漩渦之美
我們常可以在自然界中發現漩渦的存在,但其存在的形體與性質也不盡相同,為了研究漩渦的結構與形體,筆者分析出多種會對漩渦產生影響的因素:開始放流的水而高度、放流洞口大小、有無破壞漩渦結構的阻礙、單孔落流漩渦與雙孔落流漩渦、還有流體的黏滯度對漩渦的影響, 但漩渦是一個不斷改變的流體,非常難以觀察,且自然界的漩渦也不是說出現就出現,所以必須設計一個簡易實驗器材來觀察,並用數位攝影機紀錄下來,再慢慢分析,而我們也可以在這個實驗中了解漩渦的結構,和體會到漩渦所表現出自然界的力與美的一面。‧We can always find in nature of different swirl’s forms and properties. To study the swirls, we analyzed such factors, as the beginning water level, the size of the hole, the presence of obstruction that will destroy the structure of swirls, differences between single-hole-swirls and twin-hole-swirls, and the viscosity of fluid. Because swirls change all the time, it is very difficult to observe. We designed a device .The procedure was recorded with a digital video camera and analyzed it. The study helps us understand the structure of swirls and admire the beauty of swirls.
一個也沒漏掉,一個正有理數的排序的研究
本文中我們探討一個有趣的數列。這個數列有一個非常特殊的性質:將數列相鄰兩項的前項當分子,後項當分母,所產生的分數數列,恰好會出現所有的正有理數。 這個特殊的性質表示,可以將正有理數按照這個方式作排序,這個排序將完全不同於常見的正有理數排序的方法。
(1). 在正有理數的排序的結構中,我們做出許多有關於此數列的定理。
(2). 用數學歸納法證明此分數數列涵蓋所有正有理數,且每一正有理數只出現過一次。
(3). 將數列分割後,利用試算表製成數列規則表,並整理出快速的方法將數列表達出來。
(4). 將an 數列排成“樹"的模式,可更快速的把正有理數寫下來。
(5). 最後,設計出搜尋正有理數的演算法,解決在分數數列中第n個正有理數會是多少;以及正有理數會出現在數列中第幾項的問題。
Let’s discuss an interesting sequence. There is a very special quality in it. In this sequence, choose two numbers, which are close to each other, and suppose the first number as “member” while the second one as “denominator.” Then we can get a fraction sequence that includes all of the positive rational numbers! According to this special quality, we can arrange positive rational numbers by the following method. Then we can get a brand-new way of the arrangements.
(1). We can find many theorems about this sequence according to this special arrangement of the positive rational numbers.
(2). We can prove the rule that this fraction sequence includes all of the positive rational numbers by mathematical induction. Furthermore, every positive rational number appears only once.
(3). After dividing this sequence into several parts, we can get a sequence rule list by using trial balance and find a faster method to express the sequence.
(4). Arrange the an sequence by the tree model. By this way, we can get all of the positive rational numbers much faster.
(5). Finally, we can develop the operation method to solve the questions that what position would one positive rational number be in the sequence and what is the first, second, third or nth positive rational number of the sequence.
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.
以簡易方法探討奈米銀的化學活性優於非奈米級銀粒子
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。
Reduction of free radicals and endotoxin by conjugated linoleic acid loaded in-situ synthesized poly
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
鈦鈦相傳-以新穎水熱-化學電池法製備二氧化鈦
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。
安培植物假說
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
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.