壹、研究目的：培養建構式思考方式，提高解決問題的能力。 貳、研究過程：一先查數學辭典，確定F.S.之定義。二以文字敘述替代數字敘述F.S.，並分析歸納規律性。三將發表過的有關關係式，挑選適合以代數分析研究者，研究採逆命題角度處理，共有下列七種關係式採論之。 壹、Motivation and Purpose In this study, we expect to know something about Fibonacci Sequence (F.S.) that we can understand and enjoy as a high school student. 貳、Procedure 一.Make sure the definition of F.S. 二.Use algebra instead of numerical to state F.S. 三.Select the related formulas and discuss by fundamental algebra. We get 7 types as follows

A novel and simple method was developed to determine the activity of silver in nanometer particles more than in non-nanometer particles. The conductivity of conducting polymer, polyaniline (PANI) doped with different amount of nanometer silver particles was used to evaluated the activity of nanometer silver. In polymerization of polyaniline, hydrogen chloride solution usually used to increase the conductivity of polyaniline. When 1%(w/w) nanometer silver particles doped during the polymerization, the conductivity of polyaniline was down from 2.28 s/cm to 0.65 s/cm, then increased with increasing the amount of nanometer silver doped. The conductivity of polyaniline was changed from 2.28 s/cm to 0.47 s/cm when 3%(w/w) nanometer silver particles doped, but it is increased from 2.28 s/cm to 2.44 s/cm when was doped with 3%(w/w) micrometer silver particles. The conductivity of polyaniline changed due to the formation of silver chloride (AgCl) in doping nanometer silver. Some of the nanometer silver particles were formed to silver ion in hydrogen chloride solution for the high activity property of nanometer silver. This also can be proved from the spectra of XRD and FE-SEM. Therefore; determination the conductivity of conducting polymer by doping nanometer metal particles can be used to determine the activity of the nanometer particles. 本研究為開發一個新穎的檢測奈米金屬粒子化學活性大於非奈米金屬粒子的簡易方法。方法為利用導電高分子聚苯胺，於合成過程中添加不同濃度的奈米銀粒 子，並分別偵測其成品的導電度，藉以評估奈米銀粒子的化學活性。由於聚苯胺在合成過程中通常加入鹽酸以提高其導電度，致活性較大的奈米銀粒子於氧化後，隨即與氯離子形成氯化銀的沉澱，而降低聚苯胺的導電度，如添加1﹪(w/w)奈米銀粒子的，其導電度由2.28 s/cm 降至0.65 s/cm，隨後隨著添加量的增加導電度先降後再稍回升。一般非奈米級銀粒子因氧化電位為負值，即化學活性小，而不易被氧化。由實驗結果，我們發現同樣添加3%(w/w)的奈米級銀粒子或微米級銀粒子，添加奈米級銀粒子的導電度由2.28 下降為0.47，添加微米級銀粒子的導電度卻由2.28 上升為2.44，此乃說明本方法確實足以證明奈米級金屬的化學活性的確遠大於微米級金屬，因相同條件下，微米級銀粒子未如同奈米級銀粒子一樣被氧化成銀離子。即奈米級銀粒子可以輕易的被氧化，而非奈米級銀粒子則不易被氧化。尤其也可由X 光繞射儀分析光譜圖和場發射式掃描電子顯微鏡拍攝圖證明。因此，我們可以採用添加3 %(w/w)奈米級金屬銀粒子及微米級金屬銀粒子於導電高分子的方法，並藉導電度的變化，證明奈米金屬粒子的高活潑性。

洗潔劑分散系泡膜的變化十分有趣，是否能用吹泡法比較表面張力大小？沾黏在立體的框上會怎麼樣？能否由框上薄膜面積大小討論界面劑的化學性質呢？

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.

本研究首先利用NaOH 將PAN 薄膜改質形成PAA 水膠膜表面，進一步與異丙胺鍵結形成NIPAAm 結構，以做為藥物傳輸的載體。反應所得之PNIPAAm 薄膜其溫度轉換點為34 °C 其pH 敏感性介於pH 5 至10 之間，實驗進行進一步於34 °C將PNIPAAm 薄膜浸入共軛亞麻油酸(CLA)中，取出後置入4 oC 二次水中，最後測試經改質接枝後PAN 薄膜於膽固醇、三酸甘油酯的吸收效果，並以化學冷光儀分析改質接枝後PAN 薄膜其抗氧化效率。結果顯示改質接枝之PNIPAAm 薄膜於包埋CLA 其對於血液中膽固醇及三酸甘油酯有明顯的吸收效率，此外對血液中的自由基也有明顯較未改質之PAN 薄膜穩定的趨勢。A thin layer of poly(N-isopropyl acrylamide) (pNIPAAm) was synthesized in situ on the surface of hydrolyzed polyacrylonitrile (PAN) membrane. This thin layer exhibited both pH response due to the poly(acrylic acid) moiety and temperature response due to the pNIPAAm moiety. The swelling behavior of the membranes was evaluated under various temperatures and pH. The curve of the swelling ratio for the PAN-NIPAAm showed a lower critical solution temperature (LCST). Then conjugated linoleic acid (CLA) was loaded into the pNIPAAm layer. The effects of CLA on the blood coagulation and oxidative stress were evaluated using human blood. The level of reactive oxygen species (ROS) was measured by chemiluminescence (CL) method to evaluate the oxidative stress. Furthermore, the removal of bacterial endotoxin (lipopolysaccharide, LPS) by CLA-loaded PAN-NIPAAm was measured with ELISA. The results show that the LCST swelling curve was at 37°C. In addition, the swelling ratio increased by 71% when the pH increased from 5 to 10. The concentration of LPS can be reduced by CLA-loaded PAN-NIPAAm 2.1 and 1.2 5 times of that by unmodified PAN and PAN-NIPAAm membranes, respectively. In addition, the level of ROS against CLA-loaded PAN-NIPAAm was reduced significantly than that against unmodified PAN and PAN-NIPAAm. Therefore CLA-loaded PAN-NIPAAm membrane could offer protection for patients against oxidative stress and could also inhibit LPS for clinical applications

在「植物的秘密生命」這本書中提到植物在電場或磁場中會生長的更好,我最近正好學到了電磁場如何產生,以及一些產生電磁場的方法,所以想利用螺形管線圈來產生均勻的電磁場並用安培右手定則來控制磁場產生的方向來了解電磁場在高低室溫下對綠豆生長的影響. 在本實驗中我利用鐵碗纏繞線圈的方式並通入不同的電流大小來改變磁場的強度,所進行研究所得到的結果顯示（1）綠豆只有在適當的電流大小下所產生的電磁場才可以幫助加速綠豆的生長(2)栽培綠豆的環境所架設的電磁場越高,越能持續讓綠豆的生長加速（3）綠豆的加速生長並不需要整天都通電（4）綠豆在N極朝上的磁場中生長的速率較S極朝上的磁場中要快(5)在較低的室溫下,電磁場加速綠豆生長的效應較能顯現 It has been mentioned that the plants will grow faster in the electronic or magnetic field in the book of “the secret life of plants”, I learned about the knowledge and methods of how to produce the electromagnetic field just now, I use the screw wire to produce electromagnetic field and control the direction by the Amplifier’s rule to investigate the growing speed of green beans under electromagnetic field in those different temperature. In this experiment, I use the wire to screwed around the ironed bowl, and make different electric current to generate different strength of electromagnetic field, the results indicate that (1) The faster growing speed will only exist in some strength of electromagnetic field (2) The higher ironed bowls that full of screwed wire will result in the faster growing speed (3) It will not need electromagnetic field all days (4) The green beans will grow fast in those north magnetic pole than those in south magnetic pole (5)The effect of electromagnetic field to increase growing speed will be significant in higher room temperature

In recent years, sandstorms have seriously attacked Taiwan day by day. Combining with the observations of Central Weather Bureau and the satellite images of NASA, the study has been collected the data of suspension grain in decades. And the study hopes the sandstorms’ information could be observed in early period. Still it hopes to find out the possible transmission paths in the atmosphere. Then we know how to cope with sandstorms in early time. Sandstorms attack Taiwan frequently in spring, the end of the autumn and the beginning of the winter. Compared with the charts of sandstorms and the satellite images, we could broadly aware that the moving paths of sandstorms are related to the currents and the characteristics of the atmosphere. When El Nino happens, the times of sandstorms attacking Taiwan decrease, and that increase when La Lina happens. According to the results of spectrum analysis, there might be high peaks of a year and six months short period varieties. And low peaks of 2.2 years and 7 months period, tell us that the short period aerosol varieties should be relative with season changes, the long period aerosol varieties may be relative with the El Nino and La Lina period. 近年來，大陸沙塵暴侵襲台灣的情況日趨嚴重影響。本研究中收集了近十年來懸浮顆粒資料，配合環保署空氣品質監測站、中央氣象局所觀測的資料與美國太空總署的衛星影像資料及NASA航空資源實驗室的氣流軌跡回推圖，希望能夠在早期觀測時發現大陸地區沙塵暴訊息，和沙塵暴所帶至大氣中的懸浮顆粒可能傳輸路徑。發生沙塵暴侵臺事件的季節，主要在春季及秋冬兩季交替期間發生的次數為最多。由地面天氣圖表、氣流軌跡回推圖及美國太空總署的衛星影像進行綜合比對之後，可大致瞭解大陸沙塵可能的移動路徑與大氣環流特徵有關。 聖嬰現象（El Nino）發生時，侵襲臺灣的沙塵暴次數會減少。在「反聖嬰現象」（La Lina）發生時，侵襲臺灣的次數相對增加。經由頻譜分析中得知，懸浮顆粒高峰期的變化有1年期及6個月變化趨勢，懸浮顆粒低峰期的週期變化有2.2年與7個月的變化趨勢，顯示短週期大氣懸浮顆粒變化應與季節變化有關，長期性變化或許與聖嬰反聖嬰週期有關連。

茶品的發酵程度對其香氣與口感有決定性的影響，然而業界卻缺乏相關的客觀指標與其有效的量測方法。茶品發酵的主要化學過程是其兒茶素的氧化與聚合，這些茶單寧將隨著發酵過程逐漸由還原態轉變成氧化態。所以，不同發酵程度的茶，其氧化態單寧與還原態單寧的比將有所不同。這個比值預料可由氧化還原電位間接地量測得知。本研究使用白金絲與銀/氯化銀參考電極為電極對來量測此氧化還原電位。量具則使用具高輸入阻抗(大於十億歐姆)的pH 電極用電位計以取得茶汁中微弱的氧化還原電位訊號，可於十秒內取得高再現性(相對標準差小於3%)的電位訊號所得到的電位訊號與發酵程度呈高度的線性相關(相關係數大於0.9)。Degree of fermentation is pivotal for the aroma and the aftertaste of tea, but an objective scale and efficient evaluating methods are demanded for the important quality factor. Oxidation along with the polymerization of catechins is known to be the major chemical process during tea fermentation; the tea tannins will gradually change from their reduced forms to their oxidized formats. As the consequence, the ratio of oxidized tannins to reduced tannins will differ with the extent of fermentation. The ratio can be measured simply by the redox potential. In the present study, we used a platinum wire and an Ag/AgCl reference electrode as the electrode pair to measure the redox potential. A pH meter with high input impedance (over Giga ohm) served as our voltmeter for the weak voltage signals retrieved from tea infusions. The measurement was quick (less than 10 second) and with good reproducibility (CV0.9).

In our experiment, the novel hydrothermal-galvanic couple method is used to produce nanostructured TiO2 thin film. Compared with the traditional hydrothermal method, whose process is conducted under high temperature and high pressure, the hydrothermal-galvanic couple method is a thermally and electrochemically driven process. The titanium atom is gradually oxidized on the surface driven by potential difference, and eventually become nanostructured TiO2. The advantages of the hydrothermal-galvanic couple method are numerous： they are simple, environment-friendly and energy-saving. Experimental parameters include time, concentration and types of solution. The hydrothermal method is used for comparison. By the cross-section and surface pictures of Field-emission scanning electron microscopy (FE-SEM), we can clearly observe that there is obvious change on the titanium surface, along with increased thickness and altered surface structure. The film of hydrothermal-galvanic couple method is thicker than that of hydrothermal method. Thickness increases with time and concentration as well. Both the hydrophile and decomposition of methylene blue examination indicate that the product on the surface contains photocatalyst-like feature.我們利用新穎水熱-化學電池法製備奈米級二氧化鈦薄膜。相較於一般傳統水熱法高溫高壓的製程，水熱-化學電池法結合了熱能與化學電能，讓鈦原子在電位差的驅動下於表面逐步氧化，最終形成奈米級二氧化鈦粒子，具備簡易、環保、省能的優點。實驗參數包括時間、濃度、溶液種類，並以水熱法作為對照組。由FE-SEM 橫截面圖及表面圖可清楚看到鈦的表面有明顯變化，膜厚增加、表面結構改變；以水熱-化學電池法所得的薄膜明顯較水熱法厚，而其厚度隨著濃度及時間的增加也有增加的趨勢，由試片親水性測試與亞甲基藍吸光度測試，皆顯示試片的表面產物具有類似光觸媒的性質。

許多難纏的疾病，如神經退化性疾病與糖尿病，在1998年建立人類的胚胎幹細胞後，開始露出一線曙光。但就算科學家已經從胚胎幹細胞，成功引導出特殊種類與功能的細胞，預備做細胞治療時，需透過細胞核移植技術，使排斥的情形大大減少。所以當今年3月，韓國透過細胞核移植技術成功作出人類的胚胎幹細胞株時，轟動全世界。但是，他們從242顆卵，只做出一個胚胎幹細胞株，浪費這麼多卵子就牽涉到醫療倫理的層面了。既然，每一個人都要訂製自己的幹細胞株，那麼卵子的來源就很重要了。理論上，胚胎幹細胞可以分化成所有細胞與組織，當然也應該含生殖細胞在內。去年5月底，賓州大學就利用小鼠胚胎幹細胞，體外培養出型態上非常像卵子的細胞。所以，今年暑假利用兩個月時間，有個機會參與了台大醫學院婦產科的胚胎幹細胞研究團隊，稍稍瞭解了胚胎幹細胞製造成生殖細胞的過程。我們採取一種方法，先從胚胎幹細胞株，用類胚胎體(EB)的立體環境，加上 SSEA-1的篩選，與維他命A的刺激，引導至初始生殖細胞，第二步利用細胞重組的方法，利用小鼠胚胎的性腺組織，來支持這些選擇過的細胞，希望可以培養出小鼠的卵子或精子。我們從EB得到SSEA-1細胞約為全體細胞的10%，然後經過維他命A的刺激，得到SSEA-1細胞約為全體細胞的5%，這時的細胞理論上是初始生殖細胞 (PGC)，但是之後的體外單獨培養或與胚胎性腺重組培養，發現成果並不是很理想。到最後，也許受限於時間還有能力，沒有得到明確的小鼠生殖細胞，但是過程中，我學習到生殖細胞的生理，胚胎幹細胞的特性，基本實驗室的細胞培養與組織染色，這些都令我印象深刻。我們認為，如果有一個適當的基因轉植的胚胎幹細胞株，例如GFP放進生殖細胞相關的基因裡頭，讓達到終點，或邁向目標的細胞群，可以自我顯現，實驗會更容易達成目標。Scientists discovered ways to obtain or derive stem cells from early mouse embryos more than 20 years ago. Many years of detailed study of the biology of mouse stem cells led to the discovery of human embryonic stem cells in 1998. Through years of experimentation scientists have established some basic protocols or "recipes" for the directed differentiation of embryonic stem cells into some specific cell types. One major problem that must be solved before human stem cell therapy becomes a reality is the threat of rejection of the transplanted cells by the host's immune system. One way to avoid the problem of rejection is to use stem cells that are genetically identical to the host. This could be achieved by the same techniques of somatic cell nuclear transplantation (SCNT) that produced Dolly. Low efficiency less than 0.5% (1/242) in Korea this March brought some controversies in ethical issues. Where and how to procure the large amount of oocytes that will be required? One source of eggs could come from the generation of oocytes from embryonic stem cells (ESCs), as described by Hubner et al. (2003) in the mouse. By the selection of primordial germ cells (PGCs) and re-aggregation with their stromal cells, we hope to derive mature germ cells such as oocytes and sperm from ESCs in this study. In this study, we have demonstrated some PGCs after sequential selection by SSEA-1 antigen and optimal culture conditions. We also proved some FE-J1 positive cells but no further fertilization was obtained after all. Further investigation about this mechanism may be needed to derive these germ cells from ESCs.