本文由‘‘分數7/17是否能表示成兩個相異的埃及分數之和’’這個問題出發，藉由簡單數論的性質以及反證法，得到一個真分數可表示成兩個相異埃及分數之和的定理檢驗法(定理1)。有了這個基礎，我們進ㄧ步推廣定理1 的結果，做出了嶄新的結果(定理2、定理3) 。此定理分別可以用來檢驗真分數表示成三個、四個相異埃及分數之和的存在性; 至於將真分數表示為5 項、6 項….k 項相異埃及分數之和的部分尚在嘗試。利用定理1、2，我們寫了兩個Matlab 軟體工具的電腦程式，使得我們可以檢驗任意真分數是否可以表示成兩項及三項的和，並可把所有的解列出來; 最後我們研究的是一個有關埃及分數的猜想(Erdos-Strauss Conjecture)問題，當分子為4，且分母為4k、4k+2、4k+3 時，猜想皆成立。對於分母為4k+1 而言，當k 為3r+1、3r+2 猜想亦成立，k=3r 且r 為奇數時也是成立的，因此目前需解決的問題只剩分母為24t+1 的情況了。值得一提的是，我們用Matlab 的程式檢驗出當分母為1014 至1014 +240000 之內的正整數時，猜想都是成立的，這已經超越了已知文獻的結果。This paper begins with the question: ‘‘Is 7/17 able to be the sum of two different Egyptian fractions?’’ to discuss the problem of Egyptian fractions. According to the complete division properties and the counter-evidence method, we get a back-check theorem which is about a true fraction can be the sum of two different Egyptian fractions (see theorem 1). Using the same method we obtain a new back-check theorem that is a fraction can be the sum of three or four different Egyptian fractions (thereom2, thereom3). Similarly, we can follow the same procedure to get the rule that a fraction can be the sum of five or six …or even more different Egyptian fractions. By the theorem1 and 2, we propose two programs written vie the Matlab software to examine that any true fraction can be the sum of two items and three items or not. Finally we focus on the Erdos-Straus Conjecture, which related about true fractions can be divided by three different Egyptian fractions. The conjecture is when the denominator is 4k, 4k+2, or 4k+3, the problem mentioned above can be solved. As for the denominator is 4k+1, then the conjecture also can be solved, as k equals to 3r+1 or 3r+2. Also, k being 3r and r is an odd number, the conjecture is satisfied. As for the case of r equals to even number, the problem has not been solved. But it is worth to mention here that we use Matlab software to examine the conjecture is agreeable as the denominator is between 1014to 1014+ 240000. This is beyond the results from the literatures.

This study was to explore the nature of two basic constitutes of the regular pentagon,With these two constitutes, the regular pentagon could be multiplied into any times in size. We used four multiplication methodsto show how the regular pentagon enlarge and to verify that the enlarged regular pentagons derived from computer did exist. By integrating these four multiplication rules, we were able to arrange regular pentagon of any length of side, and evidenced the equation was ( If m,n is the number of A,B of a regular pentagon respectively ) When we tried to verify if any regular pentagon could be constituted by other smaller regular pentagons, we found that it was un-dividable only if the length of pentagon side were (the number of A, B were the 2n and 2n-1 item of Lucas Sequence), otherwise, any regular pentagon is able to be constituted by other smaller regular pentagons. The divided forms could be multiple. We also found that any pentagon could be divided by two successive un-dividable pentagons, which is called “standard division rule”. We expected to derive all kinds of division by analysis of two successive un-dividable pentagons in standard division rule. 這個研究起源於一個拼圖玩具：利用兩種黃金三角形排出指定大小的正五邊形。我們的研究動機是：一、 假如無限量供應A 和B，能夠拼出哪些邊長的正五邊形？二、 哪些拼好的正五邊形不能拆成一些較小的正五邊形？我們將研究的主要結果分述如下：

近年來重金屬污染問題日益嚴重，因此檢測地下水、工業廢水中的重金屬含量為一重要課題。本實驗即是利用錄音機中的零件－石英振盪器作為電化學分析偵測的工作電極，在0.1 M KNO3（pH = 3）溶液中利用循環伏安法以50 mV/s 的掃描速度從 – 100 到 – 700 mV 持續掃描 10 圈，來穩定電極表面。 以方波陽極剝除伏安法（SWASV）模式設定預濃縮電位– 700 mV、預濃縮時間60 秒偵測重金屬的鉛離子。掃描電位範圍由 – 700 到 – 100 mV vs. Ag/AgCl 往氧化方向掃描。偵測鉛離子濃度範圍為200－600 ppb，之後可針對各種條件作最佳化的條件探討可降低偵測濃度及實際運用於地下水及工業廢水的檢測。 Heavy metal pollution becomes very serious. Lead (Pb) determination is a continuous research interest in clinical, environmental, and industrial application. The main causes for living biological media are mutagenic, carcinogenic, and teratogenic activity. The determination of trace metal in the ground and industrial waste water will be a important project. Here, we report a simple system which using quartz crystal microbalance (QCM) (use in radio machine) for working electrode. The QCM was first equilibrated in 0.1 M KNO3（pH = 3）base electrolyte for about 1 min before electrochemical experiments. It was then pretreated by continuous scans in the window from – 100 to – 700 mV at a scan rate of 50 mV/s until a stable background current obtained. The amount of Pb2+ was detected quantitatively using square-wave anodic stripping voltammetry（SWASV）. The potential range was set from – 100 to – 700 mV in the cathodic direction for most cases. The standard addition method concentration range is from 200 to 600 ppb. Analytical conditions were systematically optimized and extended to practical applications aslo.

This research introduces a new, more efficient method of age determination for eclipsing Binary through use of celestial Positioning . Statistical Analysis of x-y plots of eclipsing Binary Stars within our, Milky Way Galaxy were conducted in order to find the standard deviation of each eclipsing binary star’s distance from the celestial equator. Before the standard deviations could be considered for comparison, the medians from each of the three s-y plots were examined. There medians had to show a value close to zero in order for the standard deviations to be relevant. A value close to zero indicates a proportional and symmetrical plot with an equal distribution of stars on each side of the plot. All three plots generated indicted a median no greater than 1/100 in distance from the celestial equator. A low standard deviation indicates young relative age. The statictical analysis calculated standard deviations of 2.41 for W Ursae Majoris, 1.77 for Algol, and 1.20 for Deta Lyrae. The statistical analyses were then compared to the previously made visual and mathematical analyses conducted in previous years’ studies. All analyses conducted conclude that W Ursae Majoris is the oldest type and Beta Lyrae is the youngest type of eclipsing binary star. This method can be implemented to greatly reduce time in studying the relative ages of individual objects and types of objects within our Milky Way Galaxy.

黑擬蛺蝶(Junonia iphita iphita)為台灣地區常見的蛺蝶，其幼蟲具有築巢行為，但文獻中對其幼蟲行為的描述極少，因此本實驗探討黑擬蛺蝶幼蟲在野外的族群變化與環境之關係，並研究幼蟲築巢行為，以探討其適應環境的生存策略。首先於室內及恆溫生長箱中飼養幼蟲，以建立其生活史基本資料，並於野外統計各齡期幼蟲在不同植物上的數量變化及築巢行為的差異，以探討不同環境因素對幼蟲築巢之影響。由實驗結果得知，黑擬蛺蝶生活史短，可取食多種爵床科(Acanthaceae)之植物，其寄主植物除文獻所紀錄之台灣馬藍(Strobilanthes formosanus)及賽山藍(Blechum pyramudatum)等外，也取食大安水蓑衣(Hydrophila pogonocalyx)、無花水蓑衣(Hygrophila violacea)、易生木(Hemigraphis repanda)及翠蘆利(Ruellia brittoniana)等。黑擬蛺蝶幼蟲野外族群波動與溫溼度及雨量等環境因子並無直接關係。黑擬蛺蝶一年發生多世代且有世代重疊情形，世代波動與四季律動關係不明顯，顯示黑擬蛺蝶對環境的適應力大。黑擬蛺蝶幼蟲利用築巢以適應環境變化，應是其幼蟲良好的生存策略。且幼蟲在強風及光線強的環境下築巢率增加，降雨時則減少。Junonia iphita iphita belongs to Nymphalidae（Lepidoptera）. They can be found easily in the wilderness of Taiwan. Its larva shows nest-making behavior. However, there is little literature documenting the behaviors of its larva. Therefore, the purpose of this research is to investigate the relationship between the quantities of Junonia iphita iphita’s larvae and its natural habitat, to research its nesting behaviors, and to investigate its survival strategies to adapt to the environment. I started by raising larvae in a growth chamber under a controlled temperature in order to obtain its initial information regarding its life history. In the field, I documented the numbers and the changes of larvae at each stage on different host plants and recorded the differences in its nest-making behavior in order to find out which environment factors influence the nest-making of Junonia iphita iphita’s larvae. These experiments concluded that the life history of larvae is short. The immature intaking habit showed that the larva takes various plants of the Acanthaceae. In addition to the host plants mentioned in the literature, such as Strobilanthes formosanus, and Blechum pyramidatum, Junonia iphita iphita’s larvae also live by Hydrophila pogonocalyx, Hygrophila violacea, Hemigraphis repanda, and Ruelba brittoniana, which were not listed in the literature. Through experiments, I discovered that there is no direct correlation between the population fluctuations of larvae and it’s enviroment including factors such as temperature, humidity or rainfall. Junonia iphita iphita can produce multi-generations in a year accompanying generation overlapping. There is also no obvious correlation between the generation fluctuations and changing seasons, showing that larvae can easily adapt to the environment. Junonia iphita iphita’s larvae adapt themselves to the different environments by nest-making which should be a good survival strategy. Besides, the rate of nest-making increases when larvae are under strong winds and strong lights and decreases when the rain falls.

The purpose of this project was to create a detection device for alcoholic drunk condition in human by using the principle of vapor pressure difference between breath samplings from normal and alcoholic-drunk men. The work comprises of three major steps. The first task was an experiment to determine an average air volume that can be fully blown out from the lungs of non-drunk people as a control. Twenty adult Thai volunteers weighing between 50 - 80 kg (average 59 kg) were used. The average blown out air volume was found to be 369.9 mL, with the range in values from 340-400 mL (sample size N = 20, SD = 15.47). The second task was an experiment to measure relationship between the blown air volume (100-700 mL, both from alcoholic-drunk and control groups of people) and the resulted vapor pressure by using manometer. The vapor pressure of normal breath increased from 400 to 1,600 newton/m2 with increasing blown air volume, whereas that of the alcoholic-drunk was found to be 600 to 1,800 newton/m2. The last task was to create a detection device prototype to gauge the alcoholic content in the human body from the breath. Air volume of 300 mL was arbitrary chosen to trigger lighting up of indicator lamps. The breath samples of low vapor pressure (low amount of alcohol, 21.12-44.00 mL, equivalent to 14.00-29.17 mg%) would trigger a green lamp to light up. A moderate vapor pressure range (medium amount of alcohol, 88-132 mL, equivalent to 58.33-87.57 mg%) would trigger green and yellow lamps to light up while a high vapor pressure (high amount of alcohol, 250 mL, equivalent to 165.72 mg%) would trigger green, yellow and red lamps to all light up. None of the three lamps would light up from (non-alcoholic) breath of control people. This device has also been tested to external group of volunteers. The work in this project has successfully demonstrated a useful application of simple principle in chemistry on partial vapor pressure.

IF鋼在鹽酸溶液中之腐蝕速度隨鹽酸濃度之增加而增加。12M之硝酸溶液對IF鋼具最強腐蝕性，而最低(0.1M)及最高(16M)濃度之硝酸溶液對IF鋼之腐蝕性則相對較弱。硫酸對IF鋼之腐蝕速度則由低濃度至高濃度呈現極大變化，當硫酸濃度由0.1M漸增至3M時腐蝕速度亦隨之增加，爾後腐蝕速率減小，至硫酸濃度由8M時反而呈現極大之重量增加。由於表面腐蝕層不適於XRD分析，故由EDS結合FTIR分析得知H?SO?/8M-24hrs.情況下試片表面之腐蝕層為Fe?O?。由SEM觀察發現腐蝕速率較大之條件，如HCI/12M-1min.及HNO?/12M-1min.處理過後，試片表面甚至出現具晶體對稱性之蝕恐。由本研究之初步成果發現：是溫下可以利用中等濃度(如8M)之硫酸液來處理鋼鐵，使之表面生成一緻密之氧化鐵(Fe?O?)，達到防蝕之效果。IF (interstitials free) steel was processed in various aqueous acid solutions to observe the corrosion behavior. The corrosion rate of IF steel in HCI(aq) increases with the concentration of HCI(aq). HNO?(aq) with concentration of 12M was observed to be the most aggressive for IF steel. The corrosion rate of IF steel in H?SO? solution increases from 0.1M to 3M and then decreases gradually with the concentration. A large amount of weight gain even observed when the concentration was 8M. The protective layer produced during H?SO?/8M-24hurs. treatment was analyzed to be Fe?O? by using SEM (Scanning Electron Microscope), EDS (Energy Dispersive Spectroscopy) and FTIR (Fourier Transform infrared). Etch pits with crystallographic symmetry were observed on the specimens treated with conditions HCI/12M-imin. and HNO?/12M-1min. Processing condition H?SO?/8M-24hrs. could be employed in corrosion prevention for IF steel under ambient environment.

本研究比較2003~2005 年，冬季及夏季西經168 度之「海平面溫度異常」對「緯度」的分布圖，結果呈現在赤道附近的變動較小，在高緯度地區的變動較大，為更精確的描述此變動，將每日高緯度地區的變動以「標準差」及「最大振幅」數量化，發現在南、北半球不論2003、2004或2005 年，每7~12 天南、北半球的「冬夏季海平面溫度異常」的變動變大，上述變化在北半球較為明顯，在南半球較不規則。 與2005 年冬季1 月31 日~3月17 日的北半球地面天氣圖進行分析比對發現，溫度的變動和極地天氣系統的形成關係密切，推測原因和冬季時極地為永夜，地面空氣溫度受到兩個跟月球有關的熱源影響較大，其一為海流和極地間每日有接近2 次的潮汐交替運動，其二為月球反射日光後投射到極地時，極地大規模的冰對月光的反照，對極地微弱的加熱作用。 針對2005 年6 月1 日~7月22 日之地面天氣圖作分析，結果發現夏季緯度的溫度變異和高中低緯度天氣系統的改變關係密切，推測此時和月球對海水的吸引使地表(特別在海陸邊界)的溫度，週期性的重新分配，或對大氣應也會造成週期性的質量分配有關。 以農曆為主重製溫度的變動圖並進行比對發現，無論2003、2004或2005 年，在月相為朔及望時常出現低值。此分析結果顯示，接近朔望時，高緯度海平面溫度有較穩定且變動較小的情形。而從天氣圖、農曆標準差綜合，所得結論為地月運動應和地球上高緯度天氣系統存在某種相關性。 ;Our topic is about how the moon phase variation influences the high-latitude weather system. This study analyzes the sea surface temperature anomalies (SSTAs), along 168°W in winters and summers from 2003 to 2005. The results show that the SSTAs varied relatively small around the equator and relatively large in high-latitude regions. So we next analyze the high-latitude SSTAs by the standard deviations, the maximum amplitudes, and the north surface weather graphs. After analyzing, the result shows that the SSTAs rise for every 7 to 12 days. Moreover, they relate to the winter high-latitude weather system very much while relating to the summer medium-and-low latitude weather system a lot. We think it’s because in winter eternal night, the sunlight won’t shine on the arctic zone easily. Other heat sources may become important: (1) the tidal movements between the ocean and the arctic zone. (2) The heat radiation of the moonlight and the moonlight reflection by the polar ice shields. But in summer, the moonlight effect becomes extremely small. The tidal force becomes the bigger influence factor: (1) the tidal attraction may distribute the temperature of the border between seas and land periodically. (2) It may cause the periodic atmosphere mass distribution. Additionally, after repeating the same experiment according to the Chinese lunar calendar, we found near full-moon and new-moon time, the SSTAs are more stable. Probably because of without the moonlight, the movements of rip-tides occur and help stabilize the polar weather conditions. In conclusion, the relative movement of the moon to Earth is likely providing a crucial heat source which will affect the high-latitude climate, and the heat source size probably influences the weather system cycle.

Objective To design build and run 5 Mouse mobiles – vehicles which use mousetraps as their only source of energy. Targets- • Go up a ramp • Raise a flag • Hit something and set it free • Deliver something • Catapult Details These mouse mobiles are original creations which include some commercially produced parts. They are powered by single spring driven standard wooden mousetraps. They are 5 in number each being used for the respective tasks. Basic structure Each mousetrap consists of a 2 parallel wooden planks which has 2 holes drilled on either sides for the rear and front axles. A rod is used as the axle and CD disks are used as wheels. The mousetrap is attached to the planks. Movement and Locomotion To move the mouse mobile a string is connected to the rear axle. The string runs through 2 pulleys which change the direction of the applied force and are attached to the hammer of the spring. When the vehicle is pulled backwards on the floor tension is created in the string (as the hammer is stretched) which gets stored in the form of spring energy. When the wheels are released on the floor the rear axle starts rotating hence propelling the mouse mobile forward. Completion of objectives 1) To go up a ramp For the required task a high amount of torque would be needed .That will be sufficiently provided by the spring energy. 2) Raise a flag For the required task a rod is placed on the wooden platform. The flag is placed at the bottom of the rod; it is connected to the hammer of the mousetrap using a string. The spring and the rod are placed in the opposite directions. When the hammer is released after being stretched it pulls the string and raises the flag. 3) Deliver something For the required task 2 mouse mobiles are used. A platform of any hard and light material is attached to the rear of a mouse mobile. After reaching the desired location, when the hammer of the primary spring is fully relaxed it hits the catch of another stationary mouse mobile. The hammer of the respective catch is connected to the platform using a string. Upon activation the hammer is released, the platform is pulled with extremely high speed and the materials on the platform, due to their moment of inertia fall down. 4) Hit something and set it free. For the required task 2 mouse mobiles are used. A small mousetrap is attached to the front of the mouse mobile which is in contact to the required object. The other mouse mobile on reaching the above vehicle hits its catch using its hammer. The hammer of the stationary mouse mobile is released and the object is hit and set free. 5) Catapult For the required task 2 mouse mobiles are used. A mousetrap is attached to the front of stationary mouse mobile which is attached to a strainer and the object to be catapulted is placed inside it .Another mouse mobile approaches is and hits the catch hence activating the hammer and the object is catapulted.

流行病的傳染過程如同一個無尺度網路，但較一般無尺度網路有著更多的變數而明顯差異，因此無法直接應用一般的無尺度網路模式來描述其傳染途徑。我建立一個新模式「無尺度流行病模式」，經由比較模擬結果與疾病管制局的數據，證實此「無尺度流行病模式」是正確與確切可用，且適用於短期暴發性傳染病與長期流行病。SARS案例研究結果，顯示影響SARS疾病傳染因子的大小是：ψ>m>γ。其中降低ψ值可使SARS確定病例至5月31日止降為143人(減少確定病例190人，相當於減少死亡21人)；僅提高防疫使5=γ，亦可使確定病例減至307人(減少確定病例26人，相當於減少死亡3人)。因此強化隔離措施以減少傳染天數最為重要，且可以有效控制每日SARS新增病例，避免發生高侵襲率的現象。HIV/AIDS案例研究結果，獲知採用ψ值來進行月份模擬，則至 2005年12月HIV(+)與AIDS分別為可減少2,715與285人。而進行年度模擬結果，則至 2014年底HIV(+)與AIDS分別為可減少41,936與5,328人。無尺度流行病模式可以協助所需警戒的程度與政策決定的計畫結果。因此無尺度流行病模式在幫助政府評估社會經濟成本與健康憂慮上的有用之工具。當面臨一個全然無知的新病毒的侵襲時，如何減少死亡與傷害人數？是本研究之最終目的。因此，本研究結合了流行病、無尺度網路與灰預測，建立面對病毒侵襲，一個確切可行的對抗無尺度流行病傳染新方法，並詳細說明運作流程。\r \r \r The course of epidemic infections resembles a scale-free network. However, they are different due to more variables in the epidemic infection. Therefore, the model of scale-free networks is not enough to satisfy the reality epidemic infections. In this study, I propose a new the Scale-Free Epidemic Model. Comparison of the simulation results with Taiwan CDC report data for SARS and HIV/AIDS cases show that the Scale-Free Epidemic Model is accurate and useful. This model can be used in the short-term outbreak of infectious diseases and for the longer-term epidemics. In the SARS case study, the results show that the sequence of effect of the epidemic factors was: ψ>m>γ. The SARS confirmed cases would decrease to 143 cases (reduced 190 confirmed cases or 3 death cases) calculated to May 31, 2003, if the average infection time was reduced to two days (an optimum value of ψ). Therefore, vigorous action in isolation quarantine and treatment for SARS cases is most effective policy; the number of new cases and the attack rate would also decrease. In the HIV/AIDS case study, the simulation results of the Scale-Free Model indicates that the reduced numbers of HIV(+) and AIDS in the monthly simulation calculated to December 2005 are 2,310 and 361 and the annual simulation by December 2014 are 27,161 and 3,710. The Scale-Free Epidemic model can help determine the level of caution needed and the projected results of policy decisions. Therefore it is a useful tool in assisting the government to balance socio-economic and health concerns. The fight against a new epidemic and how to reduce the number of deaths is the main purpose of this study. So, a new method to fight against epidemics is proposed. Detailed procedures of this method are explained.

本實驗的目的在於探討凌日時的黑滴效應。實驗以投影機在螢幕上投射出亮區模擬太陽，以保麗龍球模擬內行星橫越太陽表面，以相機作為觀測記錄器材，結果發現在內行星與太陽的第二及第三次接觸時會有黑滴現象。黑滴效應在光源顏色越接近紅色、拍攝相機的光圈值越小越明顯、相機對焦比實際值越小越明顯；光源的明亮度對黑滴效應沒有顯著影響。金星大氣、地球大氣不是造成黑滴現象的主因，而影響黑滴效應的因素與光的繞射相同。實驗結果發現，黑滴效應的成因主要發生在觀測紀錄的器材上面。This study is conducted to explain the black drop effect for the transit of a planet. A video projector projects a bright square on the screen to simulate the Sun. A ball simulated the planet crossing the sun’s disk. And a digital camera takes the images of transit. The Black-drop Coefficient is defined and a computer program is designed to analyze the image of black drop. The results show that the resolving power of the observation instrument is the main factor in the effect. The atmosphere and the solar limb darkening do not directly respond to it.

Light diffraction and interference are two of most basic experiments, but they’re the most powerful evident of wave properties of light. Due to the lack of high-quality and fairly accurate equipment, these important experiments are limited to the simple demonstration of the phenomena. Especially, the spatial intensity variations of diffraction and interference patterns are, however, completely not drawn to scale. In order to precisely measure the diffraction and interference patterns intensity, we consult lots of reference, search for suitable materials and reuse waste old and useless laser printers. Finally, overcoming disadvantages of time consumption and poor spatial resolution, we develop two accurate, practical and delicate methods. We use optical power control circuit created on our own to steady the brightness emitting of laser diode. Then the high linear photoelectric detector is stored on XYZ axis micro movement control platform. Next high degree of reflection rotating polygon mirror employing optical lever is collocated with low vibration blushless motor. Thus, a self-scanning intensity pattern plotter is accomplished. At the same time, it overcome difficulties like time wasting and low reliability during doing these kind of optical experiments. In this article these two dependable and worth popularizing measurements of light diffraction and interference is going to be introduced. 光的繞射與干涉實驗是光學中最基本的實驗之一，也是證明光的波動性質之最主要的依據。在一般的高中物理實驗室中受限於器材的等級與精度，只能對光的繞射與干涉做近似定性的實驗，尤其是繞射、干涉圖形上的光能量分佈，完全無法以現有的器材做精準的測量。 在這一年的專題研究中，我們小組針對測量光的繞射、干涉能量分佈為目標，參閱許多相關文獻，四處尋找適用的材料及零件，發揮廢物利用的精神，克服萬難，發展出兩種精巧、實用又準確的測量方法，我們以自行發展的光功率控制電路使雷射二極體的光度穩定，並且以高線性度的光感測元件裝載在自行設計的X.Y.Z微動機台上，同時利用光槓桿原理所構成的高反射度的旋轉六面鏡，配合低震動的無刷馬達，完成了一套能自動掃瞄繞射能量分佈曲線的測試儀，經實際使用相當地穩定可靠，可以快速而精確地獲得大量的實驗數據，比對這些數據不僅能驗證繞射理論，並能更深入地延伸理論的探討。