新穎光子晶體材料的研究與開發
本研究目的1.探討催化劑對光子晶體SiO? 合成的影響，依據催化劑對光子晶體製作的數據，統整歸納出不同濃度的氨水催化劑對於SiO? 的吸收光譜與粒徑大小等性質的影響。2.尋找簡易的方式進行光通道的製作。 採用溶膠凝膠法將tetraethylorthosilicate(TEOS) 以氨水做催化劑在乙醇溶液中的水解及縮合反應製作單分散SiO?粉體。 嘗試將細線附著在玻片上進行排列，排列完成後將細線拉起企圖製造一條溝道。 實驗結果,催化劑會影響合成SiO? 的顆粒大小，隨著催化劑濃度增加，顆粒大小也隨之增加。使用細線可成功製造出凹陷的孔道，但目前採用之線仍嫌太粗，欲尋找奈米線材加以取代以製造出更適用之光通道。 ;The purpose of this research is 1.to find out the influence of the catalyst on compounding silica photonic crystals . According to datum , I can generalize the connection between the consistency of catalyst and the particle size of photonic crystal. 2.to find easier method of making the passage of light. I used tetraethylorthosilicate (TEOS) as a reactant and ammonia as the catalyst to react hydrolysis ,water condensation and alcohol condensation in ethanol. I tried to put fine lines on sheet glasses. After the arrangement of the silica particles, I took apart the lines attempting to make sunken ditches. The outcome of this ecperiment show that partical size increases with the consistency of catalyst. We can use fine lines to make the sunken ditches, but the line is not fine enough that I should find much finer lines to make it.
黑擬蛺蝶(Precis iphita iphita)的生存策略
Beings inherit various morphs and natural ability properties from their genetic parents to adapt to the environment and survive; Precis iphita iphita , for instance, is a best example of it. Although few literatures on Precis iphita iphita is found, through long-term field observation on the food intake, nest building, avoiding predator of immature stage, and living domain, the oviposition, plant preference of the adult, different stages of morphs and changes of behavior can be classified obviously when there are environmental or weather changes. The above can help investigate how they interact and influence with plants. This study aims to record and describe various behaviors and surrounding changes for Precis iphita iphita. 生物為適應環境求取生存，從親代遺傳許多形態、本能；黑擬蛺蝶（Precis iphita iphita） 的生活史就是個很好的例子。雖然文獻報告對黑擬蛺蝶的形態與行為描述不多，但藉由野外 長期實地觀察幼蟲的攝食、築巢、躲避天敵，以及成蝶的領域、產卵、食草選擇，可明顯區 分當環境、氣候產生變化時，黑擬蛺蝶不同蟲期的蟲體都有許多外在行為的改變，可作為探 討其與植物間的交互作用和影響。本研究旨在描述黑擬蛺蝶各種不同的行為與當時環境的狀 態，並將實際觀察所得詳實記載，以供他人比較參考。
由心血管超音波影像之動態分析研究主動脈硬化
我們的研究工作有兩項重要成果：首先，根據物理學的彈性體振動模型發現：主動脈硬化的定量分析訊息可由測量主動脈相對於心臟運動的延遲時間明確得知，而且可用目前臨床使用中的心臟超音波儀器直接進行此一測量。在對23 個樣品、每個樣品分析大約50至100 次心跳的初步研究中發現，此一延遲時間是確實存在的，而且延遲時間超過大約0.17秒時，樣品就可能具有動脈硬化的現象。其次，在比照過10 組樣品的數據後發現，上述之延遲時間確定可由體外的胸前超音波掃描（TTE）準確測得，而不需要採用侵入式的經食道超音波掃描（TEE），以免除受測者的不適，及避免副作用的風險，使得此一新方法更具有方便、普遍的優點。而且此一方法也可能由數據的分佈發覺心血管之其他病徵。未來仍需應用此一方法對較多樣品進行研究以進一步確定此診斷方法之可靠性。 Two important results were achieved in this research. Firstly, according to the physical model of elastic oscillation, we found that the qualitative analysis of aorta stiffness could be obtained by a measurement of the delay time of the aorta motion relative to the cardiac motion. This measurement could be carried out with the conventional echocardiography. A preliminary analysis based on 23 samples, with 50 to 100 heartbeats per sample, confirmed the existence of this delay time. Also, a delay time of greater than 0.17 sec might imply the symptom of aorta stiffness. Secondary, after a comparison of 10 samples, the aforementioned delay time could be measured with TaransThoracic Echo (TTE) instead of TransEsophadeal Echo (TEE), in which the later is invasive while the former is not. Therefore, the discomfort of the patient and the risk of invasive operation can be avoided, making this new method more convenient and more common to accomplish. This method could also clearly discern some abnormal cardiac performance. A large-scale study with this method should be conducted in the future.
超聲波應用之研究
在實驗用共振法測量聲音在固體、液體、氣體中的駐波聲場，測量各介質中的聲速。研究超聲波在液體中的空腔效應，鋁箔在不同液體受空腔效應所破損面積與時間略成正比，並發現在水與各濃度的洗潔精水溶液中以水的破損效果最明顯。另外利用1.65MHz 高頻超聲波打入水中，因駐波使水有疏密不同產生狹縫，以雷射通過狹縫有光的繞射花紋產生，由干涉條紋可推估駐波波長。利用閃頻共振法研究光彈材料超聲波場，且發展出以肉眼觀測的裝置，由光彈材料的花紋級數與應力研究中，發現花紋級數與應力成正相關，由聲場中的花紋顏色判斷所受應力大小，並發現超聲波不僅有聲場產生並伴隨熱效應，會影響觀測花紋級數。This project began by studying the fundamental properties of acoustic waves, the relationship between its velocity, frequency and wavelength. Experiments regarding the distribution of sound waves in different mediums, and the induction of resonance in solid, liquid and gaseous materials were conducted. Results from utilizing suspending method to confirm theoretical prediction of sound velocity was accurate, and the sound wave patterns in photo-elastic materials were observed. It was also observed that an aluminum foil would be cut in an ultrasonic cleaning device. The effects of different liquids such as water and detergents on cleaning effectiveness were then experimentally determined, taking into account factors such as viscosity. From reference materials, we learned that ultrasonic waves would create Caritation in liquids. Traditionally, sound waves are expected to exhibit only longitudinal waves, yet in this study it was discovered that the residual\r stresses from resonance in photo-elastic materials also indicate the existence of transverse waves.
輸贏一線間-淘汰賽的相關探討
單淘汰賽是一種失敗一次即遭淘汰的賽制；在此假定每位選手都有一相對應的能力數值，本文主要探討在均高的單淘汰賽程表之下，若賽程安排完全依照種子安排原則(亦即最強的選手對最弱的選手、次強隊次弱….)，則對於能力越強的選手越有保障，直觀上而言能力最強的選手應有最大的奪冠機率，探討此種賽程安排是否滿足能力較強的選手有較大的勝率？因發現在某些特殊的選手能力數值分佈之下會發生次強選手勝率大於最強選手的情況，令A、B代表最強與次強選手，P(A)、P(B)代表A、B奪冠的機率，故擬定P(B)/ P(A)為參考依據，尋求P(B)/ P(A)的最大值發生處作為最極端的狀況。發現四位選手的情況下，P(B) / P(A)最大值 = 1；八位選手的情況下，P(B) / P(A)最大值=(196+98) / 343=1.0938，當選手數為2n時，P(B)/ P(A)最大值隨n的增加而遞增。
Knockout Tournament is a highly competitive system in which any player losing a game can no longer play in the tournament. Here we suppose that every player has a numerical value that corresponds to his ability. We consider a totally-seeded knockout tournament with 2n players where in the first round, the strongest player matches the weakest player, the second strongest player matches the second weakest player, and so on. We examine whether a stronger player always has a greater probability of winning the tournament. The answer is in the affirmative for n = 2. For a tournament with eight players(n = 3), the situation is much more complicated. In certain cases, the second strongest player has the greatest probability of winning the tournament. Specifically, let A and B denote the strongest and second strongest players, P(A) and P(B) their respective probability of winning the tournament. We find that the maximum value of P(B)/P(A)equals (196+98) / 343 = 1.0938. For n > 3, we have not obtained the maximum value of P(B) / P(A) . However, it can be readily seen that the maximum value of P(B) / P(A) is non-decreasing as n increases.
拖線溜點
原題目是環球城市盃中，一個圖論的問題。而題目提供了一個證明，是證 明此種連線都是偶數的圖形，一定會在三的倍數邊形成立。在經過一番思考過 後，我們希望能將原本的偶數連線性質加以驗證，並確定奇存在性。此時，我們 也不禁聯想到：奇數是否也有所特別的性質。因此，我們也向奇數連線做研究。 就在平面得到了部分結論的同時，我們想到這個問題是否可以推廣至三維 空間。然而在推至三維空間的過程中，我們又聯想到，另一種平面：球面。在球 面上放點，能否也找到一些不同的性質。因此，我們分別從平面、球面、立體圖 下手。 基本上，探討平面和立體問題的方法，是以土法煉鋼的方式來求出結果。 然而這種圖論的問題，不可能嘗試到無限多點的情形。因此，我們是著找出一個 關鍵的key，那就是結合性質和外接合性質。以這兩種方法，我們可以將一個簡 單的基本圖形，推向無限多點和無限多邊的情況。 接下來，還有討論一些特殊狀況，例如： deg v＝3n+1，探討其結果。 最後得到的結論是： 1、平面偶圖成立的條件為：此多邊形為三倍數邊形， 而且除了內 部一、二、四點以外， 其他點數都可以成為偶圖。 2、平面奇圖成立的條件為：奇數邊形的情形下，除了三點以外，其 他的內部奇數點的都可以成為奇圖。偶數情形下， 除了四 點以外， 其他的內部奇數點的都可以成為偶圖。 3、三角形平面圖，d eg n 皆為m 成立的條件：2＜ m＜ 6( m? N ) 4、三角形內外任意點d eg 皆為3n ( n ? N )的成立條件： 三角形內部4 x+1 個點( x ? N )。 5、三角形內外任意點d eg 皆為3n+1 ( n ? N )的成立條件： 三角形內部3 x 個點( x ? N )。 6、立體偶圖n 頂點(n＞4)面體的成立條件為： 內部點數為5m+ n- 3、5m+ n- 1、5m+ n、5m+ n +1、5m+ n +3。(m 為大於或等於零的整數) 7、立體奇圖四面體的成立條件為： 內部點數為偶數皆存在。 The original problem is a question of Graph Theory in IMTOT ,which provides\r a proof that proving the figure which its linking-line number is even ,should also be\r contented in the triple-sides figure. After profound consideration ,we try to make sure\r the existence of the properties the we mentioned above. Meanwhile ,it also occurs to\r us that whether the properties would be contented ,in the figure which its linking-line\r number is odd. So we make our way to it. Additionally ,three-dimensional and\r spherical figures are part of our research as well.\r Basically ,we discuss the problem in two-dimensional and three-dimensional\r aspects with the simplest method .However ,it is impossible to discuss the problem in\r unlimited dots .Hence , we are going to find a “key” to solve this problem .As a\r result ,we can find a simple basic-picture , and expand to infinite-multiple lateral\r pictures.\r Next step ,we also discussed some special situations , for example: for each\r point v , deg v=3n+1.\r At last the conclusion is following:\r 1、The conditions of linking-line number is even: triple-sides. And the amount of\r points inside the figure is without 1,2,and 3.\r 2、The conditions of linking-line number is odd: In the odd-sides figure , all number\r of the points inside the figure can be content without 3 point. In the even-sides\r figure , all number of the points inside the figure can be content without 4 point.\r 3、In a triangle , each point’s deg is the same number m: 2
Dynamic Geometry and Problem Solving
Within the framework of the new educational model for mathematics based on constructivism, results are presented of the design, application, and evaluation processes of a series of didactic sequences aimed at developing the student’s abilities for problem solving as part of the geometry curriculum for technological preparatory schools, using the Cabri-Geometre II software. In this case, subjects of study were ten newly enrolled students from CETis 18 preparatory school in Mexicali, Baja California, Mexico. The theoretical basis for this work is the constructivist approach, mainly emphasizing Mashbits views (1997) regarding problem solving. This didactic proposal was longitudinally applied in a quasi-experimental qualitative design under the following analysis categories: problem solving skills and the impact of Cabri- Geometre II in geometry learning. Recognizing the potentiality this research can have with the proper follow-up, it is intended to include it in the preparatory school curricula. For this purpose, teachers should be trained to focus their work on learning instead of on teaching. As a result of this, designing educational programs will require for teachers to become more knowledgeable not only in discipline, but in the use of computer technology, the teaching process, learning, and the students themselves. The final objective of this project is to instill educators to play this new role. As a final point, conclusions on various psychological, pedagogical, and technological aspects are given placing emphasis on the creation of learning situations with their appropriate theoretical support. Using the Cabri-Geometre II as a resource, these situations will provide geometry teaching with a more dynamic and interesting concept applicable to real-life situations.
討論顯微鏡下的化學反應
由於想了解化學反應的微觀形態，我們設計微型化學反應裝置來比較巨觀(傳統型)與微觀(創新型)化學反應間的差異，並探討其實用及環保方面的問題。在顯微鏡底下，我們觀察化學反應的沉澱結晶及電解反應，嘗試以各項變因(溫度、濃度、聲波…等)來觀察其結晶的型態。我們已成功地將實驗藥品用量減少到一滴(約0.04ml)，並以微觀的角度觀察化學反應的過程。在實驗中，發現反應進行時，粒子會不斷流動，經查證後為愛因斯坦所提出的布朗運動，並且測得硫顆粒的直徑大小約4.2 ~ 6.7 微米。不同聲波所造成硫粒子的移動速率不同，而不同溫度的部份，我們發現→每增加十度硫粒子移動速率增加約兩倍。在面積4.392×10-4cm2 範圍內大約有250~300 顆硫沉澱的粒子。本實驗成功地將顯微鏡應用在化學領域上，若將此實驗推廣，可達到污染少、觀察實驗的時間短、用量少的目標。此實驗是邁向化學微觀世界，一種值得嘗試且創新的方法。In order to compare the differences between the chemical reactions of macroscopic reactor and microscopic reactor, we have designed a device of chemical reaction and researched into the problems of their environmental protections and practical aspects. Under the microscope, we observed not only their precipitating crystal compound from the chemical reaction and electrolytic reation but their types of crystal. We have successfully reduced the dose to one drop ( about 0.04ml) and observed the process of their chemical reaction from the angle of microscopic reactor. During performing the experiment, we found the particles would keep flowing while the reaction was working. It was proved as "Brown motion" introduced by Einstein. The diameter of these particles were around 4.2~6.7μm. We find that different sound waves and temperatures,the motion speeds are quite different. And the movement rate increases about two times as the sulfer particles increase 10℃ each time .Within the measure of area of 4.392×10-4cm2,there are 250~300 sulfer particles.The experiment has successfully used a microscope in the field of chemistry. If we popularize the experiment, we can reach the goal of less pollution, fewer the dose and time-saving observation. It’s an innovation to step to the world of chemical microscope world.