines of force between point charges. We can find that the pattern is a series of circle by means of algebraic and geometric proofs. And proven by trigonometric functions, we canconclude that they satisfy the equation :x2+{y-rtan[π/2-(θ-?)]}2)]}={rsec[π/2-(θ-?)]}2)]}\r Thirdly, a set of lines of equal spacing is overlapped with a second set of lines whose spacing are derived from a Gaussian curve. A series of Gaussian curves is reproduced in a moire pattern. Reducing the angle of intersection between the two figures steepen the curvature. We discussed the relation between the curvature and the slope of inclined lines.
多重電極並聯情況下交、直流電解水的比較研究
The temperature of the water was commonly higher and both of electrodes were oxidized during electrolysis by using alternating current, but the above happenings were only found at the positive electrode by using direct current. It can be explained by the principle of the microwave stove. The exchange of the current causes the water molecules to release heat. The strength and weakness of electrolytes, the length and width of the electrodes, and the frequency of the alternating current can affect the rate of electrolysis of water. Commonly speaking, the stronger the electrolyte is, the faster the rate of electrolysis will be. NaOH and HNO3 are strong electrolytes, but the amount of the gas is zero during electrolysis by using alternating current. Maybe both of electrolytes react with stainless-steel electrodes to form some kinds of protective layers to affect the conduction of current. When copper bars, carbon bars, and iron nails are used as electrodes, either the alternating current or direct current is used, the amount of the gas is very small. Maybe these electrodes react with oxygen produced during electrolysis to form oxidized layers to block the conduction of current. Long and wide electrodes produce more amount of the gas. The amount of the gas increases when the frequency of the alternating current increases. The longer the distance between electrodes is, the smaller the amount of the gas will be. The smaller the angle between electrodes is, the smaller the amount of the gas will be, too. When the number of multiple electrodes in parallel increases, the total amount of the gas almost increases. The amount of the gas is smaller at the farther electrode. The amount of the gas at the electrode at the same distance becomes smaller when the number of multiple electrodes in parallel increases. At the same voltage, the effective current of the alternating current is about 0.707 of that of direct current. So we can predict that the total amount of the gas elect rolyzed by alternating current must be about 0.707 of the total amount of the gas electrolyzed by direct current. When we used stainless-steel electrodes and the electrolyte- H2SO4, we found the ratio was about 0.4286. Maybe the system of the electrolysis of water doesn’t obey the ideal linear system of Ohm’s Law and some part of electrical energy is wasted by increasing the temperature of the water and the oxidization of electrodes.
交流電解普遍水溫較高且兩極都有被氧化現象，直流電解則只有正極有上述現象，可能是交流電有類似微波爐的原理，電流交替時造成水分子震盪發熱。電解質強弱、電極種類、電極長短粗細、交流電頻率會影響電解水速率：強電解質較快，但NaOH 、KNO3 雖是強電解質，在交流電解時，氣體產生量幾乎是零，這可能是他們與不銹鋼電極反應形成某種保護層而影響導電；以銅棒、碳棒、鐵釘為電極時，不管是交流電或直流電，氣體體積都很小，這可能是這些電極和產生的氧氣反應，形成氧化層阻礙了導電；長的和粗的電極氣體產生量較多；交流電頻率越大，則電解所產生的氣體量也隨之增加；電極之間的距離越大兩極的氣體體積越小；兩電極之間的角度越小，兩極的氣體體積越少；多重電極並聯的個數越多，總氣體體積約略越大，距離越遠的氣體體積越小，同距離的氣體體積隨並聯的個數越多氣體體積越小。在相同電壓下，交流電輸出的均方根電壓(電流)為直流電電壓(電流)的0.707 倍(1/√2)，所以推測交、直電解水的氣體總體積比值也應為0.707，但我們以不銹鋼為電極、H2SO4 為電解液下比值為0.4286，這可能是本電解水系統並非為遵守歐姆定律的理想線性系統，且電解水時部分電能被消耗在水溫的升高及電極的氧化上。
打破語言隔閡-以圖點餐之數位餐廳
本次研究利用Web Sevrice軟體系統和Microsoft SQL Server的全文搜尋(Full-Text search)並藉由使用者選擇的圖片組合排列從系統資料庫中檢索比對，篩檢出正確或者最相似的餐點。Web Service 是建立於網際網路上之系統架構，且為一個具開放性、分散式的軟體元件，其基礎建立在HTTP、XML、SOAP、WSDL和UDDI等標準協定上，此研究即是透過Web Service系統與資料庫伺服器的連結進行。很多數位化資訊是以沒有結構化的文字資料，存成純文字檔及格式化的文件。這一類的文字資料儲存在檔案系統，而許多組織現在將這一類資料儲存到關聯式資料庫。這樣做就可以廣泛利用資料庫的好處-包括高效能存取、查詢能力、對使用者而言簡單的應用程式使用者介面，以及安全的遠端存取、查詢能力、對使用者而言簡單的應用程式使用者介面，以及安全的遠端存取。運用此功能即可在配對完成時搜尋最佳的結果並加以排名。「打破語言隔閡-以圖點餐之數位餐廳 」不只消除語言隔閡，更讓點餐手續方便許多，並讓錯誤的可能性降低。另外圖片資料庫的增減簡單快速、介面明瞭易懂。希望這些應用及創新能讓人們用餐方便及餐廳事業蓬勃發展。This research uses Web Service software system and Microsoft SQL Server. To choose the correct or the most similar meals by checking the combination and arrangement of the pictures chosen by users form the system data banks. Web-Service is a system structure establishes at the Internet. And its an open, dispersed software part. Its foundation is established at the standard agreement of HTTP,XML,SOAP,WSDL, and UDDI. The research proceeds by linking Web Service system and data-bank server lots of digital data are stored as words files and stylization documents without any structural words data. This kid of ward data are stored at file system, and many organized systems now store them at connected data banks. By doing this, people can make the most advantage of data banks- including efficient access, inquiry abilities, simple applies user’ interface, and safe remote access. People can find the best results and place them when this function finishes matching. It can not only eliminate language barriers but also make order procedure more convenient. It can also lower the mistake possibilities. In addition, we can increase or decrease pictures of data banks easily and fast. We can make the interface understood easily. We hope the applications and innovations can make it more convenient for people to order meals. And the business of restaurant can be developed successfully.
遞迥數列及渾沌現象
給定一個P∈(0,1),令k0=0, p0=p，定義k1為能使 的最小正整數k，而 ; 相同的，對於給定的kn-1, kn 為能使的最小正整數k, 。若存在kn 使得，則稱p∈ In; 若對於所有n 與kn ，，則稱p∈ I∞。如此區間(0,1)可分解成集合I1,I2,…,I∞。
影像的色偏校正
The human eyes can adjust automatically the color of object under different illuminants. But digital camera does not have such mechanism, must join the white balance to simulate the color constancy of human eyes. There are many existing white balance methods. They can be categorized into two types. The first type utilizes the widespread assumption on the dealing natural scenery, which has the advantage of simplicity. Another type explores knowledge of the semantic content, which has the advantage of accuracy. In this study we modify and enhance the widespread assumption methods that can adopt the advantage of the simplicity and accuracy. Our proposed method is structured in two main parts: a color cast detector and a color cast remover. The detector first analyzes the color distribution of the image with simple statistical tools to determine whether or not the image has color cast. The remover, a modified and enhanced version of the widespread assumption methods ( gray world and max RGB ), is then applied on the color cast image. From the experiment results, it demonstrates the efficacy and performance of the proposed method.人類的視覺能夠自動修正因光線變化而改變的物體顏色，但是數位取像設備的感光元件卻不具有這樣的功能，必須加入白平衡的功能，才可模擬人眼維持色彩恆常的特性。現有的白平衡演算法可分為兩大類型，第一類型為廣泛假設型，具有運算速度快、與取像設備無關的特性，但是平均誤差會較大；另一類型為預知特性型，其特徵為準確性較高，但是運算較速度較慢、建立色彩特性資訊時所需的成本較高，本篇研究針對廣泛假設型的演算法做些修正與增強，使其具有較小的平均誤差以獲得較佳色彩品質的影像。我們將影像的色偏校正分為色偏偵測與色偏移除等兩個階段來進行，由於僅有被偵測出有色偏的影像才需要進行色偏的移除，所以可以避開將無色偏或固有色偏的影像做錯誤的修正，由實驗的結果看來，我們的方法確實有效，除了具有運算速度快、與取像設備無關的優點外，其色偏校正能力也較現有的方法好，使得影像色彩更能與人眼所見相近。