完美長方形
正方形和長方形是每一個人都非常熟悉的圖形，但其中卻隱藏了非常多奇妙的“數學之謎”。 所謂「完美長方形」是：在一個長方形中 (長、寬不等)，能否分割出最少大小相異的正方形。 這個研究中，首先用「草圖」的解題方法研究完美長方形，接下來利用「平面圖形」的解題方法可簡化計算的過程，最後利用「對偶關係」證明出：完美長方形的最少階數為 9 階。 進而，我們將這個問題擴展至三維空間，思索在一個長方體中（長、寬、高都不等長） ，能否仿照二維空間，分割出最少大小相異的正方體，而完成這個研究。 Square and the rectangle are figures that everyone knows well very much, but what a wonderful " mystery of mathematics " is hidden among them. What is called the perfect rectangle is whether in a rectangle (its length and width is different ) could cut apart two squares as the least difference in size . In this research, the solution approach of "the sketch map" is used to study the perfect rectangle at first, then the solution approach of "the level figure" to simplify the complicatied calculation of the solving course , and "the dual relation" is finally used to prove 9 orders are the least orders for a perfect rectangle . And then, we expand this question to three-dimensional space, considering in a cuboid (its length, width, and height is different) whether could follow the two-dimensional space model to cut apart two squares as the least difference in size, and finish this research.
有毛!沒毛!哪個好!?探討石田螺及其螺殼上附生藻類與環境因子之關係
This research is about two ponds in the Ｂ park’s and the Ｄ park’s snail(Square Mystery Snail：Sinotaia quadrata) in Taipei city of Nei-hu District for research object, carry out the study of the following research proceed: 1.Discriminate the algae species that are growth on the snail shell and which is a kind of interaction with the snail; 2.The influence of the snail and algae with difference of temperature, salinity, pH value and dark ; 3. The factors affect algae growth on snail shell; 4.Use the variation of snail and algae to be a biological incator. The result manifestation: the algae that are growth on snail shell have two kinds, one is Cyanophyta and the other is Cladophora sp. The interaction between algae and snail belong to communalism, but under the condition of lacking of food, the snail then will eat the Cladophora sp. which grow on the shell of other snails. The temperature adapts aspect, upper limit of the feat existence of the snail should be low in 28℃. When over than 28℃, Cladophora sp. as the most strong, Cyanophyta is secondly, and the snail then is most poor. For the maximum tolerance of the salinity, the snail is about 4.375?, Cyanophyta is about 5.0?, Cladophora sp is then about 7.0?; Under the different salinity for the tolerance , the Cladophora sp. still the most strong, Cyanophyta is secondly, and the snail then is most poor. Under the dark environment, the speed of Cyanophyta begin to be bleaching is very fast than the Cladophora sp.. In the tolerance of pH value range: The snail is about pH=5～10, Cyanophyta is about pH=7～8, Cladophora sp. is about pH=6～8; When the pH value range is in the pH=5～8, the speed of the Cyanophyta occur changing is very fast than Cladophora sp.. The algae are growing on snail shell very different between two ponds, the main reason is water pH value dissimilarly: When pH value over than 8.5, there is no Cladophora sp. to grow on the snail shell, after the pH value to decrease, Cyanophyta then will compare early than Cladophora sp. to grow on the snail shell. Calculate by the classification of the freshwater biological incator : Two organic pollution degree of the ponds may be lain in theβ-mesosaprobic to theα-mesosaprobic, and the polluting degree of the Ｄ pond is more seriously. As for two ponds, have already faced what level of eutrophication? Belong to actually which stage of pollution grade? Not only added the classification data of floating and fixative algea in two ponds, and also according to the parts of chemistry analysis method measure of the data makes the substantial evidence, then could carry out the more accurate and thorough study in the days to come steadily studying process.本研究是以臺北市內湖區兩個綠地公園(Ｂ公園與Ｄ公園)池塘內的石田螺(Sinotaia quadrata)為研究對象，進行以下研究目的之探討：1.鑑別石田螺螺殼上藻類的種類及其與石田螺的互動關係；2.溫度、鹽度、酸鹼值及黑暗等環境因子的差異，對石田螺及螺殼上附生藻類的影響；3.影響藻類附生於石田螺螺殼上的因素；4.將石田螺及螺殼上附生藻類的變化作為監測環境因子或水質變異的指標現象。結果顯示：附生於石田螺螺殼上的藻類有藍綠藻(Cyanophyta)與剛毛藻(Cladophora sp.)兩類；與石田螺的互動關係應屬於片利共生(communalism)，但在缺乏食物的情況下，石田螺則會採食同伴殼上的剛毛藻。溫度適應方面，石田螺適宜生存的溫度上限應低於28℃，超過28℃水溫環境的耐受程度，是以剛毛藻為最強，其次是藍綠藻，而石田螺則為最差。對於環境鹽度最大耐受度方面：石田螺約為4.375??，藍綠藻約為5.0??，剛毛藻則約為7.0?；在不同鹽度環境下，鹽度的耐受程度，仍以剛毛藻為最強，其次是藍綠藻，而石田螺則是最差。在黑暗環境下，藍綠藻褪色產生白化現象的速度明顯地比剛毛藻要快了許多。在環境酸鹼值耐受的範圍方面：石田螺約在ｐＨ＝5～10 之間，藍綠藻約在ｐＨ＝7～8 之間，剛毛藻則約在ｐＨ＝6～8 之間；而酸鹼值範圍在ｐＨ＝5～8 時，藍綠藻產生變化的速度明顯地比剛毛藻還要快。而兩樣區池塘水體酸鹼值的不同，應是造成石田螺螺殼藻類附生現象差異的主要原因：當酸鹼值超過8.5 時，螺殼上就無剛毛藻附生，當酸鹼值降下後，藍綠藻則會比剛毛藻早出現在螺殼上。藉由淡水生物指標的分類推測：兩樣區池塘水體有機污染程度，可能介於β-中腐水性(β-mesosaprobic,βm)至α-中腐水性(α-mesosaprobic,αm)的範圍之間，而Ｄ池塘受污染的程度應會比Ｂ池塘還要更嚴重些。至於兩樣區池塘水體，已面臨了何種優養化的程度？究竟是屬於哪一個階段的污染等級呢？除須補充水體中浮游性及附著性藻類分類的詳細觀察資料外，仍必須參照部分水質化學分析法所測得的數據作佐證，才能在日後持續地研究過程中進行更精確及深入的探討。
黑龍仔知人間冷暖
為了瞭解黃斑黑蟋蟀叫聲和溫度之間的關係，我應用物理熱平衡原理，自製水浴槽控制環境溫度，以電腦錄音程式分別錄製15℃、20℃、25℃、30℃、35℃時的蟋蟀叫聲，利用Sound Forge軟體分析並比較不同溫度下的各種特性。結果發現所分析的chirp、chirp period、syllable period、pause均和溫度呈負相關，而單位時間內的叫聲次數則與溫度成正相關，並推導出15~35℃範圍內蟋蟀叫聲次數與溫度成正相關的公式。最佳直線為：﹙15秒內叫聲次數＋19.385﹚÷2.483=當時溫度﹙℃﹚，呈高度正相關﹙相關係數：0.9398﹚。本實驗也比較母蟋蟀對不同溫度下雄蟋蟀叫聲的偏好程度，發現母蟋蟀較偏愛25℃時的雄蟋蟀叫聲，此結果可能與雄蟋蟀在25℃時叫聲的波形最為穩定有關。為探測蟋蟀觸角上的溫度感受器位置，我們曾將不同部位的觸角加以剪除，結果顯示觸角剪除面積越大的雄蟋蟀越不傾向鳴叫，但無法證實是否為溫度偵測異常所導致。本實驗除供學術研究外，因黃斑黑蟋蟀在世界各地均有分布，所以希望能藉由分析溫度與蟋蟀叫聲的相關性實驗，未來嘗試能探討其在不同環境的適應行為亦或種化的可能性。另外，全球暖化問題日益嚴重，也希望能藉由相關實驗探討暖化對蟋蟀生態上的影響。最後，我們的實驗證明了蟋蟀叫聲和環境溫度確實有極大的關聯性，未來或許能參考蟋蟀感覺溫度的機制，製作出一個天然零污染的溫度計。 To find out the relationship of cricket’s calling and temperature, we use a hand-made water-bath tank to control the temperature and record the callings with microphone and software, Sound Forge. After analyzing the collected data, we’ve found that cricket’s chirp, chirp period, syllable period, and pause are indeed affected by temperature (15 degrees - 35 degrees C). Moreover, we also compare female cricket’s preference to the callings, and the result indicates that female cricket’s preference is changing with temperature. In the last, we tried to find out where the thermoreceptors are by cutting out the antennae. After cutting, crickets tend to not to make any calls at all, so we conclude the antennae might play an important role in sensing and calling. The experiment proves that this communication system is temperature coupled. Because the cricket, Gryllus bimaculatus, is a worldwide species, we may learn the accommodation or the possibility of performing a new species by researching the relationship of temperature and cricket’s callings. By the way, the Green House Effect is getting more and more serious, so we want to search for the influences on crickets that are caused by Green House Effect. The last but not the least, according to the report, maybe we can investigate the mechanism of sensing temperature and then make a natural thermometer that is no pollution in the future.
魂「縈」夢「牽」－談重金屬污染
近年來重金屬污染問題日益嚴重，因此檢測地下水、工業廢水中的重金屬含量為一重要課題。本實驗即是利用錄音機中的零件－石英振盪器作為電化學分析偵測的工作電極，在0.1 M KNO3（pH = 3）溶液中利用循環伏安法以50 mV/s 的掃描速度從 – 100 到 – 700 mV 持續掃描 10 圈，來穩定電極表面。
以方波陽極剝除伏安法（SWASV）模式設定預濃縮電位– 700 mV、預濃縮時間60 秒偵測重金屬的鉛離子。掃描電位範圍由 – 700 到 – 100 mV vs. Ag/AgCl 往氧化方向掃描。偵測鉛離子濃度範圍為200－600 ppb，之後可針對各種條件作最佳化的條件探討可降低偵測濃度及實際運用於地下水及工業廢水的檢測。
Heavy metal pollution becomes very serious. Lead (Pb) determination is a continuous research interest in clinical, environmental, and industrial application. The main causes for living biological media are mutagenic, carcinogenic, and teratogenic activity. The determination of trace metal in the ground and industrial waste water will be a important project. Here, we report a simple system which using quartz crystal microbalance (QCM) (use in radio machine) for working electrode. The QCM was first equilibrated in 0.1 M KNO3（pH = 3）base electrolyte for about 1 min before electrochemical experiments. It was then pretreated by continuous scans in the window from – 100 to – 700 mV at a scan rate of 50 mV/s until a stable background current obtained.
The amount of Pb2+ was detected quantitatively using square-wave anodic stripping voltammetry（SWASV）. The potential range was set from – 100 to – 700 mV in the cathodic direction for most cases. The standard addition method concentration range is from 200 to 600 ppb. Analytical conditions were systematically optimized and extended to practical applications aslo.
黑棘蟻聚落的生物時鐘
This study is to investigate whether colony of the spiny-weaver ant, Polyrhachis dives, have biological clock so as to observe the locomotion activities of the ants in the nest and find out if the Light period will interfere the rhythm. The conclusion is the colony of the ants get the rhythm is 23.8 hours during in L:D=12:12.There are ants not significant difference between large colonies and small colonies. While in Dark (D:D)the ants appears free running with 23.1 hours as the rhythm, so, the colony of the ants has obvious light-rhythm movement, showing that the biological clock will act on group and being controlled by light period. 本研究是在探討黑棘蟻 (polyrhachis dives) 聚落是否有生物時鐘(biological clock)，以觀察黑棘蟻在巢裡的活動情形，找出週期並探討光是否會影響週期。結果觀察出黑棘蟻 的聚落在有光的時候(L:D=12:12)以23.8 小時為週期，沒有光的時候(D:D)黑棘蟻仍呈現自由律動(free running)，以23.1 小時為週期，所以黑棘蟻的聚落有明顯的日週律動，顯示生物時鐘能作用在聚落上，且受光週期之調控。
跛腳皇后
高斯曾經提出八皇后問題：八個皇后在8 × 8 的棋盤上有幾種放法可以使任意兩皇后不會互相攻擊？我們在原來的問題上加上一些條件，改變皇后攻擊規則，使得皇后失去一條對角線的攻擊方向，稱之為「跛腳皇后」。我們稱一個在棋盤上放置最多跛腳皇后使其不互相攻擊的放法為好放法；研究跛腳皇后放置在各類棋盤上其好放法的個數和性質。我們分別在六種棋盤上做討論：（1） 在平面n x n 棋盤上，我們證明了其好放法與完美極致史考倫型數列之間的對應關係，並歸納出相關的性質和定理。（2） 在平面m x n 棋盤上，我們固定一邊長度n，做出n 較小時好放法數的通式；我們也將其好放法對應至廣義史考倫。（3） 在環面n x n 棋盤上，我們說明了其好放法與完全剩餘系排列之間的對應關係，並歸納出相關的性質和定理。（4） 在環面m x n 棋盤上，我們固定gcd（m,n），做出gcd（m,n）較小時好放法數的通式。（5） 在柱面n x n 棋盤上，我們證明其與環面n x n 棋盤等價，說明其好放法具有和環面n x n 棋盤好放法相同的性質和定理。（6） 在柱面m x n 棋盤上，分成左右柱面以及上下柱面來做討論。我們歸納出相關性質和定理；並固定一邊長度n，做出n 較小時好放法數的通式。Gauss had researched about putting eight queens on the chessboard on the way that doesn’t make any queen attacks another one. Thus, we added some rules on the question: the queen loses one diagonal attacking-way and become the “lame queen”. We call a way that doesn’t make any lame queen attacks another one “a good way”. We have been investigating the amount and properties of good ways based on six kinds of chessboard: （1）We found the correspondences between the “good way” on n × n plane chessboard and the Perfect extremal Skolem-type sequence, and concluded some associated properties and theorems. （2） On m× n plane chessboard, we fixed the length n of one side of the chessboard, and accomplished the amount of good ways when n is small. We also correspond the good way to the Generalized Skolem.（3）We found the correspondences between the “good way” on n × n torus chessboard and the arrayal of complete residue system, and concluded some associated properties and theorems.（4）On m× n torus chessboard, we fixed the gcd(m,n) （greatest common divisor of m and n）, and accomplished the amount of good ways when gcd(m,n) is small.（5）On n × n cylinder chessboard, we proved that this kind of chessboard is equal to torus chessboard. So the good ways, characters, and theorems on cylinder chessboard are the same as on the torus one.（6）On m× n cylinder chessboard, we separate it into two cases: left-right cylinder chessboard and up-down cylinder chessboard. We concluded some associated properties and theorems, and we also fixed the length n of one side of the chessboard and accomplished the amount of\r the good ways when n is small.
外來植物的入侵－非洲大鳳仙的生態探討
Generally speaking in order for a exotic plant life to dominate over the local ecology, the following factors must hold true: 1. A close proximity of the environment (including geographical and climatic factors) 2. A lack of nature enemy and competitor 3. A strong reproductive and adaptability capacity. Base on the above factors, We will be using Field Observation record, Sample placement, virtual environment factor experiment and other methods to conducing our investigation. This study shown the African Touch-Me-Not（Impatiens wallerana） has a strong reproductive and adaptability capacity. Even under adverse condition the African Touch-Me-Not survive for a period of time. It can produce flowers then fruits all year round, within each fruit there is on average 45 seeds with, under the right condition, near 100% germination rate. It can also reproduce asexually via cutting. Taiwan’s warm and humid geographical condition is similar to its origin of Africa. And so far haven’t found any obvious natural enemy. In the future this plant will be likely to spread on the low to mid. level mountain region. It also can be seen that the divergence within its habitat is low. Therefore it will decrease the variety, the density and the diversification of the local eco-system. Here to advise the government’s forestry and agriculture department, to study the relevant ecological information on this species, when they are considering popularization this plant. Using the information to evaluate the impact of this plant may have on the environment, and use it as a guideline for their plant conservation policy. 一般而言，外來植物入侵本地原生植群成功的條件有：一、相似的環境（包括地理、氣候等因素）。二、缺乏天敵及競爭對手。三、旺盛的繁殖力和適應力。針對上述條件，利用野外觀察記錄、樣區設置及模擬環境因子實驗等方法，來探討非洲大鳳仙未來是否會在臺灣蔓延、擴展進而影響本土的生態系。結果顯示非洲大鳳仙有旺盛的繁殖力和適應力，?使在不利的環境下，短時間不會死亡。一年四季皆可開花結果，每粒果實平均有四十五粒種子。環境適宜時，有接近百分之百的萌發率，亦可用莖進行無性繁殖。另外，臺灣溫暖多雨的地理環境亦與其原產地非洲相似，且未發現明顯天敵，未來極有可能在中低海拔山區蔓延。調查也發現它生長的地區岐異度明顯偏低，使其他植物種類、密度減少，生物多樣性降低。因此建議政府、森林、園藝和農業工作人員在推廣時，多吸取相關物種的生態學資訊，評估其對環境可能造成之影響，以作為植物保育之重要參考。
藉由lotus effect 之原理來探討超疏水性表面的製備
超疏水表面(superhydrophobic surface)因其自我清潔效果在近年來引起廣泛的研究及探討，目前世界各大公司皆積極投入自潔性產品(超疏水表面)的研發，但是截至目前為止除了塗料及織物有產品外，其他尚在研發階段。降低表面能及增加表面粗糙度為製作超疏水性表面的兩種方法。本實驗我們針對使用不同方法去仿照自然界植物「蓮花效應」，將二氧化矽粒子適當的分佈在基材表面，以增加粗糙度，製造出超疏水性表面。我們發現鍛燒會使其二氧化矽粒子黏聚在一起，對接觸角的增加無幫助。而在溶膠凝膠的配置過程中直接加入OTS(Octadecyltrichlorosilane)，並利用光散射儀比較二氧化矽奈米顆粒的平均粒徑及粒徑分佈隨時間變化的情形，一段時間後發現會有明顯大顆粒沉澱，塗佈在玻璃基材表面後容易脫落，不適合往後實驗或其他用途。而以氨水催化的溶膠凝膠以不同流速滴入TEOS (Tetraethylorthosilicate，四乙氧基矽)對接觸角的影響也不大。最後我們利用砂紙在基材表面上刷磨，可以使二氧化矽粒子分佈均勻，明顯增加接觸角。塗佈速率的改變搭配疏水性矽烷單分子膜的改質，我們已可以製造出159°的超疏水性表面。Superhydrophobic surfaces are generally made by lowering the surface energy and increasing the surface roughness. In this experiment, we use different methods of spreading silicon dioxide nanoparticles properly on the surface in order to increase the surface roughness and also make superhydrophobic surfaces. In the beginning, we find that the calcinations can cause its silicon dioxide nanoparticles to stick together instead of increasing the contact angles. Then, add OTS (Octadecyltrichlorosilane) directly to manufacture process of sol-gel, and observe the situations of the average length and the spread of silicon dioxide nanoparticles with the time goes by. After a period of time, we will discover that many obvious big particles deposit and spin-coating on the glass surfaces flop easily. Hence, this phenomenon is n’t proper for the following experiments or other uses. However, the contact angles have nothing to do with dropping the sol-gel catalyzed ammonia to TEOS(Tetraethylorthosilicate) by different flowing rates. Finally, it is crucial for us to use the sandpapers to brush on the surfaces because it may cause the silicon dioxide nanoparticles to spread well and obviously increase the contact angles. Combining the silicon dioxide surfaces with the change of spin-coating rate and the cover with hydrophobic SAM, we have made the superhydrophobic surfaces of 159°.
灰階影像內容之檢索技術
資訊時代的來臨，促使我們的社會型態大幅改變，無一不朝數位化的方向邁進。網際網路與資訊科技的快速發展，近年來影像資料庫和數位圖書館大量的成立，關於影像資料檢索的研究已漸漸成為一門極為重要的研究議題。在本研究報告中，我們提出一種植基於向量量化編碼法的灰階影像檢索技術。向量量化編碼法是一種極為簡單的影像壓縮技術。我們應用這個編碼法，來萃取出灰階影像內容的特徵值。同時我們也計算出整張影像與影像中間位置的像素平均值，作為日後檢索影像時過濾掉影像資料庫中不需要比對特徵值的依據。\r 我們所提出的方法能有效地萃取影像內容的特徵值並且讓使用者可以快速且正確地查詢到所需要的影像。當影像資料庫中存在與查詢影像完全相同的影像時，我們的檢索技術都能在第一時間第一順位檢索出這張影像。即便影像資料庫中不存在與查詢影像完全相同的影像時，我們的檢索技術平均74.3%也能在第一時間前五個順位檢索出最相似的影像。\r \r With the coming of the information age, our sociological system change extensively, and everything has moves toward digitization. Due to the rapid development of Internet, information technology, the rapid growth of image databases and digital libraries recently, the related researches of image retrieval have become a very important issue. In this memoir, we propose an image retrieval scheme based on the vector quantization to retrieve similar images from the image database according to the pre-collected image features. Vector quantization is a very simple image compression scheme. We have applied vector quantization to extract features from grayscale image. In order to speed up the retrieval process, we also calculated the mean pixel values of whole images and the central part of the image to filter the images, which are significantly dissimilar to the query image.\r The experimental results show that our proposed approaches can effectively extract features from the image and enable users to retrieve images from image database quickly and accurately. When images stored in image database match query image, the proposed scheme can instantly retrieve the stored image at the first rank. Even though images stored in image database query image exactly, the proposed scheme can instantly retrieve the stored image over 74.3% at the first five ranks.