2006年

Feeding behavior is the action which animals depend on maintain livelihood. Snakes usually use the three following ways to catch their preys: winding, venom-releasing and pressing their game to death. However, previews study is rare about the feeding behavior of Ramphotyphlops braminus. This puzzles us, prompting us to do in-depth research on it. When performing an experiment, we will use the camera with infrared function to record entire experiment and the obtained data will transform the graph. Our result shows the feeding behavior of R.braminus is a new way to catch their game, and the minute process of this special way is also written down in our report. We hope that the result can let everyone be clear about Ramphotyphlops braminus of soil ecosystem status, and it is an essential contribution for building the archive of Family Typhlopidae. 攝食行為是動物賴以維生的行為。在蛇類中，常見的捕捉方式有：纏繞、 使用毒液、壓斃等三種類型。但，文獻中卻沒有任何有關於鉤盲蛇(Ramphotyphlops braminus)的捕食行為。這使我們感到疑惑，並想深入探討。在實驗進行當中，我們使用紅外線攝影機將實驗全程錄製下來，並將所得的數據轉化成圖表。而其結果顯示鉤盲蛇(Ramphotyphlops braminus)的捕食行為是一種全新的模式，這種模式的詳細過程也被我們全部收錄到報告中。我們希望做出來的結果能讓大家對鉤盲蛇(Ramphotyphlops braminus)在土壤生態系中的地位更加了解，而且對於建立盲蛇科(Typhlopidae)資料庫有實質的貢獻。

The Look and Say sequence is produced by describing the appearance of the previous row. For example, start with “1,” which can be described as “one 1,” and therefore the second row is “11,” which is "two 1s," making the third row “21,” the fourth row “1211,”and so on. The main goal of this study is to work out the exact formula for this sequence, which means given the row number n, we can know at once what the n-th row is without having to start from the first row and doing the look-and-say iteration for n-1 times. Some of the methods used include dividing groups, repetition and cracks. The formula we derived speeds up the calculation and gives us a better understanding of the look and say sequence.「外觀數列」為依照外觀產生下一列的數列，第一列為「1」，第二列描述第一列「1 個1」而為「11」，第三列則描述第二列「2 個1」而為「21」，第四列「1211」，依此類推。本研究針對外觀數列的各項數學性質作研究探討，並由此推導出外觀數列的一般式，即給定第n 列就可知道該列的內容。我們運用了分組、重複性以及裂縫的方法分析數列，最後得到了其一般式，此一般式有助於運算速度的加快以及我們對數列性質的了解。

本實驗利用喇叭、薄膜電極、波型產生器、鎖相放大器、及750 介面卡組合一套系統,此系統可使偵測精密度大幅提升(±4*10-5cm),使得水槽及地表模型尺度變小(40*22*35cm),因此可節省實驗的成本與時間我們在坡度實驗中,發現坡度在3 度左右,淺化係數都超過3. 對照台灣沿岸發生海嘯的歷史記載,確實在台灣東北角及西南沿岸等坡度為三度之地區都發生較明顯的海嘯危害. 反之,坡度在四度以上的東岸其海嘯波高都非常低.最後再藉著硬體系統及電腦2D 動畫模擬的整合,使我們可方便掌握波浪在不同坡度及位置,其波長及波高變化比,如此有助於預估及說明海嘯隨地形變化的狀況.By using the horn, membranous electrodes, function generator, phase-locked amplifier, and Science Workshop 750, we plan to assemble a tsunami simulation system in which the precision can be getting increased (±4*10-5cm) .Because of the improvement of its precision, the size of the tank and of the surface models will become smaller .As a result, the money and time spent on the experiment will be spare. When experimenting on the influence of inclination of the landforms, we observed that when the inclination reaches about 3 degrees, the shoaling coefficient exceeded 3 .The result of our experiment can provide an explanation to the tsunami on the northeast and southwest coast of Taiwan .According to the historical records, the disastrous tsunami happens frequently on the northeast and southwest coast of Taiwan where its inclination is also about 3 degrees as well .On the other hand, on the eastern coast, the wave height is lower and its inclination exceeds 4 degrees .Apparently, our experimenting result is correspond to the natural phenomena in Taiwan’s coast . Besides, with the help of hardware system and computer 2D animation simulation, we can easily measure the wavelength and wave height scale of the wave in different inclinations and positions. Therefore, this tsunami simulation system can provide a great help to estimate and explain the phenomena of tsunami which may change its condition in different landforms.

Size-exclusion chromatography (SEC) is often used to determine the molecular weights of and separate polymers and proteins. The porous packing of the SEC column effects the separation of molecules, with larger molecules eluting earlier. Interest in high-speed SEC for larger molecules has been building, especially for combinatorial polymerization reactions and online SEC-MS applications. Mechanical stability of the packing, which siliceous materials have more of than polymeric ones, therefore needs to be improved. Several silicas have been explored but limited pore sizes and pore volumes have restricted their usage to separating small molecules. Siliceous MCF templated using oil-in-water microemulsions has good potential for SEC packing because it has ultralarge pore size (20-50 nm), high porosity and sturdy skeleton. However conventional MCF consists of highly irregular particles and hence cannot be used as packing.

The paper is to research the method how to prevent the torque down under the higher rotation of the single cylinder with two stroke’s engine and increasing the engine’s torque oppositely. By the process of adjusting （1）changing the weight and the position of the balance block（2） adjusting the exhausting time of the outlet valve（3）to decrease the weight and structure of the crank itself adequately. it is find that the engine’s torque was increased at the situation of higher rotational engine. After the adjusting of the process we have the following result：（1）at the higher revolution zone of the engine. the torque can be maintained and increased（2）the higher revolute efficiently value can be obtained by the correct adjusting of the exhaust time of the outlet valve without increasing the fuel.本研究主要是探討單汽缸二行程高轉速引擎在高轉速時扭力能延遲下降，使扭力增加。我們是利用二行程引擎高效率的結構和現有空間來提升引擎效能。經(1)改變曲軸配重塊之重量及位子移動 (2)調整引擎排氣時間 (3)適度減輕曲軸重量及結構等三項，改良後證明，確定能使扭力提升，和延伸到較高的轉速區。經過調整程序，可獲下列重要結果：(1)在引擎高轉速時，可增加較大的扭力值 (2)藉由適當的排氣時間調整，在不增加燃油供給條件下，可獲得較高的迴轉效率。

本研究利用麥克風與相關電腦設備，結合成自製頻譜儀用以觀測多種情況下蜜蜂的聲音頻率。若將蜜蜂的翅膀加以修剪，可測得有不同的頻率，解析頻率發現「翅膀為主要發聲點，但去除翅膀仍有高頻的發聲，且有三種不同的頻率。」將蜜蜂置於不同溫度下，解析頻率得知「一定溫度範圍內，溫度越高蜜蜂發聲頻率越高，反之亦然。」幼期在胸部塗顏料使絨毛無法生長，去除雙翅後，仍有頻率相近的發聲，得知「胸部絨毛不是造成高頻的原因。」靜置５分鐘，待蜜蜂停止發聲後，剪去腳、挑弄蜜蜂會發出高頻，得知「情緒是引起高頻的原因。」將蜜蜂的翅膀加以修剪，分別放回蜂窩口，發現「同一族群蜜蜂可用發聲頻率來辨別同伴。」比較義大利蜂及中華蜜蜂，得知「在多種情況下中華蜜蜂發聲頻率皆較義大利蜂高約７０Hz。」因此本實驗之結論並不受蜂種影響。The study, capitalizing on a hand-made frequency divider, the microphone and computerized equipment, observes a variety of frequency of sound given off by bees. We read different frequencies from the apparatus when the bee’s wings were trimmed. Analyzing it, we discover that the bee’s winds are major source of its sound, but it still gives out high-frequency sound when the wings were completely cut off.” After analyzing the frequency, we discover that within a certain temperature range the higher the temperature is, the higher the frequency is, and vice versa. In one experiment, we painted the thorax at its pupal stage to stop the bee from growing fine hairs. Even though the wings had been removed, it still gave out high-frequency sound. We, therefore, conclude that fine hairs on the thorax have nothing to do with the making of the sound. In another experiment, bees were placed in an undisturbed environment until they are completely silent. Then, some of the bee’s legs were cut off, while others were provoked. And all the bees make high-frequency sound in the process. We make a hypothesis that emotion could be the cause of bees’ sound-making. The bees with different trimmed wings were put back to the beehive; the bees can still recognize one another by the different sound frequencies. If we compare A. m. ligustica with A. c. cerana under different conditions, we find that the frequency from the latter is about 70 Hz higher than that form the former.

In our daily life, objects and the contacts between objects they will have mutually affect each other, some initially chaotic systems after a sufficient amount of time will mutually correct each other, and finally achieve synchronization (example: the speed of bird and fish migration, market prices, infantry…), although some are unable to achieve this. We will illustrate and explain the synchronization system, its process and discover the conditions for synchronization. Using linking concepts, we will integrate the coupled map lattices with global coupling and coupled map lattices with intermediate-range models into a synchronization mode in order to simulate a synchronization system. We first used a small system of n≦50 to obtain results that will demonstrate the linking concepts: 1. The more chaotic a system, a longer period of time is required for synchronization. 2. An increase in the number of individual objects requires an increase in the range of concepts and the amount of time in order to achieve an in depth synchronization. 3. Initial concept values which randomly effect synchronization critical point conditions are not obvious in a mathematically incorrect graph. In a closer look, when we increased the synchronization to n≦400 and the number of times to t-->100,000 we discovered:1. Using the function G(x) we hoped the results from the graph after apply the function and correction able to overlap and test with “Scaling and Universality in Transition to Synchronous Chaos with Local-Global Interactions”, but the part which overlapped the measurements was not identical: 2. We can use the significance of the critical point and the Interactive Process to find the approximate value of the critical value up to 4 digits following the decimal point. 3. We can also use the approximate value to find out the range for the simultaneous conditions and the various points on the system itself, as well as obtain a negative correlation between them, and then it can be similarly expressed with using a curve. A computer can calculate values with this kind of enumerating method, even without any special resolution capabilities to quickly obtain large amounts of approximate values of simultaneous conditions, this is especially true when calculating unfamiliar systems. 日常生活中，物件與物件的接觸，彼此會互相影響，有些原本雜亂的系統再經過充裕時間的互相修正後，最後竟能達成同步(例如：鳥群、魚群遷徙的速度、市場價格、行軍步伐…)，有些則不能。因此，我們試著利用描述同步系統的模型，觀察系統同步的過程，並且找出同步的條件。由連結的觀點，我們將Coupled map lattices with global coupling 和Coupled map lattices with intermediate-range 模型的優點整合成Synchronization mode 去模擬同步系統。我們先用小系統(n≦50)得到能印證連結觀點的結果：(一)、系統越雜亂，就需要稍長的時間同步；(二)、個體數越多時，各點需要更大範圍的點數去影響於每單位時間內以及更深的影響才能同步；(三)、起始值隨機影響同步臨界條件並不明顯，在誤差範圍內。更進一步，我們將系統推向n≦400 點,t→100,000 次，我們發現：(一)、在”G(x)”我們希望能將圖形經過函數修正之後能疊和，驗證”Scaling and Universality In Transition to Synchronous Chaos with Local-Global Interactions ”中的結果，但只有部分疊和，尺度不相同；(二)、可以直接利用臨界點的意義用十分逼近法求出臨界值的近似值到小數後四位；(三)、我們用近似值也能發現同步條件與系統各點本身可跳躍的數值範圍是負相關，可用曲線去近似。這種窮舉方式，交由電腦運算，不需要特別的解析能力就能夠快速且大量求得同步條件的近似值，尤其在運算不熟悉的系統時。

在先備知識中，我們知道在缺少營養鹽及紫外線傷害下，浮游藻類的葉綠體會因為過氧化物（R.O.S.）的增加而受到破壞，進而影響光合作用的進行，甚至導致死亡。所以確實了解常見浮游藻類生理狀態和環境的影響，以期待未來可利用大幅度提高浮游藻類生產力的方式有效降低溫室效應的影響為本實驗的主要目的。故實驗設計針對兩種常見的海洋種浮游藻類（Tetra、Ske），在不同紫外線光譜（UVAB、UVC）的照射下，觀察R.O.S.的產生量和T-T dimer的表現狀況，並對照兩者之間的關係。結果我們發現：綠藻（Tetra）和矽藻（Ske）在UVAB、UVC 的照射下皆會產生R.O.S.，且綠藻產生的量較少；但在UVC 照射下皆有DNA 損傷（產生T-T dimer）。故推估並不是綠藻（Tetra）擁有紫外線的特殊防禦機制，而是能較有效地代謝R.O.S.。As we know, under the condition of unorganized salt’s shortage and the harm of the ultraviolet ray, the phytoplankton’s chloroplast will be destroyed because of the increasing peroxide (R.O.S.). Furthermore, the ultraviolet ray will have an effect on the process of photosynthesis, and even result in the death of phytoplankton. So, we intend to promote the production of phytoplankton in order to lower the influence of greenhouse effect by probing into the environmental influence on the physiology of phytoplankton. The experimental is designed to observe two common marine phytoplankton: Tetra and Ske. By close observing Tetra and Ske exposed to different wavelength of ultraviolet way (UVAB and UVC ), we contrast the production of R.O.S. with the appearing of T-T dimer. We observe that both Tetra and Ske will produce R.O.S. after being exposed to UVAB and UVC , but Tetra produce less than Ske, and that UVC will do harm to both the DNA of Tetra and Ske (producing T-T dimer). Based on the result of the experiment we estimate that Tetra can catobolize R.O.S. efficiently instead of having a unique defensive mechanism against ultraviolet ray (UVAB and UVC under discussion in this experiment.)

本研究報告以Brocard Point 為核心，所用到的性質均先證明，以確認其正確性，並推演出一些其他的性質，藉由這些性質導出幾何不等式。內容可概分為四部份：(1)以Brocard Angle 及已知的或推演出的基本性質，導出一些不等式。(2)結合「法格乃諾問題」、「費馬點」、「尤拉公式」導出幾個幾何不等式。尤其是三角形邊長與面積，外接、內切圓半徑與邊長間的不等關係，頗為有趣。(3)以向量為工具，分別計算內、重、垂心與Brocard Point 間的距離，並導出邊長的不等關係。其中由內心及重心所導出的不等式，清楚俐落；垂心所導出的不等式則較為複雜。(4)以Brocard Cirle 與內、重心間的關係，導出一系列的不等式。其中Weitgenberk 不等式的無意發現，令我們印象深刻。The Discovery of Geometry Inequalities by Brocard Point This paper takes Brocard Point as a core. We proved some properties about Brocard geometry to confirm its accuracy, and deduce some other properties, and then derive some geometry inequalities by these properties. The content may divide into four parts: a) Derives geometry inequality by Brocard Angle, Crux Mathematicorum and properties which known or deduced. b) Unifies "Fagnano problem", "Fermat Point", "Euler formula" to derive several geometry inequalities. In particular the inequalities between triangle area and length of side, or circumradius inradius and the length of side, is quite interesting. c) Derives geometry inequalities about length of sides in triangle by the distances between incenter centroid circumcenter and Brocard Point. Especially, these inequalities were elegant which derived by incenter and centroid, but it was complicated derived by orthocenter. d) According to the relation about incenter centroid and Brocard Circle derives a series of inequalities. Discover Weitgenberk inequality makes us excited.

本研究主要的目的是在開發二氧化碳製造、過濾與循環的整合型水族養殖系統。二氧化碳的產製是以基於發酵原理，並搭配具有純化二氧化碳作用的水濾裝置，發酵環境溫度以水族箱內的水來維持，循環過程中並搭配外部過濾器，所有容器均由保特瓶改裝完成，整合成一套價廉、環保且具有高效率的水族養殖系統。由實驗結果可得知，二砂糖發酵對於二氧化碳產生率而言，其最佳發酵環境溫度範圍25℃~35℃，一般水族箱的水溫即可保持在此一溫度範圍。過濾系統則使用光電比色計與一般市售過濾器相比較，亦有令人滿意的效果。本實驗除了研究以二砂糖發酵之外，還希望更進一步地朝向廚餘減量方面開發其他發酵材料，希望能為環保盡一份心力。;The purpose of this study is to develop an integrated system of aquatic breeding with the functions of producing carbon dioxide, filtering and circulating, where carbon dioxide is produced based on fermentative theorem and purified by the water filtering; the environmental temperature of fermentation is maintained by the water in the aquarium and circulating is through an external filter. All the containers are made of PET bottles and thus integrated a cheap, environmentally friendly and high efficient system of aquatic breeding. According to the experimental result, for the producing rate of carbon dioxide, the best fermentative temperature of NO.2 granulated sugar is 25℃~35℃. With a photocell colorimeter to compare the function of the self-made filter with that of the filters on the market, one can find it’s comparable. In addition to the fermentation of NO.2 granulated sugar, the study is also expected to develop other fermentative materials to reduce kitchen waste for environmental protection.