讓美麗永恆
我一直在想，為什麼植物的美麗不能永恆呢？美麗的花朵，伴隨答淡雅的香氣，往往能美化環境，更能淨化人心，自小生長在鄉間的我，更能感受到這份來自花草的神奇力量，因此深深愛上這花草世界．但為何花朵的美麗總是短暫，為了想讓植物開花的時間長久，於是，我著手進行在自然科技雜誌及網路上搜尋相關的資料及訊息，但是找到的大多都是使生長速率變快的報告，卻找不到使生長速率變慢的報告。終於，曾經有人運用圓周運動的原理，而成功的使動物的生長速率變慢，於是，我針對直線運動及圓周運動分別依速度快及速度慢來分成四組，以及一組靜止狀態的綠豆，將五組實驗後的數據相互作比較，結果發現，除了陽光、水、空氣、土壤、養分及本身具有的胚胎外，在不同的運動狀態下也會影響到植物的生長速率 ·I was thinking about the reason why the beauty of plants couldn’t last forever. The beauty of flowers that accompanied with sweet-smelling could beautify the landscapes and purify our heart. I felt strongly about the magic power of the plant because I lived in the country in my childhood. Therefore, I loved plants deeply. Why was the beauty of flowers transient? As a result. I started to search for the related data and information on science and technology magazines and Internet. Most of the reports increase the growth rate of plants, but I cou1dn find the reports about slowing down the growth rate.At last, someone had successfully used the principle of circumference movement to slow down the growth rate of animals. Therefore, I focused on linear and circumference movement and divided them into four groups and one group of green beans with still state. I compared the data of five groups, and found that different movement affected the growth rate of plants m addition to sun, water, air, soil, and embryo.
外接正多邊形法與對稱性
Motivated by Napoleon theorem, we study the properties of the triangles obtained by moving the midpoint of each side of a given trianle along the perpendicular bisector of corresponding sides, and extend the results to the case of quadrilaterals. On the other hand ,we consider the method of erecting a regular M-gon to each side of a given N-gon and joint the N centers of these M-gons to form a new N-gon. (abbreviated as CRG method),and get the following results. 1. We characterize some kinds of N-gons that can be transformed to regular N-gons via CRG method. 2. Of M,N are nature numbers with M|N, then it is possible to find a N-gon that can be transformed to a regular N-gon by CRG method. \r 3. If a polygon P is symmetric with respect to a fixed point or a fixed line, then P can be transformed by CRG to a polygon with similar symmetries. 4. If a polygon P is transformed by CRG to ′P,there exists a commonpoint G such that ΣGA=0 andΣGB=0, where A and B runs through vertices of and P′P, respectively. 本研究將拿破崙定理加以延伸。先探討由各邊中點沿中垂線延伸得出之三角形的性質並推廣至四邊形之情形條列式報告成果。另一個推廣是將給定的多邊形的每邊外接一個正多邊形，再以這些外接的正多邊形的中心為頂點造出一個新的多邊形。我們發現此幾何變換具有以下性質：（1） 「哪些多邊形能被變換成正多邊形呢?」，我們觀察出能被變換成正多邊形的多邊形其限制條件隨邊數增加而增多，並進一步區分了哪些多邊形可以被變換成正多邊形。 （2） 在將非正N邊形做變換時，不一定須外接正N邊形才能得到正N邊形，我們區分出可外接哪些正多邊形而得到正多邊形。 （3） 對給定的多邊形作此變換時，若原多邊形有點對稱或線對稱等性質，則新多邊形也將具有相同的性質。 （4） 此變換得到的新多邊形會與原多邊形共重心，亦即新舊兩多邊形內到各自的頂點向量和為0的點會是同一點。
電話網路全方位監控系統
In this paper, we use telephone network to remote-control household appliances and monitor security system through the implementation of software and hardware. The purpose of developing this system is to build up a system that makes everyone take advantage of the telephones through pay phone network everywhere as and when he needs to set up the household appliances, meanwhile two-ways system of monitoring household security. In addition, due to the advances of communication technology and the remarkable boom of those products, the popularity of cell phones for local people is developing tremendously. We can link the portable cell phones up to the household appliances and monitoring household security through the offer network of communication companies. This system adopts public telephone network via multiple frequency to receive KT31 70 IC which is connected to EM78P45 i p Chip. And then the Chip is connected to the driving external circuit in order to control electric appliances, sensors on doors and windows. The utilization of LEPROM (93C66) memory to set up telephone and mobile phones number equips the telephone network with two-ways system of remote-controlling electric appliances and monitoring household security. In the part of controlling electric appliances, a monitor is used to display the status of electric appliances, to control the appliance switches and to set up the timer. In the part of monitoring household security, we use the system to receive the instant images of the house and to report on the closing or opening of doors and windows. The system will be informed on any occurrence of abnormalities. The memory of the system can record and update new data at any time and is able to set up twenty sets of telephone and mobile phone numbers. Besides, the system adopts identification codes to avoid malfunctioning and thus upgrade system reliability.本文旨在應用電話網路作遠端遙控家用電器及防盜保全歟控系統軟硬體之規劃與設計 。本系統研製的目的，是希望建立一套系統，讓每個人不管身置何處，都能利用電話透過公眾電話網路，輕易地控制家中的電器設備及進行環境設定，以達到控制家電及防盜保全之雙向監控系統。此外，由於通訊的進步與通訊產品的熱賣，使國月雍有手機的普遍性相當高，若能透過隨身攜帶的手機，經由通訊業者所提供的網路通訊管道，連結到家庭自動化與防盜保全系統亦可達到進行遠端遙控的目的，彌補出門在外無法使用室內電話的空檔。本系統利用公眾電話網路經複頻接收 IC ( KT3 170 ）連接至單晶片（ EM78P45 IP ) ，透過單晶片驅動外部電路與家中電器及門窗的監視感測器連接，再利用 EEPROM ( 93C66 ）記憶體設定電話及手機號碼，藉由電話網路傳輸，以達到控制家電及防盜保全之雙向監控系統。在家電控制部份，採用顯示器可隨時瞭解家電使用狀況及控制其開啟或關閉，且可設定使用時問。在防盜保全部份，可隨時監控家中門窗，若有異狀可即時通告。記憶體可隨時記錄或更新資料，並可設定二十組電話及手機號碼。此外，本系統採用確認碼設定，可防止產生誤動作，系統可靠性高。
埃及分數之固定項數分解問題
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.
黑擬蛺蝶(Junonia iphita iphita)的幼蟲生存策略
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.
月相變化對極地天氣系統的影響及其引發高緯度天氣變化之探討
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.
翻轉「膜」力
The starting point of this experiment is to study the structure of soap-film. By changing the height of the triangular prisms, cuboids and pentagonal prisms, I observed the patterns set by the soap within the frameworks. It is surprised that when the proportion of prism is in a specific range, the phase in the middle of the structure will overturn 90 degree and then transmitted into another kind of balance pattern. I named this process “phase transition”. According to the experiment ,we can conclude the change of film patterns within variable prisms are all applied to this regular cycle:：
We know the soap films are forever attempting to minimize their energy. It stands to reason that surface tension tend to set up the film in its minimal surface. From the point of Mathematic, each structure should have only one single balance pattern, which is set up on the base of Fermat point and this pattern should stand to the minimize of it’s energy. However, we discovered that in some specific cases, one structure can allowed two kinds of balance films-patterns to exist. In these cases, any small vibration can cause the happening of “phase transition”. To sum up, I presume some structures have two different types of balance film-patterns: one of which stands to the local minimum (in this condition the pattern’s surface area isn’t the smallest); the other stands to the absolute minimum (in this condition the pattern’s surface area is the smallest).
There is an energy valley separate local minimum from absolute minimum. The second pattern (local minimum) will appear when the structure is blocked from attaining its absolute minimum, but surface intention is not powerful enough to support the film jumping over the energy valley. In this condition, if we works on the structure (such as blowing), which would provide the film of energy to cross the valley, and then phase transition take place. Vice versa, we can also force the film to jump from absolute minimum to local minimum and phase transition will occur as well. In a word, phase transition can happen in each two way, which connects the two types of balance pattern.
This report lays stress to find out the condition of phase transition. We also analyze the structure of soap-film by its included angles and surface area in hope to go deep into the science of soap-film.
我們實驗的出發點在於研究泡膜的立體結構。藉由改變正立方柱的高，觀察其平衡薄膜形式，意外的發現當正立方柱的邊長比在某個範圍時，泡膜結構中央會瞬間90 度翻轉，形成另一種平衡型式，我們將這個過程命名為面轉變(Phase Transition)。為了進一步了解面轉變發生的相關因素，我們設計了一連串的實驗，針對正三角柱、正四角柱、正五角柱、正六角柱發生面轉變的時機和條件分析討論。此外，我們還分析了泡膜結構中膜與膜夾角的特性、最小表面積和表面能之間的相關性，對於泡膜的立體結構做了一系列深入的探討。
以圓錐套和熱電半導體來改善傳統電風扇效能的研究
電風扇在炙熱的夏日中為冷器以外不可或缺的生活用品。一個典型的電風扇是由架在可調高度鐵柱上的馬達及風扇構成。現行傳統電風扇有幾個缺點，一、馬達風扇(即重心)位置高，有易傾覆的缺點。二、風力分散，風速不高。三、吹出不可調室溫溫度的風。四、外觀呆板，傳統無奇。五、多噪音等。本研究根據這幾點傳統電風扇缺點，試著設計新的電風扇。首先將柱子移除使重心降至接近地面處。接著根據連續方程式(continuity equationρ1A1V1 ＝ρ2A2V2)製作圓錐狀「號角」裝置套於電風扇上以集中風力並減少噪音。最後企圖使用熱電半導體的致冷器降低輸出風的溫度。研究結果發現號角裝置有效達到預期的集中風力增加範圍目的。不幸發現以熱電半導體降溫的方式效率低且耗損過多能量所以可行性較低。雖然沒有降溫功能，本電風扇仍較傳統電風扇多出許多好處，例如加強的安全性、集中的風和強大擴充性。號角裝置可包含空氣清淨甚至音箱功能充當喇叭。Electric fans are a necessity during summer, especially in a hot and humid place such as Taiwan. A typical electric fan is primarily composed of an electric motor with fans mounted on a strut with user adjustable elevations. This setup presents several problems, including (a) the danger of an accidental tip-over due to the fan's elevated weight center (the heavy motor), (b) high wind dispersal rates, (c) room temperature winds, (d) excessive noise and (e) old, antiquated exterior appearance. This particular study attempts to alleviate all these problems. First the weight center is lowered to ground level by removing the entire strut and placing the motor close to the floor. Next by using calculations from the continuity equation(continuity equationρ1A1V1 ＝ρ2A2V2)a cone shaped “horn” device is placed over the fan in order to concentrate the wind, effectively increasing its speed while decreasing the audible noise level. Finally, an attempt was made to lower the temperature of the air in the interior of the horn by the placement of a thermoelectric semi-conductor cooling device. Our results were that the horn device worked, significantly lowered the wind dispersal rate and achieved an important objective. However, the thermoelectric cooling solution proved to be highly inefficient unless accompanied by precise wind speeds. Even without the cooling function, this new electric fan still has many distinct advantages over traditional fans such as improved safety, concentrated winds and high expandability. For instance, filters can be integrated to purify air, even an audio speaker can be made into the form of this fan.
n x n 方格表中的計數問題
對4 × 4 方格表中計數問題的二個解題方法(1..解方程式的方法， 2.分割圖形的方法)作分析和研究後，首先我推廣分割圖形的方法來証明 : “好的n × n 方格表” 存在若且惟若n 為偶數。同時証明這種“好的n × n 方格表”內所有n2 個數的總和f(n) 為n(n+2)/4。當討論一般的n×m 方格表時，發現分割圖形的方法盲點，無法繼續推廣來証明。再經過深入分析與推廣解方程式的方法，藉由n×m 變數方格表，我們終於找到構造所有“好的n × m方格表”的方法。同時計算“好的n × m 方格表” (n≦m)內所有mn 個數的總和f(n,m), n≦7和証明好的nxm 方格表會有2(n+1)行一個循環的現象。We first studied two solution methods (1.solving equations,2.dissecting diagrams.) for calculations on 4x4 checkboard. Using the method of dissecting diagrams, we proved that``good nxn checkboard'' exists if and only if n is even. Furthermore, the sum f(n) of those n2 numbers in a ``good'' nxn checkboard is equal to n(n+2)/4.In studying the more general nx m checkboards, we found that the method of dissecting diagrams does not work, However, by extending the method of solving equations, and by considering nx m variable checkboards, we obtained a way of obtaining all ``good nxm checkboards.'' By way of computing the sum f(n,m) (n≦7) of those mn numbers in a ``good nxm checkboards,'' periodicity in every 2(n+1) rows is observed.