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.”
小小細菌立大功-油類生物復育模式的探討
20 世紀初，石油的量產造就了人類文明前所未有的繁榮，然而由於運送、廢棄處理等因素，使得油類污染成為環境保護的重大議題。本實驗中，我們的研究主題為在受油污染的土壤中純化並鑑定出可分解油類之土壤菌和綠膿桿菌對可分解油類之土壤菌與這群土壤菌彼此之間的交互關係，藉此了解它們間的互動對環境生物復育的影響。我們由受油類污染的行道樹土壤中分離了約12 種的土壤菌，其中我們得到3 種對油類分解效果效果極佳的非綠膿桿菌(暫時命名為P7A、P7C、P7D)。經過菌種鑑定發現P7A、P7C、P7D 均為格蘭氏陽性菌。為了解這群可分解油類之土壤菌間的互動關係，我們針對分解效果最佳的P7A、P7C、P7D 作為研究對象，將菌落接種至含有鹽類與機油的液體培養基中震盪培養，並每隔一定時間測量其O.D 值。結果發現P7A、P7C、P7D 間的互動會導致其在以機油為單一碳源的培養液中之生長速度的改變，因此在行環境生物復育時須注意土壤菌間交互關係對其分解污染物速率的影響。此外我們由受油類污染的行道樹土壤中亦分離出了一些綠膿桿菌，因文獻指出，綠膿桿菌所分泌的綠膿素降低受油污染土壤中土壤微生物相的多樣性；因此，我們將由行道樹土壤中純化出的綠膿桿菌T3 與可分解油類P7A、P7C、P7D 進行交互作用觀察，發現T3 會侵占P7A、P7C、P7D 的既有菌落區，而平板培養基亦可清楚看出和T3 交接的P7A、P7C、P7D 菌落區寬度有明顯降低，因此我們認為T3 可抑制或殺死P7A、P7C、P7D，可得知綠膿桿菌會對可分解油類之土壤菌產生抑制或競爭關係。In early 20th century, the exploitation of petroleum transformed human civilization into a tremendously prosper stage. Because of the transportation and disposition of petroleum, the oil pollution has become a important issue in environmental protection. Besides, Chloropseudomonas spp. which can survive in many different environments and decompose lots of organic compounds. In this study, we want to find the bacteria which can utilize oil from machine oil-contaminated soil, investigating the interaction relations between Chloropseudomonas spp. and these oil-degrading soil bacteria. First, we classified these oil-degrading bacteria by the book called“Bergey’s Manual of Systematic Bacteriology.”We find three species of oil-degrading bacteria (P7A、 P7C、P7D) which are all grams-positive bacillus, possibly belonged to Aureobactreium、Curtobacterium、Cellulomonas、Oerskovia、Brochothrix、 Caryophanon. Second, in the study of the relationship between Chloropseudomonas spp. and the oil degrading soil bacteria, we found that Chloropseudomonas spp can considerably inhabit the growth of oil-degrading bacteria. Besides, there are also a great variety of interaction between three species of the oil-degrading bacteria. According to the result , the interaction might considerably affect the efficiency of oil bioremediation. Due to our analysis, we suggest that it is necessary to pay more attention to the interaction between bacteria when undertaking oil bioremediation.
表面粗糙結構對疏水性影響之應用與研究
本研究從大自然中之「蓮花效應」引發學習興趣與研究動機，在蒐集相關資訊與文獻後，發現疏水功能不只是防水，還關係著日常生活品質之許多材料特性，包括防水、撥水、防潮、防銹、防蝕、抗菌防污、自清潔…等。而影響固體表面疏水性之兩大特性，包括物理之表面粗糙度與化學之超低表面能，本研究針對物理之表面粗糙度與疏水性之關係做探討，以相同之化學特性來比較不同號數之工業用砂紙之疏水行為，並就廣泛被引用之兩種模擬表面粗糙度與疏水性關係之模式：Wenzel and Cassie model，比較現有文獻對兩種模式之特性，選擇Cassie model 來進一步實驗驗證，以量測之平均接觸角 Θ 推算Cassie model 之表面粗糙係數Φ 值，並簡化不同砂紙顆粒模型為相同粒徑之球狀，以簡化之方程式來求得水珠與砂紙顆粒之實際接觸面積與球心夾角 θ，以提供高中學校能在經費與設備之限制下，仍能有效應用與印證Cassie model，獲得砂紙顆粒直徑與球心夾角 θ 自然對數值之關係。並就疏水性之生活應用，建立接觸角與 Φ 之關係曲線，驗證實驗之方程式，與延續過去之科展成果，以實驗成果提出可行性應用之建議。The interest and motivation of the present work was introduced from “lotus effect” in nature. After we collected related literature and information, we found that the function of the so-called “superhydrophobicity” behaves not only water repellency, but also a variety of real-life applications, including anti-fog, anti-corrosion, anti-bacteria, anti-fouling, self-cleaning, and so on. Pervious studies have pointed out that two criteria affecting the performance of hydrophobic surfaces are physical (roughness) and chemistry (surface tension) properties. This study focused on influence of physically surface roughness on hydrohyphobicity. Based on an identical surface chemistry, we employed different types of industrial sandpapers to mimic the lotus leaf, and investigated the relationship between roughness and hydrophobicity by using two famous models: Wenzel and Cassie models. Comparing with their basic assumptions to our study, we applied Cassie model to confirm our experimental results, in where one Cassie parameter (?) was proposed to simplify the Cassie equation. This superhydrophobic behavior can be well predicted by the Cassie model. This study continues previous achievement and offers some practical utilization according to our\r experimental results.
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.
旋光性介質對電磁波影響的分析與討論
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。
利用滾動實驗測量摩擦係數
A cylinder rolling on an inclined plane and a sphere on grooved tracks are discussed in details.Using elementary mechanics, the formulas are derived for the time interval (t) and the final speed (vas a function of release height (h). (1) A cylinder is rolling down an inclined plane. The speed and time of the center of mass ofthe cylinder which changed with position (x) are recorded by a motion sensor. We can get theplots of v vs. √x and t vs. √ x, and find that the acceleration of the center of mass of thecylinder is constant, whether the cylinder is in rolling or a combination of rolling and slipping. (2) A sphere is rolling down an inclined grooved track. The final speed at the bottom of thetrack can be calculated from the physics of projection motion after the sphere leaves the track to thefloor. The time t for the sphere starting from rest to the bottom can be recorded by using photogate detectors. From the v-√h and t-1/√h graphs, μs between the sphere and track can be obtained. (3) When a sphere is released from the vertical height h of a cycloidal slide, the time tof pure rolling is the same independent of release position. But, when the sphere moves at a combination of rolling and slipping, the time t' will be different from t. We measure t and t' with photogate detectors and get the plot of t vs. h. The value ofμs can be calculated from the t - h graph. 圓柱或鋼珠從斜面或有槽曲面形成的軌道上滾下時，利用基本力學，可推導出時間 (t) 、速率 (v) 隨高度改變的函數關係。 (1) 利用運動感應器記錄圓柱由斜面上滾下時，圓柱質量中心的速度及運動時間隨位置 (x) 的變化，可繪出 v 對√ x 及 t 對 √x關係圖，由v－√x 及 t－√ x圖可知不論圓柱純滾動或滾動兼滑動，其質心均等加速度運動。 (2) 鋼珠由有槽斜板滾下時，到達底端的速率可由從底端至地面的拋體運動算出，而其時間t則可利用光電計時器直接記錄，利用 v－√h 圖及 t－1/√ h 圖可求出鋼珠和軌道的靜摩擦係數 μs。 (3) 鋼珠從旋輪線上方純滾動至底端時，所經歷的時間 (t) 和釋放高度無關，但是當鋼珠滾動兼滑動時，所經歷時間 t' 會改變，利用光電計時器量出 t 及 t'並作圖，利用 t－h 圖可出 μs。
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。