未得獎作品

本研究探討運用磁場來達到非接觸煞車的功能，本實驗採用兩種方式來探討磁煞車力，分別為馬達有外加電流及沒有外加電流的情況。首先本實驗提供一穩定的電源使鋁盤轉動，觀察加上磁場及把電源切掉後鋁盤轉速的變化。實驗發現，當馬達沒有外加電流時，磁煞車力與轉速及磁場平方皆成正比；馬達有外加電流時，電流差會與轉速平方差成正比。探討磁煞車力與厚度及介質的關係，實驗結果發現，渦電流常數與厚度成正相關，且當兩片鋁片中夾有介質時，渦電流常數較小。 This experiment is based on the magnetic brake’s practical uses and braking forces. We want to calculate the braking force, and also examine the factors that cause the braking force to differ.We attached a metal disk to a motor to make the disk rotate, then we control the distance between the magnet and the metal disk, therefore measuring the relativity of the distance and the rotational speed. We discovered that when the metal disk received a large quantity of the magnetic field (close distance), the breaking force and the rotational speed increased. On the other hand, when the metal disk received a small amount of the magnetic field (far distance), the breaking force and the rotational speed decreased. The magnetic braking force will convert into kinetic energy, thus, by using this connection and also by increasing the electric current to measure the resistance, we calculated the magnitude of the magnetic braking force. Hence we perceived an inverse ratio between distance and the braking force, that is to say, the closer the distance, the stronger the magnetic braking force; the further the distance, the weaker the magnetic braking force.

流體旋轉時，外圍及底部流體，因槽壁及槽底摩擦力的影響，流速較慢，相對的壓力也較大，導致外圍的水流會轉入中心。發現本實驗的渦流為強迫與自由漩渦組成。實驗中，探討f(轉動器的頻率)、H(總水深)、y(?入深度)、R(轉盤半徑)四者與角形數間的關係。若y、R 愈大、H 越小，隨著f 的增大，可觀察到的形狀邊數越多；反之，若y、R 愈小、H 越大，則f 愈高，所形成的圖形半徑愈大，易超過轉盤，不易觀察。依白努利方程式，外層水流的流速較慢，而內層水流的流速較快，故外層壓力大而內層壓力小，水會由外往內流，而此渦動流於轉動液面產生的剪力，可能為產生N 邊形漩渦的主要原因之一。流體旋轉系統中，因轉動而產生流體離心力與內外層壓力差交互作用下，於某特定相關的因素條件下，形成特定角形數漩渦，是本實驗的重要發現。When fluids are in rotation, fictitious force given by the container brings about the relative decrease of speed of the bottom and outer layer of water, which causes its pressure to increase, and water to spin inward, resulting in a vortex motion with N-corner polygons formed at the surface of the rotating plate. During this experiment, we discover that the vortices consisted of free and forced vortex and the polygons vary as control parameters f(rotation frequency), H(height of fluid), y(depth of the plate), and R(radius of the plate) change. The larger y and R are,the smaller H is, the more corners show up as f increases. On the contrary, the smaller y and R are,the larger H is, few polygons are identified since the rotating radius of polygons are larger than the plate. According to Bernoulli’s principle, smaller velocity of the outer-layer water causes water pressure to increase and water to spin inward. During this process, shear force is developed at the surface of the rotating fluid, which we believe is the main cause of N-corner polygons. In a rotating system, the interaction of centrifugal force and differential pressure causing a certain Ncorner polygon to be formed under different controlled parameters is our main discovery.

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！

This research is about two ponds in the Ｂ park’s and the Ｄ park’s snail(Square Mystery Snail：Sinotaia quadrata) in Taipei city of Nei-hu District for research object, carry out the study of the following research proceed: 1.Discriminate the algae species that are growth on the snail shell and which is a kind of interaction with the snail; 2.The influence of the snail and algae with difference of temperature, salinity, pH value and dark ; 3. The factors affect algae growth on snail shell; 4.Use the variation of snail and algae to be a biological incator. The result manifestation: the algae that are growth on snail shell have two kinds, one is Cyanophyta and the other is Cladophora sp. The interaction between algae and snail belong to communalism, but under the condition of lacking of food, the snail then will eat the Cladophora sp. which grow on the shell of other snails. The temperature adapts aspect, upper limit of the feat existence of the snail should be low in 28℃. When over than 28℃, Cladophora sp. as the most strong, Cyanophyta is secondly, and the snail then is most poor. For the maximum tolerance of the salinity, the snail is about 4.375?, Cyanophyta is about 5.0?, Cladophora sp is then about 7.0?; Under the different salinity for the tolerance , the Cladophora sp. still the most strong, Cyanophyta is secondly, and the snail then is most poor. Under the dark environment, the speed of Cyanophyta begin to be bleaching is very fast than the Cladophora sp.. In the tolerance of pH value range: The snail is about pH=5～10, Cyanophyta is about pH=7～8, Cladophora sp. is about pH=6～8; When the pH value range is in the pH=5～8, the speed of the Cyanophyta occur changing is very fast than Cladophora sp.. The algae are growing on snail shell very different between two ponds, the main reason is water pH value dissimilarly: When pH value over than 8.5, there is no Cladophora sp. to grow on the snail shell, after the pH value to decrease, Cyanophyta then will compare early than Cladophora sp. to grow on the snail shell. Calculate by the classification of the freshwater biological incator : Two organic pollution degree of the ponds may be lain in theβ-mesosaprobic to theα-mesosaprobic, and the polluting degree of the Ｄ pond is more seriously. As for two ponds, have already faced what level of eutrophication? Belong to actually which stage of pollution grade? Not only added the classification data of floating and fixative algea in two ponds, and also according to the parts of chemistry analysis method measure of the data makes the substantial evidence, then could carry out the more accurate and thorough study in the days to come steadily studying process.本研究是以臺北市內湖區兩個綠地公園(Ｂ公園與Ｄ公園)池塘內的石田螺(Sinotaia quadrata)為研究對象，進行以下研究目的之探討：1.鑑別石田螺螺殼上藻類的種類及其與石田螺的互動關係；2.溫度、鹽度、酸鹼值及黑暗等環境因子的差異，對石田螺及螺殼上附生藻類的影響；3.影響藻類附生於石田螺螺殼上的因素；4.將石田螺及螺殼上附生藻類的變化作為監測環境因子或水質變異的指標現象。結果顯示：附生於石田螺螺殼上的藻類有藍綠藻(Cyanophyta)與剛毛藻(Cladophora sp.)兩類；與石田螺的互動關係應屬於片利共生(communalism)，但在缺乏食物的情況下，石田螺則會採食同伴殼上的剛毛藻。溫度適應方面，石田螺適宜生存的溫度上限應低於28℃，超過28℃水溫環境的耐受程度，是以剛毛藻為最強，其次是藍綠藻，而石田螺則為最差。對於環境鹽度最大耐受度方面：石田螺約為4.375??，藍綠藻約為5.0??，剛毛藻則約為7.0?；在不同鹽度環境下，鹽度的耐受程度，仍以剛毛藻為最強，其次是藍綠藻，而石田螺則是最差。在黑暗環境下，藍綠藻褪色產生白化現象的速度明顯地比剛毛藻要快了許多。在環境酸鹼值耐受的範圍方面：石田螺約在ｐＨ＝5～10 之間，藍綠藻約在ｐＨ＝7～8 之間，剛毛藻則約在ｐＨ＝6～8 之間；而酸鹼值範圍在ｐＨ＝5～8 時，藍綠藻產生變化的速度明顯地比剛毛藻還要快。而兩樣區池塘水體酸鹼值的不同，應是造成石田螺螺殼藻類附生現象差異的主要原因：當酸鹼值超過8.5 時，螺殼上就無剛毛藻附生，當酸鹼值降下後，藍綠藻則會比剛毛藻早出現在螺殼上。藉由淡水生物指標的分類推測：兩樣區池塘水體有機污染程度，可能介於β-中腐水性(β-mesosaprobic,βm)至α-中腐水性(α-mesosaprobic,αm)的範圍之間，而Ｄ池塘受污染的程度應會比Ｂ池塘還要更嚴重些。至於兩樣區池塘水體，已面臨了何種優養化的程度？究竟是屬於哪一個階段的污染等級呢？除須補充水體中浮游性及附著性藻類分類的詳細觀察資料外，仍必須參照部分水質化學分析法所測得的數據作佐證，才能在日後持續地研究過程中進行更精確及深入的探討。

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.

This study is to investigate whether colony of the spiny-weaver ant, Polyrhachis dives, have biological clock so as to observe the locomotion activities of the ants in the nest and find out if the Light period will interfere the rhythm. The conclusion is the colony of the ants get the rhythm is 23.8 hours during in L:D=12:12.There are ants not significant difference between large colonies and small colonies. While in Dark (D:D)the ants appears free running with 23.1 hours as the rhythm, so, the colony of the ants has obvious light-rhythm movement, showing that the biological clock will act on group and being controlled by light period. 本研究是在探討黑棘蟻 (polyrhachis dives) 聚落是否有生物時鐘(biological clock)，以觀察黑棘蟻在巢裡的活動情形，找出週期並探討光是否會影響週期。結果觀察出黑棘蟻 的聚落在有光的時候(L:D=12:12)以23.8 小時為週期，沒有光的時候(D:D)黑棘蟻仍呈現自由律動(free running)，以23.1 小時為週期，所以黑棘蟻的聚落有明顯的日週律動，顯示生物時鐘能作用在聚落上，且受光週期之調控。

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.

高分子發光二極體乃是利用電子和電洞在發光工作層結合而形成激子，激子在形成後隨即以光的形式衰退，而發出光來。一般而言，高分子發光二極體是一種三明治的形式，電子注入層/發光工作層(高分子)/電動注入層，而通常我們會選擇加入電子傳遞層和電動傳遞層，來增加其發光效果。本研究係針對聚苯胺做為電洞傳遞層對發光二極體之影響，分別對有電洞傳遞曾和無電洞傳遞層之發光二極體作導電度測量、循環伏安法、電位-電流測量、亮度-電位測量。發光二極體中所須之高分子層，須利用旋轉塗佈機，將其均勻的披覆在載體上，由於本校並無此儀器，所以將離心機改造成簡易旋轉塗佈機，並觀察其披附之效果。另外，在封裝元件時，係因學校缺乏真空蒸鍍的儀器，所以將利用電鍍法把鋅鍍在ITO玻璃上，或將鋁片和ITO玻璃緊靠在一起，針對此二替代方法，本研究將探討其所製出原件成效。Polymer light emitting diode (PLED) utilizes the energy gap between the layer of electron and electric hole that emits the light due to the decay of solitron. PLED is always in the sandwich from, that means the conducting polymer is contained between metal as an cathode and indium tin oxide as an anode. It is used the addition of another electric transfer layer and electric hole transfer layer to improve the lighting efficiency of PLED. The purposes of this study are to discuss the effect of polyaniline as the electric hole transfer layer. The study methods are conductivity measure, the cyclic voltametry, the luminance-voltage curve. The simplified spin coating machine was designed to coat the polymer onto the ITO. The zinc was electroplated onto the graphite as an cathode.

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。

高斯曾經提出八皇后問題：八個皇后在8 × 8 的棋盤上有幾種放法可以使任意兩皇后不會互相攻擊？我們在原來的問題上加上一些條件，改變皇后攻擊規則，使得皇后失去一條對角線的攻擊方向，稱之為「跛腳皇后」。我們稱一個在棋盤上放置最多跛腳皇后使其不互相攻擊的放法為好放法；研究跛腳皇后放置在各類棋盤上其好放法的個數和性質。我們分別在六種棋盤上做討論：（1） 在平面n x n 棋盤上，我們證明了其好放法與完美極致史考倫型數列之間的對應關係，並歸納出相關的性質和定理。（2） 在平面m x n 棋盤上，我們固定一邊長度n，做出n 較小時好放法數的通式；我們也將其好放法對應至廣義史考倫。（3） 在環面n x n 棋盤上，我們說明了其好放法與完全剩餘系排列之間的對應關係，並歸納出相關的性質和定理。（4） 在環面m x n 棋盤上，我們固定gcd（m,n），做出gcd（m,n）較小時好放法數的通式。（5） 在柱面n x n 棋盤上，我們證明其與環面n x n 棋盤等價，說明其好放法具有和環面n x n 棋盤好放法相同的性質和定理。（6） 在柱面m x n 棋盤上，分成左右柱面以及上下柱面來做討論。我們歸納出相關性質和定理；並固定一邊長度n，做出n 較小時好放法數的通式。Gauss had researched about putting eight queens on the chessboard on the way that doesn’t make any queen attacks another one. Thus, we added some rules on the question: the queen loses one diagonal attacking-way and become the “lame queen”. We call a way that doesn’t make any lame queen attacks another one “a good way”. We have been investigating the amount and properties of good ways based on six kinds of chessboard: （1）We found the correspondences between the “good way” on n × n plane chessboard and the Perfect extremal Skolem-type sequence, and concluded some associated properties and theorems. （2） On m× n plane chessboard, we fixed the length n of one side of the chessboard, and accomplished the amount of good ways when n is small. We also correspond the good way to the Generalized Skolem.（3）We found the correspondences between the “good way” on n × n torus chessboard and the arrayal of complete residue system, and concluded some associated properties and theorems.（4）On m× n torus chessboard, we fixed the gcd(m,n) （greatest common divisor of m and n）, and accomplished the amount of good ways when gcd(m,n) is small.（5）On n × n cylinder chessboard, we proved that this kind of chessboard is equal to torus chessboard. So the good ways, characters, and theorems on cylinder chessboard are the same as on the torus one.（6）On m× n cylinder chessboard, we separate it into two cases: left-right cylinder chessboard and up-down cylinder chessboard. We concluded some associated properties and theorems, and we also fixed the length n of one side of the chessboard and accomplished the amount of\r the good ways when n is small.