具有長短兩軸的對稱性剛體，譬如半橢球，在施加適當質量配重後，給予其Z 軸方向的 初角速度，將會逐漸上下震盪、搖擺，而後改變原先的角速度方向，朝相反的方向逆轉回來。 此現象稱為「逆旋現象」，本研究分析關於配重、質心距離與表面摩擦係數等因素的影響，利 用光點投影方式判讀其軌跡，並建立數學模型以驗證物理原理。研究發現，動摩擦垂直長軸 的分力所造成的力矩，將會導致逆旋的發生，並且，對本研究的剛體模型而言，加以20g 配 重，與長軸夾45°距質心5.5cm 且動摩擦系數為0.1227 時，逆轉角度有最大值。當長短兩軸 的震盪頻率相近時，甚至會發生兩軸能量的耦合現象，而有不只一次的逆旋。 The phenomenon was found for rigid bodies with long and short symmetrical axes, such as half-ellipsoids. We add extra masses ( Δm ) to a stone of the shape of half-ellipsoid and then give it an initial angular velocity ( 0 ω ) to make it spin. While the stone spins, the two symmetric axes start oscillating up and down. Then, remarkably, the spin of the stone slows down while the amplitude of oscillation increases until the direction of angular velocity reverses. This process is called “Rattle Back Spin-Reversed Phenomenon.” Our study involves the effect of several parameters on the above phenomenon, such as the shape of the stone, the added mass, and the friction between the stone and the table surface. We try to build a physical model to explain the spin-reversed phenomenon which can be recorded by tracing the motion of the stone with optical means. According to our study, the shape of the stone and the distribution of the added mass played crucial roles. The torque generated by kinetic friction along the long axis also helps the spin to reverse. Furthermore, in our experiment, we record a maximum reverse angle with following settings: two sets of 10 grams of mass are symmetrically added to the flat side of half-ellipsoid, in the distance of 5.5 cm to the C.M. of stone and an included 45 degrees angle with a long axis. And the most surprising finding is that when the oscillation frequencies of two symmetric axes are close to each other, the spin of the stone can reverse twice.

File compression has become a very important tool in the technology field because it allows faster data transfer rates over the internet and decreased file size on data disks. File compression aims to reduce file size while still retaining the quality of the file. Lossy file compression methods are not very efficient because the compressed files end up losing more data than what is usually intended causing a considerable loss in quality. Lossless file compression methods, on the other hand, take time to process since they require decompression to retrieve the original file. In this study, a lossless algorithm which does no require decompression was created. The resulting Fractal File Compression (FFC) algorithm contains two parts, the IFS algorithm and the Huffman Tree generator. Both algorithms were created using Java language and JCreator. The finished program was tested on an image file with 2542 x 1944 pixels dimensions. The image file was compressed using JPEG, BMP, PNG and FFC formats. For each method, the image file was compressed at three different resolution settings; low, medium and high. All the compressed images were then viewed under 500% zoom using Adobe Photoshop CS2. In an area of 40 by 40 pixels, the number of distinct boxes, which served as a measurement of image quality, was determined. Compressed images for JPEG, BMP, and PNG for both the low and medium settings have low image qualities, while the fractally-compressed images have a high image quality. For the high resolution setting, both JPG and fractally-compressed images have Page 2 of 2 high qualities while BMP and PNG still have low qualities. Based on the measurements obtained from the box-counting method and the file sizes, the absolute image quality for each compressed image was calculated. The absolute image qualities of the compressed images used for each setting were then compared. Coupled with large file size and small pixels per area count, the conventional methods have lower absolute image quality than the images compressed using the FFC method. This was true for the low and medium settings, however, JPG compression has a higher absolute image quality than the fractally-compressed images. This meant that JPG compression is more efficient than fractal compression when an image has a high resolution. The resulting FFC algorithm is lossless since it uses pattern searches and replacements in order to decrease the file size. To make the program more suitable for high resolution images, the FFC algorithm may be modified. Most of the changes in the FFC algorithm should be done in the IFS generator. High resolution images can be compressed fully if the pattern that was used for compression is more representative, but even shorter. A more representative bit pattern would create a high quality, high resolution image with a smaller file size.

在全球一片節能環保的趨勢下，綠色能源的開發也越來越快速，未來連植物，也可能成為「發電來源」。我們根據前人的研究方法就想到要利用這一種身邊常看到的花草樹木利用酸鹼性的不同來當作電池的電動勢，因而藉此來發電。透過在學校、家裡附近的街道、公園等等地方的植物，用指示劑來檢測它的範圍，觀察其是酸還是鹼。利用現有的網路資源。尋找各種植物的名稱和圖片，一種一種的慢慢去找。所以我們此篇文章討論的是植物的酸鹼性來做電池的正負性。讓我們解決現代「電」的不足。用植物電池並配合串聯、並聯的接線方式，除了可以應用於低功率的負載，如點亮LED燈，甚至在並聯了兩組改良式電極模組之後，再嘗試讓小鎢絲燈泡發電。 我們進行新．神農氏嘗百草，但我們不是為治病，而是拯救地球能源短缺的問題。 Based on previous studies, we expect to make use of plants to generate electricity.We collected plants form school, streets and parks, detecting their pH values with indicators .Through lnternet resources, we find out the names and pictures of various plants. Therefore, we conduct this research to make the pH values of plants act as the positive and negative of batteries. Furthermore, we will help to solve the problem of electricity shortage.

A novel method of electrolytic Y3Al5O12 (YAG:X, X=Ce, Eu, Tb) phosphor thin-film coating on sapphire was investigated in yttrium, aluminum, cerium, europium and terbium nitrate solution. By means of X-ray diffraction (XRD), scanning electronic microscopy (SEM) observation, and cathodic polarization tests, the most efficient potential of deposition was found in the region between -1.2 V~-1.5 V. The YAG phosphor thin-film was successfully synthesized by the cathodic deposits were heat-treated at 1200 ℃ for 4 hours. The excitation photoluminescence (PL) spectra of Ce3+ in YAG consists of a strong maximum at about λ＝520~530 nm that show yellow emission peak, and a red emission was observed at about λ＝595~700 nm by additional Eu3+. The excitation PL spectra monitored inλ＝480~500 nm with the amount of Tb3+ and that show green emission peak. The fabrication of YAG phosphor thin-film will be useful to improve the emission intensity of the white LEDs in the future.由電解沈積陰極的電位—電流關係圖、Ｘ光繞射分析、SEM 觀察及實驗反應的經驗式我們可以知道要在導電的sapphire（氧化鋁單晶）基材上電解沈積合成燒結YAG 螢光薄膜所需之各類氫氧化金屬，其合適的電解沈積電位為-1.2 Ｖ~-1.5 V，我們利用電化學沈積法可以成功地合成欲燒結成YAG 螢光薄膜所需之氫氧化金屬，將所合成之氫氧化金屬放入高溫爐以1200 ℃高溫燒結4 小時後，依據我們目前以光螢光激發(PL)這些YAG 薄膜的光譜結果，可以成功地得到YAG:Ce(λ=520~530nm)黃光螢光薄膜、YAG:Eu(λ=595~700nm)紅光螢光薄膜及YAG:Tb(λ=480~500nm) 綠光螢光薄膜，證明以新的電化學方法可以成功製備YAG 螢光薄膜，相信這些研究成果未來應用在研發提昇白光LED 發光效能上有極大之助益。

台灣地區高蹺?（Himantopus himantopus）的度冬族群出現月份是九月中旬至隔年四月，棲息地主要是在台灣西部沿海之鹽田、魚塭、沙質河口及少數內陸河川，而 1994年成立的台南四草野生動物保護區更是其在台灣的主要繁殖區。 本研究主要從2001年3月~2003年10月進行八掌溪嘉義市段高蹺?族群數量的調查，在 2001.12 月計數到最高數量約 1200 隻，2002.10 月有 1540 隻，連續兩個年度都是全國最高數量，分析環境因子及食物來源皆優於其他各沿海棲地。 在 2003 年 5 月至 9 月調查嘉義沿海高蹺?繁殖配對情形，在 5 月 24 日發現鰲鼓溼地巢數 25 個、幼鳥 14 隻，布袋七區鹽田巢數 9 個，顯示除了台南四草繁殖區外還有其他的繁殖地。 The winter residents of Black- winged Stilts in Taiwan appear in mid-September to next April. Their main habitats are the salt pans, water ponds, sandy river mouths and few inland rivers in western Taiwan. Furthermore, the “Taina Szu-Tao (四草) Wildlife Sanctuary” established in 1994 is their major breeding area. This research is the investigation of the amount of Black- winged Stilt in Pajhang River（八掌溪）, Chia-yi city（嘉義市） in 2001, Mar.~ 2003, Oct. The highest amount in 2001, Dec. is about 1200 and in 2002,Oct. is 1540. The amounts of these continuous two years are the highest in Taiwan. To analyze the reasons, the environment and food sources are better than other coastal habitats. In 2003, from May to September, the investigation of mating situation of Black-winged Stilt in Chia-yi coastal areas, twenty five nests and fourteen young birds in Ao-Ku(鰲鼓) wetland; nine nests in Pu-dai （布袋） seven salt pans are found on May 24th. It shows that there are other breeding areas except the breeding areas in Tainan Szu-Tao.

間歇泉是一種十分奇特的地質景觀，地下水受到火成岩入侵所帶來的穩定熱源加熱，產生水蒸氣，利用水蒸氣形成的空氣柱壓力推動水由地底噴發出地表，也因為熱源穩定使得噴發時間差接近一定值，形成所謂的「週期性」。而根據實驗結果發現，管壁較薄的管子，在噴發之後，會使管中殘餘的水稍作降溫，加上補充的冷水使系統降溫；管長愈長時，蓄水槽中的水量較多，提高溫度所需的時間也較長，而延長了噴發的週期，最後歸納出間歇泉形成及存在的三個主要條件：(1)穩定的熱源;(2)細長的孔道;(3)豐沛的地下水。英文摘要：The geyser is a very amazing sort of geologic scenery. Its principle is that the heat source of invasive volcanic rock heats the underground water to produce steam that results an air-columnar with a large pressure to erupt through the underground on the surface. Because of the steady supply of heat source, the period between eruptions is closed to a constant called “periodicity.” According to the result of the experiments, the tube that have thin wall can lower the remaining water’s temperature a little and the cold water’s supply can also lower the plumbing system’s temperature after eruption. Besides, the water in the longer tube needs more time to higher its temperature to protract the period because it have more water in its reservoir. Eventually, there are 3 essential conditions of the geysers’ existence concluded: (1) steady supply of heat; (2) a thin and long standpipe; (3) abundant underground water.

藉由結合液晶與奈米線，本研究設計出新型的光電元件，我們發現這些新設計具有先前元件很難達到的新穎特性。首先，我們研究液晶分子與一維磁性奈米線之結合，很有趣的是磁性奈米線在液晶元件內，會沿著液晶方向作整齊排列，更重要的是經由一外加電場，即可調控磁性奈米線之磁場方向。藉由電場調控磁場，是很久以來許多科學家追求的目標，然而成效不彰，本研究提供了一個簡便的方法，克服了長久以來的障礙。第二個例子，我們研究液晶分子與一維半導體奈米線結合之元件，我們證實了半導體奈米線所發射瑩光之電場偏極方向，可以經由外加電場來調控，這個特性對於資訊科技的應用，將很有用處。本研究所觀測到之結果，皆可利用下列事實來理解，奈米線具有很大的表面積，因而增加了與液晶分子之交互作用，經由此增大的交互作用力，奈米線會沿著液晶分子方向排列。值得強調的是，本研究利用了已成熟的液晶顯示器技術，其未來應用性將有很大潛力。New devices based on the composites of liquid crystals and one dimensional nanowires have been designed, fabricated, and characterized. It is discovered that these novel devices own interesting properties that are very difficult to be obtained by conventional ones. As the first example, the liquid crystal device with built-in one dimensional magnetic nanowires has been studied. It is found that the magnetic nanowires can be well aligned along the orientation of liquid crystal molecules. Quite interestingly, the direction of the magnetization of magnetic nanowires can be easily manipulated by an external electric field at room temperature. The phenomenon of electric manipulation of magnetization has been studied since nineteen century, but the achievement is rather limited. Here, we provide a convenient alternative to overcome the long quest search. For the second example, the liquid crystal device with built-in semiconductor nanowires has been investigated. We demonstrate that the polarization of the emission arising from semiconductor nanowires can be easily controlled by an external electric field, which is one of the basic requirements for information technology. All of our observed results can be well understood in terms of the inherent nature of a large surface to volume ratio of one dimensional nanowires, which induces a strong interaction between embedded nanowires and liquid crystal molecules. Therefore, the nanowires can be driven along the orientation of liquid crystal molecules. It is stressed here that our newly designed devices are based on the well established liquid crystal display technology and therefore their practical application can be realized in the near future.

The didactic prototype for the teaching of the pneumatic Basic is designed, so teachers can instruct knowledgement of pneumatics focused to identification, handling and application of its elements based on constructivist theory in which the student learns making, working on projects and in a collaborative way. This implies that his presentation should include the basic elements to be used in this study area, as well as allowing that the student can interact with it, still easy to use, and take them by the teacher into his area of education, which can be a classroom, room, Auditorium, workshop, lab, and even training courses to the industry, the only thing that requires is compressed air (2 to 4 bars). As well as, to create a secure environment for the user when this is manipulating. Its construction based on a compact, lightweight and ergonomic, structure to ensure that it can be transported without difficulty. Also that must comply with the minimum essential to enable the student to acquire competencies in the curriculum which consider the identification, handling and application of pneumatic elements; IE has the following 2 directional valves 3/2 NC, 1 directional valve 3/2 NC-operated with a knob, 2 valves 3/2 pneumatic drive, a 5/2 valve NC NC of stable pneumatic drive, 1 valve of simultaneity or function, and 1 valve selector or function, or double effect with pressure regulator piston1 piston of double effect, 1 piston for simple effect, 1 valve 3/2 NC with motorized drive and roller.

1. 將 cos nθ以cosθ 形式依高次降羃排列展開，觀察各項係數，找尋其變化規律，進一步求得各項係數的一般項公式。2. 將 sin nθ以sinθ 形式依低次升羃排列展開，觀察各項係數之變化規律，進一步求得各項係數的一般項公式。3. 找出cos nθ 與cos(n-1)θ，cos(n+1)θ 之間的關係式。4. 找出sin nθ 與sin(n-1)θ，sin(n+1)θ 之間的關係式。5. 利用cos nθ 的係數間的遞迴關係，找出其相對應的特徵方程式。

3C產品及LED燈多以藍光照明，長期照射易導致視網膜黃斑部病變。其作用機轉是藍光引起視網膜細胞過氧化物質 (ROS)增加，造成細胞的氧化壓力進而引發細胞凋亡。幾丁寡醣 (Chitosan oligosaccharides, COS) 藉由減少自由基產生和抑制轉錄因子NF-κB傳導路徑而有抗氧化及抗凋亡的作用。 本研究以ARPE-19細胞株，在添加不同濃度的COS下，經照射LED藍光處理後，分析色素上皮細胞活性、ROS表現量及細胞凋亡情形，並透過PCR、西方墨點法、JC-1及免疫螢光染色分析作用機轉。實驗證實COS能抑制過氧化物質 (ROS)的產生，減少視網膜色素上皮細胞因藍光所造成的細胞凋亡。PCR和西方墨點法的結果顯示COS可以抑制發炎介質HO-1、iNOS、Caspase-3、Bcl-2、ERK，及基因iNOS、MCP-1的產生。免疫螢光染色顯示COS能抑制NF-kB核易位。總結來說，COS能藉由抑制NF-kB的活性，減少其下游基因的表現量，降低細胞氧化壓力和發炎反應來避免視網膜色素上皮細胞損傷。COS在臨床上有潛力成為一種預防LED藍光造成視網膜傷害的有效保健食品。

蝴蝶定理（Butterfly theorem）是在一個圓形中，設M為圓內弦PQ的中點，過M作弦AB和CD。設AD和BC各相交PQ於點X和Y，則M是XY的中點。 在此份研究中，我們探討正方形邊上兩個動點、正方形內一個定點以及邊上動點與內點的連線，延伸交四邊的另外兩點，所構成的「蝴蝶形狀」的「蝴蝶線」。主要利用兩個動點在邊上的位置，以及內點在正方形內的位置，尋找上述條件與蝴蝶線的關係。由於邊上四個點的分布對於蝴蝶線有很大的影響，所以又依照四點分布位置進行分段討論。另外，我們也尋找正方形內接蝴蝶形的特殊性質。