本研究欲探討垂直水柱遇障礙物成節的形成機制。以數位照相機、光電計時器等進行觀測。 實驗結果如下： （一）因往返水柱波速不同，而且節無波腹大幅振動現象，故節不是駐波現象。 （二）細針插入水柱表面時，當針上方超過某長度後，針下方產生Ｖ字形震波。但不論針相對水柱的速度是否超過波速，針上方都有節，故不是震波所產生的現象。 （三）根據水波槽模擬實驗，不論木條是否超過波速，木條前方均產生波紋。木條前方的水受到木條推動，往前方加速，因此顯現出波紋了。 我們認為，在水柱中所看到的節，不是震波或駐波，而是相對於木條往前傳遞的波。波源是撞擊物，改變了水柱表面的壓力，而成為波源，水柱的水因受撞擊，某個範圍內流速會小於波速，使得撞擊物前方存在波紋。This experiment uses digital camera and photoelectric timer to discuss the mechanism of causing spouts to form nodes on its surface. Because the downward wave velocity of the spout is different from that upwardand there are no significant vibrations of antinodes, standing waves are not the mechanism of causing nodes. In the experiment of inserting a needle into the spout, we found out that while the needle was inserted above a certain length of the spout, v shaped bow waves emerged. However, no matter the velocity of the needle related to the spout is over the wave velocity, there are always nodes above the needle. Therefore, bow waves are not the mechanism of causing nodes. According to the ripple tank simulating experiment, no matter whether the speed of the wooden stick is faster than the wave velocity or not, there are always waves forming in front of the wooden stick. The wooden stick pushes water in front of it and causes the water to accelerate forward. Therefore, waves appear. We think that the nodes we see on spouts are neither standing waves nor bow waves. The nodes are rather caused by the relatively moving wooden stick. The object, which impacted the spout (wooden stick), changed the pressure of the spout’s surface and became the source of wave. Because of the impact, the velocity of the water current of a certain area became slower than the wave velocity and causes nodes forming on the surface of the spout.

桃園虎頭山是位於林口台地南端的低海拔(約240~260M)丘陵地,表土層屬於紅土層,紅土主要成分為細沙(直徑>50μm，約佔50%)、粉沙(直徑2~50μm，約佔30%),其餘以黏土為主,加上少量含鐵礦物,採樣地點字圖二中的三聖宮旁的登山步道,其坡面面向東南方,對位處北緯25度的桃園屬於向陽波,經日曬適當時間後所產生的龜裂現象,是我們探討的對象;We have focused the study on the sun cracks found in the Mts.Hu-To are located in the southern part of the Mesa Lin Kou, which are 240m to 260m above the sea level. Mainly red clay, the surface soil is a composition of fine sand(diameter>50μm,up to50%)and silt(diameter>2~5 μm,up to 30%),including clay and a limited amount of iron minerals. The soil sample was gathered at the trail beneath the Hil Gue-Lun(241m,see pic.1)from the southeastern latitudes.

稀子蕨（Monachosorum henryi Christ）生長在台灣中海拔山區，是少數具有特殊生殖方式(不定芽)的蕨類。本研究對東眼山的稀子蕨族群進行物候調查，以了解其進行孢子繁殖及不定芽繁殖的過程，並試圖探討稀子蕨的不定芽是否可增加其族群對環境的適應性。研究結果顯示稀子蕨的孢子體及原葉體都無法在乾旱的環境下生存，常有大規模乾死的現象；而其不定芽則具有很強的耐旱性，無論是在季節普遍性及幼苖發育程度上，生殖芽都比孢子繁殖較佔優勢。而且其不定芽於旱季結束後，可迅速萌發，長出的孢子葉可隨之進行有性(孢子)及無性(不定芽)生殖，使其族群不至於在旱季中有地區性滅絕之虞。;Monachosorum henryi Christ , which exists in the middle elevations of the mountainous regions of Taiwan, is a fern with a special reproductive system seldom found in other ferns.This study investigates the phenology of Monachosorum henryi population in the Don Yang mountain region. Its purpose is to understand the sexual and asexual reproductive cycles of these ferns and to interpret whether or not the buds can increase the fitness of their population during the dry season.The results show that it is extremely difficult for the sporophyte and prothallus of Monachosorum henryi to survive in a drought. However, the buds have a much stronger drought endurance. According to this investigation, the adventitious buds of Monachosorum henryi are superior to the spores in seedling development in every season. Adventitious buds are able to germinate soon after the dry season as well as in any other season, and are able to grow spores and buds on their fronds enabling both a sexual and asexual way of proliferation. In this way the fern avoids a district extinction of their population.

As electronics continue to shrink in size, the cost and environmental impact of current methods of production are increasing dramatically. The purpose of this experiment was to lay the groundwork in another potential method of creating nanowires and printed circuit boards. We believe that through the exposure of supercritical CO2, metalized electrospun fibers with gold nanoparticles will have increased conductivity. In addition, the adhesion of metal to polymer thin films can be controlled with a poly (ethylene oxide) (PEO) mask on both silicon and Kapton substrates. This study found that a specific concentration of gold nanoparticles can make a solution of poly (methyl methacrylate) (PMMA) in chloroform that cannot be electrospun, spinnable. Scanning electron microscopy also confirmed that scCO2 smoothes the surface of the fibers and makes them more uniform. EDX analysis also found that exposure to scCO2 also removed all residues of solvent and cross.sectional transmission electron microscopy showed that the nanoparticles were conglomerated near the surface. In conclusion, scCO2 and gold nanoparticles respectively enhanced the morphology of the fibers and made the electrospinning process more robust. Cross.sectional analysis also showed that the nanoparticles attracted the deposited gold into the fiber making prongs reach from the deposition into the fiber, but there was no test to quantify the adbesion. Using the spray bottle test, the gold still remained on wires. The resistivity of the micro wires was extremely close to that of gold creating resistances within hundreds of ohms over hundreds of micrometers of wires. Thin Films masked with PEO were exposed to scCO2 and metalized with gold or copper. Atomic force microscopy analysis shows unique crystallization formations of poly (capro lactone) (PCL) after scCO2 exposure. ASTM standard peel tests determined that the process was successful with PCL thin films. On the Kapton samples, peeling patterns reversed when the thickness became too great to melt in scCO2.+ Through perfecting these processes, the electronics industry can continue in its miniaturization while the environmental and monetary costs.

The purpose of the research is to investigate the settling mode of the viscid micro-particle, such as the ones from the “Miso Soup”, in static liquid. We constructed the “constant temperature environment” by constant temperature trough and transparent glass trough. The data is gathered from pictures captured from DV and then analyzed by Media Player. We did a stability test prior to the start of the experiment and found the system with good stability. The results of the experiment are as followed: 1. The settling mode can be divided into four phases: (a) Initial accelerated phase (b) Maximum phase (c) Gradually decelerated phase (d) Stationary phase. 2. The lower the fluid concentration is in the fixed temperature: a. the faster its settling interfaces appears; and the deeper it becomes for the depth of its settling interface. b. the faster the maximum sedimentation rates of the settling interface becomes and the slower it appears. 3. At the fixed concentration, the higher temperature: a. has the bigger maximum sedimentation rates of the settling interface b. gets to the stationary phase sooner c. has shallower stationary settling interfaces d. the time when the settling interface appears is independent with the temperature 4. The shape of the container has no effect on the settling mode as the settling interface is always perpendicular to gravity field. 5. If we add salt into the liquid, the stationary settling interfaces of the result will be higher than non-added ones.本研究的目的在於探討味噌這樣的微小黏性顆粒，在靜止液體中的沈澱模式。運用恆溫槽與透明玻璃水槽所建構之恆溫環境透過數位攝影機，以電腦播放軟體於特定時間擷取畫面進行分析。在正式實驗前，進行了穩定性試驗，發現穩定性良好。實驗的結果發現：一、 沈降模式：可以分為四個時期，分別為（一）起始加速期（二）高峰期（三）逐漸穩定期（四）完全靜止期。二、 在固定溫度下，溶液濃度越低：(一) 出現沈降交界面的時間越短且穩定距離距液面越深。(二) 沈降面沈降速率最大值越大且出現的越晚。三、 在固定濃度下，溶液溫度越高：(一) 沈降面沈降速率最大值越大。(二) 沈降交界面完全靜止期出現的時間越短，也就是越快達到穩定。(三) 沈降交界面的穩定距離距液面越淺。(四) 沈降面沈降速率最大值出現的時間與溶液的溫度無關。四、 容器內部的形狀與沈降面的沈降行為並沒有影響，都是成與重力場垂直的水平線沈降。五、 添加食鹽之後最終穩定沈降面比同濃度同溫度的高了許多。表示添加了食鹽對於味噌溶液有阻止沈澱的效果。

源自於Thinking Mathematically這本書的一道題目, 關於正方形的切割問題：將一個正方形切成不重疊的正方形, 所得的個數就可被稱作NICE(好的), 問有哪些數是NICE數？ 在平面的正方形切割的問題, 透過分割技巧, 我們得出了重要的結果：除了2、3、5以外的自然數都是NICE數, 並推導出：若k為NICE數, m為自然數, 則k+3m為NICE數。我們將問題推廣至立方體：將一個正方體切成不重疊的正方體, 所得的個數就可被稱作very NICE(非常好的), 問有哪些數是very NICE數？我們也得出重要的結果：大於47的自然數皆為very NICE數, 並推導出：若 是very NICE數, 且m是自然數, 則k+7m為very NICE數。

本研究整合了碎形圖形的迭代運算方法與基因交配觀念來達到音樂創新，並透過音樂和諧性判別機制來提高創新音樂的悅耳程度。利用基因觀念之交配的方法來解決長短的問題。這個方法是把原始音符輸入後，找出它們的中心點，以這個中心點為準，其他的音符按照一定比例向外延展，成為新的迭代點。再利用這些迭代點，迭代出新的音符。把製造好的音符染色體放置到交配池中，以隨機的方式在交配池中選取其中之一個染色體進行交配的動作，此二音符染色體會交換彼此的基因，產生下一代新的代表音符長短之染色體，隨後以「模仿母體判斷式」來判斷這新一代的音樂是否與母體音樂相似，藉此淘汰掉「不肖的」下一代，而若新一代與母體的相似程度高的話，它的悅耳性相信也會相對提高。最後把這些技術應用於數位音樂創作，以衍生新穎應用與創新的結果。Fractals can be produced by IFS (Iterated Function Systems). By iterative computation of many times, we can obtain the similar graphics. In my research, the methods to generate the iterative algorithms were presented. In addition, I would discuss the regularity and the content as well as the properties of those digital patterns. At last, the advanced application of fractals to digital music pieces was presented. The program took a note of several measure of music as the beginning point, and made the IFS calculations for each new note in each measure. But there was no difference in beats if you just make the IFS iteration. So I changed the beats with genetic crossover method. In this research, the expression of the DNA to each beat of note was adopted. The same way, it took a note as a beginning point. And the system obtained the new DNA from the old notes for new ones randomly. After producing the new pieces of music, I want to know if it is good to listen. So I used the algorithm that checks the simulation to the shape of mother music. If its shape is similar to the mother music, the probability that the new music is pleasing may even increase. That would make a piece of brand new music. What I want to do in this research is improve the multiformity of music and find what the relationship is of ‘good music’ and mathematical algorithms

It is always fascinating to see water droplet’s dancing around on a Japanese teppanyaki hotplate surface. The water usually does not evaporate immediately, but form interesting shapes, dance around and follow by evaporation of gaseous water and disappear. In this experiment, we designed a very simple experimental set-up to observe the little water droplets dancing on a heated hotplate. A homemade stainless plate and a small heater attached to the plate, and a thermal couple was assembled. With this simple setup, we observed the variation of water droplet’s shape as a function of the hotplate temperatures. The temperature of the water droplets, the duration of the water on the hotplate, and the shape number were measured. The shape formation mechanism was proposed. We found when the water droplet was subject to high heat due to the contact of the surface and the hotplate, the abrupt evaporation of the water molecules and violent vibration cause the formation of the various shapes to reach thermal equilibrium; the number of the shapes and the oscillation can be described by Laplace’s equation,Using a high-speed camera, we found the higher the temperature of the water, the more variations of the water droplet shapes can be observed. In addition, at a certain temperature range, the number of the water shapes did not change, suggesting a similar phase transformation behavior on the shape formation. 緣起： 邂逅專題研究、水珠漫舞、剪輯影片，引起我們想更進一步揭開它的神秘面紗。 緣續： 了解熱平台上水滴大小的變化及水珠基本的形狀及變化律動。 緣繫： 進一步研究水珠多變的面貌，並探討水珠的大小、溫度、停滯時間及變化規律相關機制。 緣定： 糾纏在水珠圓舞曲中有如大珠小珠落玉盤的曼妙，其中埋藏了平均圓與能量量子化的律動。

The ASSOR is a device that allow to perform the sterilization function in hospital areas, the most important sectors of the hospital where it is required to implement this type of systems are the operating rooms, intensive cares, baby care, pathology, etc. The principle of the present project is a system that enables or either disables a valve that allows the fluid of the product, antiseptic or sterilizing, inside the room to be sterilized. The main application of this system is, after the manual cleansing of the room, in a control board, the procedure is turned on. The ASSOR consists, in general, of an electro valve that controls the fluid of the antiseptic into the room, a fan system, the electronic control circuit for the application of the product and electronic circuit to have a synchronized control of the system, and finally the product application in the target room.

在這篇研究報告中,我用了三種觀點來推廣幾何中的反演變換,首先,把反演變換視為是一種圓內與圓外的一種1-1且onto的映射,第一種推廣,是將變換中心移到視圓心以外的圓內的地方,馬上我們得到一個結論「反演半徑會隨著動點而改變」,接著,我們實驗了一下反演變換用有的一些性質,保角性,保圓性,…等在這個變換視中是否依然存在;接著我們用第二種方法來推廣反演變換,我們將邊界的形狀由圓視改成別的形狀(如三角形,四邊形…等等),然後也試試看在這種變換之下是否還擁視有反演變換的一些性質;第三種推廣,則是在研究的過程中,我發現了一種新的幾視變換,承接第一種推廣,我們將原先為定點的變換中心改為動點,將原先的動點改為定點,做出來的一種新變換。In the study, a new geometric Inversive transformation through three points is discovered. Here is the main result：（1）The first, onto cycle of inside and outside can be proved under invasive transformation. It is changed moving the center from center of cycle, we can get a new ” Inversive radius can be changed by moving drop. (2) We hope to find the answer to this problem by experiment, it is exist with the inversive properties. (3) A new geometric transformation is discovered, a fixed drop can be changed moving drop, then the first moving drop shifted the fixed drop. This leads to a new construction if the new transformation.

中文摘要：\r 本研究旨在探討，在TCP/IP 協定之下，最大網路傳輸效率之MTU\r （Maximum Transmission Unit,最大傳輸單位）值。根據IEEE 所公\r 佈Ethernet 之標準，經實地模擬實驗，本研究之結論如下：（1）在\r 單純兩台電腦直接串接時，由於幾乎無任何干擾與封包的碰撞，可設\r 定之MTU 最大值以1500bytes 為最佳；（2）但在模擬真實的大型廣域\r 網路時，由於碰撞增加及雜訊增多，經模擬實驗顯示，MTU 值為\r 1500bytes 時無法在資料傳送、接收及重組時取得平衡，最佳之MTU\r 值落於500 到600bytes 之間，進一步研究顯示MTU 值設在500 到\r 600bytes 時可提升傳輸效率約50%。同時，本研究亦討論將此機制應\r 用於未來新網路標準之可行性及其必要性。Abstract：\r The main purpose of this research is to explore the best network\r transmission efficiency's Maximum Transmission Unit under TCP/IP\r protocol. According to the Ethernet's standard of IEEE and simulated\r experiments, the outcome of this research are :( 1) When connecting two\r computers serially, there is almost no interference and impact of packets,\r the best MTU that we can set up is 1500bytes ;( 2)When simulating the\r truly wide area network, interference and impact are rising. The result of\r this simulates experiment shows that when MTU is at 1500bytes, it's\r unable to keep balance when sending, receiving and re-composing. The\r best new MTU is between 500bytes and 600bytes. And when MTU is\r between 500bytes and 600bytes, the network transmission efficiency can\r be promoted about 50% higher. At the same time, the research is also\r discussing the feasibility and necessity of applying it to the standard of\r the future network.

Sicherman 已經找出與兩顆六面的正常骰子有相同機率分布的Sicherman 骰子，並進一步獲得與三顆六面的正常骰子有相同機率分布的骰子必為一對Sicherman 骰子與一顆六面的正常骰子之結果，我們試圖由已知的Sicherman 六面骰子的處理方法出發，透過對割圓多項式的分析來累積足夠的相關資料，以處理由兩顆四面骰子至兩顆三十面骰子，處理由三顆四面骰子至三顆三十面骰子的各種Sicherman 骰子的答案，來探索兩顆與三顆的n 面Sicherman骰子存在的充要條件與求法，並進一步將所得之結果分類，得到 ”有相同標準分解式的類型的數n，會具有相同組數的Sicherman 骰子”之猜測結果與特殊情形下的證明。 Sicherman has found out the Sicherman dice which have the same probability distribution as the normal two six-sides dice. Furthermore , he also found out a pair of Sicherman dice and a normal six-sides dice has the same result as 3 normal six-sides dice . We try to begin with the given algorithm of six-sides Sicherman dice , through the analysis of Cyclotomic Polynomials to accumulate sufficient related information then to come up with the solution from discussion of 2 four-sides dice to 2 thirty-sides dice , from 3 four-sides dice to 3 thirty-sides dice to explore the existence of necessary and sufficient condition and solution of 2 n-sides Sicherman dice and 3- sides Sicherman dice , and even to classify the results to come to a conclusion of the guessing results and proofs under special cases about “the numbers n which have the same Canonical Prime Factorization will have the same numbers of n-sides Sicherman dice.”