臺灣

我們試著尋找所需最小的城堡個數以看守整個a × b × c (a,b,c ? N) 的長方體。所謂城堡是一種棋子，當放置城堡的位置是(x, y, z) ，則(x, y,t)、(x,t, z)、(t, y, z) (t 是任何不超出邊界的正整數)是這個城堡可以看守的格子。我們用這些城堡來完全看守長方體，試著找出其最小值。在2005 年我們猜測了a = b = c 、a = b c 、a > b > c 的上界，而在2006 年時完成了a = b = c 、a = b c 的大部分情況的證明，少數不能解決的部份也提供了不錯的上界。目前我們在a = b = c 、a = b c 的情況幾乎完全解決，目前正在向a > b > c 的部份發展。A generalized searching method of finding the minimum number of castle which can oversee all over the rectangular box, defined as a × b× c (a,b,c ? N) , is presented. The castle here is defined as one kind of chess. The castle positioned as (x, y, z) can direct the lattice points of (x, y,t) 、(x,t, z) 、(t, y, z) (t is the positive integer and smaller than the box size). These castles we use here is to oversee the rectangular box and to help us to find the minimum number. In 2005, we got the upper bound of overseeing the rectangular box in the conditions of a = b = c、a = b c、a > b > c , while in 2006 we complete the proofs of the minimum number of castles based on the conditions of a = b = c 、a = b c . The further work we want to attain is to complete the case of a > b > c.

本研究使用鋁板探究快速解凍法，利用熱傳導，嘗試排水導流和增加接觸面積；利用熱對流，使板面立體或加裝風扇，增加空氣對流，解凍速度再升級，自製出第一代魔力解凍板，並且改良研發第二代魔力解凍板成為綠色環保產品。我們發現： 一、鋁板厚度達2mm時，解凍速度可增加5~10倍，但持續加厚解凍效率趨緩。 二、「孔洞導流鋁板」兼具排水與接觸面積的優點，因此解凍速度優於其他鋁板。 三、增加冰塊與鋁板的接觸面積可以加速解凍，最佳解凍板組合為上層4mm下層2mm，解凍速度較單層快2.3倍。 四、第二代解凍板使用鋁扁管與第一代解凍板使用風扇之解凍效果相當。 五、第二代解凍板解凍豬排的速度優於市售解凍板，較自然解凍快11.5倍，低於平均市售價格達1707元。

Based on Ampere，s Law, the magnetic field intensity of the solenoids is B=μ0μr?n?I, where μ0 is the magnetic permeability of free space, μr is the relative magnetic permeability, n is the number of coils per unit length and I is the solenoidal current. The end magnetic field of the solenoid must multiply by one half. According to the above result, it can be greatly strengthened by the addition of a ferromagnetic core. First, we observe three different inserted materials of coils (wood, iron and magnetite), whose magnetic induction in different solenoidial current. By experiment, when the iron and magnetite materials were inserted into the coil, it would produce larger magnetic induction. The calculated relative magnetic permeabilities of wood, iron and magnetite materials are 0.57, 18.37 and 18.32, which are close to the reported paper (1). When the driving field is removed, the fraction of the saturation magnetization of the magnetite is retained, which is called hysteresis and is related to the existence of magnetic domains in the material. In the second part, we change the frequency of circuit switch, which induced different current. Compared with the result of the first part, it would fit the result, which is the induced magnetic field is proportion to the solenoidal current. 根據安培定律，螺線管的磁場為B=μ0μr?n?I。其中μ0為真空中的導磁率，μr為相對的導磁率，n為單位長度的線圈匝數，I則為通入螺旋管的電流。至於螺旋管的端點磁場須再乘上1/2。所以根據上述的結果，當螺旋管插入鐵磁性物質，會增強螺旋管的磁場。首先，觀察三種不同的芯物質；非鐵磁性材料，軟磁材料，硬磁材料（木棒，低碳鋼棒，磁鐵棒）在不同的外加磁場下的感應磁場，得到芯物質的磁化曲線，而計算出來的相對導磁率分別為0.57, 18.37 和18.32與參考文獻(1)接近。而當外加磁場移走時，硬磁性物質的磁性仍然存在，稱為殘磁現象。在第二部分，我們改變線路開關的頻率。發現不同的開關頻率，會得到不同的螺旋管電流，而造成不同的感應磁場。再度驗證了感應磁場大小是正比於螺旋管電流的大小。

在相對較高氧化電位下的前處理，這樣的活化步驟已被普遍接受。藉由這樣的活化步驟，廢煤渣（傳統鋼鐵業）轉變成能夠有效偵測微量鉛金屬離子的催化劑。微量鉛金屬離子的偵測是藉由方波剝除伏安法進行。在最佳化參數下，偵測鉛金屬離子的靈敏度為11.482μA/ppm(斜率??)，線性範圍為0.1－2ppm。最後，照光設備之應用亦可用來提升偵測鉛金屬離子時之靈敏度。最終實際應用則取天然的水進行實驗之驗證。The preactivation process (i.e., preanodization) at very positive potentials has been accepted as the prime activating procedure. By using the preactivation process, waste cinder (from steel industry) were converted into an efficient catalyst in the determination of Pb2+ in cinder-modified carbon paste electrodes. The possibility of determining Pb2+ at trace levels was examined by square-wave anodic stripping voltammetry. Under the optimized analytical conditions, the sensitivity, linearity, and detection limit are 11.482 μA/ppm, and0.1－2 ppm (r = 0.974). Finally, the lighting was also used to raise the sensitivity of the determining Pb2+. The practical applications were demonstrated to measure trace Pb2+ in natural waters.

將水加入溶液上方會造成溶質向上擴散，而造成濃度和濃度梯度的變化。我們使用簡易的實驗儀器算出不同時間各位置的濃度和梯度變化。書上大多假設濃度梯度成鐘型曲線分佈的簡單模型描述擴散過程，但只能用在擴散係數為定值的情況。從實驗或參考資料顯示，擴散係數會隨濃度而變，因此擴散現象常呈現非高斯之分佈，故我們以自己設計的實驗分析溶液在較高濃度時的「非高斯型擴散」，直接測量並計算不同濃度下的擴散速率、擴散係數。研究分子擴散行為理論未完全建立，擴散目前屬於半實驗的科學，此實驗設計與分析方式可供作擴散理論發展的參考。

本實驗中利用二氧化鈦能在常溫下經紫外線催化，分解空氣中的水分子，產生自由基的特性，攻擊幾丁聚醣中碳與氧鍵結的部分，使chitin 的分子量成功的從近50000 降解至3000以下；並可利用照射時間的不同，降解出分子量不同的chitin。此法不但大大排除利用化學法降解時廢液處理上的問題，而且還能利用照紫外光時間長短的不同來控制分子量的大小；又奈米級二氧化鈦(TiO?)在紫外光在短短四個小時之內就有很好的降解效果，除了節省了反應所需的時間外，降解前後幾丁聚醣的濃度也很高，因此所需的成本也遠低於當今利用酵素降解的方法。In the experiment, we used the properties of TiO? that can be catalyzed by UV rays and breaking the molecules of H?O and produce free radicals, which free radicals can attack the chemical bond between carbon and oxygen in chitin, successfully degrading chitin's molecular weight from 50000 to 3000.We also use different shining times to degrade chitosan into different molecular weight. In this way, we not only readily solve the problem of treating waste liquids produced by chemical degradation, but also control the molecular weight by different UV ray shining time. For another thing, TiO? in the nanometer level has excellent effect on degradation within 4 hours under UV ray shining. It not only cut back the reaction time but also produced high concentration of the chitin after degradation. As a result, the cost is much lower than that of using enzyme to degrade chitin.

本文中我們探討一個有趣的數列。這個數列有一個非常特殊的性質：將數列相鄰兩項的前項當分子，後項當分母，所產生的分數數列，恰好會出現所有的正有理數。 這個特殊的性質表示，可以將正有理數按照這個方式作排序，這個排序將完全不同於常見的正有理數排序的方法。 (1). 在正有理數的排序的結構中，我們做出許多有關於此數列的定理。 (2). 用數學歸納法證明此分數數列涵蓋所有正有理數，且每一正有理數只出現過一次。 (3). 將數列分割後，利用試算表製成數列規則表，並整理出快速的方法將數列表達出來。 (4). 將an 數列排成“樹＂的模式，可更快速的把正有理數寫下來。 (5). 最後，設計出搜尋正有理數的演算法，解決在分數數列中第n個正有理數會是多少；以及正有理數會出現在數列中第幾項的問題。 Let’s discuss an interesting sequence. There is a very special quality in it. In this sequence, choose two numbers, which are close to each other, and suppose the first number as “member” while the second one as “denominator.” Then we can get a fraction sequence that includes all of the positive rational numbers! According to this special quality, we can arrange positive rational numbers by the following method. Then we can get a brand-new way of the arrangements. (1). We can find many theorems about this sequence according to this special arrangement of the positive rational numbers. (2). We can prove the rule that this fraction sequence includes all of the positive rational numbers by mathematical induction. Furthermore, every positive rational number appears only once. (3). After dividing this sequence into several parts, we can get a sequence rule list by using trial balance and find a faster method to express the sequence. (4). Arrange the an sequence by the tree model. By this way, we can get all of the positive rational numbers much faster. (5). Finally, we can develop the operation method to solve the questions that what position would one positive rational number be in the sequence and what is the first, second, third or nth positive rational number of the sequence.

我們從網路看見一位國外網紅破解了星光配方，重現星光耐火效果！讓我們對耐火黏土產生興趣，自製檢測裝置進行耐火黏土配方與原理探討。 我們分析耐火黏土的基本組成有「黏土粉、黏膠、膨鬆劑、添加物」四類材料，測試出最佳耐火配方①黏土粉：玉米粉、②黏膠：白膠雄獅或糯米膠、③膨鬆劑：小蘇打、④添加物：增加軟度—漿糊；降低溫度—明礬、硼砂、滑石粉。歸納出黏土耐火原理是表面受熱產生膨脹碳泡沫，內部產生千層派或多孔洞麵包結構，小蘇打產生的CO2取代孔隙的空氣，產生耐火效果。 我們調配自製三種耐火黏土配方「白膠雄獅明礬」、「糯米膠硼砂」、「糯米膠滑石粉」，其耐火效果都優於國外網紅配方，且可塑性更佳，甚至誤食對身體無害。

本研究設計了兩個風洞實驗裝置，分為水平風洞與垂直風洞，兩者皆進行飄浮模擬試驗進而推算微小物質的運動量，並以小保麗龍球作為標準圓球，確保儀器的可用性，最後再透過醫檢儀器進行驗證。水平風洞利用機率的觀念統計孢子的分布，透過孢粉落下的高度差，帶入公式求得質量。垂直風洞則使用高倍率攝影鏡頭觀察孢子飛行，利用三力平衡的觀念推算其微小質量。最後，無論是自製風洞測出的質量、精確度、成本、測量速度和加速度的能力以及花費時間的長久，本實驗的儀器皆有優勢。 

這是一種可在膨脹狀態及未膨脹狀態間轉換的膨脹收縮瓶塞。本設計之瓶塞包含一彈性橡膠之塞座及一剛性塑膠之旋轉控座。該瓶塞在未膨脹狀態，可將瓶塞置於平口內將瓶塞順時針方向旋轉90度使瓶塞由未膨脹狀態轉換至膨脹狀態將瓶子密封；欲開瓶時將瓶塞逆時針方向旋轉約90度使瓶塞由膨脹狀態轉換至未膨脹狀態，可輕易將瓶塞從瓶子內拉出。根據顧客之需求設計瓶塞並選定適當之塑膠材料以製作旋轉控座及適當之衛生橡膠以製作塞座，依廠商提供塑膠及衛生橡膠之特性資料做有限元素分析預測橡膠元件受撐大之變形量，進行加工與製造印證分析之結果，與預期目標有相當的差異，故製作簡易之試件進行探求塞座內縮量與瓶塞膨脹量之關係， 探求瓶塞膨脹量與瓶子所能承受的壓力之關係，進而逆向設計瓶塞之塞座內縮量。 This is a kind of bottle plug that can change at the situation of swell or unswell.The design of this bottle plug includes a rubber plug and a rigid plastic controller that can revolve around. We can put the bottle plug at the top of the bottle and rotate it 90° c.w., the bottle pug will be at the situation of swell and then seal up the bottle. If we want to open the bottle, we just rotate 90° c.c.w., and the bottle plug will be at the situation of unswell and then we can pull the bottle plug out easily. I design this bottle plug according to the need of the customers; choose the certain plastic material to make the rigid plastic controller, and the properly rubber to make the plug; analyze and predict the amount of deformation by Finite Element Method in accordance with the characteristics of rubber and plastic supplied by the factories. However, the result and the expected result are quite different. In order to solve the problem, I make an easy sample to search for the relationship between the contraction of the rubber plug and the swells of the plastic controller and also the relationship between the swells of the plastic controller and the pressure that the bottle can endures. Then I design the contraction of the rubber plug on the base of the result of the experiment I made above.