MTU值與網路效率的關係
中文摘要：\r 本研究旨在探討，在TCP/IP 協定之下，最大網路傳輸效率之MTU\r （Maximum Transmission Unit,最大傳輸單位）值。根據IEEE 所公\r 佈Ethernet 之標準，經實地模擬實驗，本研究之結論如下：（1）在\r 單純兩台電腦直接串接時，由於幾乎無任何干擾與封包的碰撞，可設\r 定之MTU 最大值以1500bytes 為最佳；（2）但在模擬真實的大型廣域\r 網路時，由於碰撞增加及雜訊增多，經模擬實驗顯示，MTU 值為\r 1500bytes 時無法在資料傳送、接收及重組時取得平衡，最佳之MTU\r 值落於500 到600bytes 之間，進一步研究顯示MTU 值設在500 到\r 600bytes 時可提升傳輸效率約50%。同時，本研究亦討論將此機制應\r 用於未來新網路標準之可行性及其必要性。Abstract：\r The main purpose of this research is to explore the best network\r transmission efficiency's Maximum Transmission Unit under TCP/IP\r protocol. According to the Ethernet's standard of IEEE and simulated\r experiments, the outcome of this research are :( 1) When connecting two\r computers serially, there is almost no interference and impact of packets,\r the best MTU that we can set up is 1500bytes ;( 2)When simulating the\r truly wide area network, interference and impact are rising. The result of\r this simulates experiment shows that when MTU is at 1500bytes, it's\r unable to keep balance when sending, receiving and re-composing. The\r best new MTU is between 500bytes and 600bytes. And when MTU is\r between 500bytes and 600bytes, the network transmission efficiency can\r be promoted about 50% higher. At the same time, the research is also\r discussing the feasibility and necessity of applying it to the standard of\r the future network.
滿足
之M點是否為重心之探索
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.
奈米複合材料與空氣分子的愛恨情仇-探討奈米碳管對空氣滲透率之影響
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.
由６面Sicherman骰子來分析ｎ面的Sicherman骰子
Sicherman 已經找出與兩顆六面的正常骰子有相同機率分布的Sicherman 骰子，並進一步獲得與三顆六面的正常骰子有相同機率分布的骰子必為一對Sicherman 骰子與一顆六面的正常骰子之結果，我們試圖由已知的Sicherman 六面骰子的處理方法出發，透過對割圓多項式的分析來累積足夠的相關資料，以處理由兩顆四面骰子至兩顆三十面骰子，處理由三顆四面骰子至三顆三十面骰子的各種Sicherman 骰子的答案，來探索兩顆與三顆的n 面Sicherman骰子存在的充要條件與求法，並進一步將所得之結果分類，得到 ”有相同標準分解式的類型的數n，會具有相同組數的Sicherman 骰子”之猜測結果與特殊情形下的證明。 Sicherman has found out the Sicherman dice which have the same probability distribution as the normal two six-sides dice. Furthermore , he also found out a pair of Sicherman dice and a normal six-sides dice has the same result as 3 normal six-sides dice . We try to begin with the given algorithm of six-sides Sicherman dice , through the analysis of Cyclotomic Polynomials to accumulate sufficient related information then to come up with the solution from discussion of 2 four-sides dice to 2 thirty-sides dice , from 3 four-sides dice to 3 thirty-sides dice to explore the existence of necessary and sufficient condition and solution of 2 n-sides Sicherman dice and 3- sides Sicherman dice , and even to classify the results to come to a conclusion of the guessing results and proofs under special cases about “the numbers n which have the same Canonical Prime Factorization will have the same numbers of n-sides Sicherman dice.”
攀蜥，攀棲－由台北市內湖金面山區生態因子分析夜晚黃口攀蜥之停棲策略
For this research, the nocturnal perching habits of the lizard, Japalura Polygonata Xantbostona, were examined. Nighttime observations were made from July 2002 to March 2003 in the area along the mountain brook in the south valley of the King-Mien Mountain in Nei-Hu District. The study comprised a series of analysis with discussion of the lizard’s (Japalura Polygonata Xantbostona) perch based on the temperature of living environment and the manner of perch including the dissimilarity between male and female, adults and juvenile lizards in selecting their perch conditions. During the period of study 452 lizards were marked and examined. 163 were female, 168 were male, and 121 were young lizards. The study considered four particulars: (1) orientation, (2) angle, (3) manner of perch, and (4) height of the perch above ground. As for the orientation, most of the lizards chose to perch in an inward (towards the tree) and in an upward direction; the angle of perch was mainly within 1°~ 45° and slanted to 180°. Second, the manner of perch chosen by most of the lizards was holding the stem or trunk by arms. All four groups of lizards exhibited no difference in the orientation, angle and manner of perch. However, male lizards tended to perch at a greater height above ground than the female and juvenile lizards did. The study produced other findings as well: A tendency correlation curve was plotted showing that temperature related with the number of lizards taking perch, and from the curve the optimal temperature of the living environment was determined to be approximately within the range of 19° ~24°. Additionally, there was a relationship between temperature of living environment and the size of lizard and the number of lizards taking perch. A further positive relationship was observed between temperature and the height of perch above ground. Also, the study showed an apparent positive relationship between the temperature of sample living area and the snout-vent length(SVL) of the lizard. Finally, the Japalura Polygonata Xantbostona tended to take their nocturnal perches within a rather fixed home range. 本研究由2002 年7 月至2003 年3 月，於臺北市內湖區金面山南麓溪谷進行黃口攀蜥夜 晚停棲策略研究，以溫度和各項停棲行為進行來分析探討，包括黃口攀蜥的成幼蜥、雌雄蜥 停棲選擇上的差異。 研究期間，共標記到452 隻攀蜥，其中雌蜥163 隻、雄蜥168 隻、幼蜥121 隻。將停棲 的情況分為方向、角度、停棲型態、離地高度四項來分析，在方向上多以朝內、向上為主； 角度多以小角度的1°~45°及180°為主；在停棲型式多以環抱莖枝為主。進一步分析成幼蜥、 雌雄蜥不論在方向、角度、停棲型式的選擇上皆無差異。離地高度的部分則以成蜥及雄蜥的 停棲高度較高；以溫度分析黃口攀蜥的成幼蜥出現停棲隻次、停棲高度、出現停棲攀蜥體型 的相關性，溫度對出現停棲隻次可以做出趨勢相關曲線，估算攀蜥的停棲有一最適宜溫度範 圍約在19~24℃間；溫度與其停棲高度呈現正相關性；每次測得樣區溫度與出現停棲攀蜥平 均吻肛長有顯著的正相關。而黃口攀蜥夜晚婷棲時則會傾向於較固定的範圍內。
氣候變遷對台灣地區異常降水的影響
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。