為了瞭解黃斑黑蟋蟀叫聲和溫度之間的關係，我應用物理熱平衡原理，自製水浴槽控制環境溫度，以電腦錄音程式分別錄製15℃、20℃、25℃、30℃、35℃時的蟋蟀叫聲，利用Sound Forge軟體分析並比較不同溫度下的各種特性。結果發現所分析的chirp、chirp period、syllable period、pause均和溫度呈負相關，而單位時間內的叫聲次數則與溫度成正相關，並推導出15~35℃範圍內蟋蟀叫聲次數與溫度成正相關的公式。最佳直線為：﹙15秒內叫聲次數＋19.385﹚÷2.483=當時溫度﹙℃﹚，呈高度正相關﹙相關係數：0.9398﹚。本實驗也比較母蟋蟀對不同溫度下雄蟋蟀叫聲的偏好程度，發現母蟋蟀較偏愛25℃時的雄蟋蟀叫聲，此結果可能與雄蟋蟀在25℃時叫聲的波形最為穩定有關。為探測蟋蟀觸角上的溫度感受器位置，我們曾將不同部位的觸角加以剪除，結果顯示觸角剪除面積越大的雄蟋蟀越不傾向鳴叫，但無法證實是否為溫度偵測異常所導致。本實驗除供學術研究外，因黃斑黑蟋蟀在世界各地均有分布，所以希望能藉由分析溫度與蟋蟀叫聲的相關性實驗，未來嘗試能探討其在不同環境的適應行為亦或種化的可能性。另外，全球暖化問題日益嚴重，也希望能藉由相關實驗探討暖化對蟋蟀生態上的影響。最後，我們的實驗證明了蟋蟀叫聲和環境溫度確實有極大的關聯性，未來或許能參考蟋蟀感覺溫度的機制，製作出一個天然零污染的溫度計。 To find out the relationship of cricket’s calling and temperature, we use a hand-made water-bath tank to control the temperature and record the callings with microphone and software, Sound Forge. After analyzing the collected data, we’ve found that cricket’s chirp, chirp period, syllable period, and pause are indeed affected by temperature (15 degrees - 35 degrees C). Moreover, we also compare female cricket’s preference to the callings, and the result indicates that female cricket’s preference is changing with temperature. In the last, we tried to find out where the thermoreceptors are by cutting out the antennae. After cutting, crickets tend to not to make any calls at all, so we conclude the antennae might play an important role in sensing and calling. The experiment proves that this communication system is temperature coupled. Because the cricket, Gryllus bimaculatus, is a worldwide species, we may learn the accommodation or the possibility of performing a new species by researching the relationship of temperature and cricket’s callings. By the way, the Green House Effect is getting more and more serious, so we want to search for the influences on crickets that are caused by Green House Effect. The last but not the least, according to the report, maybe we can investigate the mechanism of sensing temperature and then make a natural thermometer that is no pollution in the future.

微孔珊瑚是優良的生物氣候記錄器，可準確記錄海水表面水溫、陸源沉積物通量和其他微量海水組成等，已成為熱帶氣候變遷研究的重要工具。然而，珊瑚成長速率則顯著受限於海水表溫影響（邱景星，1999）。太陽是地表能量最主要來源，其活動狀態能深遠掌控地球氣候變化，因此其週期性變動規律，已成為近期地球科學家探討環境變遷的重要資訊。 本研究以台灣東南外海綠島採集的微孔珊瑚骨骼樣本，藉由X-ray精確測量其年平均生長速率及觀察骨骼內微量腐殖酸螢光特性，並透過比對太陽輻射量、珊瑚生長與太陽黑子數目的相關性分析，以推倒百年來控制地表氣候變遷的主要因素。 本研究經由頻譜分析、主變量計算、平均標準差和太陽輻射角修正，獲得正確太陽黑子數目、地區性輻射、海水表面溫度和珊瑚生長速率等資料，並討論其間的相互關係。 結果顯示，太陽輻射、海水表面溫度和氣溫有高度正相關（r2>0.62），證實太陽對地球氣候系統的重要性。太陽黑子與輻射資料，則因大氣折射、日照時數等因素影響，正設法解決這些干擾效應；而珊瑚生長速率與海水表面溫度的相關性，則涉及雙極化效應（註）及其他未知因素影響，尚待進一步釐清。 （註）：雙極化效應指珊瑚在過高或過低的環境下，生長速率皆會停止 The skeleton of Porites corals is one of the most useful biogenic recorders, which provide relevant information of abrupt climate change, such as sea surface temperatures (SSTs), riverine sedimentary flux, and seawater compositional variations. Information retrieved from coral skeleton, therefore, has become a powerful tool for studying tropical climate change. The annual growth rate of Porites corals, however, was affected strongly by local SSTs (Chiu, 1999). On the other hand, the climatic condition on Earth surface is regulated significantly by solar activity. Subsequently any intensity or periodicity variation in sunspot activity will cause major global environmental changes. This research aims to study coral skeleton collected from the Orchid Island (Lan-yu) offshore southeastern Taiwan for precise measurement of annual growth rate using X-ray density bands, as well as the luminous characteristics of trace humic acids in skeleton. A systematic comparison among solar irradiation, SSTs and coral growth rate will provide critical information on major factors that may affect environmental changes occurred during the last millennium. In this study, we apply spectrum analyses, principal component, mean standard error method, and modified sun irradiation angle to correct biases presented in the available data of observed sunspot number, local irradiation, SSTs and coral annual growth rate and to examine possible relationships among these factors. We have found excellent correlation coefficient (r2>0.62) in solar irradiation, SSTs and air-temperature, which support the importance of solar irradiation to the earth surface climate. However, effects on cloud and length of sun irradiation need further investigation to emphasize the importance of sunspot activity to the annual growth rate of Porites corals. No straight forward relationships were observed between coral growth rate and local SSTs due to complicated biological effect (1*) or other unknown factors, waits for further investigation in the near future. 1* Complicated biological effect means that coral may stop growing their skeletons when the temperature it lives in is over range for growth.

In this study, we mainly explore the geometric construction in 3D. By conducting some problems about constructing circles, we define the PLC construction in 2D as constructing a circle, either passing through a given point (P), tangent to a given line (L) or tangent to a given circle (C). Besides, we aim to discuss the properties of the PLC construction and the relations between each other. We discover if we find a plane satisfying certain conditions in space, the properties in the PLC construction can apply to such a plane. Furthermore, we extend the properties in PLC to the PES construction in 3D, defined as constructing a sphere, either passing through a given point (P), tangent to a given plane (E) or tangent to a given sphere (S). Also we discuss the relations among them.這個研究主要在探討3D 的尺規實作。藉由歸納某些有關作圓的題目，我們定義2D 中的PLC作圖─作圓，過已知點（P）、切已知線（L）、切已知圓（C）。並探討PLC 作圖的性質及彼此的關聯性。而我們發現：在空間中只要找到滿足特定條件的平面，則2D 幾何作圖性質在該平面仍能沿用。此外，運用PLC 作圖性質，我們進一步推廣到空間中的PES 作圖─作球，過已知點（P）、切已知面（E）、切已知球（S），並探討各個類型間的關聯性。

日光燈是我們最常用的照明設備。傳統的日光燈是屬於電感性的負載，接上電源後其電壓與電流的波形會產生異相位的問題，造成無效功率。本研究是以簡單而且經濟的方法在日光燈的兩端並聯電容器以改善其電流落後電壓的情形，減少無效功率，降低電力的消耗。研究中測量日光燈的等效阻抗，並加以相應的補償電容，從電路實驗中觀察，得到功率修正的結果。Fluorescent lamps shine our lives everywhere. However, traditional fluorescent lamps are inductive loads and produce a phase angle between voltage and current when connected to an alternating power supply, which leads to considerable electricity losses. This project uses parallel capacitors with the fluorescent lamp to compensate the phase difference between current and voltage, and thus reduces power consumption. In the study the impedance of a CFL (Compact Fluorescent Lamp) bulb has been measured and compensated with corresponding capacitance. Finally, the power consumption reduction is verified with experimental results.

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！

一 Motivation and Purpose: In this study, we want to completely know about “The number abc…de, which times m/n, 1≦n≦m≦9?N can get ed… cba?”, and also expect to find out “The good rule within them”. 二 Procedure:Using method of enumeration, induction to collect sample of all and beginning from two digits to get information “good rule”. When get some useful idea, put them into the following research for the step easy go on, the method try and error is a very tiresome works, especially when we deal higher digits. till enough information is obtained, we solve problem and find new one, then likewise again research steps, just the basic science research ways, we are glad have the key of these problem. 三 Result and conclusion :Those number we named “converse No.” There are two groups: S=m+n=10 and 11 S=11, then Q=m/n=9/2,8/3,7/4,6/5=4.5,2.6,1.75,1.2 S=10, then Q=m/n=9/1,8/2,7/3,6/4=9,4,2.3,1.5 Each group have four type. When S=11,Q=7/4=1.75,if converse No.each digit is a multiple of 3, then can cancellation or extension of fraction to get another 3 or 4. Growth up rule: Converse No. = type factor x heritable factor x growth factor=rx hx g S=11,r=2~5,h=9, s=10, r=1~4, h=99 一 研究目的：盼能找出”顛倒一族”的族譜。二 研究過程：確定研究題目為ab…cde×m/n=edc...ba,0≦n≦m≦9?N 求ab… cde？以窮舉法收集觀察資料，歸納演繹尋求規律。1.先觀察兩位數，分析共有顛倒對36對。2.建立乘數Q=m/n一覽表，共有27個3.設計顛倒對大/小及其商一覽表，以利觀察、歸納獲得規律。4.接著觀察三位數，共有360對，綜合二、三位數規律，找出選擇式窮舉法：9之倍數法。5.再接著找出四位數，再綜合而知另有 全調法 重現法 半調法 GCD遺傳基因法等來繁衍高位數顛倒數。6.於是依諸法找得六位數資料，得知GCD遺傳基因法為繁衍通則，完成族譜建立模式。7.研究顛倒數位數與其個數間關係式，完成研究。研究結論：1.顛倒一族有兩大類：S=10與S=11 S=m+n。2.每一大類有四型： S=10中，Q =9/1,8/2,7/3,6/4(9,4,2.3,1.5)S=11中，Q =9/2,8/3,7/4,6/5(4.5,2.6,1.75,1.2)3.每一型均有一個顛倒數，除了S=11中，Q=7/4=1.75者可約、擴分而得3or4個。4.顛倒數原則上均為9之倍數，除了Q=7/4經約、擴分可能得非9倍數者。

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.

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。

The larceny is always annoys our family and our society. They usually steal on the day when people working in the office or studding in the school. They always wait for people leave the house, and try the bell until them confirm the owner of the house leaved and nobody at home. Then they will open the door or break the lock of door. So we can find that if any body home or the lock is very hoard to open or to break. Then the thief is always choice to give up. That prove if we con let the thief think the house is some body home. Then it can to avoid larceny. This project is about how to design a system which is used AI technology to be a robot that is like a human. That robot can talk to the thief and can be a special lock when the thieves try to break the lock of door. The goal of this project is to design a robot that will be a door angel. It will let thief thinks that is some people always in the house. So they can not to steal in this house. We use the AI speech recognition & house environment control I/O system to be a robot which is setup in the door. It is like an angel to protect our home and family. And can stop the larceny. 「住宅竊盜犯罪」一直持續困擾著人類社會，住宅竊案最常發生於大白天，小偷常趁著家中成員上班、上學等時機，稍加觀察，再加以測試（按門鈴） ，確定家中無人，下手破壞鎖具侵入搜括；小偷只要遇到非常難開的鎖或認為有人在家就不會進一步的行竊。所以這證明只要讓小偷認為家裡有人，就能防止竊案的發生，而我們的研究目的就是如何在小偷還在徘徊尋找目標時，就要讓他感到這一家不能偷，如何讓他感覺家裡有人，進而打消入侵行竊的意念。我們希望能設計一套系統，利用AI人工智慧語音辨識及家庭環境控制，來建立一個充滿智慧的門神機器人，來事先嚇阻小偷的行動，就像門神一樣，可以預防竊案的發生，並整合大門門鎖內鎖與家電，形成智慧型的門神機器人，來保佑我們的家庭，也讓竊盜率降低，作為竊盜犯罪防治的利器。

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.