臺灣

一般人從小就知道如果要判斷西瓜有無成熟，只要用手輕拍瓜皮，利用聲音的特性就可以知道西瓜是否成熟，此技術看起來容易，卻需有多年經驗之西瓜商始可為之。本研究利用拍擊西瓜所造成之聲音進行非破壞性音波檢測，來探討西瓜之成熟度。換言之，本研究希望在依照西瓜商拍擊的習慣下，從客觀的科學角度，探討存在於西瓜商手上「聽音辨瓜」的奧秘。由研究結果得知，西瓜的拍聲在頻譜中可分為三個頻區，即西瓜殼所造成的高頻區，水及含水量高的果肉所形成的中頻區，及由空洞及含水量低的果肉所造成的低頻區，而西瓜商就是藉由這三種音頻所表現出的綜合效果進行判斷。The method, tapping the watermelon rind and listening to the sound, has been often used to judge whether the watermelon is mature or not. Although it is not difficult to tap the rind of a watermelon, it is not so easy to have a correct judgment of the maturity just from the sound you heard, unless you are an experienced watermelon farmer. In order to investigate the secret that the farmers have, this research detects and analyzes the sound of tapping watermelons in an objectively scientific way. According to the experimental results, the sound could be approximately partitioned into three regions in the frequency spectrum, denoted as high-frequency, mid-frequency, and low-frequency regions. The high-frequency region and mid-frequency region are resulted from the hard solid rind and the juicy flesh of a watermelon, respectively. As for the low-frequency region, it comes from the vacant holes or flesh with little amount of water. Based on the experiment, it can be concluded that the maturity of a watermelon can be correctly judged from the combination of these three frequency regions, just like the farmer’s method.

George Sicherman discovered that it is possible to take a couple of 6-sided dice re-labeling them with different positive integers (1,2,2,3,3,4) and (1,3,4,5,6,8) having the same probability distribution as rolling a standard pair of 6-sided dice. Such unique pair of dice is calling Sicherman dice. The secret behind the Sicherman dice can be studied by combining the powerful mathematical tool “Generating functions” with the symbolic manipulation software “Derive 6”, The same procedure may be applied to studying the possibility of the generalized Sicherman dice along the consideration of :\r (1) Adding more dice. (2) Changing the number of faces. To this end, we introduce the concept of the Sicherman Bound. For a given integer n, the number of n-sided Sicherman dice is finite. We computed manually such numbers for n?50 based on the method of “Elimination of negative terms”. Sicherman Dice 就是一對點數配置與正常骰子(6 面正立方體，點數為1到6)不同的骰子，它所拋擲出的每一種不同點數和(2,3,4...,12) 的機率恰好與一對正常的骰子相同。這種骰子是美國的Col. George Sicherman 所發現的。 Sicherman 更進一步指出：在不使用Sicherman Dice 的情形下，不可能找到一組大於或等於三顆的非正常骰子，它們拋擲出的每一種不同點數和的機率恰好與一組同數量的正常骰子相同。本研究的目標在於1. 尋求計算「Sicherman Dice 的組合和正常的骰子有相同的出現機率」的方法2. 證明Sicherman 結論的真偽及是否適用於其他正多面體(4 面/ 8 面/12 面/ 20面) 的標準骰子3. 修正Sicherman 的結論，並定義Sicherman 極限(Sicherman Limit)。在假設n面正多面體(n 為自然數， n ? 50 )存在的情形下，探討每一個正多面體的Sicherman 極限4. Sicherman Dice (Crazy Dice) 的延伸探討(1) 不同面數骰子的組合，是否可以找到面數組合相同，但點數配置不同的Crazy Dice( 如4 面與6 面的標準骰子組合，找到4 面與6 面的Crazy Dice)(2) 多個面數相同或不同骰子的組合，是否可以找到面數、個數及點數配置皆不同的Crazy Dice ( 如3 個4 面標準骰子組合， 找到2 個8 面的Crazy Dice)在研究的過程中，我發現以下的現象：(1) Sicherman Dice 的產生，是生成函數因式重新組合的結果(2) Sicherman Dice 是否存在，則視上述重新組合的結果是否有負項產生由於上述的觀察，我使用自行發展的「負項消去」法來檢驗Sicherman 結論的正確性及求得n 面正多面體其對應的Sicherman 極限。同時我也和Col. George Sicherman 取得聯繫， 討論當年他發現Sicherman Dice 的經過及其結論的限制條件，作為本研究未來發展的參考。

相剋作用是指植物在代謝過程中釋放出有毒物質以抑制本身或鄰近植物種子萌發及植株發育生長的過程。一般認為，榕樹是具有相剋作用的常見植物，但很少見到相關的文獻探討。本實驗利用榕樹不同組織萃取液，以小白菜、結球白菜與阿拉伯芥作材料，探討該萃取液對上述植物發芽與生長之影響，結果顯示榕樹葉萃取液所造成之影響較顯著，不同榕樹組織的萃取液、不同濃度的萃取液對不同植物所產生的效果不盡相同，針對不同生長期的植物進行處理所造成的影響亦有差異。進一步以管柱層析法與高壓液相層析法（HPLC）分離葉萃取液，結果發現以正己烷和乙酸乙酯75：25為沖提液的條件下，於HPLC的層析圖中分離時間約8分時所流出的物質具最明顯的抑制作用。電泳剖面分析顯示處理與未處理間有些許蛋白質條帶差異，此變化蛋白可能與植物幼苗對該萃取液之耐受性有關。利用核酸微陣列(microarray)對榕樹萃取液處理之阿拉伯芥植物進行基因表現分析，發現榕樹萃取液對植物部分基因表現也有促進和抑制的情形，經由基因體與蛋白質體分析法可推論出一些受影響之相關基因。 Allelopathy was defined as a phenomenon which certain plant species, by secreting metabolites to the environment, can suppress the growth of themselves, seed germination and/or growth of other plants in the same habitats. Banyan （Ficus microcarpa L.f.） is a plant species in our campus likely to have allelopathy effect. However, documents describing such action on allelopathy were rare. In this study, we applied the crude tissue extracts including leaves, stems, roots of banyan onto the germinating seeds of Pai-Tsai （Brassica rapa L.ssp.chinensis（Rupr.（Olsson）））, Chinese cabbage （Brassica pekinensis Rupr.） and Arabidopsis（Arabidopsis thaliana, ecotype Columbia-0） to study the effects of such plant extract on the germination and seedling growth of other plants. It is found that allelopathic effects on seed germination vary among different tissues used for extract preparation. Different concentration of the extract also yield various degree of allelophathic effects. It is also noted that the application of extract onto the post-germinated sprouts has less effects on plant growth. The extract of leaves was subsequently chromatographed over silica gel using hexane/EtOH gradient solvent system and HPLC. The result showed that there was one fraction about 8 min in the chromatography of HPLC eluted with 25% EtOAc in hexane had the most inhibitory effect. SDS-PAGE analysis on the electrophoretic profiles of water soluble proteins has explored a different band pattern between the treated and non-treated sprouts. The observed band difference might provide a clue for exploring proteins which reacted differently upon the application of extract. DNA microarray analysis on the effect of banyan extract on Arabidopsis gene expression has also been employed to characterize genes responsive to the allelophathic treatment. Cross-comparison between the differential transcript and protein profiles will reveal key regulators in plants experiencing allelophathic condition. \r

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.

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.

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.

蟋蟀聲音與行為的關係密不可分。取北部四種蟋蟀樣本，以數位錄音筆錄製及電腦軟體分析蟋蟀的聲音，並用PCR技術萃取蟋蟀的粒線體DNA(16S)加以分析，藉此和傳統的形態學分類相互比較。結果發現蟋蟀聲音的頻率特性中主頻率的差異在親緣遠近有關聯性，但聲音的時間特性方面則沒有特定關聯，不過聲學分析圖仍可作為單一種的鑑定指標。此外，研究發現此4種蟋蟀的聲音頻率範圍有重疊現象，但主頻率、脈衝比、唧聲率及唧聲長不同，推測雌蟋蟀應是綜合這些特性辨別同種。另一方面，以黑蟋蟀作為研究對象，進行干擾實驗，觀察並繪製出其聲音行為模式; 並將此作為對照，結果發現蟋蟀的生殖行為主要受到雄蟋蟀的聲音支配，而雄蟋蟀則以嗅覺辨別雌蟋蟀位置，決定下一步行動，與視覺較無關係。 Cricket's voice is closely related to the behavior. We select four species of crickets from the northern Taiwan to study the acoustic and mating behaviors. The digital sound recorder and acoustic software are used to analyze their acoustic characters. Furthermore, the PCR technology is used to amplify and sequence parts of mtDNA sequences and the results were compiled as the comparison to the traditional morphological character. The result shows that the resolution in acoustic characters of main frequency, pulse number, chirp rate, and the length of chirp are different among four species, though the minor frequency pattern is overlapping. Moreover, we find that frequency characteristic difference among four species is partly related to their phylogenetic relationship, yet is not seen in time characteristic. It is obvious that difference of acoustic behavior can be regarded as identified index among species. Results of acoustic analysis impel us to infer that the female crickets take the comprehensive acoustic behavior to distinguish their specific male. In addition, behavior pattern and model of Gryllus bimaculatus are established as the comparison of interfering experiment is undertaken. Which results suggest that the mating behavior in cricket is dominated by males’ acoustic behavior, and is initiated by male’s olfactory sense rather than that of sight.

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.

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。

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。