Drought and inundation are two unusual natural disasters in Taiwan. The two natural disasters\r have some relation of abnormal rainfall become more and more in Taiwan. So it let me think about\r can climate vicissitudes make the chance of abnormal rainfall become more?\r The study have researched the chance of abnormal rainfall by "rainfall duration" and "total\r rainfall". It collect the day by day total rainfall from 1960 to July 2002, collect locals are Taipei,\r Taichung, Kaohsiung and Hualien. Than enter the data into the computer, let computer calculation\r total rainfall, rainfall days, heavy rain days, pouring rain days and torrential rain days. Then\r analysis the tendency of long-term change.\r According to the analysis, the chance of abnormal rainfall happened become more in Taipei,\r Taichung, Kaohsiung and Hualien. The ratio of Hualien and Kaohsiung is the most obviously. It's\r also find that there temperature and total evaporate became higher, the total sunshine duration\r became lower. Then El Nino have some influence in abnormal rainfal. In El Nino year, total rainfall\r will become lower. When La Nina year, the total rainfall will become more in Taipei and Hualien.\r Then the long influence is clearly in Taipei.\r 乾旱與水災是台灣地區相當常見的二項天災，這二項災害的發生都與異常降水有直接的\r 關係。近年來台灣地區因異常降水造成的天然災害，似乎有逐年增加的趨勢。因此讓人聯想\r 到氣候變遷是否會導致異常降水頻率增加。\r 本研究主要由「降雨時數」與「降雨量」二方面探討異常降水發生頻率。先收集台北、\r 台中、高雄、花蓮四地自1960 年至2002 年七月三十一日之逐日雨量資料，將資料輸入電腦\r 後，統計各站歷年降雨量、降雨日數、大雨、豪雨、暴雨日數，並分析長期變化趨勢。\r 分析結果，台北、台中、高雄、花蓮四地異常降水發生機率，有增加的情形；其中以花\r 蓮及高雄變化的比例最高。再與其他各地氣象要素比較可發現，可能與氣溫及蒸發量數上升，\r 以及日照時數縮短有關。另外聖嬰現象也可能對異常降水有長期性的影響。一般而言聖嬰年\r 雨量減少，反聖嬰年台北、花蓮地區雨量反而會增加。而長期性的影響，以台北地區最顯著。

在這篇研究報告中,我用了三種觀點來推廣幾何中的反演變換,首先,把反演變換視為是一種圓內與圓外的一種1-1且onto的映射,第一種推廣,是將變換中心移到視圓心以外的圓內的地方,馬上我們得到一個結論「反演半徑會隨著動點而改變」,接著,我們實驗了一下反演變換用有的一些性質,保角性,保圓性,…等在這個變換視中是否依然存在;接著我們用第二種方法來推廣反演變換,我們將邊界的形狀由圓視改成別的形狀(如三角形,四邊形…等等),然後也試試看在這種變換之下是否還擁視有反演變換的一些性質;第三種推廣,則是在研究的過程中,我發現了一種新的幾視變換,承接第一種推廣,我們將原先為定點的變換中心改為動點,將原先的動點改為定點,做出來的一種新變換。In the study, a new geometric Inversive transformation through three points is discovered. Here is the main result：（1）The first, onto cycle of inside and outside can be proved under invasive transformation. It is changed moving the center from center of cycle, we can get a new ” Inversive radius can be changed by moving drop. (2) We hope to find the answer to this problem by experiment, it is exist with the inversive properties. (3) A new geometric transformation is discovered, a fixed drop can be changed moving drop, then the first moving drop shifted the fixed drop. This leads to a new construction if the new transformation.

帶電的離子受到垂直的磁場與電場作用，會因為受到洛倫茲力而產生有趣的轉動現象。我們利用上述原理設計簡易的裝置設備，探討電解質溶液不同濃度、不同離子電荷數，受到不同離子間靜電力，產生不同的離子移動速度。經由所測量的時間與圓周運動的距離，可計算電解質的絕對遷移速度。由實驗結果推論在固定電場下，當電解質濃度降低，正、負離子間的相互作用力降低，離子遷移速度(migration velocity)加快，莫耳電導率 Λ（mole conductance)也隨之增加。同濃度時，電解質2-1 價型硝酸銅與2-2 型硫酸銅離子強度(ionic strength)不同，2-2型硫酸銅離子強度較大，遷移速度較小，莫耳電導率Λ 也較小。Because of the effect of Lorentz force, charged ion will have interesting rotation under the vertical magnetic and electric field. We use the above principle to design a simple instrument or tool, in order to evaluate and study the formation of different ionic mirgration velocities. The velocity of the charged ion in the instrument is affected by differences in the electrolyte, the charge differences of the ion tested and the differences in electrostatic forces between ions. From the experiment we can deduct that at a fixed constant electric field, when the concentration of the electrolyte is reduced, the interaction of forces between positive and negative ions will be reduced. When the migration velocity of ions increase, the mole conductivity Λ (mole conductance ) will also increase. At the same concentration, the ionic strength between copper nitrate ( 2-1valency type ) and copper sulfate ( 2-2 valency type ) are not identical. Copper sulfate, a 2-2 valency type has higher ionic strength, the velocity is slower and the mole conductivity Λ is also smaller.

滿足之M 點，我們稱之為Pi(i=1…n)的均值點。當n=3，M 恰為△P1P2P3 的重心 (G); n=4 時，M 亦為三角錐P1P2P3P4 的重心！因此不免引人遐思：滿足之M 點是否皆為其重心？ 我們藉由電腦幾何作圖軟體GSP 協助觀察，掌握了圖形變化間之不變性，再配合向量解析及推理，得以發現均值點、多邊形的重心、以至多面體的重心、及平行多邊形的一般性作法。附帶又發現：任意相鄰三頂點即可決定一平行n 邊形。並進而證實：平行四邊形為四邊形M＝G 的充要條件。但當n≧5 時，平行n 邊形只是n 邊形M＝G 的充分非必要條件！一般而言，具有對稱中心O 的n 個點所構成的圖形必可使M 與G 重合於O 點上。 The point M satisfying is called “the mean point of Pi(i=1…n)”. As n=3, M is the center of gravity (G) of the △P1P2P3. If n=4, then M is also the center of gravity of the triangular pyramid P1P2P3P4. Therefore, I began to wonder if the following assumption stands: The point M that satisfies is always a center of gravity. By using the computer software GSP (The Geometer’s Sketchpad) to observe figures. It is found that when a figure is changing there is still constancy. Furthermore, supported by the analysis based on vectors, general constructions can be established concerning the mean point, the center of gravity of polygon, the center of gravity of polyhedron, and the parallel polygon. Also, I find that any three neighboring vertexes decide a parallel polygon. And thus it is verified that the parallelogram is the sufficient and necessary condition for quadrilateral M=G. As n≧5, the parallel n-sides shape is the sufficient, not necessary condition, for n-sides shape M=G. In general, a central figure of n points having the center of symmetry O can make M and G meet on O.

本文研究風洞中之風帆在不同條件下，受風吹拂所產生之升力與阻力關係，並探討及成功 的以數學模型解釋其原因，此研究結果可應用於帆船帆面之設計。其主要探討之變因為以下 之五種： (一) 風速大小對帆船帆面之受力關係：當帆面與風向垂直時，在低風速時，實際測值較接近 風速的一次方的函數關係。高風速時，實際測值接近為風速的二次方的函數關係。 (二) 帆面積大小與受風推進力之關係：當帆面與風向垂直時，在風速固定風速下實驗，得到 面積與風對帆推力成正比。 (三) 順風航行時，帆面之攻角(θ)與受風推進力之關係：航行方向的力與sin 2θ 成正比關係。 (四) 側風航行時，帆面之攻角(θ)與受風推進力之關係：帆面在攻角大於 45°時，航行方向的力與sin θcosθ 有相當程度的吻合，而在攻角0°~45°之間則與飛機攻 角升力資料相接近。 (五) 初步探討雙桅帆與單桅帆面受風推進力之不同：發現其在側風時能有效的減少失速的現 象，在帆面高攻角時，能減少失速現象，依然可以持續穩定的航行，我們也可推想出飛機 的機翼前段的縫翼功能也是如此。 This article is derived from our research of relation between lifting power and its resistant power produced via wind-blow in a wind tunnel under different terms and condition, also to discuss and to explain their causes successfully via mathematics models, thus, the result of this study may be applied in designing of sail-surfaces of sails boats. Its major discussion can be included into the below 5 kinds: - Relation of (1) Relation of sizes of wind-speed against reacceptance of aerodynamic forces over sail-surface: When sail-surface and wind direction becomes horizontal, under low coin-speed, practical measured-value is rather close to wind-speed's linear function relation. When in nigh wind-speed, the practical measured-value is rather close to wind-speed's quadratic function relation. (2) Relation of size of sail-surface and pushing power of wind: When sail-surface and wind direction becomes horizontal, an experiment was made under fixed wind speed, the result obtained is sail-surface size and pushing wind power toward sail is in direct proportion. (3) When it is in “round-the-clock wise” navigation the angle of attack (θ) of sail-surface and the relation with wind's pushing power: Strength of navigation direction and sin2θconforming direct proportion. (4) When it is in side-wind navigation, the angle of attack (θ) and pushing power by wind relation; When the sail surface is in the angle of attack (θ) greater than 45o, the navigation direction power and sinθcosθhas certain extent of conformity, and between angle of attack e 0o-45o, happens to be very appropriate with aircraft's angle of attack and lifting power data. Fundamental discussion of Double Masts Sail boats and Single Mast Sail boats comparing differences of wind-aided pushing power: It was found that stall phenomena could be decreased effectively, when it is side-winded, especially, when the sail-surface is at high angle of attack, it could decrease Stall phenomena, and could maintain stable navigation. We can also assume that the front section of aircraft aide-wing’s function exactly the same.

本實驗使用聚醚亞醯胺溶液製備基本薄膜，由於玻璃態高分子薄膜過於緻密，一直是高分子薄膜在應用上的一大限制，為了在薄膜上製造缺陷，又不會使薄膜之選擇性降低，因此選擇將酸化之奈米碳管(孔徑10~20nm) 加至聚醚亞醯胺薄膜中。本實驗主要為探討添加不同濃度的酸化奈米碳管對聚醚亞醯胺薄膜的滲透率與選擇率的影響，藉由添加0.5 wt%、1 wt%、1.5 wt%、3 wt%、4 wt%等不同濃度的酸化奈米碳管至15 wt% 的聚醚亞醯胺溶液中，並製作薄膜，測試其基本性質與五種氣體(H2、CO2、O2、N2、CH4)的滲透率及不同空氣分子之間的選擇率。我們總共測試了三種薄膜的性質，分別是表面特性、熱穩定性及結晶型與層間距，薄膜的表面性質，能觀察到奈米碳管在薄膜中製造奈米孔隙結構，增加氣體滲透的孔道，能有效增加氣體的滲透率。增加奈米碳管的量，能有效升高第一階段熱裂解的溫度，雖然熱裂解在本實驗中沒有很大的差異，但是還是可以從熱重分析圖中推測不同量的奈米碳管會影響熱穩定性。在X 光繞射實驗中，添加奈米碳管的薄膜與純聚醚亞醯胺薄膜，在結晶相上都屬非結晶型薄膜，添加了奈米碳管的高分子複合薄膜的層間距明顯增大。在氣體滲透實驗中，我們比較了不同氣體或濃度不同的奈米複合薄膜的氣體滲透率，在不同氣體時，氣體的滲透率會隨著奈米碳管濃度增加有明顯的提升，五種氣體滲透率大致依照H2>CO2>O2>N2>CH4 這個趨勢增減。奈米碳管對1.5%增加到3%或4%的奈米複合薄膜滲透率的影響卻減小，由此可以推斷奈米碳管對空氣滲透率並非無限制的增加，在1.5%以後就漸漸趨近最大值。H2為14.89barrer，CO2 為9.51barrer，O2為6.34barrer，N2為6.48barrer， CH4 為3.75barrer 。本研究總共比較了三組氣體的選擇率，分別是CO2/CH4，O2/N2，H2/CH4，分離率最高的是H2/CH4 的，兩分子的粒徑大小差對分離率有極大影響，差愈大，其分離率也愈高。奈米碳管的量改變並不會使薄膜的氣體選擇率明顯增加或減少，但是加入太多奈米碳管其選擇率會變低。在五片薄膜中，1.5%的薄膜有最好的選擇率，奈米碳管的添加量超過1.5%選擇率就會開始下降。綜合滲透率及選擇率可以分析出，添加1.5%奈米碳管的高分子奈米複合薄膜有較高的滲透率，又不會降低選擇率，在利用上比其他濃度的奈米複合薄膜在有害氣體過濾及空氣的分離回收方面產生更好的效果。;This experiment uses Polyetherimide polymers solution to make basic membranes. Because glassy polymer membranes are too dense for gas permeations, it is one of the limitations in their applications. To increase gas permeability and maintain air selectivity, I made some nanogaps on the surface of the membranes by an acidification multi-wall carbon nanotubes (MWNTs, kinetic diameter 10~20nm) in the PEI membranes. We mainly want to find if it has some influence between the consistency of acidification MWNTs and gas permeability or selectivity. We mixed 0.5wt% 、1wt%、1.5wt%、3wt%、4wt% acidification Carbon nanotube in 15wt% PEI solution, made membranes and tested the character, five kinds of gas permeability (H2、CO2、O2、N2、CH4) and the selectivity between different gases. We have tested the three nature of membranes, including surface characteristic, TGA and XRD. We can see some nanogapes made by carbon nanotube in the membranes. It could availably increase gas permeability. Mixing more carbon nanotube in the membranes could increase the temperature of the first heat-decomposition. Though the heat-decomposition in this experiment didn’t change a lot, we could say that different percent nanotube would affect the membranes’ heat-decomposition. By the experiment of XRD, the membranes with carbon nanotube and the pure PEI membranes attach to amorphous membranes. Nanocomposite’s de-spacing is bigger than pure membranes. In the experiment of air permeability, we compared different kinds of gas or different percent carbon nanotube of nanocomposite if they have some change of permeability. The conclusion is that air permeability increase as the quantity of nanotube increase. The five kinds of permeability the direction：H2>CO2>O2>N2>CH4.The influence of permeability will decrease when the quantity of carbon nanotube increase from 1.5% to 3% or 4%. We can get the conclusion that the increment of gas permeability isn’t limitary. It drifts towards maximal about 1.5%. H2 is 14.89barrer. CO2 is 9.51barrer. O2 is 6.34barrer. N2 is 6.48barrer. CH4 is 3.75 barrer.This experiment totally compared three groups of air selectivity. They ’re CO2/CH4, O2/N2 and H2/CH4. The maximum of selectivity is H2/CH4. The difference of kinetic diameter affects air selectivity a lot. The quantity of nanotube doesn’t associate with the air selectivity, but mixing too much nanotube will decrease air selectivity. The 1.5% nanocomposite has the highest selectivity. If the consistency of the membranes is higher than 1.5%, the air selectivity will decrease. Depend on the gas permeability and the air selectivity, the 1.5% nanocomposite has higher permeability and constant air selectivity. That shows the 1.5% nanocomposite has a better effect on air selectivity and recycling.

在眾多的蝴蝶中有不少是具有眼斑。傳統上認為眼斑的功能是驚嚇天敵或欺騙天敵。有關眼斑本身結構的瞭解很少。我們利用臺灣及馬祖產的蝴蝶，分別記錄圖鑑上峽蝶、眼蝶及灰蝶合計 60 種以上，以及鳳蝶幼蟲七種的眼斑特性。記錄的眼斑特性包括數目、組成的色彩結構，以及記錄眼斑在翅的腹面或背面明顯。進一步測暈孔雀峽蝶、台灣波眼蝶、蘇鐵小灰蝶等三種蝴蝶的眼斑和翅面積。眼斑在腹面及背面都有，但以腹面明顯者佔多數，而眼斑數 l 一 7 個都有，在後翅者佔多數。眼斑慕本是由數個同心圓組成，分別為輪廓、眼白、虹彩及障孔。在峽蝶及眼蝶的結構都相當完整，輪廓為褐或深褐，眼白為黃色為主，虹彩都為黑色或深褐色，障孔為白色或淡藍色。在灰蝶的眼斑較不完整，大都輪廓不清晰，眼白的黃色或橙色部份比例高，但都缺少障孔。幼蟲有眼斑成蟲不一定有。鳳蝶的幼蟲（ 8 種）都為綠色，其眼斑輪廓黑色，眼白為白色及紅色但明顯比上述成蟲的眼斑之眼白部位要小，而黑色的虹彩都很大。幼蟲的障孔為白色的細線形，我們認為這和立體形狀的幼蟲及成蟲平面翅的差異所造成，在文中也討論到水棲蝶魚的眼斑和蝴蝶眼斑的差異。眼斑和翅面積的相關分析結果變異很大，在統計上正相關及負相關都有。眼斑數目的不定及和翅面積並沒有一定關係，我們討論到蝴蝶的眼斑在不同種類有些可能有求偶生殖上的功能。這方面值得科學家大量投入研究。Quite a few species of butterflies have colorful eyespots on their wings. The main functions of these eyespots were considered to startle or deceive predators by most scientific researchers. In fact, only limited literatures dealt with the basic structure and color patterns of butterfly eyespots. The purpose of this study is to study the basic structure and color patterns of these eyespots. We measured the surface area of eyespots v.s. wings from specimens. From the color plates of Taiwan and Matsu butterfly field guide, we recorded the eyespots either on ventral or dorsal side of wings, and the color patterns for more than 60 species. \r The number of eyespots on wings varies from I to 7 among individuals we checked. Majority of eyespots were found on ventral side of wings. The basic structure of eyespots were formed by I to 3 concentric circles, i.e., outboundary, cornea, iris and pupil . Pupil was not found in certain species. The color in cornea section is yellow and in iris is black or dark brown. The contrast in these two areas is quite prominent just as the contrast showed in warning coloration of after animals. The pupil is either white of light blue. Caterpillars with eyespots were found in Papilionidae, their adult stage were without this character. We checked 8 species of caterpillars, their basic structure of eyespots were similar to other butterflies, with cornea, iris and pupil. The cornea is either red or white color, and the iris is black in colors. The ratio(iris/cornea) is much higher in caterpillar than in butterfly. The pupil is a thin thread shape instead of a tiny spot like the one in butterfly wings. We discussed the difference of pupil between juveniles and adults from the aspect of dimension structure of a subject. In the paper we also discussed the difference of eyespots between butterfly and butterfly fish in the coral reef. Base on the no significant relationship between the surface area of eyespots and wings. We suspect that butterfly eyespots may have another function, such as intersexual selection between males and females beside startling and deceiving predators.\r

本研究以碳化矽(SiC)奈米粉末加入去離子水中，插入銅電極加以電壓進行其表面帶電性的研究。研究中發現SiC奈米粉末的表面帶有負電荷，且加以電壓後，SiC奈米粉末會沉澱下來。利用場發射掃描式電子顯微鏡(SEM)及X-光繞射儀(X-RD)檢測其性質，發現加以電壓使奈米粉末失去電荷而聚集沉澱。同時經由製作不同酸鹼度SiC奈米粉末溶液的陽極極化曲線發現pH值越大，SiC奈米粉末表面電位越高，開放電路電位越小。本研究實驗過程中發現pH值2之SiC奈米粉末溶液加過電壓後，正極生成一透明薄膜狀物質，極有可能是導電鍍膜，應用價值極高。本研究已先進行微硬度試驗與金相實驗，將由長庚大學機械系研究所進行更深入檢測與研究。The electrochemical behavior of the SiC-nanopowder in deionized water was studied. The electrochemical cell was composed of two pure copper electrodes, across which different voltages were applied. The morphology of the nanopowders or even with reacted products was examined using field emission electron microscope(FESEM) and the corresponding phases were identified with X-ray diffraction method(XRD). The experimental results show that tha nano-powders precipitated at the surface of the anodic copper electrode and in the same time the nanopowders in the solution aggregated when 20 volts were applied across two electrodes. That is, net negative charge could be induced around the nanopowder. Deposition rate of the aggregated powders in the various pH-value solutions was evaluated and the aggregated powders were examined with FESEM. The higher Zeta potential of the SiC-nanopowder was examined as the nanopowders immersed in the higher pH value solution. The nanopowders aggregated themselves as the pH value under 2. The anodic polarization behavior of the copper electrode in SiC- nanopowder solution was measured and the results were compared with the aforementioned tests.

This experiment mainly aims at three kinds of solution - Dextrose, Saccharose, and Fructose. By changing its temperature, density, length of tube, as well as different wave length factor of polarized light, we observe the influence of the direction of polarization by those factors. The experimental result showed as follow. The Dextrose and the Saccharose can cause the polarized light with the rotary direction of clockwise, so both are ‘dextrorotatory’. The Fructose can cause the polarized light with the direction of counterclockwise, so it is the ‘laevorotatory’. For the Dextrose, when the\r temperature is lower than 20℃, the direction of polarization has changed observably, but doesn’t have any rule. When the temperature is higher than 20℃, the direction of polarization increase slowly. For those three kinds of solution, when\r density increased, the polarization increased observably. When the polarized light passed through the solution with longer path, the direction of polarization has more change. When the wave length of the polarized light changed, the direction of polarization has been changed observably. When the wave length of the polarized light is shorter, the direction of polarization change increased.本實驗主要針對葡萄糖、蔗糖、及果糖等三種旋光性溶液，改變其溫度、濃度、容器管長、以及不同波長的偏振光等因子，觀察這些因素對偏振方向所造成的影響。實驗結果顯示：葡萄糖與蔗糖會使得偏振光的偏振方向以順時針旋轉，屬右旋性之光學異構物；果糖會使得偏振光的偏振方向以逆時針旋轉，屬左旋性之光學異構物。若溶液為葡萄糖，當溫度低於20℃時，偏振光的偏振方向會有明顯的改變，但無規則可尋；當溫度大於20℃時，偏振方向旋轉角位移則以非常緩慢的方式增加。當此三種溶液之濃度增加時，偏振光的偏振方向有明顯遞增的現象。此外，當容器長度越長（即偏振光在介質中的行程越長）時，偏振方向的改變亦越明顯。當偏振光的波長改變時，偏振光的偏振方向有明顯的變化，且當偏振光的波長越短，偏振方向的改變越大，似乎與波長呈反比，但此結果與理論值（即旋光度與波長平方成反比）仍有一些差距。

k(2αβ ,α2 ? β2,α2 + β2 )是大家熟悉畢氏定理的通式解，且一般書籍的証明大都採用代數的手法證明。以國中生而言，上述的代數方對國中生來說不夠直接且較無推展的實用性。因此幾何觀點出發發展另一種思考方式，利用角平線的性質給予畢氏定理比例解另一種全新的詮釋，並賦予比例解中的參數α 、β 在幾何的意義。在推理的過程中，我們得到一個相當有用的對應關係：一個有理數對應到一個直角三角形、兩個有理數對應到海倫三角形，再將此對應關係運用到各種幾何圖形上面，即可證明出他們所對應的通式解。最後我的興趣鎖定在海倫三角形、完美海倫多邊形與超完美海倫多邊形上的做圖方法上，善用我們所發展的對應關係，上述的問題皆可迎刃而解。k(2αβ ,α2 ? β2,α2 + β2 ) is a popular formula in Pythagoras Theory, often proved in algebra approach among books. Nevertheless, in light of junior high students, the aforementioned algebra method is neither direct nor practical. Hence, a different thinking method is derived from geometry perspective, using the straight line concept to reinterpret Pythagoras Theory and define the geometric meanings of α andβ . In the process of logical development, a useful correlation emerges: a rational number correlates with a straight-angled triangle, and two rational numbers correlate with Heron Triangle. This correlation can be applied to all kinds of geometrical diagrams to prove the correlated homogenous solution. Ultimately, my interest lies in the diagram methods of Heron Triangle, Perfect Heron Polygon, and Super Perfect Heron Polygon in order to apply our developed correlations to solve the above mentioned problems.