形?與形外
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.
直角三角形生成關係的研究與發展
k(2αβ ,α2 ? β2,α2 + β2 )是大家熟悉畢氏定理的通式解，且一般書籍的証明大都採用代數的手法證明。以國中生而言，上述的代數方對國中生來說不夠直接且較無推展的實用性。因此幾何觀點出發發展另一種思考方式，利用角平線的性質給予畢氏定理比例解另一種全新的詮釋，並賦予比例解中的參數α 、β 在幾何的意義。在推理的過程中，我們得到一個相當有用的對應關係：一個有理數對應到一個直角三角形、兩個有理數對應到海倫三角形，再將此對應關係運用到各種幾何圖形上面，即可證明出他們所對應的通式解。最後我的興趣鎖定在海倫三角形、完美海倫多邊形與超完美海倫多邊形上的做圖方法上，善用我們所發展的對應關係，上述的問題皆可迎刃而解。k(2αβ ,α2 ? β2,α2 + β2 ) is a popular formula in Pythagoras Theory, often proved in algebra approach among books. Nevertheless, in light of junior high students, the aforementioned algebra method is neither direct nor practical. Hence, a different thinking method is derived from geometry perspective, using the straight line concept to reinterpret Pythagoras Theory and define the geometric meanings of α andβ . In the process of logical development, a useful correlation emerges: a rational number correlates with a straight-angled triangle, and two rational numbers correlate with Heron Triangle. This correlation can be applied to all kinds of geometrical diagrams to prove the correlated homogenous solution. Ultimately, my interest lies in the diagram methods of Heron Triangle, Perfect Heron Polygon, and Super Perfect Heron Polygon in order to apply our developed correlations to solve the above mentioned problems.
趨光性及族群壓力的探討
The purpose of the research was to find the relationship between the fruit fly’s attraction to light (or heliotaxis) and their genes. Fruit flies, because of their short life span of approximately two weeks, and their simple requirements for survival, are ideal candidates for the study. With a specially designed device "Mi Gong" for the experiments, fruit flies could be separated and cultivated in accordance to their preference to specific wavelengths of light. They received cross-breeding and were studied to learn the ratio of the resulting offspring in their preference to the light. It was observed that the majority of the fruit flies were more attracted to violet light. It was also found that the next generation of the fruit fly inherited higher sensitivity to the light than their parents. Knowing that there could be potential margin of errors in the experiments, the results of the study demonstrated that light, as an external source, had limited impact to heliotaxis of fruit fly. The study suggested that insects with heliotaxis, including fruit fly, inherited heliotaxis in their genes. The study also pointed out the potential benefits of employing heliotaxis in many areas especially in the agricultural development. Furthermore, heliotaxis can be utilized to study the difference in the behavior of nightlife insects before and after the invention of manmade light source.這項研究，主要是在探討果蠅的趨光性和遺傳的關係。很多種昆蟲都具備趨光性，我們之所以以果蠅作實驗，主要是因為其生活週期短，大約兩週，且易於培養。實驗內容是以「迷宮器材」來鑑別果蠅對某一特殊色光的偏好，將該群果蠅分離出來培養，令其繁衍後代，觀察其後代對此一色光偏好的比率，我們所用的果蠅大致上對綠色光較敏感，而其子代的敏感度較親代高。因此，我們推論趨光性會遺傳，且受光影響，但並非全由光影響，故這可能是實驗中的誤差成因。雖然此實驗是以果蠅為對象，但亦可假設其它具趨光性的昆蟲，也可能是因遺傳而導致其子代有趨光性，而我們可利用其趨光的一些特性，減少農作物因害蟲類的果蠅而損失，並且希望可以得知,在人造光源還未出現在世上時，夜行性昆蟲是否有差異。
野外實測嗜酸性溫泉紅藻光合作用能力之特性
台灣溫泉資源豐富，不同的溫泉泉質適合不同的溫泉藻類生長。溫泉藻屬於極端生物，其應用資源極待研究開發。本研究根據細胞型態、藻膽蛋白種類分析以及rbcL 基因定序等結果推測北投溫泉藻屬於一種溫泉紅藻，其種類近似於Galdieria sp. (Rhodophyta)。此外，本研究利用葉綠素螢光分析儀於野外實測北投溫泉紅藻於不同光強度下，光合作用能力的差異，發現適應於不同光強度的溫泉紅藻，其電子傳遞速率並無顯著的差異。推測其原因可能與北投溫泉紅藻的phycocyanin 含量會隨著光量有所調整，藉此達到最佳的光合作用能力有關。另外，本研究發現隨著光強度的上升，溫泉藻的NPQ 值有上升的趨勢，然而低光區的溫泉藻有較高的NPQ 值，此與一般理論不符。利用HPLC 分析北投溫泉紅藻的類胡蘿蔔素種類組成，其種類分別為Lutein、α-carotein、β-carotein 與Zeaxanthin，未發現Violanxanthin 與Antheraxanthin，北投溫泉紅藻並不俱有葉黃素迴圈。因此根據研究結果，我們認為NPQ 值與色素的關係仍有討論的空間Taiwan is resourceful in hot springs. Various hot spring algae are adapted to different types of hot springs. Hot spring algae applications are still under developing. In this work, based upon the morphology, analysis of phycobiliproteins, and rbcL sequences, the hot spring algae of Peitou is found to be Galdieria maxima (Rhodophyta). In addition, the dependence of the photosynthesis of Galdieria maxima on the light intensity was measured by Diving-PAM. The results show that the light energy availability efficiency of Galdieria maxima adapting to different light intensity exhibited different, although the electron circulate rate differed insignificantly. This suggests that the concentration of phycocyanin in Galdieria maxima may vary to attain optimal photosynthesis. Furthermore, the NPQ of Galdieria maxima increase with the light intensity. However, contradict to the theory; even under the same light intensity, the NPQ of Galdieria maxima was higher at low light zone. The carotene composition of Galdieria maxima was analyzed using HPLC and found lutein, α-carotene, β-carotene, and zeaxanthin. Violaxanthin and antheraxanthin were not present. Therefore, Galdieria maxima do not exhibit xanthophyll. Based on the results of this study, the correlation between NPQ and pigment still needs to be investigated.
應用垂直循環層流淨化水質之研究
The results of the thermal diffusion experimental show that the separation efficient\r increases with increasing ΔT, but decreases with increasing Q at C0 constant. When\r Q is kept constant, the efficient of change ΔT are small, and the maximum at C0 about\r 545 mg/L. The purification efficient of raw water for thermal diffusion is low.\r And it is high energy consumption, difficult operation, and high costs. So the potential\r of the application is low. Therefore, the vertical circulatory laminar flow apparatus\r was developed in this study. And the separation equation of this apparatus was also\r set up. The results of vertical circulatory laminar flow experimental show that\r the efficient increase with increasing V, and the optimum conditions are at about\r Q= 1.05 L/min, C0=800±50 mg/L, and V=26 cm/min. The separation efficient of the\r vertical circulatory laminar flow apparatus is higher than thermal diffusion apparatus.\r And its energy consumption and costs are low, and easy to operate. Since all interior\r moveable plates have two operation sides, so the multiple channel apparatus is application.\r Therefore, the multiple channel apparatus can treat large amount raw water and has\r low costs. The efficient of the experimental all are better than the theoretical\r values that may due to: (1)the assumed partical diameter is too small,(2)the flow\r is not real laminar flow, and (3)the end-side effect is not considerate.
\r 熱擴散實驗結果顯示在固定C0下，分離成效隨ΔT增加而增高，但隨進料流率增加而降低。在固定ΔT下，分離效率亦隨進料流率增加而降低。固定進料流率下，增加ΔT對分離效果的影響不大，以C0=545±10\r mg/L時，顯現出最佳成效。採用熱擴散裝置雖對降低原水中之懸浮微粒含量效果有限，且能源需求高，造成高成本和操作複雜，不具實用潛力。為提高分離原水微粒之成率，以及簡化操作與降低成本，本研究開發垂直旋轉帶裝置來製造出上下循環水流，並導出水流與微粒於其中之流速分布式，以及頂部、底部出口之微粒濃度計算式。垂直循環轉帶實驗結果，顯示提高V值有助於降低Ct/Cb比值；Q=\r 1.05 L/min左右、C0=800±50 mg/L下與V在26 cm/min左右，均有較低之Ct/Cb比值。垂直旋轉帶裝置分離成效明顯優於熱擴散裝置，且設備簡單、能源需求低與操作容易。由於旋轉帶之兩面均可以做為移動平板，因此不僅可以用來處理大量之高濁度原水，也能更具經濟效益。由理論與實驗結果之比較，顯示理論成效較實驗差，探討其原因可能是：(1)平均粒徑之假設值偏低、(2)流場並非全然以層流流動、(3)兩端終端效應未加考慮等。
抑制水果黑色素形成之新理論及研發美白保養品之新概念
PPO 是一種含銅的多酚氧化? (E. C. 1. 14. 18. 1)，主要是將酚類 (phenol) 氧化成二酚類(diphenol)，更近一步的變成quinones，後者是一種不溶於水的褐色聚合物，在植物中造成褐化最主要原因，然而在人類皮膚則產生黑色素 (melanin)。我們提出有一種揮發性的抑制劑存在動植物體內，此種抑制劑會抑制生物體內PPO 的活性。植物在收成後，揮發性的抑制劑逐漸消失，導致內生性的PPO 活性逐漸上升，因此植物便會產生深褐色的斑點。在本研究中，我們以玉蘭花作為例子，以生化酵素動力實驗、部分純化黑色素抑制劑來解釋揮發性抑制劑在植物體內的存在及其作用，更進一步對水果快速褐化提出一種新的理論。研究發現PPO 的褐化反應就像是人體內酪氨酸? (tyrosinase) 的催化反應，酪氨酸?可以使人體產生黑色素而累積在皮膚上形成黑斑，利用〝人工皮膚〞模擬揮發性黑色素抑制物的作用，證明，防止PPO 抑制劑之揮發可能在未來美白保養品工業裡扮演一極具潛力的角色。Polyphenol oxidase (PPO) or tyrosinase (E.C. 1.14.18.1) is an important and ubiquitous enzyme responsible for browning in plants and melanization in animals. PPO is a copper-containing enzyme that catalyzes the chain-oxidation from monophenol or polyphenols to o-diphenols and subsequent o-quinones. The resulting quinones are large wate-insoluble polymers with dark brown color. We proposed that volatile inhibitors are associated with the plant PPO and block the PPO activity in vivo. While post-harvesting the volatile inhibitors evaporate, the endogenous PPO is then activated and therefore instantly produces dark quinone pigment. In the present study using magnolia flowers as an example, we show the presence of a potent volatile inhibitor(s) for PPO in plant. The novel finding clarifies the mechanism involved in the browning phenomenon of post-harvesting for most fruits. Since the PPO is also know present in human as tyrosinase responsible for the formation of “darkening spots” on skin, the finding of evaporation of potent PPO inhibitor may be potentially used as a strategy in developing a novel cosmetic product.
單細胞浮游藻類對紫外線防禦機制之探討
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.)
別鬧了，辛普森先生
We investigate the machinery producing successive Simpson’s paradoxical reverse. Taking advantage of algebraic and geometric techniques, we obtain the following results. Take playing baseball for example. In our study, we find that Simpson’s paradox only occurs when the hitter’s hits over 3 times in one game. Set n equal to the times I will hit in one game. If my batting average in each game is at least(n ?1)/2 times higher than the others’; then I am sure that my total batting average would not be invert by the others. In order to find how many the lattice points in the triangle, we use Pick’s formula. But sometimes, the Pick’s formula is not appropriate to triangles whose vertex are not all lattice points. So we develop New Pick’s formula to estimate the number of lattice points in such kind of triangles. Besides, we also find an iterative algorithm to produce successive “Simpson reverse” phenomenon by using C++ language, and we can therefore produce as many “Simpson’s set of four sequences” terms as we like(not beyond the computers’ upper limit).Moreover, if both sequences of ratios converge, then they must have the same limit.我們探討了一般人乍看之下顯得頗弔詭的辛普森詭論。我們配合GSP 作圖，用解析幾何、設立直角座標系和C++ 程式的運算，找出在特殊情況下或一般情況下所產生的辛普森數列組和特殊的性質，並且以棒球場上的打擊率為例子來做印證。通常一場棒球賽中，每個人平均上場3 次～4 次，經過我們的討論，發現要發生逆轉的機會只有在上場達到4 次或以上時才會發生。?了求出在直角座標系中可以滿足的格子點個數，我們用了Pick公式，但?了更準確的估計，我們引進了虛點的概念，重新推導出了新Pick 公式。另外，我們還發現，假設兩個人上場比賽，若打了2 場，且每場最多上場打擊K 次，其中的一個人的打擊率只要是另一個人的(k-1)/2倍以上就保證不會被逆轉。我們又找到了連續產生辛普森逆轉的演算法，利用C++ 寫出程式，經由演算法和遞迴式，製造出項數可任意多(只要電腦能夠承受)的辛普森數列組，且我們發現若兩個比值數列接收斂，則極限趨近於同一個數值。