在做這實驗之前，我花了很長一段時間思考一個問題：我如何能得到同\r 樣大小（均勻）的水珠陣列？我在家中各個角落放置許多水瓶，看看哪\r 個地方能培養出顆粒相同的水珠？ 往往肉眼見到整齊排列的水珠，一經\r 顯微鏡觀察，可就大小不齊整了。\r 第一篇中的實驗，幾乎是「水珠日記」，記載冷凝過程；其中我特地比對\r 「穩定的水蒸氣氣流」與「擾動的水蒸氣氣流」、「水蒸氣氣流與凝結盤\r 間溫度差別」、「凝結盤密度差別」、「凝結因子的重量百分濃度差別」、「水\r 蒸氣氣流之流速差別」，並加以複合比對。希望能找到產生均勻排列的條\r 件–探討水分子的自我組裝機制（Self Mechanism of Water Droplets）。\r 這其中提出『均勻假說』： 當條件合宜時，冷凝下降的細微水珠會產生\r free vortex ring，形成整齊的渦環組合，進而產生均勻排列的細微水珠陣\r 列。\r 實驗是藉由溶液密度小於水的設計，讓水蒸氣冷凝於液面上，並且因密\r 度較大而下沉。設計的要點是：儘量減少細微水珠自冷凝後的堆疊\r （coalescence），以呈現水珠原貌。\r 在第二篇實驗中，將對渦旋比例尺修正。渦旋本身難測大小，在空氣中\r 也不易觀察，但是若由水中觀看，可藉由空氣蕊長短估算。這次更進一\r 步考慮到排水速率、水深、排水口形狀、與極值。\r \r I have tried to ask a famous math professor if he can create a formula\r describing the ordered array of water droplets。〝Then, I should study Physics\r first !〞He said。\r Condensation is the thing we live with , being found everywhere, passing\r without notice。But we never know0 when it does start？\r This experiment presented here is actually the diary of the growth of water\r droplets through condensation。Through convection and vortex ring, it\r discusses the self assembly mechanism of water droplets and peep into the\r uniformity of the size of water droplets。\r Here, vortex ring plays an important role in the self assembly mechanism of\r water droplets which is not triggered in the daily life。\r By coalescence, water droplets grow bigger, but are not round again。We used\r the polymer film as template and designed the solution lighter than water, so\r the minute droplets will sink to the bottom and layer by layer。After seconds\r we may have multilayers of ordered array。\r This is the first step in discovering the uniformity of water droplets, besides, I\r made some correction to the Vortex-Ruler。Vortex-Ruler will be useful in\r researching the flying mechanism of butterfly and dragonfly as to judge\r which one induces more vortices。

We study the magic power of dark energy and dark matter by using theoretical derivation and numerical simulations. We found that: 1. The dark energy will gain kinetic energy from the moving dark matter through gravitational interaction. Due to the law of energy conservation, the motion of the dark matter will slow down and satisfy Ek(t)−Ek0 ∝ρDE1.92 t, where Ek(t) is the kinetic energy of the dark matter, Ek0 is its initial kinetic energy, ρDE is the energy density of the dark energy, and t is the time. 2. The formation history and the structure of galaxies will be different due to the existence of dark energy. The more the dark energy, the earlier the formation of the galaxy core. In addition, the kinetic energy Ek(R) as a function of R will be different if the ρDE is different. Thus we can observationally measure the Ek(R) of galaxies, compare it will our results here, and then deduce the ρDE in our universe. The results here can be applied to the observations in the near future. 我們藉由理論的推導，配合電腦模擬的手段，來探討宇宙中黑暗物質和黑暗能量的神祕力量。我們發現：一、黑暗能量會透過重力交互作用而從運動中的黑暗物質獲得力學能，而且因力學能守恆，致使黑暗物質的速率減慢，滿足 Ek(t)−Ek0 ∝ρDE1.92 t, 其中 Ek(t) 為黑暗物質的動能， Ek0 為其初始動能， ρDE 為黑暗能量的密度，t 為時間。二、星系的形成過程及結構，會因黑暗能量的存在而改變。黑暗能量越多時，星系的核心會越早形成。而且動能 Ek(R) 隨著至星系中心距離 R 的變化，會因 ρDE 的不同而不同，因此可以試圖量測宇宙中星系的 Ek(R) ，然後和這裡的結果比對，即可推導出宇宙中的 ρDE 。這些研究成果，將可直接應用在未來的觀測結果上。

本研究探討象鼻蟲製作捲葉前在葉面上戳洞行為與圓柱狀捲葉關係。研究過程中測量葉面上孔洞記號的連接距離，發現可呈現許多相似等腰三角形，將所畫出的三角形組合成七邊形後，再利用三角函數及餘弦定理來驗證孔洞與捲葉間數學的規律。探討全等性質的等腰三角形及相似等腰三角形面積關係，並以手作摺紙及GSP軟體繪製圖形觀察。結果可以得知： (一)在一面積相等的正七邊形中，全等三角形合併時（內部為中心點）與相似等腰三角形合併時（內部為任意點）的面積公式為a/2(h1+h2+...hn)=n*a/4(cosθ/2)2*sin2π/n ，則可知兩者面積相等。 (二)我們利用餘弦定理進行演算，結果發現等腰三角形頂角約為 ，底角約為 ，與正七邊形內角相近，所以可得知捲葉搖籃內部約為正七邊形，而有接近圓的模式，符合捲葉搖籃的外觀形態。

Synthesis of halooximes has attracted much attention given their importance as precursors to proline derivatives1, unnatural amino acids2 and a host of alkaloids3. Halooximes have numerous industrial and biological applications 4, for example oxime ethers increases specific channel opening activities, acting as potential targets in drug treatment for various diseases 5, most adrenergic β-receptor blocking compounds also conform to the structure of oxime ethers 6. They also have vitro antifungal activities against certain plants7. A known method for the synthesis of 3 using Me3SiX as a Lewis acid, via intermediate enamines with acyclic/ cyclic bis(oxy)enamines, gives yields between 21-68%. Low yield stems from lack of reaction specificity2. In this work, we investigate coupling nitrogen-oxides with CoBr2 to synthesise halooximes in high yield. Initial cyclic/ acyclic bis(oxy)enamines were prepared by reacting 1 equiv. nitro compound with 2.4 equiv. in excess of dichloromethane under argon atmosphere at a temperature of 0ºC. 2.2 equiv. of TMS-Br was further added and left to stir till thermal equilibrium with room conditions. The cyclic/ acyclic bis(oxy)enamine was isolated upon aqueous work-up, filtration and evaporation. Synthesis of halooximes was carried out by reacting 8mL to 1mmol equiv. of THF and 2 equiv. of CoBr2 under argon atmosphere and left to stir till CoBr2 dissolves. 2mL to 1mmol equiv. of CH2Cl2 was added to 1 equiv. of bis(oxy)enamines. The reaction mixture was left to stir at room temperature for 2 hours, after which aqueous work-up, filtration and evaporation were carried out. Our results are summarized in Table 1. We also obtained relatively high percentage yields for the direct synthesis of bromooximes from cyclic nitronates via a one-pot procedure: Low yield stems from lack of reaction specificity2. In this work, we investigate coupling nitrogen-oxides with CoBr2 to synthesise halooximes in high yield. Initial cyclic/ acyclic bis(oxy)enamines were prepared by reacting 1 equiv. nitro compound with 2.4 equiv. in excess of dichloromethane under argon atmosphere at a temperature of 0ºC. 2.2 equiv. of TMS-Br was further added and left to stir till thermal equilibrium with room conditions. The cyclic/ acyclic bis(oxy)enamine was isolated upon aqueous work-up, filtration and evaporation. Synthesis of halooximes was carried out by reacting 8mL to 1mmol equiv. of THF and 2 equiv. of CoBr2 under argon atmosphere and left to stir till CoBr2 dissolves. 2mL to 1mmol equiv. of CH2Cl2 was added to 1 equiv. of bis(oxy)enamines. The reaction mixture was left to stir at room temperature for 2 hours, after which aqueous work-up, filtration and evaporation were carried out. Our results are summarized in Table 1. We also obtained relatively high percentage yields for the direct synthesis of bromooximes from cyclic nitronates via a one-pot procedure:

複雜系統廣泛地存在每個人生活的周遭，儘管這些系統在表象上有明顯的差異，卻不約而同的都呈現出臨界現象。一個簡單的物理概念卻能廣泛地使用在許多不同的場合當中，這是令人始料未及的。這份報告在尋找，是什麼原因導致這許多似乎與物理沒什麼關聯的系統，都呈現出臨界現象？以及這類系統是如何演化的？臨界現象在系統的演化歷史中，又是扮演怎樣的一個角色？一開始，先介紹臨界現象在實際系統中表現的形式，在這以文字系統作為範例。接下來，進入思考的階段，猜測系統個體間存有的關聯性，提出如何影響的假設，並建立模型。從模型結果，可以了解複雜系統隨時間演化的趨勢改變，並發現臨界現象在系統中扮演的角色以及代表的意義。這份報告有三項結論：1. 臨界現象在複雜系統中呈現的形式 2. 模型結果與實際系統十分相似 3. 臨界現象代表著系統的穩定態。The theory of Scaling Law and Universality was originally used in researching Critical phenomena, and now we find it existing in our normal life. A simple physical concept can be used extensively in different courses. This study try to find out the relation between individuals which causes Critical phenomena appear in such different courses in our normal life, and figure out the effect time brings about. To begin with, we introduce the sights of Scaling Law and Universality by exploring the formation of complicated system. Facing a complicated word system as a real example, we observe an extraordinary phenomena, and find out the Universality and Scaling Law in different kinds of linguistics. In the main part, to think further, what’s the relation between the individuals that leads to Critical phenomena? We will give hypotheses and build a model to simulate complicated system from the view of Universality, trying to find out the cause of the interaction of complicated system. From this model, we could understand: When a complicated system evolves with time, the Critical phenomena will naturally occur in this system that could be considered as dynamic equilibrium. From this study we found out(1) The Universality and Scaling Law in complicated systems, here we use linguistics as an example.(2) Under the hypotheses, the simulation is almost as same as the real result of linguistics system.(3) Time plays an important part in the Critical phenomena which can be found in many different complicated systems, and Critical phenomena symbolize a stable state of such systems.

要檢測膠體粒子是否存在於溶質中，並不能以一般的光學顯微鏡觀察得出，若是用廷得耳效應觀察光線散出的量決定，則將運用到大量昂貴的精密儀器，與繁複深奧的化學理論，本實驗主旨即在運用自製的簡單儀器測量待測膠體流經強磁場因磁電效應產生電壓，藉著改變沈降劑種類或劑量使電壓產生波動的現象，藉此評估各種沉澱劑對膠體溶液沉降效果好壞與最適當的劑量，並將此結果應用在實際污水處理作業的先期測試上。Wanting to know colloid particles exist in solute by a normal optical microscope is impossible. If we use Tyndall effect, to observe the quantity of dispersive beams, to prove whether colloid particles exist in solute, then we will use amount of expensive and precise apparatuses and even complex and abstruse chemical theory. The gist of this experiment is using simple apparatuses that made by us to measure the volt generated by colloid flowing through the strong magnetic field(magnetic-electric effect).Then we try to change the sort or dose of precipitant to let the volt undulate, so that we can compare the impression on precipitating of each of the precipitant and the most applicable dose. Finally the result can be applied to forward trial of practical sewage disposal system.

Chitin, a polysaccharide common in biocomposites, has an interwoven organic framework that can act as a scaffold for mineralization in natural systems. Acidic amino acids, namely aspartic (Asp) and glutamic (Glu) acids, are the primary active molecules at biomineralisation interphases in mollusks and play an important role in controlling the polymorph and morphology of the associated mineral.\r In this study, chitin was extracted from squid pens and used as a scaffold for crystallization. The chitin scaffold was functionalized with glutamic acid and aspartic acid separately to create an artificial microenvironment for the study of biomineralization of calcium carbonate. The objective was to investigate the usefulness of the extracted chitin to serve as a scaffold for calcium carbonate crystallization, especially the fidelity of the polymorph nucleated to the amino acids and proteins used.

The definition of "Fermat Point" is that a dot, which lies in a triangle, has the minimum distance to the three apexes. In other words, "Fermat Point" has the minimum distance to three dots which are not on the same line. In the broad sense, then, in a N polygon, a dot which has the minimum distance to the N apexes could be named "Fermat Point." But what if we link up the N apexes and find out that they cannot make a convex polygon? The above is what we wish to fully discuss. Our inspiration comes from a paper on"Fermat Point." It just describes N convex polygon, so we think of putting the case to naturally polygon. The case may be that it is a concave polygon or part of the apexes which lies on the same line. We would not base our study on the conventional methods. Moreover, strictly defined, the repeated line segment will not be taken into account. That is, if the "Fermat Point" drops on the line with more than two dots on it, we just count the\r line segments except for the shorter line segments which were originally included in other studies. According to the theorem, our conclusions are as follows: 1. If N points lie on the same line segment, then the "Fermat Point"can be any point on the line segment. 2. If (N-1) points are on the same line segment, then the "Fermat Point" is on the point which two lines join together. One is that the line segment, and the other is the one which passes the remaining point and\r perpendicular to the first line segment. 3. Now there are (M+N) points. Among them, M points will make a M jog-polygon. The others all drop in the polygon. As the diagram shown beneath, we know that the "Fermat Point" drops on the point which two lines join together. The two lines must pass as many points as possible. 所謂的「費馬點」是指三角形內到三頂點距離和最小的點。換言之，「費馬點」就是到平面上不共線三點距離和最小的點。因此，我們可定義，廣義的「費馬點」即是n 多邊形內到各頂點距離和最小的點，亦即到平面上不共線n 點距離和最小的點，但若平面上n 點不能恰為n 多邊形的頂點呢？這就是我們所要討論的。由於我們的靈感來自一份關於「費馬點」的科展作品，所以我們想到，當平面上n 點不能恰為n 凸多邊形的頂點，甚或其中有一部分的點共線時，將不能以n邊形的方法來探討，但我們可以將之化為m 邊形內（n-m）個點來討論。而更重要的是，我\r 們增加了另一個限制，重複的線段將不被我們列入計算。亦即當所求點落在某一多點共線的線段上時，我們只計算該線段的總長，而不計其中重複的較短線段。根據這個原則，我們試行證明平面上三點、四點、五點及六點的可能情況，期望能從中找出足以推廣至平面上n 點的一般性。結果雖不完美，但我們總算差強人意的歸納出了下列結論：1.若n 點共線段，所求點可為所共線段上任一點。2.若（n-1）點共線段，則由該不共線點引一線與共線段垂直，其交點即為所求。3.若（n+m）個點中有m 個點為一m 多邊形的頂點，另外n 個點落在該m 多邊形內，則由兩個外頂點引直線盡可能通過最多點，該兩直線的交點即為所求。

台灣西海岸的河川，常飽受嚴重的水污染，其中最嚴重者莫過於重金屬離子所造成的危害了。所以，本作品即探究：從了解【電解水的氧化還原反應】到設計【小型多重兩極分流電解槽】上，希望藉此設計能給相關單位參考，以為農田引水灌溉及養殖水域做把關的工作。最後並對長期以來校內涉及電解、電鍍…等含重金屬離子的實驗做徹底的減廢設計，以排出無污染性的廢水。;Rivers along the west coast of Taiwan have been seriously polluted for a long time, the most hazardous one of which has been caused by heavy metal ion. As such, this article aims at how to discharge a pollution-free wastewater by understanding first from the oxidation- reduction reaction of electrolytic water to design of a miniature multiple bipolarity divided-flow electrolyser. It is hoped that this design would provide related government regulatory agencies with adequate information so that they may be capable of doing a responsible pollution-prevention job in water irrigation for farming land and water for marine farming as well. Finally, the author may further add that this design has been through constant laboratory tests involving electrolysis and electroplating of heavy metal ion in the hope that a perfect design to eradicate wastewater can be produced so as to discharge pollution-free waste water.

Deficiencies in clearance of apoptotic cells predispose to the development of autoimmune disease. This is evident in mice lacking the receptor tyrosine kinases Tyro3, Axl, and Mer that mediate uptake of apoptotic cells. Deficient mice exhibit an increased abundance of apoptotic cells in tissues and manifest diverse autoimmune conditions. To test these mice for the presence of autoantibodies to apoptotic cells, we generated spontaneous splenic B cell hybridomas and used microscopy to screen for clones reactive with apoptotic Jurkat cells. From hybridomas secreting IgG antibodies reactive with apoptotic cells, we selected one that recreated the major serum specificity for apoptotic cells. The antibody, LHC7.15, bound to an antigen that is differentially distributed between the nucleus and the cytoplasm in live and apoptotic cells. In late apoptotic cells, the antigen coalesces into aggregates that form blebs at the cell surface. Immunopurification of the antigen, followed by mass spectrometry, identifed a protein of 69kD whose partial sequence matched hnRNP P2. This multi-functional protein binds DNA, RNA, and several known RNP autoantigens. Our observations suggest that an RNP complex, formed and translocated to the cell surface in apoptosis, participates in the induction of linked sets of anti-RNP autoantibodies. Our results also implicate hnRNP P2 as a potential novel antigen involved in initiating and sustaining systemic autoimmune diseases.

人眼所見點光源四週的光芒（我們稱為"星星長角"），夜間瞇眼時所見向上下方向射的特別長的光芒（我們稱之為"炫光萬丈"），這二種視覺中的光學現象無法用相機拍攝，但眼睛卻能夠看見。書上及網路上均無法找到合理的解釋。因此，我們設計了數個實驗來研究這些光學現象的成因。我們發現了星星長角的成因是由光對眼睛表面刮痕的繞射和光對眼睫毛的繞射雙重原因所產生。而炫光萬丈的成因則是光線經過眼球表面淚膜層的部分反射及部分折射所造成。The purpose of the research is to verify possible reasons of some optical phenomenon in human vision, including the star shape of a dot light source and glare upward or downward when one narrowing his/her eyes. These optical phenomenon can be seen by naked eyes but can not be taken photos with a camera. We find no detailed explains which can explain the cause of glare upward or downward on the internet or in books. So we designed several experiments trying to find out the cause of these optical phenomenon . In experiments, we figured out that diffractions by notches on the surface of eyes and eyelashes are both responsible for the star shape of a dot light source. The cause of glare when narrowing eyes is that partial reflection and partial refraction of light take place between boundary of air and tear film and boundary of tear film and cornea. The appearance of glare is closely related to the thickness of the tear film . When we narrow our eyes , the tear film is thicker. The thicker the tear film is ; the longer the glare is .Also, bended extent influence the length of glare. We figured out that the more bended the tear film is ; the longer the glare is.