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.
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。
台灣和東亞地區的氣候變遷
由人類活動造成的溫室效應可能導致地球溫度升高,聖嬰現象加劇等現象與災害,本文利用個氣候中心發展出的模式,推估台灣和東亞地區未來氣候變遷的情況,我們發現當大氣中的二氧化碳濃度增加為現在的1.9倍時,台灣地區的年平均溫度將升高0.85-2.50度C而東亞地區將會升高1.46-4.07度C,在同條件下個模式的平均推估量也顯示,台灣地區將每天增加0.10公厘的降水，而東亞地區每天將增加0.08公哩,我們希望這個研究結果可以做為其他相關研究的基礎,使大家提早因應未來氣候變遷所可能引發的種種變化;Greenhouse effect, incurred mainly by human activities may result in lots of phenomenon and damages such as the increasing of the world's average temperature and he aggravation f the "ElNino" effect. In this research, we simulate future metrological values by employing several simulation modes developed by different climate centers and predict future climate changes in Taiwan and East Asia area. We found that when the concentration of carbon dioxide exceeds 1.9 times than current value, the estimated range of the increased year-average temperature are0.85-2.5℃ and 1.46-4.07℃ for Taiwan and East Asia, respectively. Under the same condition, the ensemble mean reveals that the precipitation raises will be 0.1 and 0.08mm per day, for Taiwan and East Asia respectively. We hope our work can be the foundation of other related researches, and all the researches together can help for coping with possible damages caused by future climate changes.
塑膠海岸－臺灣東北海岸微小塑膠污染之研究
一、目的：1.找出基隆沿岸是否受到塑膠微小物的污染，建立塑膠成分的簡易檢定法，3.分辨所發現塑膠微小物成分，4.試圖分析其污染源，並尋求減輕汙染方法。二、結果：本研究為首篇證實東北部海岸已遭受塑膠微小物污染之本土研究。我們想出了不用昂貴儀器的位之塑膠簡易成分判別法，發現海面漂浮的油渣含有塑膠微小物，還觀察到海岸生物（藤壺）由本來附生在岸邊的石頭上轉而附著於漂浮的塑膠垃圾及漁民和釣客所使用的浮標、漁網、浮桶等。三、為減少海岸的塑膠微小物污染，建議政府立法規定業者主義塑膠原料運送中產生的問題，並提倡垃圾分類，人民本身也應自我覺醒。Taiwan is an island, and the sea is very important for us. So in this study, we tried (1) to examine the small plastics (resin pellets and plastic fragments) pollution of the northeast coast, (2) to identify the components of unknown plastics by burning, soluability in organic solvents and relative weight but without using expensive instruments, and (3) to classify the small plastics we found and to find out where were they from. Our study is the first grassroot research proving that the northeast coast of Taiwan has been polluted by small plastics. We attempt to identify the components of unknown plastics without using expensive instruments. The present study discovers that there are many small plastics in the floating oil scum. The relation between the oil scum and small plastics needs more study. We finds marine life (bamacles) growing on floating small plastics. The ecological importance of this discovery needs more study. We also make suggestions for reducing the minute plastic pollution of the coasts: (1) the government should ask big companies to be more careful on the transport of plastic pellets, (2) people should be aware of the problems caused by small plastics.