2005年

在這篇報告中，特別針對了凝膠的機制去做探討，以許多的實驗數據，再輔以凝膠的基本定義，去臆測各種有關於凝膠的老化機制，並藉由其過程中推斷出一些有趣的性質： 1. 當膠體內水分含量不同，與凝結後的醇類膠體有相當的影響。 2. 凝膠老化後形成的結晶形狀，因凝膠溶質、溶液內互溶性的不同，形成了不同凝聚程度的絮聚現象。 3. 同種陰陽離子在不同碳數的醇類凝膠中，因為與水溶液的互溶性也有所不同，間接影響了凝膠的形成速度，這對於安定來說，包含了很大的意義存在。 4. 對於其老化的速度，會因其安定程度而有所影響。 5. 老化後的溶液內的陰陽離子濃度，會直接影響其再次安定與老化的情形。 In this report, we especially do the discussion to the mechanism of the gel. With a lot of experimental data and the basic definition of gel, we conjecture various kinds of aging mechanism about the gel, and infer some interesting problems from its course: 1. Moisture content in the gel effect the gel’s quality after alcohol condensed greatly. 2. Because of dissolving difference between the alcohol and the other substances, crystallization forms after the gel aged have formed different degrees phenomenon of gathered. 3. The same kind of negative and positive ion among the alcohol gel that have different carbon atoms. Because of dissolving difference between the ions and the solution, the ions influence forming speed of gel indirectly. To being stable of the gel, this phenomenon includes very great meaning. 4. Stable degree of the gel can influence its speed of aging. 5. The consistency of negative and positive ion in the aging solution of the gel can influence its stable and aging situation again directly.

本研究目的是探討大豆卵磷脂對於老化及學習記憶能力是否有改善之功能。以 24 隻 SAMP8 小白鼠，分為大豆卵磷脂組及對照組，飼養 8週。經由主動迴避試驗、單次被動迴避試驗，測其學習記憶能力；另測量其腦部丙二醛(MDA)之含量，評估其老化的程度。由實驗結果顯示，在主動迴避試驗中，大豆卵磷脂組被電擊次數有減少趨勢；在單次被動迴避試驗中，大豆卵磷脂組停留在明室的時間高於對照組。而在 MDA方面，大豆卵磷脂組腦中MDA含量低於對照組。由上結果推測大豆卵磷脂對於抗老化及學習記憶方面都有改善的功能。 The purpose of this research was to study the effects of soybean lecithin on improving the aging process and learning and memory abilities. The first part of the experiment is to raise 24 SAMP8 mice eight weeks, and divided them into group A and Group B. We tested them memory power by Active shuttle avoidance test and Single-trail passive avoidance test, and tested their degrees of the aging by the content of MDA. The result demonstrated that there was a decreasing tendency in times of being hitting in group A during Active shuttle avoidance test. The time which group A stayed in the bright room was higher than group B during Single-trail passive avoidance test, and the content of MDA in group A was apparently all less than group B in the experiment of MDA. So we can get the message that Soybean Lecithin has the improvement of ameliorating the speed of oxygenation and increasing memory power.

這是一種可在膨脹狀態及未膨脹狀態間轉換的膨脹收縮瓶塞。本設計之瓶塞包含一彈性橡膠之塞座及一剛性塑膠之旋轉控座。該瓶塞在未膨脹狀態，可將瓶塞置於平口內將瓶塞順時針方向旋轉90度使瓶塞由未膨脹狀態轉換至膨脹狀態將瓶子密封；欲開瓶時將瓶塞逆時針方向旋轉約90度使瓶塞由膨脹狀態轉換至未膨脹狀態，可輕易將瓶塞從瓶子內拉出。根據顧客之需求設計瓶塞並選定適當之塑膠材料以製作旋轉控座及適當之衛生橡膠以製作塞座，依廠商提供塑膠及衛生橡膠之特性資料做有限元素分析預測橡膠元件受撐大之變形量，進行加工與製造印證分析之結果，與預期目標有相當的差異，故製作簡易之試件進行探求塞座內縮量與瓶塞膨脹量之關係， 探求瓶塞膨脹量與瓶子所能承受的壓力之關係，進而逆向設計瓶塞之塞座內縮量。 This is a kind of bottle plug that can change at the situation of swell or unswell.The design of this bottle plug includes a rubber plug and a rigid plastic controller that can revolve around. We can put the bottle plug at the top of the bottle and rotate it 90° c.w., the bottle pug will be at the situation of swell and then seal up the bottle. If we want to open the bottle, we just rotate 90° c.c.w., and the bottle plug will be at the situation of unswell and then we can pull the bottle plug out easily. I design this bottle plug according to the need of the customers; choose the certain plastic material to make the rigid plastic controller, and the properly rubber to make the plug; analyze and predict the amount of deformation by Finite Element Method in accordance with the characteristics of rubber and plastic supplied by the factories. However, the result and the expected result are quite different. In order to solve the problem, I make an easy sample to search for the relationship between the contraction of the rubber plug and the swells of the plastic controller and also the relationship between the swells of the plastic controller and the pressure that the bottle can endures. Then I design the contraction of the rubber plug on the base of the result of the experiment I made above.

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.

Farmers in many countries are legally required to identify livestock with some sort of tagging system. Tagging is required for ownership, breeding and as a means of tracking livestock during a disease outbreak.\r New Zealand farmers are required to fit all livestock with two ear tags (one in each ear). Ear tags are applied in a similar way to the piercing of human ears. The two tags are of different sizes and are known as the primary and the secondary tags. The primary tag is physically bigger than the secondary tag.\r We farm deer and have noticed that after tagging some deer develop ear infections at the site of tagging.\r A randomized controlled trial was undertaken in 105 fawns to test the hypotheses:\r ‧ Pre treatment of the ear tag with liquid iodine will reduce post tagging infection.\r ‧ A reduction in ear infections as a result of tagging will lead to more rapid weight gain.\r The treatment group had iodine applied to the sharp part of both primary and secondary tags immediately prior to tagging of the fawns. The control group was tagged in the usual fashion. Fawns were then assessed for infection at 6 and 11 weeks after tagging. Each ear was individually graded for infection and recorded against the number of the animal. Grading was on a scale of 0-3: zero having no infection; 1-slight redness; 2-a larger ring of redness and possibly some dried blood; 3-as for grade 2 plus swelling of the ear around the pin.

洗滌用的界面活性劑分散系，沾在吸管可吹成泡，沾在框上則生成特定形體的薄膜；兩種不同現象，依據各自的性質原理，分別設計為可測量的裝置，研討表面張力與濃度間的關係，發現『兩泡連通法』，測量的靈敏度較佳，並且；薄膜總面積法則會因為框的形不同，測得薄膜總面積與表面張力大小的變化趨勢不一樣，而且數據誤差都比『兩泡連通法』大。市售的洗劑有肥皂與合成清潔劑兩類，它們溶於水的分散系，表面張力與濃度大小的變化趨勢正好相反；肥皂的濃度愈大表面張力愈大，合成清潔劑的濃度愈小表面張力愈大。這種現象發生的原因，和分散質是否含苯環結構無關。用數位照相輔助毛細管上升法，觀測『兩泡連通法』標準液的張力與濃度關係，數據顯示兩泡連通法與毛細管上升法，兩者比較各種分散系張力與濃度大小的結果相同。因此，用『兩泡連通法』比較不同分散系張力大小是簡便生動的可行方法。The dispersion of surfactant used for the purpose of cleasing,if dipped on a blowpipe,can be blown into bubbles and,if dipped on a frame,will form a certain shape of membrane.For these two different situations,according to the principle of their quality,measuringdevices can be respectively designed to explore the relation of surfact tension to its concentrate.It is discovered that,with the measuring device of the Two Bubble Connection Method,the sensitivity measured is better;and that,because of the difference of the structures of the frames,the total area of the membrane and the change trend of the degree of the surface tension will also be different and the probable error of the measured digits is always larger and it is not easy to find regularity. For the two categories of dispersion,soaps on the market and synthesis detergent,when they are measured with the Two Bubble Connection Method about the relationship of their surface tension to the degree of their concentrate,the trend of change is exactly opposite.The surface tension and concentrate of the category of soap are in right proportion whereas,for synthesis detergent used for cleaning bowls and plater and washing clothes,when its concentrate is less,its surface tension is more intense.Based on the findings of this study,the concentrate and the change trend of the degree of tension have no connection with whether there is benzene structure in the solvent. With the Capillary Rise Method assisted by digital photography to observe the relation of the tension of standard solution to the concentrate,we have found that they totally correspond to the result measured with the Two Bubble Connection Method designed in this study.

The physiochemical properties of fullerenes have aroused wide interest, such as its ability to accept and lose electrons and relatively high reactivity that permit various modes of structural modifications. However, obstacles to further research include its complete lack of solubility in water and low processability.\r This project investigated the morphology and microstructure of a fullerene-grafted polymer as a potential candidate for better and novel systems for drug delivery. In this research, hydrophilic functionalities were introduced to the C60 fullerene by chemical modifications, through the attachment of poly(acrylic acid) (PAA) chain. The objective was to investigate the dynamics and the self-assembly properties of this polymer in aqueous solutions, and the knowledge gained would enhance the development of such system for potential applications in drug delivery and nanotechnology.

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。

任意一個三角形要如何分割成四個彼此相似的組成三角形呢？我們透過嚴謹的數學推理，先對三角形作二、三分割的可能情形進行驗證，並藉由已完成相似二、三分割的三角形，運用「內分」和「外加」的觀念，使相似四分割的討論變得明快，並得以將各式三角形的所有相似四分割的圖示作完整而有系統的呈現。 \r 我們也對「比例四分割」的作圖法與其相關幾何性質，進行猜想與討論，並驗證得出一些結果。尤其對「黃金三角形」經比例四分割後，組成三角形之對應邊長的比值也是「黃金值」，以及使用五條摺痕線的摺紙方式，可以摺出一張黃金三角形紙張的比例四分割，這些研究結果都令我們感到獲益良多。 How to divide a triangle into four similar little triangles？ Possible situations of dividing a triangle into two or three parts could be testified by strict mathematical inferences, and then the concepts of “internal division” and “external addition” could be applied to make our discussion clearly and briefly. With above discussions, figures about four similar divisions of all kinds of triangles could be presented completely and systematically. Some results were come up after making some conjectures and discussions about the geometric constructions and geometric properties of “four proportional divisions”. We learn a lot by these researches especially on the discoveries that the ratio of those corresponding sides in each four similar triangles which form a golden triangle, is also golden ratio; and that we could divide a golden triangle into four similar triangles by using five folding lines.

Root growth is related to the acquisition, distribution, and consumption of water and nutrients of plants. As a vital organ, roots directly take the effect of environmental change and its behavior is closely related to the growth of the whole plant. With such, the importance of root systems has motivated botanists to seek a better understanding of root branching complexity. This complexity, which has been difficult to comprehend using simple Euclidean methods (i.e. lines and circles), is important to the survival of plants, especially when the distribution of resources in the environment is scarce. Mathematical models using fractals and computers can be applied to accurately understand the growth and form complexity of plant root systems. This study was conducted to analyze the root growth of gamma-irradiated cashew and mangosteen using fractals.