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.
愛的教育，鐵的紀律-果蠅的學習與記憶
The main purpose of this study is to explore whether fruit flies (Drosophila melanogasters which background is 2U) can distinguish and memorize different colors and smells by learning. Futhermore, to find out the relation between age and learning ability, and analyze the influence of repeated training on how long the memory would last. According to our experiment, in smell training, the fruit flies are able to distinguish and memorize different smells, and young fruit flies have better memory than old flies. In color training, the fruit flies can distinguish and memorize different colors, but the effect was less than that of smell training. In intensive learning, proper times of learning increased the memory ability, but excessive learning exhibited an opposite effect. In the labyrinth experiment, we select and nurture the fruit flies having the best color memory in order to further understand the gene correlated with the memory learning. In addition, in one-time training, fruit flies are able to remember the smells and colors in four minutes, and young ones have the better ability. In six-time training, fruit flies have the ability to remember the smells and colors in twelve minutes. In the end, we hope you can know more about the learning and memory ability of fruit flies through our report. 本實驗主要探討果蠅是否可經由學習分辨、記憶顏色與氣味，並探討年齡與學習能力的相關性、分析多次訓練對記憶時間的影響。由實驗結果得知，氣味方面，果蠅有辨識記憶氣味的能力，以年輕果蠅的效果較佳；顏色訓練方面，果蠅亦可分辨記憶顏色；密集學習方面，適當學習次數內，有助於增加果蠅的記憶能力，但過度的學習刺激會降低學習效果。並且，我們選顏色訓練中記憶較佳的一組進行迷宮實驗，經三次的岔路選擇，選出對顏色記憶最佳的果蠅，希望能探討訓練過的果蠅子代能否有較優良的記憶。至於記憶時間方面，一次氣味學習，果蠅在四分鐘內皆有記憶，且年輕果蠅記憶效果較強，達六分鐘；另外，多次氣味學習，果蠅於第四次訓練效果最佳，且記憶能力可達十二分鐘。希望藉本實驗報告，以期更瞭解果蠅學習與記憶的資料。
利用Google Maps 建立高中地理資訊系統
台灣通史「婆娑之洋，美麗之島」，身為台灣人，應知台灣事，本研究本維 基百科（Wikipedia）所揭示的「海納百川，有容乃大」精神，以Apache 網頁伺 服器為平台，MySQL 為資料庫，利用AJAX、PHP 網頁技術，並使用Google Maps 提供之服務，建立符合Web 2.0 精神的的b04地理資訊共享系統。在此系統下， 我們允許教師(編輯者)以合作方式上網提供與課程相關的地理資訊，並可進行資 訊修改或刪除，希望集合所有教師之力，提供給學生最豐富、最正確的b04地理 資訊系統。 In this paper, we propose a new map-based collaboration environment “MyGIS” for geographical information distribution. In MyGIS, the publishers/teachers can easily collaborate to annotate a spot with contents such as messages and links. The annotations of a spot are updated on the map in real-time which enables the receivers/students to correctly study at anywhere and anytime. To ensure the trustfulness of the content, the publishers are authenticated using login mechanism. In this study, several technologies inc lu ding Apache, PHP, MySQL, Ajax are involved. Finally, We implemented MyGIS on Google Maps and evaluated its feasibility and usefulness.
安培植物假說
在「植物的秘密生命」這本書中提到植物在電場或磁場中會生長的更好，我最近正好學到了電磁場如何產生，以及一些產生電磁場的方法，所以本研究即利用螺形管線圈來產生均勻的電磁場，並用運用安培右手定則來控制磁場產生的方向，來探討電磁場在不同條件下對實驗植物－綠豆生長的影響。本實驗使用銅質線圈纏繞鐵碗的方式，且通入不同大小電流來改變磁場的強度，以探討對實驗植物－綠豆生長的影響。本研究所得到的結果顯示：(1)綠豆在通入電流50mA 時所產生的電磁場可促使綠豆達到最好的生長效果；(2)栽培綠豆環境中所架設的電磁場較高，可使綠豆表現出較為明顯的生長速率；(3)促進綠豆的生長並不需要二十四小時都通入電流；(4)綠豆在N 極朝上的電磁場中生長的速率較S 極朝上的磁場中要快；(5)在較低溫度環境中，電磁場促進綠豆生長的效應較為顯著。;It has been mentioned that the plants will grow faster in the electronic or magnetic field in the book of “the secret life of plants”, I learned about the knowledge and methods of how to produce the electromagnetic field just now, I use the screw wire to produce electromagnetic field and control the direction by the Amplifier’s rule to investigate the growing speed of green beans under electromagnetic field in those different temperature. In this experiment, I use the wire to screwed around the ironed bowl, and make different electric current to generate different strength of electromagnetic field, the results indicate that (1) The faster growing speed will only exist in some strength of electromagnetic field, (2) The higher ironed bowls that full of screwed wire will result in the faster growing speed, (3) It will not need electromagnetic field all days, (4) The green beans will grow fast in those north magnetic pole than those in south magnetic pole, (5)The effect of electromagnetic field to increase growing speed will be significant in higher room temperature.
STATIN類降血脂藥物對血管平滑肌細胞之作用
動脈硬化是個致病率和致死率相當高的慢性發炎疾病，為台灣十大死因之一。在病理過程中血中濃度過高的膽固醇為動脈硬化的一大危險因子，其會誘發一連串的發炎反應驅使血管壁內皮細胞功能喪失，血壓上升，平滑肌細胞增生等。Statin 是臨床上十分有效的降血脂藥物，雖然其作用機制已知在於抑制膽固醇合成酵素 HMG-CoA reductase 而有降血脂功效，但近年來探討 statin 在抗發炎方面的作用也漸受重視。nitric oxide synthase (NOS) 代謝產物如 nitric oxide (NO)，cyclooxygenase (COX) 代謝產物如 prostaglandin (PGE?、PGI?)，及 heme oxygenase-1 (HO-1) 代謝產物如 carbon monoxide (CO)，均有文獻指出可以改善血流，而可能在動脈硬化上扮演保護角色。相反的，matrix metalloproteinase (MMP) 的表現會誘使更多的免疫細胞浸潤到血管壁，並增加動脈硬化斑破裂，引起栓塞和中風的發生。在此實驗中，我們利用培養的大鼠主動脈血管平滑肌細胞作為研究材料，發現了 statin (lovastatin 、pravastatin、atorvastatin 、fluvastatin) 具有一些和降血脂無關的直接保護血管壁能力。包括會增加 interleukin-1β (IL-1β) 所誘導 iNOS 蛋白的表現及NO 的產生; statin 本身會增加 COX-2 和 HO-1 蛋白的表現及 PGE? 和PGI? 的產生，及抑制 MMP-2 和 MMP-9 蛋白活性的表現。此外分析調控 iNOS 基因轉錄最為關鍵的基因轉錄因子 NF-κB，發現適量的 statin 會增加 IL-1β 活化NF-κB 的作用。值得一提的是雖然適量 NO 有維持血管恆定的功能，過量時則會造成血壓過低休克的現象，這就是細菌感染後因內毒素 lipopolysaccharide (LPS) 作用引發敗血性休克的主要原因之一。為更進一步釐清 statin 是否會影響受細菌感染病人的生命危險，我們也探討 statin 對LPS 作用的影響。結果發現 statin 反而會抑制 LPS 誘導大量 iNOS 蛋白的表現，NO 的產生及 NF-κB 的活化。這些新的實驗結果提供更多證據支持 statin 可以藉由維持血管舒張，減緩血管壁的發炎反應，穩定動脈硬化斑的作用，以有效控制動脈硬化各個病程的進展。這發現能讓我們更透徹明白 statin 的作用，且對將來研發 statin 在心血管疾病方面新的臨床治療用途是有所助益的。 ;The 3-hydroxy-3-methylglutaryl (HMG)-CoA reductase inhibitors, statins, are potent inhibitors of cholesterol synthesis and have wide therapeutic use in cardiovascular diseases. Recent evidence, however, suggests that the beneficial effects of statins may extend beyond their action on serum cholesterol levels. In this study, we investigated the effects of lovastatin, pravastatin, atorvastatin, and fluvastatin on cultured rat vascular smooth muscle cells. We found statins can inhibit LPS-induced iNOS expression and NO production, while they can potentiate IL-1β-elicited responses. Moreover, statins themselves can stimulate COX-2 expression, PGE?, PGI? formation, and HO-1 induction. In contrast, statins can inhibit basal and IL-1β-induced enzyme activities of MMP-9 and MMP-2. In studying the activity of NF-κB, which plays an important role for iNOS gene induction, we found that statin can increase IL-1β-induced NF-κB activity, while inhibit that induced by LPS. All these results suggest that stimulation of iNOS expression in the presence of IL-1β, togeth1er with the increased COX-2 and HO-1 expression might contribute to the beneficial effects of statins in atherosclerotic process in terms of vasodilation and inhibition of smooth muscle cell proliferation. The inhibition of MMP activity might enhance plaque stability and reduce the development of atherosclerosis. All these results strengthen the pleiotropic actions of statins in anti-inflammation and anti-atherosclerosis.
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°.