耐熱性酵素生產菌Bacillus Subtilis WLA12 之分離與定性
本實驗針對一取自台北縣烏來南勢溪下游之溫泉菌，進行微生物學、生物化學、分子生物學三方面之觀察與實驗，期能得到一可生產特定酵素之菌種，且具耐高溫之抗逆境能力。對其酵素進行定性，並嘗試轉殖出相關基因，使之可大量表現。目前已篩選出一種可生產多種酵素之菌種〔依其採集地點暫稱WL-A12〕經菌種鑑定為Bacillus subtilis WL-A12。藉由菌落檢測法以及Zymogram 的方式做酵素分析，並以電導轉形等技術，希望能成功轉至E. coli 上表現。另外，也對該菌種作了一些基本微生物方面的觀察〔如需氧情況、最適生長溫度〕。We isolated enzyme-producing thermophilic bacteria from hot springs near downriver of Nan-shi, Wulai, Taipei (北縣烏來南勢溪). Through microbiological, biochemistry and molecular biological analyses, a multiple enzyme-producing Bacillus subtilis strain, designated WLA12, has been isolated. The growth condition of WLA12 was observed. Using basic colony assay and zymogram analysis (gel electrophoresis) to observe the expressed enzymes, molecular weight and gene size of the enzymes were revealed. With comparison to E. coli control strain, the related enzymes were only found in WLA12. To express the Bacillus genes in E. coli, molecular cloning and gene transformation via electroporation was carried out.
東沙島海灘的變遷與復育：由龍擺尾停擺說起
政府最近公佈在東沙群島設立第一個國家海洋公園，顯示國人重視海洋資源的保育與復育；但是東沙島特殊的自然景觀「會擺動的沙嘴」—龍擺尾，卻因興建八座消波塊構築的突堤而消散停擺。本研究以一個高中生的觀點，設計及進行一系列的模型實驗，探討東沙島的形成機制、各種環境因素對海灘及龍擺尾的演化、驗證龍擺尾的現況及如何讓龍擺尾復活，再由東沙島海灘復育看世界的海岸問題。雖然設備很克難，但都能完成預定的目標，證實東沙島的海灘演化。希望此次對東沙島海灘的研究成果與初步探討，能應用於世界上遭受侵蝕而需復育的海岸。In 2007, our government proclaimed Dongsha archipelago as the first national marine park, signifying her emphasis on the conservation and restoration of marine resources. However, the sand spit on Dongsha island, a unique natural wonder commonly referred to as the “swaying dragon tail”, has become motionless since the construction of a total of eight groins along its SE and NE coast during the period between 1993 and 1996. This study has conducted a series of model experiments to verify several fundamental issues, ranging from the formation and the factors affecting the stability and the status quo of Dongsha island and its spit. The experimental results find several favorably outcomes, giving the coast evolving evidences of Dongsha island. Furthermore, strategy to stabilize the coast and revitalize the spit are then considered, which could hopefully benefit the coast suffering erosion on the world’s coastline.
國民身分證相片規格驗證暨浮水印防偽系統
政府全面換發國民身分證，並訂定新式身分證之規格，以防範遭不法偽造之情事，確保民眾權益。然而其中的照片規格，有十多條規格的限定，若用傳統的辨別方式，近1876 萬張照片是否合乎規定，那將耗費多少的人力呢？於是本次研究主題「新式國民身分證相片規格驗證暨浮水印防偽系統」即產生，設計一套程式，提高換發國民身分證的工作效率及確保換證使用相片的正確度。並且延伸研究出使用內崁式的數位浮水印〈Digital Watermarks〉，將全國民眾的身分證照片統一建立資料庫，並自動加入個人資料浮水印。日後，照片只需透過本程式分析，即可知道其姓名、身分證字號、有無犯罪前科等個人資料。希望藉此達到降低偽造身分證之犯罪率，以保護民眾之權利。 The government is launching to renew national identification cards with new norms, to avoid fake ones. However, there are more than ten limits on photos, it could be wasting time to discern by people. Thus, I launched a research on "The xamination on new national ID card photos and watermark forgery-proof system". The program will help both to enhance efficient renewal process and to use correct photos. Also we developed the embeded Digital Watermark technology, which would create a database for ID cards of the nation and could add personal infomation automatically. With the help of the program, simply run the photo analysis, we could find out the names, ID number, criminal background, etc.We hope to decrease crimes via fake ID cards, and protect the national right.
聽音辨位--聲波的測量應用
本實驗設計主要是以波的傳送速度(特別是聲波)，以及接收收到的時間值來做實驗、運算、討論。而其特點是為了應用於實際生活中，做了許多異於平常測量方法的設計。主要是使用時間差(｜t1–t2｜V=發聲器到兩感應器的距離差 )來消彌掉一般測量時，需要採取同步的條件，說明如下：
1. 由以上的圖中，t1’ = T + t1 為實際由感應器開始感應到感應器#1 接收到訊號的時間；同理，t2’ = T + t2 為實際由開始感應到感應器#2 接收到訊號的時間。而T 為感應器開始感應到發聲器開始發聲的的時間(之後的 T 皆為如此)。由以下式子得知：
｜t1’ - t2’｜=｜( T + t1 ) - ( T + t2 ) ｜=｜t1 - t2｜及為本實驗所需的時間差。利用減法將T 消除，便及為發聲器與感應器不必採取同步，此為本實驗目標以及優點之一。
2. 之後的公式推導中，實際由感應器開始感應到感應器接收到訊號的時間中，表示為t1、t2、t3……以此類推。
像是市面上販售的反射式測距器由於其直線性的限制，在我們可負擔的情況下，就只能做一維的測量，而在本實驗中，我們使用多個感應器，而可測量至二、三維空間，並使測出的物體由相對位置轉為絕對位置。再加上正在計劃中的測量儀器改良與自製，例如利用電腦的音效卡接上麥克風或是其他感測器，以及電子零件、電路的組合與設計。而在於一般的實際應用面上可配合工業的破壞性檢測，甚至是橋樑的斷裂處、各種振源的測量，亦或是人員的搶救，都應有不錯的效果與利用價值。
1.The major design of experiment is to spot the location of an object by experiment, calculating and discussing of such figures like the transmission speed of the waver (especially sound wave), plus time value of the receptor and so on to get the result. 2.In practice, the ordinary measuring method has to be implemented under the circumstance of synchrony: however, the distinguishing characteristic in the experiment is to overcome such restriction with the use of the “time lapse” concept. 3.The reflecting measuring instrument on the market is limited by its “straight-line characteristic.” Instead, we use multiple sensors to spot the absolute location of an object in its 1-D, 2-D, 3-D form. 4.We have now been working on the improvements of the measuring instruments, for instance, using sound cards to connect to the microphone to make a new sensor; also, the redesign and combination of other electric parts and circuits are also under construction. 5. We plan to apply the experiment not only in spotting the location of an object but also in further spotting the location of vibration coming from various objects (e.g. in the use of rescue).
繪身繪影-正三角形磁磚設計方法與碎形密舖之研究
本研究主要以正三角形作為基本單元，透過窮舉討論得到正三角形邊的作用方式只有五種，再經由排列組合歸納出11 種正三角形密鋪磁磚設計方法。進一步，運用我們的研究結果，配合數學簡報系統製圖，創作新圖樣，也彌補了Escher 在手繪時所造成的誤差，達到完全密鋪的效果。碎形磁磚的部份，我們也依據其背後的數學理論創作幾套結構圖，利用結構解析，碎形密鋪磁磚將變得十分容易，學習者將可輕鬆製作富有創意的新圖樣。 ;This research mainly takes the regular triangle as the basic unit. Through the enumeration, we obtain that there are only five operations for edge of the regular triangle, and then 11 kinds of regular triangle design methods are induced. Even more, utilizing our findings and Mathematical Presentation System (Math PS), we created the new pattern which makes up Escher’s errors and achieves the tiling. As to Fractal Tiling, we create several sets of structure drawings according to its mathematics theory. Using structure analysis, the Fractal Tiling will become extremely simple, and the learner can make the rich creative new pattern easily.
口琴簧片振動與氣流的影響
本研究主題在測量口琴簧片受到各種氣流因子影響後，所產生音色、音頻等變化之探討。在過去我們認為，一片簧片不論如何吹奏，其發出的頻率皆相同。但是事實上，演奏家控制氣流的強弱、方向、渦流等，便可吹奏出多樣的音頻。探討形狀因子對簧片頻率的影響，如：長度、寬度、厚度對頻率所造成的影響。自製口琴，利用變壓器控制送風機風速。探討氣流因子對簧片主頻之影響，利用各種不同的自製吹嘴，改變風速、角度、渦流…等，找出可能使簧片改變頻率的氣流因素。實驗結果發現改變風速會影響簧片主頻的變化，風速越大，頻率越大，為一條平滑線。但並非一直都會上升，當簧片頻率上升至某一極限，便無法再利用風速使頻率上升。例如實驗四吸音標準狀態下，風速大於8 Kt 後，頻率一直停在429Hz。在外加障礙物時(模擬吹奏舌頭時隆起)和標準狀態(正常零度入射)下頻率比較吹音和吸音有明顯的差異。吹音時，同風速下，其頻率比標準狀態高，發生音升；吸音時，同風速下，其頻率比標準狀態低，發生音降，具應用性。我們發現在頻率改變時，簧片的振動型態會有所不同，所以利用高畫素像機拍攝和電腦相位差算出簧片之曲折點至尾端的距離，發現頻率和簧片之曲折點至尾端的距離成正向關係。如實驗五中頻率從414 至419Hz，簧片的曲折點到振動端距離也明顯變大。我們發現吹嘴和口琴只要稍有一點空隙(大約在0.2cm 左右)，便會和完全吻合時有顯著的頻率差距(吻合後大約比有空隙低20Hz 左右)，此實驗頻率變化現象和現實壓音頻率變化極為相近。實驗過程中發現，改變簧片吹嘴的吻合程度，吹入口琴的風速相近，但頻率變化卻也有壓音的音頻變化。在實驗三加入各種氣流因子發現入射角度和標準情形差異不明顯，因此推論壓音的頻率變化和風力強度、入射角度關係不大，壓音主要為渦流所造成的現象。簧片振動模式改變，導致簧片振動頻率發生變化，且簧片的自然頻率不變。當壓音產生時，氣流在振動面造成妨礙簧片振動的抗力，但琴格內部同時也給簧片的風壓，使簧片產生一種非自然振動的頻率。The theme of the research is to explore the changes on its timbre and frequency after the harmonica reed is influenced by each kind of air current factor .In the past ,most people think no matter how to play the reed ,the frequency it produced was supposed to be the same. But in fact the frequency will be changeable under different direction, turbulent flow and air intension by the perform. First to explore the basic feature of harmonica reed, for example: The length, the width, thickness cause the influence on the frequency. To make the self-made harmonica, using the transformer control air feeder wind speed. To discussion the influenced caused by air current factors,and use each kind of different self-restraint to boast, change the wind speed, angle, turbulent flow ,in order to discover possible factors the reed causes to change the frequency of the air current factor. The experimental result discovered the change of wind speed can affect the change of basic frequency , the stronger speed cause the bigger frequency, It will be a curve. But it will not be rising continuously, when the reed frequency rise to some limit, it is unable to cause the frequency rise again by using the wind speed. For example experiment four sound absorption standard conditions, after the wind speed is higher than 8 Kt, the frequency continuously stops in 429Hz. To compare obstacle (simulation plays when tongue sticks out) and the standard condition (normal zero degree incidence) , comparison blows the sound agreement sound absorption to have the obvious difference. When blows the sound, under the same wind speed, its frequency is higher than the standard condition, has the sound to rise; When sound absorption, under the same wind speed, its frequency is lower than the standard condition, has the sound to fall. The harmonica terminology for presses the sound, extremely has the application. We discovered when frequency change, the reed vibration condition have differently, therefore use the camera photography and the computer phase different figures out the reed winding point to the end distance, discovered the frequency and the reed winding point relate to end distance is being connected. If tests five medium frequencies from 414 to 419Hz, the reed winding point is away from to the vibration end also obviously changes . The different reed vibration condition cause the frequency to change. Natural frequency is constant. When cause “bending” (the frequency is lower than the standard condition), the airflow make a force keep from reed vibration. But the chamber air pressure still drive reed. therefore cause the reed to give off not natural frequency sound
溫度與光週期對淡黃蝶的影響
為了了解淡黃蝶Catopsilia pomona無紋型crocale-like及銀紋型pomona-like中間受到環境因子的差異。先比對兩型的粒線體ＤＮＡ，之後模擬夏季和冬季自然環境進行實驗。得知兩型為同種。另一方面進行溫度和光週期的實驗，顯示淡黃蝶幼蟲和成蟲雌雄個體各部位會受到此兩環境因子的影響。In order to realize if Catopsilia Pomona and Catosilia crocale are the same species, we analyzed and compared the DNA sequences of Mitochondria, and the result revealed they are indeed the same species. Then we observed the developmental process of the butterfly, and inspected the effects of different factors: photoperiod and temperature were shown to affect the phenotype of the butterfly; lower temperature and shorter day resulted in phenotypic shift from crocale-like to pomona-like, and vice versa. Also, the conflicting factors produced intermediated form. (e.g. lower temperature with longer day) Not only changed the phenotypes of adult with photoperiod and temperature, those of larvae also did. However, the mechanism how photoperiod and temperature affect the phenotype of the butterfly is unknown.
Double Pedal Curve
設Γ為一平面曲線而 P 為一定點 , 自P 向Γ所有的切線作對稱點，則所有對稱點所成的圖形Γ1 稱為曲線Γ對定點P 的double pedal curve , Γ1 對定點P 的double pedal curve Γ2 稱為曲線Γ對定點P 的2-th double pedal curve , Γ2 對定點P 的double pedal curve Γ3 稱為曲線 Γ對定點P 的3-th double pedal curve ,…… 。以下是本文主要的結果：結論A：當Γ為一圓形而P 為圓上一點時 , 計算其n−th double pedal curve 的方程式。結論B：當Γ為任意平滑的參數曲線而P 為任意一點時 , Γ的 double pedal curve 的切線性質。結論C：當Γ為任意平滑的參數曲線而P 為(0,0)時, 計算其n−th double pedal curve 的方程式。
Given a plane curve Γand a fixed point P ,the locus of the reflection of P about the tangent to the curveΓis called the double pedal curve of Γwith respect to P.We denote Γ1 as the double pedal curve of Γwith respect to P, Γ2 as the double pedal curve of Γ1 with respect to P , Γ3 as the double pedal curve of Γ2 with respect to P ,and so on , we call Γn the n-th double pedal curve of Γwith respect to P. If Γ is a circle, and P is a point on the circle, we got the parametric equation of the n−th double pedal curve of Γ with respect to P. And, for any parametric plane curve Γ; we got the method to draw the tangent of the double pedal curve of Γ.