出國代表作品

光學滑鼠會以很高的速度不斷地對著接觸面拍照，藉由比對每幅影像間的變化來偵測滑鼠移動的速度與方向，本研究利用此特點而設計一個簡易的光學量測系統，其中包括透鏡、光源與接觸面材質的選擇，以及利用Raw Input 模式讀取個別滑鼠移動訊息而發展出來的量測程式，使得此系統可以在無接觸與無摩擦的情況下來測量外界物體的移動速度與距離，經由實驗證明，在光學感測器還可以感應與追蹤的範圍內，量測的數據還蠻精準的。接觸面到光學感測器透鏡的距離越遠，能夠測得移動物體的極速也越高，但是會造成感測器的解析度下降，如此限制了接觸面的材質種類，無法量測表面較為光滑的物體，但是在設計得宜的情況下，仍有蠻多方面的用途，日後若能採用較高效能的光學感測器並加上測距儀的輔助，相信此系統的應用層面會更為廣泛。Optical mouse can take continuous snapshots very quickly of the contact surface and compare the images sequentially to detect the direction and amount of movement. This study uses this feature to design a simple optical measurement system, including lens, illumination and contact surface choice, as well as the measurement program using raw input model to accept the movement information from the mouse. This system can measure the distance and speed of the motion object under the non-friction condition. From the experiment test result, this optical measurement system is workable and satisfactory. Contact surface to optical sensor distance farther, can measure the higher speed of the motion object, but will cause the lower resolution of the optical sensor. This will limit the variety of the contact surface; superficial smoother object is unable to measure. In the future if we can use the high performance optical sensor and assist with rangefinder, believed this system can have more widespread applications.

Starting from the problem in AMC competition of Australia, we try to find out the locus and its length when a point in a regular polygon rolls in a circle. The result is that the locus has a wonderful and regular cycle.Next, we discuss the regularity of the cycle when a regular polygon（n sides） rolls in another regular polygon. Furthermore,we discuss the the equation of the locus by changing the radius and the angle of rolling. we find out the argument function of the locus of a point inside when a a regular polygon（n sides）rolls in another regular polygon （m sides）： ， Aj is the summits of the regular polygon（m sides）, Bjcorresponds Aj when a point inside the regular polygon (n sides) rolls, ) And then, we do some moving simulation with some computer math software, such as Cabri Geometry、Mupad, etc. We discuss the regularity of the locus and its equation of a point inside when some special cycloids, like asteroids, cardioids, etc, roll in a certain condition. Moreover, with the result of research 2, we create the “plate＂ and apply for a patent on it. We hope to study math by playing games. 從澳洲AMC 競賽題出發，嘗試探討一正n 邊形中的一點在單位圓內滾動軌跡及其軌跡長度，發現該軌跡均會產生奇妙的循環規律。 接下來，推廣探討正n 邊形在其他正多邊形中滾動時循環的規律，並利用旋轉半徑及角度之間的變化深入探討其滾動軌跡方程式，發現正n 邊形繞正m 邊形滾動時其內部一點軌跡參數式為，其中， Aj 為 正m 邊形之各頂點、Bj 為正n 邊形中內部一點旋轉時對應 Aj 之點，。 進一步想嘗試使用數學電腦軟體如：Cabri Geometry、Mupad 等對以上研究去做一些動態模擬，並再探討一些特殊擺線如：星狀線、心臟線…等，在條件下相切滾動時，圖中某一點的軌跡規律性及其方程式。另外，應用研究二中的結果，創造出寓數學於遊戲的「圖形板」，並申請了新型專利。

We operated the misexpression screen between the EP lines and the pattern lines with the genotypes of eq1>dll, eq1>abdA, eq1>Ubx, eq1-GAL4, ey-GAL4 or dpp-GAL4. After the screening, we found that five of these 1,800 strains of filial generation had special phenotypes. It had shorter antennae and defects in the anterior equatorial region of eyes. We used plasmid rescue and IPCR to sequence the certain target gene, and found that it was escargot, abbreviated as esg. To identify when, where and how the overexpression of escargot induces such phenotype, we operated the staining of eye-antenna disc in third-instar larval period of wild type, eq> esg×UAS-GFP and eq>GFP with anti-dll, anti-caspase3 and anti-esg. The result shows that escargot cannot be detected before puparium formation. But the expression of dll, a gene controls the eye development, was reduced in the eye disc. We except the overexpression cause the defect of distal antennae and the anterior equatorial region of eyes mainly in the 3-day-long pupal life.我們用異位表現法篩選出和eq1>dll、eq1>abdA、eq1>Ubx、eq1-GAL4、ey-GAL4或dpp-GAL4 這些pattern lines有交互作用的EP lines。在這1800種的果蠅子代品系中，有五種具有特殊的性 狀。它們具有觸角短化以及複眼前緣中央區有缺刻的現象(形成心型眼)。我們使用質體救援 法以及IPCR的方法來定序這段未知基因序列，發現這是一個叫做escargot的基因(簡稱esg)。 為了了解過分表現此基因會造成何種分子影響，以至於產生此種性狀，因此我們使用 anti-dll 、anti-caspase3 和anti-esg 進行野生型、eq>esg×UAS-GFP 和eq>GFP 三齡幼蟲的 eye-antenna disc的螢光免疫染色。結果在幼蟲成蛹前都沒有偵測到esg的表現現象；不過在eye disc中，控制眼睛發育的基因dll的表現有被抑制的現象。因此我們推測過分表現esg的過程因 該是發生在為其短短三天的蛹期。也就是說，這種表型應該是在化蛹後形成。

在一個有障礙的平面上，給三個定點，我們探討連接此三點的最佳網絡。我們討論了諸如直線、射線、線段、圓、網格狀、三角形……等類的障礙，當網絡每穿越障礙一次，就必須付出代價，例如「拖延5 分鐘」。所以，設網絡穿越障礙的次數為y ，則網絡除了原本的總長度之外，還額外加入y 倍某固定數值的損耗。我們以費瑪點的各種性質及三角形不等式等方法為工具，就不同的穿越障礙次數綜合比較，而找出最佳網絡。在某些情況下，最佳網絡不是以費瑪點來連接三點，而是在障礙(如：直線)上找出符合某種與餘弦值相關特殊性質的點，以該點來連接三點，而此網絡可用GSP 軟體相當精確地作出。另外，我們也探討在考慮障礙造成損耗的情況下，兩點間的「實際距離」為何。 最後，我們考慮「混合障礙」問題。在此類問題中，除了前面所討論的障礙，還另加了如同「河流」的兩平行直線間區域之障礙，在這種障礙區域中，網絡的長度要乘以數倍來計算。我們發現，此類問題的最佳網絡也可用特定的正弦條件配合GSP 而相當精確地作出來。;Considering various kinds of obstacles in a plane, such as a line, a segment, a ray, a circle, a triangle or chessboard grids, which function like a red light, we research into the problem of finding the optimal network connecting three given points A, B, C in the plane amidst obstacles described above. Each time when the network crosses an obstacle, it will cause losses, such as five minute’s delay or a loss of one hundred dollars. Taking advantage of Fermat points, some basic inequalities concerning triangles and some special qualities about sine or cosine functions, we obtain the optimal networks in different situations. Besides, we consider what the “real distance” between two points is when there are obstacles in a plane. We also put another obstacle, including a line and a weighted region between two parallel lines, into consideration. In the region, like a river or a muddy ground in real life, the length of the network should be multiplied by a fixed time. Furthermore, we can use GSP to make the networks very accurately.

本研究是[對於正n 邊形A1A2…An邊上一點P(含頂點)，想像自定點P 朝鄰邊發出一條光線，若依逆(順)時針方向依序與每邊皆碰撞一次，經一圈而可回到P 點，則此路徑稱為「光圈」。過程試著追蹤在正n 邊形內能形成光圈的光線行進路徑及其相關問題。 本研究令，且以逆時針得光圈來討論： 1.根據[光的反射原理]，探討光圈之存在性，發現除定點P 在正2m 邊形或正三角形的頂點外，其餘皆有光圈。 2.將可形成光圈的路徑圖展開成[直線路徑圖]來探討。 3.由[直線路徑圖]，觀察到形成光圈的光線行進路徑，可能存在下列情況： (1)不通過正n 邊形的頂點，且產生路徑循環與不循環問題。 (2)通過正n 邊形的頂點。 4.發現正2m 邊形光圈皆為[完美光圈]。 5.發現正2m+1 邊形光圈之路徑與有理數、無理數之特質有關。即當s 值為有理數時，路徑會循環；當s 值為無理數時，路徑不循環。 The research is about [on Point P (including the angles) on the side of regular polygons A1、A2…An , imagine the light goes from Point P to the closest side, then bumps each side sequentially counterclockwise. After going a circle, it’s back to Point P. The track is called “the circle of light.” I try to trace the light track of the circle of light and other correlative questions.] In this research, we suppose,and we discuss the circle of light according counterclockwise direction:1.According to the light reflective principles, we discuss whether the circle of light exists or not. And then we discover that the circle of light really exists except when Point P is on the angles of regular triangle or regular 2m polygons. 2.Spread out the circle of light’s track to [rectilinear track.] 3.By [the picture of rectilinear track], observing there are two kinds of the circle of light’s track: (1)If the light doesn’t go through the angles of regular polygons, it can be a circulative track or a non-circulative track. (2)When the light goes through the angles, it stops. 4.We discover that all the circles of light in regular 2m polygons are [the perfect circles of light.] 5.We discover the circle of light’s track is correlative with rational numbers and irrantional numbers. When s is a rational number, the track is circulative, if s is a irrantional number, the track is not circulative.

給定一平面E，A為平面上一點。取r>0，則我們知道到其距離為定值的點形成一圓，而A為此圓圓心。如果把A改成一平面圖形，則到其距離為定值的點形成的集合會是什麼樣子？類似地，給定平面上兩焦點F1及F2在平面上，則到其距離和為定值的點形成橢圓。同樣的，若把F1及F2改成平面圖形，其圖形會是什麼樣子？藉著GSP的輔助，到目前為止，我們得到了以下的結果： \r 1. 給定一平面E及此平面上的一個凸多邊形, 我們描繪出在此平面上到此凸多邊形之距離為定值的點所形成的圖形。\r 2. 設F1和F2分別為平面E上之點或線段或多邊形（未必是凸多邊形），我們利用包絡線描繪出所有滿足d(P,F1)+d(P,F2)=k（k夠大）的點所形成的圖形。 \r 3. 設C1,C2為平面E上之兩圓，我們討論所有滿足 d(P,C1)+d(P,C2)=k\r （k夠大）的點形成的圖形並討論其性質。 \r 4. 設L1和L2分別為平面E上之兩線段，我們討論所有滿足d(P,L1)+d(P,L2)=k（k夠大）的點形成的圖形並討論其性質。 \r 5. 設A為平面E上之一點，Γ為平面上一凸多邊形，我們討論所有滿足d(P,A)+D(P,Γ)=k（k夠大）的點形成的集合並討論其特性。 \r 6. 藉由和圓作比較，我們研究了變形圓的光學性質；而對變形橢圓也做類似的討論。\r Let E be a plane and A a fixed point on E. Given , it is known that all of the points on E with distance to 0r>rA form a circle and the point A is called the center of this circle. What is the corresponding graph if we replace the point A with a set (for example,a segament or a polygon) contained in FE? Similarly, what is the case when we modify the two focuses and in the definition of an ellcpse to sets and (or example,two segments or two polygons) contained in 1F2F1F2FE ? Taking advantages of GSP and analytic geomety, we research related situations and so far we have obtained the following results:\r 1. Let Γ?E be a segment, a convex polygon or a circle , etc. and r>0 be fixed. We sketch the graph of points on E with distance r to Γ and study properties of such graphs.\r 2. Let F1 and F2 be singletons, line segments , polygons(may not be convex), or circles,etc., on E Taking advantage of envelopes, we sketch the graph of those points P on E satisfying d(P,F1)=k(K>0 is large enough).\r 3. Let C1 and C2 be circles on 1C2CE. We sketch the graph of the points P on E that satisfiy d(P,C1)6d(P,C2)=k (k>0 is large enough) and study properties of this graph.\r 4. Let L1 and L2 be two line segments on E and be a large enough constant. We sketch the graph of points P on E that satisfy d(P,L1)+d(P,L2)=k(k >0is large enough) and research properties of this graph. 0k>\r 5. Let A?E and be a convex polygon on ΓE. We sketch the graph of points on E that satisfy d(P,L1)+d(P,L2)=k(k>0 is large enough) and research properties of this graph.\r 6.We compare the optical properties of metamorphic circles with circles and we deal with metamorphic ellipses similiarly.

「風笛」是台灣原住民鄒族的信號用具及祈雨法器，由一條繩子綁一支竹片構成。轉動風笛時，竹片會繞繩子自轉並拍打空氣而發出聲音，並有上下飛舞的現象。風笛產生聲音的原因，為竹片拍打空氣而造成的渦流共振現象；又由於繩子扭力大小及方向改變，使風笛的音調忽高忽低、響度忽大忽小、且竹片會在兩個平面上公轉，而有週期性變化。施力使風笛公轉轉速加快時，竹片自轉速率也變快，使其音調愈高、響度愈大；而繩愈短、愈粗時，竹片的公轉週期將愈短。The wind whistler was once used by Tsou aborigines as a tool for message transfer. It is composed of a string and a bamboo flapper. When swung around, the flapper spins, beats the air, and makes sounds. Moreover, the flapper flies up and down during the revolution. The spinning flapper beats the air, causes the vortex resonance phenomenon, and thus produces sound. As the twist torque and direction change, there is periodical variation in the sound volume, sound pitch, and the movement of the flapper, which orbits up and down at two planes. If given force to speed up its revolution, the flapper，s spinning frequency also increases, which makes the sound pitch higher and the sound volume greater. Besides, when the string is shorter or thicker, the flapper，s revolution period will be shorter.

由於結網性蜘蛛視覺不靈敏，如何在網上藉振動進行獵捕，這是長久以來頗令科學家困惑的難題，當周遭環境各種振源觸網時，首先會產生不同振盪，蜘蛛是否藉由這些振盪得知獵物資訊？如何迅速準確的定位？又有那些決策條件影響蜘蛛的捕獵行為？更特別的，為何蜘蛛在捕獵過程中會“扯網”？本研究以台灣最大型結網性蜘蛛－人面蜘蛛為研究對象，並設計出一套非接觸式的測量方法，就上述謎題作深入的探討後，成功的解開人面蜘蛛的捕獵機制。簡單來說，其機制分為兩大系統：(1)當獵物擾動不明顯，人面蜘蛛會立即扯網，藉有無產生阻尼振盪，以判斷有無獵物存在；在阻尼振盪產生時，蜘蛛將感知其中具有最大阻尼振盪之放射絲為獵物所在方向，而振盪週期長短，係蜘蛛用以判斷獵物遠近之有效因素。(2)當振源明顯時，蜘蛛直接判斷各種擾動的振幅大小、頻率高低、波形模式、振源質量輕重，決定是否啟動捕獵或逃離反應，並在反應前先行定位，亦即以步足腳勾偵測並比較各放射絲之振盪大小，以振盪最大之放射絲為獵物方向，其次藉由第二對步足之位移所產生之準光角，判斷獵物之遠近。蜘蛛正確的將獵物定位後，會以適當的速度往前衝，一口咬住獵物，以蛛絲重重包裹後，拖往網中央並進行吸食。 Giant wood spider, Nephila pilipes, is the biggest orb web spider in Taiwan. The mature N. pilipes may even grow to exceed 5 cm body length. While waiting for the prey, its giant body hangs quietly on the hub of the web. Owing to its ineffective vision and sense of smell, the spider depends almost on detecting the vibration signal of the struggling of web cause by the struggling prey. When various kinds of sources from the environment contact the web, they will generate various types of vibrations which cause the spider to judge whether they represent danger, prey, or irrelevant signals. Our results suggest that if the disturbance is obvious, through discriminating the amplitude and frequency of the vibration, the spider will make a decision whether to attack or escape immediately. Yet, before any decision is made, it will need to locate the source of vibration. For example, it will locate prey correctly by comparing the vibration transmitted from the radiating strings. The radiating strings that transmitted the largest vibration are where the prey is entangled. The displacement of the second pair of legs will generate a quasi visual angle which enables it to comprehend the distance of prey. When the vibration signal is obscure, it will jerk the radiating string immediately. After jerking it, if there is damping oscillation on the web, then the spider can judge the location of the prey. When there is damping oscillation, the radiating string that transmitted the greatest damping oscillation is where the prey is entangled. Furthermore, the frequency of damping oscillation helps the spider to judge the distance of the prey. After locating the prey correctly, N. pilipes approaches the prey fast, wraps it with silk then drags the prey to the hub to feed.\r

本專題的目的是研究以任意實數 a1 、 a2 、 a3 為起始的M&m Sequences 之穩定性質。我們主要關心的問題是：(1) 是否任給定三數a1 、 a2 、 a3 為起始的M&m 數列皆會穩定？(2) 若上述的M&m 數列穩定，則其穩定的長度與a1 、 a2 、 a3的關係為何？(3) 其穩定的值與a1 、 a2 、 a3的關係為何？我們研究的主要步驟及結果如下︰1. 當1 2 3 a 1) 為起始的M&m 數列。3. 我們證明了下列性質：(1) 若M&m 數列中前n 項所成數列的中位數為n m ，則下式成立： (2) 當存在 k > 4 , k ? N ，使得 ?1 ?2 = k k m m 成立時，則此數列穩定，且穩定長度p 滿足：min{ | 4 } ?1 ?2 = > = k k p k k 且m m ，其中p 必為奇數。(3) { n m }為單調遞增且, 5 1 ? ? ? a m n n n4. 如果x ? 41.625，則{?x,1, x}為起始的M&m 數列，其對應的數列有相同的大小次序且此M&m 數列會穩定，穩定值為41.625，且穩定長度為73。5. 我們觀察發現：如果x 1). 3. We prove the following properties: (1) If the median of the former n numbers of the M&m sequence is n m , we obtain (2) There exist k > 4 , k ? N such that ?1 ?2 = k k m m , then the sequence is stable and the stable length min{ | 4 }?1 ?2 = > = k k p k k and m m , where p must be an odd number. (3) { n m } is monotone increasing and , 5 1 ? ? ? a m n n n . 4. Suppose x ? 41.625, then the all M&m Sequences beginning with –x , 1 , x are the same, and the sequences will be stable, the stable value is 41.625 and the stable length is 73. 5. By the computer experiments, we observe that if x is any positive real number less than 41.625, the M&m Sequence starting with –x, 1, x, will be also stable but does not appear to follow any clearly discernible pattern of behavior. However, the stable lengths are much variant and exist some unknown relation with point format of x. Moreover, we have the following properties: (1)If x is a node, then the stable value is x and the stable length equals to the index of median of the node + 2； (2)Near the branch of 41.625, the stable length is almost a constant except at the edge area，the stable length of (-x,1,x) as x around branch 1 is chaos； (3)If x near the node (K= 3, 5, 7, …, 67, 69), then the stable length is l(K)+K?1 where the positive integral l(K) is determined by Prop1 (see Table 6 and 7).

Up to this time we have spent almost three years in studying condensation and water droplets. Little could we have done as compared with the almighty nature. However we are rewarded by the nature as we gradually found the secrets about electro-magneto field and water droplets: The size of water droplets turn smaller upon electro-magneto field and grow more uniformly especially upon electric field. This experiment presented here is actually the diary of the growth of water droplets in condensation, upon magnetic field and electric field. Through convection, it discusses the self assembly patterns of water droplets and peep into the uniformity both of the size and the distribution mode of water droplets. In former basic experiment, we focus on temperature and the speed of water moisture; generally speaking, higher temperature speeds up the coalescence procedure but does not affects the nucleation size of water droplets in simple plain surroundings; while speed of moisture does affects the nucleation size. As we went farther, deep into convection and found magneto-electric force did play an important role in the self assembly mechanism of water droplets. The topic is mostly concerned as we are surrounded by magneto-electric waves in today’s world. This experiment anchors the first step in discovering the uniformity of water droplets in different environment, and providing insights into the self assembly mechanism of water droplets upon electro-magneto field with nano sizes. 這是一系列關於水蒸氣冷凝為極細微小水珠的實驗。其中可以分為兩大部分； 第一部分是基礎實驗。將水蒸氣導入至潔淨的介面上(蓋玻片)，觀察冷凝水珠的結構。雖然看似簡單平常，但卻有令人驚奇的發現；不同溫度的水蒸氣，其冷凝最初始的細微顆粒之尺寸是相同的 ！爾後隨著溫度的升高，堆疊速率也跟著上升；以致於最後一起呈現出來的水珠大小不一，尺寸不一。 第二部分是將水蒸氣導到磁場及靜電場上，觀察其冷凝結構。這部分的實驗推翻了一般「水分子是電中性在電磁場中不受影響？」的刻板觀念 ！實驗所呈現出來的冷凝水珠，不但於附加磁場中尺寸縮小又不易長大，同時還有固定的自我組成模式( Slef-assembly pattern);而且也發現在磁場中的冷凝小水珠的尺寸比電場中的小，可是電場中的小水珠則表現出較大的均勻特質。