低雷諾數圓形及多邊形水躍的研究
打開水龍頭，水鉛直落到正下方的水平板時形成圓形水躍。我們實驗研究20＜Nr＜150 的低雷諾數圓形水躍的變因，探討圓形水躍半徑和流量、出水口高度、以及液體黏滯係數間的關係。改用高黏滯係數的液體（4：1 的乙二醇水溶液），鉛直落入板上方深h 的相同液體時，先形成圓形，h 漸大時形成環形圓紋曲面，再加大h，形成多邊形水躍，內外圍同方向旋轉，轉速ω；液中加水，黏滯係數高於及低於某定值，多邊形都消失，側面觀察，外圍液體作鉛直面旋轉。將水平板改置於旋轉盤上方，使高黏滯係數（4：1）的乙二醇水溶液鉛直落入板上方形成多邊水躍，逐漸加快旋轉盤的轉速至 ω 時，多邊形都消失；逐漸減少乙二醇的濃度，至完全用水實驗，亦有多邊形出現，我們認為；平板上方的液體的轉動是非圓形水躍的成因。When a jet of water falls vertically on to a horizontal plate, it spreads out rapidly in a thin layer until it reaches a critical radius at which the layer depth increases abruptly. This phenomenon commonly called the circular hydraulic jump. We study the variations of the circular hydraulic jump radius, as a function of volume flow rate of the jet, the drop height, and the viscosity of the fluid at low Reynold numbers (20＜Nr＜150). When a jet of ethylene-glycol mixed with water (the kinetic viscosity is 10 times of water) falls on to a horizontal plate which is immersed in the same liquid with height h. We find the circular state frequently undergoes spontaneous breaking at its axial symmetry into a stationary polygonal shape. Rather than displaying the weak angular deformation generally seen in fluids, the jump forms clear corners and edges that are often straight. Several of these polygon formations show consistency in height h. And we find the polygon structure rotates in a horizontal motion. When a jet of water falls on to a horizontal plate, and the plate is rotated by a motor ,we find the axial symmetry of the free surface of circular hydraulic jump is spontaneously broken a various number of cornered polygonal shapes. We study the number of corners as a result of the volume flow rate of the jet, the drop height and the viscosity of the fluid in the experiment. And the frequency of rotation of the plate is taking into consideration.
N 元二次不定方程式的整數解探討
傳統的畢氏定理三元二次不定方程x² + y² = z²有一組漂亮的整數解為(m² - n²、2mn、m² + n² )；中國數學家嚴鎮軍、盛立人所著的從勾股定理談起一書中記載四元二次不定方程x² + y² + z² = w²的整數解為(mn、m² + mn、mn + n²、m²+ mn + n² )，這組解被我們發現有多處遺漏，本文以擴展的畢氏定理做基礎修正了他的整數解公式，並推廣取得N 元二次不定方程的整數解公式。
There is a beautiful integer solution formula for the Pythagorean theorem equation, x² + y² = z² , such as (m² - n² , 2mn ,m² + n² ). The “m＂ and “n＂ of the solution formula are integer number. A book written by two Chinese mathematicians, Yen Chen-chun and Sheng Li-jen who expanded the Pythagorean theorem equation to the four variables squares’ indeterminate equation, x² + y² + z² = w² . They claimed that they found its integer solution formula, such as (mn , m² + mn , mn + n² , m² + mn + n² ) for any integer “m＂ and “n＂. But we found it losses many solutions. This paper corrected their faults due to the expanded Pythagorean theorem built by ourselves. Further more, we derived a general formula of N variables squares’ indeterminate equation. Now, we can get integer solutions of the equation, (for all natural number “n＂) easily by choosing integers m1 , m2 , m3 ,……, mn−1 up to you.
化學光電池之光敏劑的開發與研究
六種自行合成出來的聯吡啶釕錯合物Ru(bpy)₃、Ru(bpy)₂(phen) 、 Ru(bpy)₂dcbpy、Ru(phen)₃、Ru(phen)₂(bpy)、Ru(phen)₂dcbpy 及商用染料N3-dye，被成功的做成光敏性太陽能電池。光電流的產生率可由IPCE (incident photon-to-current conversion efficiency) 的測量可知。此類釕錯合物可以物理吸附或化學鍵結於TiO₂奈米粒子上。IPCE 的大小可以用來探討不同吸附方式的釕錯合物轉換光電流的效率。在物理吸附上Ru(phen)₂(bpy)的效率最好。化學鍵結的以N3 Dye 最好，我們合成的錯合物以Ru(bpy)₂dcbpy 較佳。此種以TiO₂奈米結構為承載基材的太陽能光電池(Dye-Sensitized Solar Cell)，染料仍以商用染料 N3-dye 最佳。本研究發現物理吸附的Ru complexes 也可產生光電流，若能最佳化，將可簡化染料錯合物之合成。
Six ruthenium complexes, Ru(bpy)₃, Ru(bpy)₂(phen), Ru(bpy)₂dcbpy, Ru(phen)₃, Ru(phen)₂(bpy), and Ru(phen)₂dcbpy were synthesized. These Ru complexes and N3 dye have been incorporated into the dye-sensitized solar cell system. The solar energy conversion of the ruthenium complexes were measured and converted to IPCE (incident photon-to-current conversion efficiency). There complexes were either chemically bonded or physically absorbed onto the nano-sized TiO₂ particles. The IPCE were utilized to compare the photon-to-current efficiency of these Ru complexes. Among the physical-absorbed dyes, Ru(phen)₂(bpy) has the highest IPCE. For chemical-absorbed dyes, the commercial N3 dye is still the best. Among the complexes synthesized in this research that are chemical-absorbed, Ru(phen)₂dcbpy has the highest IPCE
The commercial N3 dye has the highest IPCE in the dye-sensitized TiO₂nanoparticle solar cell. We found that physically absorbed dye can convert photon to current. With better solar cell assembly, physically absorbed dye can have the same conversion efficiency as N3 dye.
了解抗氧化的「旋」機-利用自製的旋光儀來探討旋光性與抗氧化成分之間的
In this research we derived heating effects on anti-oxidation by optical rotation analyses. A simple and accurate Polarimeter was devised with polar screens, laser, and photo resistor; the laser was used for light source, and the photo resistor for detection. Four kind of fruits, Hyloceeus polyrhizus, California plum, kiwi and tomato were experimented by heating them in boiling water and microwave oven. Their optical rotations versus time duration were calculated. Then we used ABTS/ the H2O2/HRP analysis system from Arnao's research to obtain the heating effects on anti-oxidation by calculating the vitamin C densities versus lag time. We found that there was a tendency of increased anti-oxidation at the beginning by heating, but decreased afterwards. Better oxidation was achieved by using microwave for Hyloceeus polyrhizus, by using boiling water for kiwi and tomato, and by using both methods for California plum. The same tendency was also found in the optical rotation analyses. Therefore we successfully developed a new method to measure the antioxidant activities by the optical rotation. We can also apply this method to simulate the fruit digestion process in the stomach, which let us understand further about anti-oxidation ( or optical rotation ) versus time. 本研究利用偏振片、雷射光為光源、光敏電阻為偵測器，組裝成一個簡易且精確的旋光度計。 我們利用此旋光度計對奇異果、火龍果、聖女蕃茄、加州李子四種水果以微波、水煮及油浴三種方式來處理，求出水果的旋光度與熱處理時間的關係。再藉由Arnao 研究的ABTS/ H2O2/HRP 分析系統，以不同濃度的維生素C與延遲時間畫圖作為標準曲線來測量總抗氧化活性，並比較熱處理後抗氧化活性的變化趨勢。 透過本研究可以了解不同熱處理方式對四種水果之抗氧化活性初期皆有增加的趨勢，但隨著時間增長則抗氧化活性降低。其中奇異果與聖女蕃茄用油浴，火龍果用微波處理，加州李子則是用任何熱處理方式均可得較佳的抗氧化活性，而熱處理後在旋光度測量上也有相同的趨勢。因為此兩種方法有一致的反應趨勢，所以證明我們成功地開發出一種可以利用旋光度來測定抗氧化的新方法。 最後，應用本方法進一步模擬水果在胃部裡的消化，讓我們更可以了解在整個消化的過程中抗氧化活性(旋光度)隨時間變化的情形。
蟲以食為天一線蟲覓食與攝食行為之探討
秀麗隱桿線蟲(Caenorhabditis elegans)為在科學界備受矚目的模式生物，對於其生殖及發育過程已有諸多研究，然而對於其覓食及攝食行為的相關研究卻仍闕如；每一種生物都有其獨特的行為模式，而為了解線蟲發展出何種覓食與攝食的行為以適應自然的環境，因此著手進行研究。本研究歸納出線蟲的七種一般行為：前進、探頭、偏移、擺頭、後退、轉向及拐彎行為，並探討其意義。其中，前進及探頭行為為恆常出現。偏移與轉向行為與攝食有關，在有菌環境中出現，可避免其遠離食物來源，而連續的後退及轉向行為也構成特殊行為之樹枝狀行為，推測應為幫助線蟲的消化所出現的行為。擺頭與拐彎行為與覓食有關，在無菌環境中出現。後退行為雖在有無菌環境中皆出現，但由後退後行為的不同可以了解後退行為在兩種環境下具有不同意義。在有菌環境中，後退後通常伴隨轉向行為；在無菌環境中，後退後通常伴隨拐彎行為，為逃離不適環境且藉以覓食的行為。經過研究，發現線蟲的覓食機制為嗅覺，且對嗅覺有依賴性及專一性，在其他氣味存在的環境下會大大降低覓食的效率，但最後仍然能正確地找到食物來源。線蟲於覓食的過程中所出現的特殊行為之混亂行為，由實驗結果發現為是E. coli 所釋放至培養基的化學物質所造成，化學物質濃度越濃，線蟲所表現出的混亂行為就越明顯。推測此種現象發生的原因，應為E. coli 釋放化學物質以干擾線蟲，以避免本身受到捕食，然而，線蟲也演化出適應的能力，因此在發生混亂行為後仍然能抵達菌落，此種特殊的交互作用表現出線蟲與E. coli 間的共演化現象。Cenorhabditis elegans has long been a model organism used for developmental biology studies. However, researches about its foraging and feeding behaviors are still limited. Every organism has its unique behaviors, and this research was conducted in order to understand more on what kind of foraging and feeding behaviors were developed by C. elegans and how they helped C. elegans to adapt to the environment in which it lives. The research concluded with seven general behaviors of C. elegans : advancing, probing, slanting, swaying, backing, turning and bending, and the meanings of it. The advancing and probing behaviors are constant. The slanting and turning behaviors, which appear in presence of food, are feeding-associated behaviors, which help C. elegans avoid leaving the food source. Continuous backing and turning behaviors also make up the branching behavior, one of the special behaviors, which help C. elegans’ digestion. Swaying and bending behaviors, which appear in absence of food, are foraging-associated behaviors. Although backing behavior appear both in presence and absence of food, the difference in post-backing behaviors show that there are distinct meanings of backing behavior in each environment. In presence of food, turning after backing is usually observed; in absence of food, bending after backing is usually observed, which indicates the act of escaping from unsuitable environment and searching for food. Studies show that the foraging mechanism of C. elegans is by olfaction, and C. elegans is highly olfaction-dependent and specific: efficiency of foraging decreases significantly under environment with scents other than that of E. coli, but C. elegans is still able to locate the food. According the experiments, the chaos behavior, one of the special behaviors, appears during the foraging process of C. elegans, and is caused by chemicals released to the medium by E. coli. The density of the chemicals and the extent of chaos behavior is in direct proportion. The theory is E. coli secrets chemicals to disturb the worm to avoid being preyed upon. C. elegans, however, also evolved the ability to adapt to the chemical so that it can still reaches the food source even after chaos behavior appeared. This unique interaction is a manifestation of co-evolution between C. elegans and E. coli.