雙叉桿菌於不同優酪乳中抗氧化性之研究
The objectives of this investigation were to evaluate the growth conditions and the antioxidant activities of fermented black bean soy milk(BBSM) with Bifidobacterium longum B6 and 15708 cultured in four media, namely, ( BBSM ( 100%)+ 1% glucose ), ( BBSM (100%)), ( BBSM (50%) + milk (50%)), (milk (100%)) . These results indicated that; (1) both strains attained viable cell numbers about 7.19~9.53 log CFU/ml after 18 hrs of incubation and were in the order of ( milk (100%))＞( BBSM (50%) + milk (50%))＞ ( BBSM (100%) + 1% glucose)＞( BBSM (100%)), (2) both strains in ( BBSM (100%)) exhibited higher pH value ranging from 4.79 to 5.50 , but lower titratable acidity(%) ranging from 0.27% to 0.61% than the three other media after 48h of fermentation, (3) both strains displayed an even smaller tolerance to simulated gastric juice at pH = 2.0 for 3h, especially in ( BBSM(100%)), while in simulated gastric juice at pH =3.0 for 3h had higher tolerance , (4) both strains had high resistance ranging from 72.51% to 92.62% to 0.3% bile solution for 12h, (5) the reducing power of ( BBSM (100%)) was more excellent than that of ( milk (100%)), (6) the scavenging effect of yogurt (BBSM ( 100%) + 1% glucose) on DPPH radicals was significantly higher than that of ( milk (100%)), (7) In general, at ten- fold dilution the chelating effect on copper ions of these four un-fermented media except ( milk (100%)) was significantly higher than that of fermented media with B.longum B6 or 15708. 本研究是探討雙叉桿菌(Bifidobacterium longum B6及15708)在四種發酵基質(【黑豆奶(100%)+1%葡萄糖】、【黑豆奶(100%)】、【黑豆奶(50%)+牛奶(50%)】、【牛奶(100%)】)中的生長情形及抗氧化活性。結果顯示： (一) 兩株菌在四種培養基中的生長菌數大小順序如下：【牛奶(100%)】＞【黑豆奶(50%)+牛奶(50%)】＞【黑豆奶(100%)+1%葡萄糖】＞【黑豆奶(100%)】。 (二) 兩株菌在【黑豆奶(100%)】的pH值比較高於其他三種優酪乳，而最終發酵可滴定酸度比較低於其他三種優酪乳。(三) 兩株菌於pH2.0環境下，在【黑豆奶(100%)】優酪乳中耐酸性很低，而於pH3.0環境下卻有很高的耐酸性。(四) 兩株菌對0.3%膽鹽之耐受性均很高為72.52%~92.62%。(五) 在稀釋10倍的四種基質中，不論發酵前或發酵後的還原力皆以【黑豆奶(100%)】為最高，【牛奶(100%)】為最低。(六) 在濃度稀釋10倍時，【黑豆奶(100%)+1%葡萄糖】對DPPH‧自由基清除率明顯比【牛奶(100%)】高。(七) 在濃度稀釋10倍的四種優酪乳中，除【牛奶(100%)】外，發酵後比未發酵的銅離子螯合率明顯降低。
Self Assembly Mechanism of Water Drotlets
這是一系列關於水蒸氣冷凝為極細微小水珠的長程實驗。其中可以分為下列三個階段：第一階段是基礎實驗。將水氣導入至潔淨的光滑表面上(蓋玻片)，觀察水珠冷凝的機制。第二階段是在外加磁場及電場作用下，將水氣導入至潔淨的光滑表面（蓋玻片），觀察水珠冷凝的機制。這部分的實驗推翻了一般「水分子是電中性，在電場或磁場中不受影響 」的刻板觀念！實驗所呈現出來的冷凝水珠，不但有明確的自我組成模式( Self assembly pattern)。並且發現：電場會增速凝結水珠的成長(Aggregation)，而磁場則會抑制凝結水珠的成長。第三階段是將水蒸氣導引至超聲波的環境中：我們先將超聲波訊號產生器(變頻、定頻)面向於載台旁，再讓水氣導入至潔淨的光滑表面上(蓋玻片)，觀察冷凝水珠的機制。當使用固定頻率超聲波波源，我們發現：在超聲波場中水珠的成長會受到抑制，且成長速率會隨著頻率的升高而逐漸減小。第一階段與第二階段的實驗結果與討論已分別發表於2004 年及2005 年的台灣國際科學展覽報告中，本作品將詳述第三階段。 This experiment explores the basic nature of the condensation of water vapor into droplets on the surfaces of cover glasses. This condensation occurs because of the difference in temperature between the water vapor and the cover glass. The condensation process is observed under a microscope. The growth of the droplets can be described as: nucleation, aggregation (piling up) and coalescence. The growth is irrelevant to surfaces or environments. It is found that the temperature difference of moist air over the cover glass do not affect the nucleation size of the droplets in simple plain surroundings; while the change of flow rate does. In general, the coalescence is speeded up at higher temperatures. Furthermore, the effects of electric fields 、magnetic fields and ultrasonic waves are also studied. It can be observed that the size of water droplets become smaller and grow more uniformly under magnetic fields or imposed ultrasonic waves; also, the aggregation rate is decreased by imposed magnetic fields or ultrasonic waves, and it is increased by imposed electric fields. These effects of magnetic fields 、electric fields and imposed ultrasonic waves might be related to the flow conditions and the vibration of surrounding air in the system. This experiment provides the first step in the understanding of the formation of water droplets and their self assembly mechanism in different environment.
Bezier曲線與蚶線間之關聯性的探討與推廣
在這篇報告中，我們以貝斯曲線的做圖原理建立出一種新的曲線－環狀貝斯曲線，進而得到不少有趣的結果。我們發現有名的古典曲線－蚶線，也是屬於二次環狀貝斯曲線。軌跡方程式為：，此時，係數恰符合二項式定理。之後我們推廣至n次環狀貝斯曲線的軌跡方程式：，也符合二項式定理。
在複數平面上，給定z0、z1、z2三點，我們定義出一個二次變換 ，若，，可映射成蚶線的圖形；若z∈實數，則可映射成拋物線。利用此結果類推我們找到一個複數平面上由 z0、z1、...、zn 所決定的n次變換將以原點為圓心的單位圓，映射成n次環狀Bezier曲線。
In this essay, we use the method of forming a Bezier Curve to establish a new curve, circular Bezier Curve, and find a lot of interesting results. We discover the famous classical curve ＂limacon＂, which belongs to the Quadratic Circular Bezier Curve. The locus of Quadratic Circular Bezier Curve is, where. Its coefficients match the binomial theorem. Then we apply it to the locus of nth-circular Bezier Curve:, and it also matches the binomial theorem.On the complex plane, we define a quadratic transformation corresponding to three points—z0,z1 and z2 as .If , where , a limacon is mapped. If z is a real number, a parabola is mapped. With this result, we will find a nth transformation defined by z0、z1、...、zn on the complex plane. It will form a nth-circular Bezier Curve with unit circle centering on the origin.
奇妙的三維世界
本實作以光學全像術為基礎，拍攝出三維立體的影像。內容主要為分別製作「穿透式」全像片、「反射式」全像片及「彩虹」全像片等三部份。其中，在反射式全像片中，嘗試以不同數量的光束來拍攝。發現以單光束法拍攝出的全像片比較容易成功，但重建影像的視角與效果都不如雙光束拍攝法來的好。在拍攝彩虹全像片的過程中我們令狹縫為變因，做有加狹縫與未加狹縫的實驗，實驗發現效果不同。並以改變狹縫的角度、方位，來觀察底片的變化。最後，觀察出豐富多樣的彩虹變化型態。全像片可重建拍攝的物光與參考光，並顯現拍攝物的三維狀態。可應用於信用卡、紙鈔防偽，廠商標籤，附加商品（如鑰匙圈、貼紙），廣告看板等，用途廣泛。 The purpose of this project is to construct the 3-dimensional images utilized optical holography. The holograms we made can be categorized into three main types: transmission, reflection and rainbow. In reflection hologram, we have tried to construct the hologram by the use of different number of light beams. It could be found that the reconstructed image of the hologram formed by a single beam is better than those of the hologram formed by two beams. However, the field of view and image quality of the two-beam hologram was better than those of single-beam hologram. In rainbow hologram, we varied the orientation and position of slit to investigate the quality of the reconstructed images. The reconstructed images displayed rainbow image diversity. In application, the holograms can display three-dimensional images by reconstructing the hologram. In addition, the holograms are in widespread applied in security applications of credit card、banknotes、labels、stickers etc.
重複圖形
「重複圖形」是本篇報告研究的問題，我們利用「方程式」建立一個尋找重複圖形，並証明其個數的方法。利用此方法得出下面的結論：1.會形成lap 2 的凸多邊形只有2 種，即三角形和四邊形。(1)「lap 2 三角形」只有1 種，即等腰直角三角形。(2)「lap 2 四邊形」只有1 種，即二邊之比為1： 且內角是45°、135°的平行四邊形。2.會形成lap 3 的凸多邊形只有2 種，即三角形和四邊形。(1)「lap 3 三角形」只有1 種，即內角為30°–60°–90°的直角三角形。3.其他的lap k 三角形：(1)任意內角為30°–60°–90°的直角三角形都是lap 3k²，其中k是正整數。(2)邊長比為1：m： 的直角三角形是lap (m²+1)k²三角形，其中m、k是正整數。
To find repeated figures, we construct a method to search them with the help of algebraic equations. Here we arrive at：1. There are only two kinds of lap 2 convex polygons, triangles and quadrilaterals. (1) The only lap 2 triangle is isogonal right-angled. (2) The only lap 2 quadrilateral is the one that contains angles 45°, 90° and two neighboring sides with the ratio 1: . 2. There are also two kinds of lap 3 convex polygons, triangles and quadrilaterals. (1) The only lap 3 triangle is the one with angles 30°, 60° and 90°. 3. Other kinds of lap k triangles are listed as following: (1) A triangle with angles 30o, 60°, 90° is a lap 3k², the k is a natural number. (2) A right-angled triangle whose ratio is 1 : m : is a lap (m2+1)k², the m and the k are natural numbers.
共點圓、共圓點
我的研究是利用一些特殊的手法來探討所有情況皆會產生共點圓或共圓點。在一個由四條直線(無平行線組、無共點)所構成的圖形中，可以找到四個三角形及它們的外接圓。我知道它會共點，在此稱其為限制點。且若再添加一條直線，則可以任意的取出四條直線，分別找出它的限制點，而這些限制點又會共圓，吾稱其為限制圓。我欲證明此種情況會不斷延續下去。即是六條線時又會有限制點，七條線時又會有限制圓…。在本研究中，我利用了數學歸納法、特殊的編號方法以及「方向角」來做出此證明。由於固定的線組對應至固定的限制點或限制圓，希望能向找出其性質的方向發展。In my study, I use some skills to discuss all the situations which satisfy following conditions. The result is that concurrent circles or concyclic points will be found in every situation. In a graph consisting of four lines, conforming to conditions that any three lines won’t be parallel or intersect at one point, I can find out four triangles and their circumscribed circles. I know these circumscribed circles will be concurrent and I call the point at which all the circles meet “restricted point”. If another line is additionally added in the graph, I can discover that restricted points determined by any four lines in the graph will be concyclic. I call the circle “restricted circle”. What I want to prove is that the above situation will go on. In other words, restricted points will exist when I have six lines, and restricted circles will exist when I have seven lines and so on. In my study, I used Principal of Mathematical Induction, special ways of numbering points and circles, and “orientated angle” to prove my hypothesis. Because of particular line groups corresponding with particular restricted points or restricted circles, the further work I want to attain is to find the relation of them.
四面體體積平分面的包絡方程探討
剛開始考慮平分物件時，我們從二維的多邊形部分著手，後來發現已經有人做過相關研究，並且得到類似的結論。這個部份顯現出面積平分線與其包絡曲線間的密切關係。我們將其中的方法和結果加以歸納、改善，為了更全面地研究，我們推導出一般性的包絡方程。之後當我們推廣到三維領域時，發現四面體體積平分面與之前的結論有些相似之處，平分的情況卻也更複雜，我們將推導的結果用電腦軟體呈現出來，以便更深入地了解它。最後嘗試了相當抽象的高維積平分，結果仍具有工整的對稱性，讓我們充分領略了數學之美！When considering bisecting a subject, at first we focused our attention on 2-D case, polygons. But afterwards, we found there were already some similar studies conducted by other students, which indicated the close relation between the area-bisecting lines of a polygon and their envelope. We rearranged their methods and results, and then made further improvement. Moreover, in order to study the bisecting problem entirely, we derived the general envelope equation. Then when extending the generalization to the 3-D case, we came to the conclusion that tetrahedrons’ volume-bisecting planes is similar to that in 2-D, but the circumstances are more complex. We tried to show our result with the aid of software, hoping to understand it fully. Finally, we tried to do the case in higher dimension, which is very abstract, and the result was clear-cut symmetrical. During the studying process, we had seen “the beauty of mathematics.”
水滴奇遇記-蓮花效應的真面目
Lotus self-cleaning effect arises because the leaves have the superhydrophobic surfaces. When rain falls onto a lotus leaf, water beads up as a result of surface tension. The water drops promptly roll off the surface, taking every dirt with them. This phenomenon is called the lotus effect. With the aid of a light microscope and an Environmental Scanning Electron Microscope, we observe and describe the morphology of the leaves of Nelumbo nucifera in detail. We successfully observe the real interface between air, water droplets and the papillae of a lotus leaf, and find the evidence of a composite surface that is formed by epicuticular wax crystals and air. These observations improve our understanding of the two-level composite surfaces that are formed by micro-scale papillae, nano-scale epicuticular wax crystals and air. We try the method of using the critical angle of a static drop beginning to roll on inclined surface to evaluate the self-cleaning ability. We then find out that it may be a more precise criterion compared to using the static contact angle for the evaluation of the lotus effect. Literature review shows that the earlier investigation lacks the height(H) and interval(I) of the projections on the lotus leaf surface. A close relationship between the self-cleaning property and the H/I ratio is found. In this study, we present the experimental data of the height and interval of the projections on four different species of plant leaves that all have lotus effect, which may be of great help to technological applications. 蓮花效應是指蓮葉表面具有超疏水性與自我潔淨的能力，當雨水落在葉面，因為表面張力的作用形成水珠，水滴迅速滾離葉面，把灰塵一起帶走。本實驗以光學顯微鏡和環境式掃描式電子顯微鏡觀察蓮葉，詳細描述其表面形態，成功的發現空氣、水滴和蓮葉乳突真實的接觸界面以及表面蠟和空氣構成複合表面的證據。實驗結果可以使乳突、奈米表面臘質和空氣構成的雙層次複合表面更容易被了解。我們嘗試以水滴傾斜滾動臨界角來評估自潔能力強弱，實驗結果比傳統使用靜止接觸角更為準確。表面高度和間距的比值與蓮花效應有很大的關係，查閱文獻顯示蓮葉缺乏這些資料，本研究提出四種有自潔能力的葉子的實驗數據，這些數據應該對科技應用有很大的幫助。
二次函數上正三角形建構之研究及探討
在拋物線上置掛正三角形看似簡單，其實不然。本篇文章研究在二次函數的各種不同情況下，可做正三角形的分佈以及其個數。
1. 在一條拋物線上時，最多只能作正三角形。
4. 在三條對稱軸相等的拋物線和共頂點開口大小不同之拋物線上，本篇文章證明一定能找出正三角形落在它們之上。但由於最多有四個分界點，要解四次方乘組過於繁複，於是本篇文章對分界點作了一些估計，找出了分界點的極限值。
5. 本篇文章證明了對於給定的正n 邊形，存在一1 元n-1 次方程式可以通過它所有頂點。
Building a regular triangle on a parabolic curve looks easy . In fact , it doesn’t . This Article researches regular triangles distributions and its numbers in different conditions.
1. On one parabolic curve can only build regular triangles , squares and other regular polygons can’t be built.
4. For three parabolic curves which has same symmetrical axis or three concurrent parabolic curves, we prove that it can build at least one regular triangle on them .But because it can have at most 4 boundary points, to solve quartic equation is to complicated. So we do some estimation of boundary points, and find out some limits.
5. This Article prove that for given regular polygons , there exists a one dimension n-1 orders equation can pass all its apexes.