In this work, techniques to explore the capabilities of multi-walled carbon nanotubes\r (MWNTs) in sorting nanoparticles (NPs) were presented. A droplet of a solution comprising of quantum dots (QDs) with various sizes was deposited on an aligned array of intertwined MWNTs. Photoluminescence (PL) and fluorescence microscopy (FM) revealed that MWNTs were effective nano-sieves that could effectively sort out QDs with a size difference of ~ 2.1 nm.\r Cadmium Selenide/Zinc Sulfide (CdSe/ZnS)core-shell QDs and Cadmium Sulfide (CdS) QDs were used to explore whether chemical properties of NPs affect the sieving capability of MWNTs. Further investigation on the effects of micro-patterning on the sieving ability of MWNTs was also carried out.PL and FM results suggested that micro-patterning could aid in separation of QDs and thus improve sieving capability of MWNTs. With the above findings, QDs emitting different colors as a result of size difference could efficiently be assembled onto the MWNTs en route to three-dimensional architectures with controlled assembly of NPs.\r Together with controlled laser power to remove desired amounts of QDs decorated MWNTs, a multi-colored display could be achieved. Further experiments were also carried out to determine the feasibility of introducing MWNTs as filters for NPs. Dilute solutions containing NPs such as gold colloid was run through these MWNTs filters by gravity. Field emission scanning electron microscope (FESEM) images of the samples showed that MWNTs were successful in trapping the nanoparticles. Explorations into the length dependent effect of using MWNTs as filters, suggested that 300μm MWNTs are better nano-sieves compared to 50μm MWNTs.

何謂無限解？若n位正整數B ，滿足xm xp mod 10n，則稱B 是xm＝xp的n位數解。例:2494＝3844124001、2492＝62001，所以249為x4＝x2的一個三位數解。當n→∞時，則稱B 是xm＝xp的一個無限位數解，簡稱為無限解。本研究主要在探討方程式x2＝x、x3＝x、x4＝x、、、、xm＝x、xm＝xp無限解的規律性及各方程式無限解的個數，並加以證明。幸運地，我們利用任意數次方後其個位數每四個循環一次的特性，藉由整數論定理的推導，並佐以Mathematica軟體輔助計算，得到以下令人振奮的結論！在Xm＝Xp的無限解中：(1)若m－p＋1為4k-2或4k(即m－p＋1為偶數)k N，則其必僅有兩個無限解。(2)若m－p＋1為4k-1，k N，則其必僅有七個無限解。(3)若m－p＋1為4k+1，k N，則其必僅有十三個無限解。

Color is not a physical quantity, but it is a characteristic of spectra. Traditionally spectra of light sources are characterized by the wavelengths and intensities of the spectral lines. We propose an alternative way of charactering spectra using colors. Using digital cameras, convex lens, and a 600 Lines/mm grating, we design a “Digital Spectrophotometer” (Pic.1), which uses no light sensors and electrical circuits that are necessary for conventional spectrometers. To analyze a spectrum using the “Digital Spectrophotometer”, we take digital images of the diffracted light through the grating emitted by the light source and then analyze the intensity distribution of the color components of the spectral lines. The structure of the “Digital Spectrophotometer” is simple and is easy to operate. The Digital Spectrophotometer includes a computer software program we have developed called the “Digital Spectrological Method”. After enlarging the digital spectrographs to a mosaic scale and regards each mosaic as a basic color block, the Digital Spectrological Method will transform every color block into a four dimensional “color coordinates” (λ (wavelength), R(red), G(green), B(blue)), where the coordinateλ is translated from the spatial position of the spectral line and the R, G, and B coordinates specifies respectively the corresponding intensity of the red, green, and blue color components. Comparing the “color coordinates” of the unknown light sources to the known, we can easily identify the wavelengths of the lights emitted by the unknown illuminant precisely. We have accomplished the following experiments by using the “Digital Spectrophotometer”: 1. Measure the spectra of various gaseous atoms, and establish the “database of digital spectra in color coordinates” (DDSCC). 2. Compare the characters of color presentation between digital camera images and positive film of the optical camera. 3. Identify the absorption spectrum of the Solar spectrum (Fraunhofer Lines) using the DDSCC. 4. Analyze the Orion αandβ spectrum using the DDSCC. 5. Identify the 589.0 and 589.6 nm wavelength difference between the “Double Lines of sodium spectrum”. 6. Measure the range of wavelength of the colored LED and register the results into the (λ, R, G, B) coordinates. 7. Compare the range of wavelength of He-Ne Laser and commercial Laser pointer. 8. Measure the Zeeman splitting of the hydrogen atom spectrum at 0.5 Tesla. 顏色雖不是物理量，卻是光譜的特性，傳統上對光譜的分析只記錄波長及對應的強度，而非以顏色來區分。我們運用數位相機、凸透鏡及600 條/㎜光柵，設計一個以顏色成分為標準來分析各類光譜的「數位攝譜儀」(Pic.1)。這個新的設計無須使用傳統光譜儀所需之光感應器及電路設計，只需拍攝光源透過光柵的繞射影像即可分析對應之光譜。我們製作的「數位攝譜儀」包含了一個自行設計的電腦軟體程式「數位光譜分析法」；將拍攝到光譜數位影像放大成「馬賽克」，作為光譜的最小「色塊」，該程式可將每個色塊轉換為一組四維的「顏色座標」 (λ (波長)，R(紅)，G(綠)，B(藍))，其中的λ 座標係由光譜線的位置轉換而來，而紅、綠、藍座標則記錄對應的紅、綠、藍色成分強度。與已知光源譜線的「顏色座標」比較，「數位攝譜儀」可精確測量各種未知光源放射出的光波波長且操作方便。利用「數位攝譜儀」的數位分析方法，我們完成以下實驗：1. 測量不同種類的原子光譜，建立「數位光譜資料庫」，包括氫、汞及鈉原子。2. 比較數位相機影像與光學相機正片的色彩顯影。3. 利用「數位光譜資料庫」，鑑定太陽光譜中的吸收光譜(Fraunhofer Lines)。4. 利用「數位光譜資料庫」，分析獵戶座α、β的可見光光譜。5. 鑑別波長589.0、589.6 奈米的鈉雙線。6. 用顏色座標(λ,R,G,B)測量發光二極體的波長範圍。7. 比較He-Ne 雷射與雷射光筆放光的波長範圍，發現市售雷射光筆所放之光並非單頻。

本研究主題主要是解決化學上複雜同分異構物的繪製以及其命名，因為物質在結構複雜時其同分異構物變化之多令人難以捉摸，於是我應用電腦強大的邏輯處理以及運算判斷的能力來讓電腦繪製。以下是我想達成的目的：(1)排列出分子式的同分異構物(2)顯示出同分異構物之示性式、結構式(3)預知尚未創造出物質的性質研究中我創造出以下原則讓我方便達成研究(1) 數位密碼：為了讓電腦方便執行我使用數碼的方式表達各種同分異構物(2) 五大原則：此原則能讓不僅是電腦甚至是各個要繪製同分異構物的人都能有架構的繪製，不會遺漏任何的組成。(3) ３Ｄ顯示：透過Ｘ３Ｄ軟體的協助我能讓使用者透過立體的方式了解到物質的結構。The purpose of this research is to solve the problem of Isomer’s structure drawing and named problem. It’s hard to predict the status of complex Isomers, so we use the powerful logic and calculational ability of computer to draw the structure of Isomers. The following points is the goal that we want to reach (1) Arrange the structure of the Isomer’s formula (2) Show structural formula of Isomers (3) Predict the chemistry of things that haven’t been created During our research, we create the following principle to help us do the research (1) Digital Codes: In order to let the computer to run the process, we use digital codes to express all the Isomer’s formula. (2) The “5 Rules”: The 5 rules can help not only computers but all the people who try to draw the structure of Isomers without losing any of compositions. (3) 3D Display: Helping our user to understand the structures of materials with the 3D images producing by the “X3D”.

本研究探討自由渦流中的穩定漩渦，自然界的漩渦分為強制渦流和自由渦流兩大類，自由渦流又可分為不穩定漩渦與穩定漩渦兩種。不穩定漩渦的水流不斷的從放流口流出，水面無法保持穩定。穩定漩渦因為有水源補充流出的水，水面則可保持恆定。本研究的測量方式有別於別的研究。我們將漩渦周邊的水壓利用儀器轉變為電壓，再利用流體力學的公式及一些自導公式將這些數值轉變為漩渦的各項數據，如水壓、流速。另外，我們也用攝影機來觀察漩渦的形狀及流線，最後總合而為漩渦周邊的結構。This study investigates vortex type 4—stable free vortexes. Vortexes can be classified into two main categories: force vortexes and free vortexes. Free vortexes can further be subcategorized into unstable free vortexes and stable free vortexes, the difference between which is that the surface and structure of unstable free vortexes do not maintain a stable condition because the water runs outward while those of stable free vortexes do because the water circulates with abundant water supply within the container. The study employed different means of measuring the vortexes from those used by previous studies. The water pressure of the spiraling vortex water flow was measured, transformed into electric power and then into exact values of water pressure and flow velocity by applying equations in flow mechanism and some self-derived equations. Besides, video cameras are also used to observe the patterns and streamlines of the vortexes. Based on the figures achieved, this study obtained a comprehensive account of the structure of the spiraling vortex water flow of stable free vortexes.

在台灣公共場合快速成長下，例如：大賣場、百貨公司、展覽會場，這些公共大型場合都有很好的消防設施，但始終有人葬身於火場？ 原因就是幾乎所有的人都不會去特別注意逃生平面圖，導致花太多的時間尋找出口，這樣生存機率就大大降低。火場裡面有太多的致命因素，像是：高溫的空氣，毒氣、濃煙…等，所以必須把握每一分每一秒。為了加快逃生速度，我們將所有的通道都設有導引警示器，逃生者只要順著導引警示器就可以安全到達出口。為了因應公共場合有龐大的人群，所以逃生路線不能只有一條，因此我們設計上是有多條路線，一、可以解決龐大人群，二、可以加快速度。;With the rapid growth of public places in Taiwan, evacuation system is of more and more importance. Actually, public places, such as hyper malls, department stores and exhibitions, are not without fire-fighting equipment, but why is that there are still people getting killed in a fire? The reason is that almost no one actually pays attention to the evacuation plans. As a result, it often takes too much time to find the exits, which lowers the possibility of survival. In a fire, there are usually too many fatal factors, which could lead to death, such as high temperature and heavy smoke; therefore time is precious when escaping from a fire. To fasten the speed of evacuation, we set guiding alarms in every passageway. By following the guiding alarms, people can get to the exits safely. Besides, owing to the huge amount of population in public places, there can’t be only one route out. With regard to this, we design many routes in order to enable and fasten the speed of evacuation of huge amount of population.

1. Purpose of the research The purpose of this research is to make a suitable experimental pattern to distinguish, by scientific method, organic cereals from non organic cereals. The reference ideas consider cereals (rice, barley and maize) as a complex system that possesses its own chemical–physical properties. These cereals are able to maintain traces of the cultivation process. In non organic cereal grains foreign molecules, from synthesis substances used during their cultivation and/or in their final processing, can be found. These kinds of molecules would be absent in organic cereals. The effect of these foreign molecules traces on the principal components (glucides, proteins, lipids) of cereals is investigated by Infrared Spectroscopy (IR). 2. Procedures The spectra of a small quantity of cereal meal are recorded by the ATR (Attenuated Total Reflectance) sampling method. The meal is obtained from selected grains of rice and barley, that are grated near the germ. On the contrary, the maize grains, are cut lengthwise and the two halves are grated on the interior surface. This procedure of preparing samples, withdraws that part of the non organic cereal grains where foreign molecules are more abundant. The meal mass amounts to only a few milligrams; so in this way the dilution effect caused by starchy and proteinic parts onto the lipid part, is reduced. The cereal packaging has to be intact, well preserved and the expiry date has to be far–off. The organic packaging has the European Certification symbol and that of the authorizing agency. The cereals used in this research, have been labelled with symbols. The experimental data are processed by the NMC (Nearest Means Classification: J.Chem. Educ. 2003, 80, 542) method, adapted to cereals. 3. Data The NMC method is based on the individuation of suitable absorption bands of the IR spectrum and, for each of them, the calculation of the following quantities: the average value of the wave number (); the (Σ) value; the |diff.|=|(ῡ–)| value and the Σ|diff.| value. At the end the sum of the Σ|diff.| for all selected bands is computed in order to obtain the Σ(Σ|diff.|). Then a graph is plotted using (Σ) and Σ(Σ|diff.|) variables. The graph has a gap between the organic cereals and the non organic ones; in other words the organic cereals are found in a particular area, whilst the non organic cereals are found in another area. The boundary between the two areas is a particular value of the Σ(Σ|diff.|). This is the pattern that distinguishes organic cereals from non organic ones. 4. Conclusions For some cereals, the gap is bigger than others; but in any case the position of the cereals on one side of the boundary line or on the other, is clear. An experimental scientific pattern that marks the difference between organic cereals and non organic ones, can be useful to organic farms, authorizing agencies and consumers. This research has planned a route to find such a pattern.

本研究透過對蕃茄施予短時間的不同高鹽份濃度刺激，觀察植株成長 情形並對果實進行品質測定，本研究對於品質之定義著重於總抗氧化能力、糖度及硬度的檢測。由實驗結果得知Na+、Cl-離子所造成的滲透壓差，確實有助於可溶性固形物及Na+、Cl-離子的累積，對於果實糖度及硬度上皆有顯著變化。但對於如何造成總抗氧化能力值的提升，在未來的研究中會再深入探討。We observe the germination of the tomatoes and assay "the quality" of the fruits in our research by giving plants short-range acridness of different high salinity. In this research, the definition of “quality” emphasizes the anti-oxidized ability, the brix, and the hardness. By the experimental result knew Na+ and Cl- ion creates the osmotic pressure, truly is helpful to the Soluble Solid Content and the Na+ and Cl- ion accumulation. Yet regarding by what the anti-oxidized ability promotes, we will treat in-depth in our intended research.

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.

本研究目的1.探討催化劑對光子晶體SiO? 合成的影響，依據催化劑對光子晶體製作的數據，統整歸納出不同濃度的氨水催化劑對於SiO? 的吸收光譜與粒徑大小等性質的影響。2.尋找簡易的方式進行光通道的製作。 採用溶膠凝膠法將tetraethylorthosilicate(TEOS) 以氨水做催化劑在乙醇溶液中的水解及縮合反應製作單分散SiO?粉體。 嘗試將細線附著在玻片上進行排列，排列完成後將細線拉起企圖製造一條溝道。 實驗結果,催化劑會影響合成SiO? 的顆粒大小，隨著催化劑濃度增加，顆粒大小也隨之增加。使用細線可成功製造出凹陷的孔道，但目前採用之線仍嫌太粗，欲尋找奈米線材加以取代以製造出更適用之光通道。 ;The purpose of this research is 1.to find out the influence of the catalyst on compounding silica photonic crystals . According to datum , I can generalize the connection between the consistency of catalyst and the particle size of photonic crystal. 2.to find easier method of making the passage of light. I used tetraethylorthosilicate (TEOS) as a reactant and ammonia as the catalyst to react hydrolysis ,water condensation and alcohol condensation in ethanol. I tried to put fine lines on sheet glasses. After the arrangement of the silica particles, I took apart the lines attempting to make sunken ditches. The outcome of this ecperiment show that partical size increases with the consistency of catalyst. We can use fine lines to make the sunken ditches, but the line is not fine enough that I should find much finer lines to make it.

自2004年4月29日至2004年8月30日止，研究不同食物量對於蓋斑鬥魚生殖表現之影響。自臺北縣水產種苗繁殖場取得40尾（北縣種苗場字第0930000192號），分成低、中、次高、與最高四個飼養食物量組（3, 6, 9 ,12 顆飼料/每隻魚），每一種食物量組進行四次重複實驗，每一個實驗箱飼養雌、雄魚一對，控制相同的光週期、溫度、密度等變因。結果顯示食物量為中食量組（6粒/隻）泡巢維持時間最長，與其他三組統計上有顯著差異，而其他生殖表現如雄魚的吐泡巢次數、泡巢間隔時間，以及雌魚產卵次數、產卵間隔時間，和魚卵孵化時間等四組之間皆無明顯差異。因此推測不同飼養食物量的處理對於蓋斑鬥魚生殖行為之影響不顯著。From April 29, 2004 to August 30, 2004, we studied the effects on breeding behavior of Macropodus opercularis in different quantities of food. We got forty fish from the nursery in Taipei County. We breed one male and one female in the tank, and the quantities food was set to low, middle, high, and highest groups (3, 6, 9, 12 granule forage per one fish). Every experiment group repeated three times. We also controlled the same light cycle, temperature, and density. We found that the longest maintenance time per one foam nest was breeding in middle group, and there is a statistically significant difference. But the other results had no statistically significant differences between different groups. Therefore, we inferred that the different allowance food feeding control had no significant effect to breeding behaviors of Macropodus opercularis.

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。