在數學課堂中，老師拋出一道甄試的口試題目，那是一道有關蟲類繁殖過程\r 中，探討子代存在位置及其規律性的題目。此問題引起我們繼續討論的興趣，並\r 試著應用至「一路領先」問題。我們試著改變其形狀來構造「一路領先」的路徑，\r 再擴張其維度來解決任一人數「一路領先」的問題！\r 由於發現Motzkin 數列和三人「一路領先」給定得票數的情況一一對應，我們\r 找到一種對應方法，將Motzkin 路徑和「一路領先」得票過程做一對一的對應！以\r Motzkin 路徑和三人「一路領先」為基礎，我們構造了「立體Motzkin 」，發現其\r 路徑走法數竟和五人「一路領先」得票過程總方法數完全相同！若限制向量(1,0,0)\r 只能出現在xy 平面上，則和四人「一路領先」得票過程一一對應！當我們在網路\r 上搜尋資料時，發現有一種lattice path 的規則和四人「一路領先」的方法數完全\r 一樣！我們一樣找到一種對應規則，讓此走法和四人「一路領先」得票過程一一\r 對應！\r 架構出「立體Motzkin 」後，我們試著架構「n維Motzkin」，發現給定有規律\r 的(2n ?1) 個n維向量，就可以構造出n人的「一路領先」！此方法對解決lattice path\r 和投票問題等有顯著的幫助！

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).

聚丙烯酸是尿布中吸水成份，若被隨地丟棄勢必對環境造成污染。分析其結構，由於存在對重金屬離子具螯合作用的羧基，因此，可用於捕捉重金屬離子，作為偵測污水離子的利器。另外，若將螯合的銀離子以化學還原法製成奈米銀，將可應用於抗菌。研究結果有： \r (1)PAA對Mn、Fe、Co、Ni、Cu、Zn、Ag等離子具有明顯螯合效果。 \r (2)螯合反應：PAA＋Mn＋ [PAA-M]n－x＋xH＋，其可利用濃鹽酸使其再生。 \r (3)螯合能力以Fe3+最強，Zn2+(Mn2+)較弱。 \r (4)螯合離子的最小極限為10-3(M)，我們採樣的廢水有重金屬污染，推測濃度大於10－3(M)。 \r (5)成功將螯合的Ag＋製成奈米銀，為金黃色，屬於球形銀，甲醛濃度愈高，奈米粒徑愈小。 \r (6)奈米銀與銀離子在抗菌上的確有明顯效果，帄均粒徑小，抗菌效果越強。

「翻車」事件令人怵目驚心，輕則車毀，重則人亡。減少翻車事件，可減少悲劇的發生。而翻車絕大多數均發生在轉彎的路段，且伴隨著超速發生。因此，本研究乃針對汽車過彎行駛，探討其翻覆的原因以及改進之道 · 本研究乃利用實驗分析法以及理論驗證法進行研究，實驗中變化不同的汽車質量，車軸寬、車身高以及車軸寬/車身高，質量重心寬、高以及寬/高、傾斜度以及迴轉半徑等九種參數 · 於自製的紅外線偵測變頻式可調迴轉模擬機上以八部模型試驗車測試其翻覆轉速，並換算為翻覆速度後逐一分析討論之。經由實驗結果，本研究得到以下結論：一、汽車轉彎翻覆與離心力有關，當離心力大於臨界側向推力時，汽車即翻覆。臨界側向推力公式為 F = mg ( tanθ + K?) / ( l -K? tanθ ) 二、最大容許車速平方與轉彎半徑及質量中心寬高比相乘積成正比；而在定車速下，飲小客許轉彎半徑與質量中心寬高比成反比．前述各項皆與質量大小無關．三、提高轉彎路面傾斜度對防止汽車翻覆有確實的效果。而最佳的過彎防止翻覆方法是降低車行速度，提高轉彎半徑，增加路面外側傾斜度，以及提高汽車質量中心寬高比”四、汽車過彎不致翻覆的最大極限速度 Vc 以及最小轉彎半徑rc分別為 vc=〔 rg ( tan θ + K ?）/ ( l 一 K ? tanθ ) ]; rc =（ V2 / g ) ( l 一 K?tanθ ) / ( tanθ + K? ) 五、本實驗所設計紅外線偵測變頻式可調迴轉模擬機，可有效的模擬汽車過彎翻覆，適用於中等學校物理、力學等學科的實驗課程。The accident of overturning a car always results in both destroying the car body and the death of the people. This project is to investigate what factors would have an effect on overturning a car and how to prevent a car from overturning.This project explores the factors by varying the mass of the cars, the distance between axes, the height of the car body, the ratio between the axis distance and the car height, the central gravity, and the declination. We test and record different overturning rotating speeds of eight model cars by a self-made adjustable simulator with a varying frequency infra-red detector. According to the experiment, the following results are obtained. I. The overturning occurrence is as a result of the eccentric force over the critical lateral force. The critical lateral force is F=mg(tanθ +K?)/(l—K?tan θ) 2. The square of allowable maximum speed is in proportion to the product of turning radius and ration of width to height for the center of mass; however, the allowable minimum turning radius is inversely proportional to the ration of width to height for the center of mass under constant vehicle speed. The above inference is independent of the mass of vehicle. 3. Increasing the declination can prevent a car from overturning. 4. The maximum speed for a car turning without overturning is Vc. The minimum turning radius is r. Both are expressed as follows:Vc=[rg(tanθ +K2)/(1—K?tanθ );rc=(’V2/g)( I —K?tanθ )/(tanθ +K?)5. The self-made adjustable simulator with a varying frequency infra-red detector can be used in the experiments of the middle school science curriculum.

豆類澱粉?抑制劑具害蟲防治與血糖調節之功效。本研究從台灣五種豆類中進行澱粉?抑制劑活性初篩，篩選出四季豆對麗蠅的澱粉?有明顯的抑制效果，粗萃後分離純化出單一蛋白質，經胺基酸定序結果得到兩個多?片段-VGLDFVLV 與TETSFNIDG ， 與已發表文獻比對推測為腰豆澱粉?抑制劑—αAI-1。經測試發現此抑制劑在85℃時仍具備抑制果蠅澱粉?之活性，為一熱安定性蛋白質，其抑制作用受pH 值影響很大，在偏酸性環境下的效果最好，且其抑制作用具特異性，可明顯抑制果蠅、入侵紅火蟻、白蟻、蟑螂及麵包蟲等昆蟲的澱粉?活性。在調節血糖方面，本研究利用豬胰臟澱粉?進行抑制活性測試，篩選出四季豆、花豆與黑豆對豬胰臟澱粉?有明顯的抑制效果，進一步利用Wistar 品系大鼠，進行豆類澱粉?抑制劑降血糖功效之活體試驗，將四季豆、花豆和黑豆粗萃經濃縮乾燥後餵食大鼠，發現花豆、黑豆在第一小時具有顯著抑制血糖增加效果；四季豆、黑豆在第三小時血糖回升，花豆仍可維持較低血糖濃度。此初步結果顯示，花豆粗萃物可能具備減緩消化吸收作用，具應用潛能，其確切分子作用機制值得深入探究。Amylase inhibitors can be applied in pest control and glucose adjustments. The study screens Phaseolus vulgaris from five Taiwan’s beans that has the most significant inhibition towards Chrysomia megacephala. The protein was isolated and sequenced two fragments, -VGLDFVLV and TETSFNIDG, highly homologous to that of αAI-1 from Phaseolus vulgaris. The pure protein still inhibits the amylase from Drosophila melanogaster at 85℃, suggesting it is thermal-stable. Its activity was specific and was affected by pH, reaching the peak in weak acidic condition. It obviously inhibits amylases from D. melanogaster, Solenopsis invicta, Odontotermes formosanus, Periplaneta Americana Linnaeus, and Alphitobius sp. In addiction, the study points out Phaseolus vulgaris, Phaseolus coccineus L. and Glycine max, which have significant inhibition toward pancreatic amylase. The amylase inhibitors’ functions of decreasing in blood glucose were detected by animal experiments on Wistar rats. The rats fed with the extracts of Phaseolus coccineus L. and Glycine max showed the inhibition of glucose increasing at the first hour, while blood glucose concentration after rats fed with Phaseolus vulgaris and Glycine max increase at the third hour, and blood glucose after rats fed with Phaseolus coccineus L. maintains low. Its premier result indicates that the extract from Phaseolus coccineus L. might postpones digestion and has potential to be applied. According to these results, amylase inhibitors are worthy to further analysis.

本篇文章從＂將aⁿ+bⁿ分解成（a+b）及ab的非線性組合＂出發，在同樣的遞迴精神下引進並定義擬-Lucas多項式 ＜Sn (X)>：

本研究的目的在觀察液滴的蒸發過程，探討影響一滴蒸發方式改變的變因。我們利用數位攝影機外加近攝鏡頭，由側面逆光拍攝液滴蒸發過程，並轉錄成電子檔利用電腦協助分析。液滴影像分隔放大投影在方格紙上，以便測量接觸角及高度的變化。結果發現蒸發情形可分為三種：Ⅰ.當接觸角大於九十度時，液滴和界面的接觸線迅速外擴，直到接觸角遞減至90度後定住不動，蒸發終了時，接觸線迅速內縮，留下縮小的實心殘跡。Ⅱ. 當接觸角小於九十度時，接觸線先些微外擴迅速外擴，之後定住不動，直到蒸發終點，液體內縮，留下環狀殘跡。Ⅲ.當接觸角小等於九十度時，接觸線始終定住不變，液滴蒸發後留下原大小的實心班跡。液滴蒸發時接觸角和高度並不是連續變化，而是交互階梯式遞減。本研究的結果可應用在探討噴漆及噴墨印表機的噴墨印刷上。The objective of this investigation is to observe the evaporation of liquid drop and find out the factors that could affect it. A digital camera with micro lens is used to film the process of the evaporation. And a close-up of the sample drop is taken with backlight. The results are analyzed with a personal computer. The magnified images of the drops are projected on grid papers for measuring the changes on contact angles, and heights of drops. We classify the evaporation of a drop into three types: Ⅰ. The contact angle is greater than 90 degrees. At first, the contact line will spread outwardly till the contact angle decrease to the 90 degrees and then be pinned until the evaporation reach its terminal. At last the contact line quickly contract inwardly, and a solid stain remain. Ⅱ. The contact angle is less than 90 degrees. The contact line will spread slightly and then be pinned. At the terminal the liquid contract inward, and a ring-like stain is formed. Ⅲ. The contact angle is equal to 90 degrees. The contact line will always be pinned, and no ring, but spot stain is left. During the evaporation, we discover that the contact angle and the height of the drop do not change continuously but alternatively decrease by steps. The results of our investigation can be applied to the aspects of paint-spraying and jet printers.

在一次偶然的機會中，我們在科學月刊上讀到一篇探討骨牌排列 (Domino Tiling) 問題的文章。文中骨牌排列問題看似單純，但其中卻有許多有趣的性質，因此，我們想對此進行更深入的研究。\r 我們將1x2的骨牌填入特別的方格中，考慮填入的順序並計算其排列情形的數量。由定義的兩個模型SDT(Standard Dominos Tableau) 與「缺一格」的GDT(Good Dominos Tableau) 為基礎，嘗試尋找它們之間的關連性，藉由對應(bijection)的方法，得知在高度的限制為奇數的情況下，SDT與GDT的數量相同，並且，兩者之間的結構有密切關聯。\r 除此之外，在這個研究中，針對SDT在高度不超過三排時，我們建構出了骨牌排列情形與我們架構的「廣義Motkzin路徑」的對應操作流程。接著，我們嘗試探討一般化的SDT與此結果的關聯性，由對應過程的想法，架構出高維度的「廣義Motkzin路徑」，並推測此路徑與SDT之間有緊密的相關性！

直接乙醇燃料電池以酒精與氧氣透過氧化還原反應產生電能，但化學反應緩慢，需利用觸媒以增加其速率。本實驗目的在於盡可能找出一個表現最佳的觸媒。本實驗利用活性碳粉作為觸媒（鉑、錫）的載體，以酸性（HNO3）與鹼性（NaOH）環境分別處理碳粉，再以含浸法與多元醇含浸法將觸媒還原。我們得到以HNO3 處理的碳粉無法保有原碳粉的型態，較利用NaOH 處理為差。在觸媒製備方面，多元醇含浸法還原效果比含浸法可得到較小的觸媒尺寸，在本實驗中，溶液中鉑與加入的碳粉重量比為3:7 時，可得到最大的反應面積。此外，當鉑與錫原子數比為4:1 時，可得到最大的乙醇氧化電流。Direct ethanol fuel cell is a kind of power source which generates electrical power by a redox reaction involving ethanol fuel and oxygen. However, this reaction takes place slowly; therefore, catalyst is needed to improve its activity. The goal of this project is to get an optimize catalysts ratio to obtain the best catalyst activity. Activated carbon is used as the support of catalyst (platinum and tin) particles in this project, which is pre-treated in acid (HNO3) and alkaline (NaOH) solutions respectively. Then, the precursor is reduced by impregnation and EG-impregnation. We learned that activated carbon pre-treated with NaOH activates better than which pre-treated with HNO3 because the latter bear less resemblance than the former. As for the catalyst, the results of EG-impregnation show smaller size of catalyst particles than those of impregnation. In this project, when the ratio of the weight of platinum and activated carbon added into the solution is 3:7, we can get the largest surface area. In addition, when the ratio of the amount of platinum and tin atoms is 4:1, we can get the largest current of ethanol oxidation.

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.