2007年

本研究自2005 年12 月開始，以臺北市內湖區大湖自公園死亡的漂浮琵琶鼠魚(Many-rayed Sailfin Sucker Catfish )為主要研究對象，探討外來物種與放生行為對大湖生態系的影響。 研究期間共觀察到死亡的琵琶鼠魚隻數計有1085 隻，可記錄到個體形質資料的隻數為910 隻，背鰭棘數則有11 棘、12 棘、13 棘與14 棘四種，分析四種不同棘數的琵琶鼠魚後發現：在體長、頭寬及吻到背鰭長度均無差異(p>0.05)，因此判斷所記錄的個體應是棘甲鯰科(Loricariidae) Pterygoplichthys 屬中的同一種魚種。由檢視魚體並分析記錄數量與環境因子相關性後推測：琵琶鼠魚死亡主因是劇烈起伏的溫度差異，其次是人為因素的刻意傷害。 所記錄到大湖池塘水棲動物有：環節動物、軟體動物、節肢動物、魚類、兩棲動物及爬行動物等六大類共34 種，其中外來物種有16 種，本地入侵物種有3 種，而這些外來動物進入大湖的主要管道應是由個人的棄養或放生行為所造成。琵琶鼠魚因繁殖能力強、具攻擊性、吞食其他魚種卵塊、可適應高污染水體及垂釣客對魚種的篩選等因素，而成為最具生存競爭能力的優勢魚種。不但造成大湖池塘呈現嚴重魚種單一化，更可由靜止水域大量擴散至流動水域。未來如何將政府相關部門、學術研究單位與民間社團等力量結合，共同防範大湖琵琶鼠魚的持續蔓延、宣導民眾正確的放生觀念、積極改善大湖水體污染狀況，並訂定完整之外來物種移除計畫，以期恢復大湖池塘物種歧異度，都將是刻不容緩的重要生態課題。;This research began in December of 2005. Focusing on dead floating Many-rayed Sailfin Sucker Catfish in Dahu Park, Nei-hu Distrct, Taipei city. We discuss the impacts of Alien and of behaviors of the release of captured animals on Dahu Park’s ecosystem. During observation period, there were totally 1085 dead Many-rayed Sailfin Sucker Catfish, of which 910 bodies were found. The number of the thorn bushes on dorsal fins includes 11, 12, 13,and 14. After analyzing four kinds of different thorn bushes, we find that no differences exist in Total length, Head width, Predorsal length (p>0.05). We hence conclude that the recorded object should be species with identical with Loricariidae Pterygoplichthys. With the inspection of the fish’s body and the analysis of the relevance of the recorded quantity and the environmental factor, we infer that the main reason of the Many-rayed Sailfin Sucker Catfish’s death is violent temperature differences and the second is attributed to human’s intentional abuse. The aquatic animals of Dahu Park amount to 34 kinds and six classes such as Annelida, Mollusca, Arthropoda, Pisces, Amphobian, and Reptilia. Among them, 16 kinds that are Alien and 3 kinds are Native Invasive Species. Intentional abandon and release behavior channel of these Alien to Dahu Park. Many-rayed Sailfin Sucker Catfish are highly productive, aggressive, and adaptable to highly polluted water. Besides, they eat ovums from other fishes. Moreover, they are not the fisher’s preference and hence often thrown back into pond once hooked . Thus, they become the most competitive survival fish species in Dahu Park. The high competitive ability of Many-rayed Sailfin Sucker Catfish causes Dahu Park to present a serious unification of fish species. This serious unification of fish species could also be spread from static water areas of Dahu Park to flowing water areas. According to our research, certain urgent ecological issues in Dahu Park are to take precautions against the spread of Many-rayed Sailfin Sucker Catfish, to promote the correct idea of releasing captured animals, to improve Dahu Park’s water pollution, and to stipulate a complete plan about eliminating Alien. Our research suggest that government’s relevant departments, academic research units, and folk corporations should be cooperated to achieve the above four goals. Once the four goals are achieved, we believe that the fish species of Dahu Park will be full of varieties again.

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：

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.

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.

The objective of this project is to investigate styrene butadiene rubber(SBR), which is the most important synthetic rubber. The project contains production methods, properties, safety methods and applications for emulsion SBR. The goal is to determine which production technique of SBR is the most beneficial. This is based on the chemical and physical properties of the final product and its quality. The process that is used in the project is emulsion SBR with combined coagulation stripping. The rubber production plant is a profitable venture. The total capital cost is estimated around $31,361,572, with an annual production cost of about $67,281,378 yearly, generating revenues of $73,801,760 per fiscal year, with an interest rate of 5%. The life of the plant is 15 years and would produce 50,000 ton/year.

台灣通史「婆娑之洋，美麗之島」，身為台灣人，應知台灣事，本研究本維 基百科（Wikipedia）所揭示的「海納百川，有容乃大」精神，以Apache 網頁伺 服器為平台，MySQL 為資料庫，利用AJAX、PHP 網頁技術，並使用Google Maps 提供之服務，建立符合Web 2.0 精神的的b04地理資訊共享系統。在此系統下， 我們允許教師(編輯者)以合作方式上網提供與課程相關的地理資訊，並可進行資 訊修改或刪除，希望集合所有教師之力，提供給學生最豐富、最正確的b04地理 資訊系統。 In this paper, we propose a new map-based collaboration environment “MyGIS” for geographical information distribution. In MyGIS, the publishers/teachers can easily collaborate to annotate a spot with contents such as messages and links. The annotations of a spot are updated on the map in real-time which enables the receivers/students to correctly study at anywhere and anytime. To ensure the trustfulness of the content, the publishers are authenticated using login mechanism. In this study, several technologies inc lu ding Apache, PHP, MySQL, Ajax are involved. Finally, We implemented MyGIS on Google Maps and evaluated its feasibility and usefulness.

正方形和長方形是每一個人都非常熟悉的圖形，但其中卻隱藏了非常多奇妙的“數學之謎”。 所謂「完美長方形」是：在一個長方形中 (長、寬不等)，能否分割出最少大小相異的正方形。 這個研究中，首先用「草圖」的解題方法研究完美長方形，接下來利用「平面圖形」的解題方法可簡化計算的過程，最後利用「對偶關係」證明出：完美長方形的最少階數為 9 階。 進而，我們將這個問題擴展至三維空間，思索在一個長方體中（長、寬、高都不等長） ，能否仿照二維空間，分割出最少大小相異的正方體，而完成這個研究。 Square and the rectangle are figures that everyone knows well very much, but what a wonderful " mystery of mathematics " is hidden among them. What is called the perfect rectangle is whether in a rectangle (its length and width is different ) could cut apart two squares as the least difference in size . In this research, the solution approach of "the sketch map" is used to study the perfect rectangle at first, then the solution approach of "the level figure" to simplify the complicatied calculation of the solving course , and "the dual relation" is finally used to prove 9 orders are the least orders for a perfect rectangle . And then, we expand this question to three-dimensional space, considering in a cuboid (its length, width, and height is different) whether could follow the two-dimensional space model to cut apart two squares as the least difference in size, and finish this research.

We study the effect of dark energy on the evolution of cosmic structure in a scenario where the dark energy is treated as free particles and thus can be localized. By theoretical derivation and numerical simulations, we found that: 1. The dark energy particles gain kinetic energy from a moving dark matter particle through gravitational interaction. Due to energy conservation, the dark matter particle will slow down with time Ek(t) = Ek0 - 9 × 10-5[|1+3w|ρDE]1.92t where Ek(t) is the kinetic energy of the dark matter particle,Ek0 is its initial kinetic energy, w is the coefficient of equation of state for dark energy, ρDE is the mean energy density of dark energy, and t is the time. 2. The formation history and structure of galaxy clusters are different in the presence of localized dark energy. The more the localized dark energy, the earlier the formation of the cluster core. In addition, the kinetic energy Ek(R) as a function of R will be different if the ρDE is different. Thus we can compare the observed Ek(R) of clusters with our results to deduce the ρDE in our universe. The results here can be applied to the observations in the near future. 我們探討宇宙結構演化受到可局部叢集之黑暗能量粒子的影響。藉由理論推導及電腦模擬，我們發現： 一、黑暗能量粒子會透過重力交互作而從運動中的黑暗物質粒子獲得力學能。因力學能守恆，黑暗物質粒子的速率會減慢，滿足 Ek(t) = Ek0 - 9 × 10-5[|1+3w|ρDE]1.92t 其中Ek(t) 為黑暗物質粒子的動能，Ek0 為其初始動能，w 為狀態方程式係數，ρDE 為黑暗能量的平均密度，t 為時間。 二、星系團的形成過程及結構，會因可局部叢集之黑暗能量的存在而改變。黑暗能量越多時，星系團的核心會越早形成。而且動能 Ek(R) 隨著至星系中心距離R 的變化，會因 ρDE 的不同而不同，因此可以將量測到的 Ek(R) 和這裡的結果比對，推導出宇宙中的 ρDE 。 這些研究成果將可直接應用在未來的觀測結果上。

在2003 年台灣國際科展之作品說明書「Concatenating Squares」中【9】與2004第三屆旺宏科學獎「SA3-119 ：與特殊型質數之倒數關聯的兩平方總和的整數分解」成果報告書中【10】，就已有令人驚訝的結果。在2005 第四屆旺宏科學獎「SA4-298 ：分和累乘再現數產生的方法及其性質探討之推廣與應用」成果報告書中【11】，更是以逆向思維進行研究推廣，創造出許多新穎且引人注意的美麗數式，由原創性的觀點來進行逆向思維的研究。正由於這些再現數充滿奇巧，且與不定方程（代數）、簡單的數整除性分析（數論）以及同餘式理論都有所關聯，我們要發展前所未有的同步關聯與研究分歧， 且是最新的發現，更以豐富的想像力、創造力與推理能力提出令人耳目一新的重要結果，得到許多從未見過世面的美麗數式，回眸觀賞時內心充滿了數學之美！;Number which when chopped into two（three）parts, added / subtracted and squared（cubed） result in the same number. Consider an n -digit number k , square it and add / subtract the right n or n .1 digits. If the resultant sum is k , then k is called a Kaprekar number. The set of n -Kaprekar integers is in one-to-one correspondence with the set of unitary divisors of 10 n m1. If instead we work in binary, it turns out that every even perfect number is n - Kaprekar for some n . We wish to find a general pattern for numbers these numbers cubed or 3-D Kaprekar. We also investigate some 3-D Kaprekar of special forms. In addition, some results relating to the properties of the Kaprekar numbers also presented. This study indicates the “interesting” and “pragmatic” natures of the research project. We have developed the original results based upon his initiatives and has thus created a new horizon through the research project. This is the proudest achievement for this study. Generalization of Some Curiously Fascinating Integer Sequences：Various Recurrent Numbers！

本研究是藉由數學手法探討；如何由一疊36 張四種花色的撲克牌中，尋找出保證可猜中最多張花色的方法。研究過程是以在適當的猜牌時機，以鴿籠原理、邏輯推理、二進位、分析與歸納……等數學原理與方法，搭配巧妙的策略運用而達到目的。猜牌方法：先約定好猜牌規則，助手將36 張牌背圖樣相同但非對稱的撲克牌，以旋轉牌背的方向傳達訊息。在本研究中得出利用數學原理與方法可「經由巧妙的猜牌方法保證可以猜中26 張花色」，並提供後續研究者利用本研究之結果繼續深入探討與研究。 The study is mathematically based with reasonable explanations behind it. We are to correctly guess as many cards as possible from a deck of 36 cards, with random numbers and four different suits. We will apply mathematical methods, such as pigeonhole principle, logic inference, binary system, and analytical reduction, upon right timing. Using careful arrangement of the principles and reasoning, we can reach our ultimate goal. To state guessing: Conference between the guesser and the assistant about the guessing rules, the assistant will have 36 cards with the same exact pattern on the back but not symmetrical. The pattern of the cards will be different when rotated 180o. The only communication between the two is by rotating cards. In the process we will obtain mathematical theory and methods assuring 26 cards correctly guessed, and the study is for further and deeper discussion.