出國代表作品

給定一個P∈(0,1),令k0=0, p0=p，定義k1為能使 的最小正整數k，而 ; 相同的，對於給定的kn-1, kn 為能使的最小正整數k, 。若存在kn 使得，則稱p∈ In; 若對於所有n 與kn ，，則稱p∈ I∞。如此區間(0,1)可分解成集合I1,I2,…,I∞。

本研究探討在給定範圍的面積下，以最省錢的方式用籬笆圍出最大的矩形土地，其中矩形的邊長為正整數，且矩形對邊使用相同單價之材質的籬笆，但相鄰邊使用不同單價之材質的籬笆。我們希望透過轉換，將單價不同的情況回歸到單價相同的情況，以便完整的解決這個問題。\r 藉由改變邊長，將 轉換成 ，使問題轉換成相鄰邊之單價相同的情況；但是經過運算找出的最佳解 轉換回 後卻不一定符合「整數邊長」的要求(即 和 不一定是整數)。為了解決這點，我們重新以不同的角度探討單價相同的情形，以找出整數的最佳解。\r 最後我們發現，若 和 切線斜率的差值大於或等於1，則 坐標愈近 的解愈佳，而在差值小於1的範圍內，我們提出一個檢驗法，可以找到整個問題的最佳解，同時讓此最佳解 轉換回 後仍符合「整數邊長」的要求，進而解決問題。

本研究探討肥皂膜與肥皂水的共振現象。在肥皂膜共振方面，我們以實驗探討皂膜的共 振模式與頻率的關係；並配合共振理論模型求出薄膜厚度，再與體積密度-厚度測量方法比 較。而又發現皂膜在共振時，皂膜保存時間較平常久，故進行皂膜生命期與頻率、強度的關 係。在進行肥皂膜實驗時，肥皂水滴落在喇叭上，振動出奇特的形狀，進而探討皂水共振的 特性並嘗試建立其數學模式。 ;The research is about the resonance of soap film and soapsuds. For the resonante of soap film, we tried to find out the relation between the resonant pattern and frequency by experiment; according to the resonante model, we measured the thickness of soap film, which was compaired with volume-dencity method. We found that the life-time of the resonant soap film is longer than the normal one, so we proceeded to study the relation between the life-time, frequency, and power. We observed special resonant pattern while the soapsuds fell down on the speaker. So we studied the characteristics of resonant soapsuds, trying to make the mathematical pattern of resonant soapsuds.

This research tries to find out how changes of weight or proportion of a reactor would affect the type and structure of a crystal. In the experiment, the Hydrothermal reaction was adopted to conduct the syntheses of Vanadium-substituted Gallium Phosphates and try to pick up the single crystal to collect data with SXRD for further illustrating the crystal structure with diamond software to know well its nature. The research result finds out a new type of crystal unseen in the existing literature produced because of the weight changes of C3H10N2, therefore the weight change of a reactor may affect the structure of crystal significantly. In the future, it is expectation that comparison among structures of other Vanadium-Substituted Gallium Phosphates can be made, and the properties of this compound can be measured, and try to find out a brand new type of structure for new exploration by changing the initial reagent. 本研究係透過改變化合物所添加之反應物的比例，以了解反應物比例的改變對晶體的型態與結構的影響。實驗採用中溫水熱反應來從事金屬釩鎵磷酸鹽的合成。並挑取單晶，以X-ray 繞射儀進行數據收集，再以diamond 軟體繪出晶體的結構圖，且進一步得知其性質。研究結果發現，經改變丙二胺的量後，產生不同於文獻上的新化合物，可知改變所加反應物的比例，對於晶體結構有相當大的影響。未來可朝向與其他的釩鎵磷酸鹽做結構上的比較、對此化合物做更進一步的性質測量、改變起始試劑測試，進而得到更新穎的結構形式等部分進行探究。

本研究的目的在觀察液滴的蒸發過程，探討影響一滴蒸發方式改變的變因。我們利用數位攝影機外加近攝鏡頭，由側面逆光拍攝液滴蒸發過程，並轉錄成電子檔利用電腦協助分析。液滴影像分隔放大投影在方格紙上，以便測量接觸角及高度的變化。結果發現蒸發情形可分為三種：Ⅰ.當接觸角大於九十度時，液滴和界面的接觸線迅速外擴，直到接觸角遞減至90度後定住不動，蒸發終了時，接觸線迅速內縮，留下縮小的實心殘跡。Ⅱ. 當接觸角小於九十度時，接觸線先些微外擴迅速外擴，之後定住不動，直到蒸發終點，液體內縮，留下環狀殘跡。Ⅲ.當接觸角小等於九十度時，接觸線始終定住不變，液滴蒸發後留下原大小的實心班跡。液滴蒸發時接觸角和高度並不是連續變化，而是交互階梯式遞減。本研究的結果可應用在探討噴漆及噴墨印表機的噴墨印刷上。The objective of this investigation is to observe the evaporation of liquid drop and find out the factors that could affect it. A digital camera with micro lens is used to film the process of the evaporation. And a close-up of the sample drop is taken with backlight. The results are analyzed with a personal computer. The magnified images of the drops are projected on grid papers for measuring the changes on contact angles, and heights of drops. We classify the evaporation of a drop into three types: Ⅰ. The contact angle is greater than 90 degrees. At first, the contact line will spread outwardly till the contact angle decrease to the 90 degrees and then be pinned until the evaporation reach its terminal. At last the contact line quickly contract inwardly, and a solid stain remain. Ⅱ. The contact angle is less than 90 degrees. The contact line will spread slightly and then be pinned. At the terminal the liquid contract inward, and a ring-like stain is formed. Ⅲ. The contact angle is equal to 90 degrees. The contact line will always be pinned, and no ring, but spot stain is left. During the evaporation, we discover that the contact angle and the height of the drop do not change continuously but alternatively decrease by steps. The results of our investigation can be applied to the aspects of paint-spraying and jet printers.

面對一個終身學習，多元化學習的社會，學習的方法不再侷限於閱讀或求教於師了，取而代之的是電腦科技的變革。上屆學長利用線上代理人融入遠距教學的作品令我印象深刻，但總覺得少了些趣味及互動性，於是本實驗嚐試將虛擬實境加入線上代理人及遠距教學，利用空間魔法師建構出來的環境，讓使可者能夠融入其中，悠遊在虛擬的世界，並配合鍵盤的滑鼠的控制移動，點選建構出來的虛擬物件，透過超連結連結至網路上的知識網頁，配合線上代理人的互動及帶領，結合了主動、趣味、互動與便利，開創未來的學習方法，一個講求效率、速度及克服空間無時無刻都能學習的環境。With the arriving of 21st century，things are widely different，including the ways of learning. Because of the revolution of multi-media，computer technology will change the traditional way of learning. I was impressed by the master piece 「Long-distance with Agent」 which was done by the schoolmates last semester. But I feel their work still have much room for improvement，so I combine to use the virtual environment with the advantages of their work. Learners can move and click the objects in the virtual reality space，and they can be linked to the knowledge website through the Internet. Learners can enjoy the interesting ，fast，interactive and efficient learning environment. This work is done by the Space Magician Ver3.0， which is used to design a 3D virtual reality environment. And the users can enjoy the net-surfing and through the hyperlinks to get the information.

本研究希望在數位顯示方面做些改進，利用電腦運算使戶外大型LED看板所使用之能源降到最低，以達到節能減碳。\r 本研究分為兩個部份:\r 第ㄧ部份:以瑞利準則探討亮點間距與觀賞距離之關係。\r 實驗中，以Photoshop繪圖模仿LED燈泡之排列，分析兩亮點之大小、距離與觀測距離的關係來設定點之尺寸，再進一步分析三原色點之觀測距離、比例及三原色點之佈點方式對混色效果之關係，並以瑞利準則判斷之。\r 得到公式如下：\r 自己所繪之點大小/點恰可分辨之最近距離=LED燈之間隔/點恰可分辨之最近距離=0.8mm/1m \r 第二部份:數位顯示—LED。\r 利用第一部份所得知的公式發現：在某ㄧ觀賞距離時，有最佳的影像品質且有最少的用電量。較近時，則影像品質降低；而較遠時，影像品質已無法提昇，而多餘的用電量則可經由實驗省去。藉由本次實驗結果，可利用所編寫之程式計算出在某ㄧ距離下最適合之燈泡尺寸及所省之電量，以達到節能減碳的效果。

19、20世紀的後期印象派中，點描派為最吸引人的畫派之ㄧ，而喬治‧秀拉(Georges Seurat)即是其畫派之代表人物，因此，設計實驗時以秀拉的畫風為中心。\r 本研究以Photoshop繪圖模仿點描派之作品，?探索物質的本質，選用三原色為混色的原色，來觀察混色後對畫作的效果。研究中，以分析兩亮點之大小、距離與觀測距離的關係來設定點之尺寸，再進一步分析三原色點之觀測距離、比例及三原色點之佈點方式對混色效果之關係做為實驗主軸，並以瑞利準則判斷之。\r 希望藉由本實驗能以物理學的角度瞭解點描畫派之作品，同時，設法將點描畫數位化，並希望找出欣賞點描畫最佳情況，提供賞畫者最好的視覺享受。

吹長笛時，按同一按鍵，以大小不同的力量去吹，會引發不同頻率的泛音，而通常越用力吹，引發泛音的頻率越高，所以我們想了解為什麼越用力，泛音的頻率會高，其間的關係究竟是什麼？風經過管口會產生各種頻率的噪音，其中某些特定頻率的聲音會因為會在管內形成駐波而放大，所以我們只能聽到某些特定頻率的聲音。當風速增加時，會在管口形成渦漩逸放的紊流現象。其渦漩頻率與流速成正比（註一）。我們以塑膠管實驗。發現以特定的風速引發該基音後，繼續增加風速，當風速達某一定強度時，才會躍遷為下一個泛音的頻率。這個現象告訴我們：在一封閉管下，風速與泛音的關係並非「線性遞增」，而是越「躍遷遞增」的關係。另一個實驗測量不同管長、其諧音之頻率的關係，我們可以得知，越短的管子，因為相鄰兩泛音間頻率差較大，越不易激發更高階泛音。經由這些實驗結果，我們能夠推論：當管子越長、基音頻率越低時，諧音間頻率的差距相對越小，繪出的風速－頻率關係圖應更加顯示了風速與頻率呈正比關係。未來我們可以以閃頻器觀測紊流渦漩的產生，再變化至不同吹入角度，及各式管口造形，這些實驗能協助我們更進一步了解樂器的發聲原理，甚至開發一個以聲音頻率測量風速的儀器。註一：林婉如、張?文2006 國際科工程組佳作作品。When we press the same key and blow a flute using different strengths, we can get different overtones. Usually, the harder we blow the flute, the high the frequency we get. We want to understand why we get a higher frequency when we blow harder into the flute and to understand the relationship between them. When wind passes through the mouthpiece, many kinds of noises will be produced. Some of the frequencies will expand because they will form standing waves in the tube. Therefore, we can only hear certain frequencies. As wind speed increases, a turbulence of the vortex shedding will be formed. The frequency of the vortex shedding and wind speed will be in a direct ratio. We experiment with plastic tubes. When we increase the wind speed and get certain magnitudes, the frequency will jump to the next overtone. The phenomenon shows that the relation, in a closed tube, between wind speed and harmonics is not a linear increase but a transition increase. In another experiment, we measured the relationship between wind speed and different lengths of tubes. We can infer that the shorter the tube, the higher high-frequency harmonics can be produced. Through these experiments, we come to the conclusion that the longer the tube, the lower frequency of the fundamental tone we get and the discrepancy in frequency between harmonics is smaller. Then we make a diagram between wind speed and frequency that indicates that there is a direct ratio between wind speed and frequency. In the future, we can use “” to observe the production of turbulence. Then we can switch to different angles when we blow into flutes. Otherwise, we can experiment with different shapes of mouthpieces. These experiments can assist us to understand more how the instrument sounds. We can develop a device measuring wind speed with frequency.

細胞脂肪分化是造成肥胖、骨質疏鬆、和糖尿病的重要前置因素。我們若要維持良好身材又想省去減肥藥的問題，那麼我們必須了解造成脂肪化的原因，才可能擁有好的預防之道。利用人類骨髓間質細胞可以分化成骨質與脂肪等細胞的特性，我們研究氧化壓力對間質細胞\r Ras基因轉換表現後骨質與脂肪分化的影響。結果發現以添加超氧根 (O2-，l5nM)形成氧化壓力，可促進正常Ras基因表現的間質細胞朝骨質分化;相反地，超氧根會促進\r Ras基因突變而不表現的細胞，朝向脂肪分化的現象。進一步研究其作可原理，發現氧化壓力可促進 RaS蛋白質啟動細胞外訊息活化酵素(ERK)，接著驅動骨質轉錄因子(CBFA1)表現，再到骨鈣蛋白質與骨結節形成。而抗氧化酵素(超氧根轉化酵素;SOD,5OOU/ml)的作用，可以抑制正常Ras基因細胞氧化壓力下骨質分化的進行;但不能防止氧化壓力促進Ras基因突變細胞，朝向脂肪分化的作用。總結而言:Ras基因的表現與否，是決定脂肪分化的關鍵切換點;也是影響氧化壓力對間質細胞朝骨質分化的樞紐。這種基因與氧化壓力互動影響骨質與脂肪分化的剖析，將有助於提醒人們:使用抗氧化劑來調節抗衰老、肥胖、和美容時，必須是在不同情況和不同基因體質的人，有所不同。 \r Human\r mesenchymal stem cells are able to differentiate into bone, muscle, cartilage or\r fat tissues. Our preliminary study with human mesenchymal cell line (HS-5) showed\r that HS-5 cells could differentiate to bone, cartilage and muscle but not fat cells\r as determined by histochemical staining of phenotypes. We have further studied the\r influence of oxidative stress on the switch between bone and fat cell differentiation.\r Results showed that oxidative stress started with exogenous superoxide, produced\r by the interaction of xanthine oxidase and hypoxanthine, promoted the differentiation\r of osteogenic lineage showing expression of osteocalcin and bone nodule formations.\r The mechanism was investigated and superoxide was found to induce ERK (extracellular\r regulated signal kinase) activation; and then the expression of osteogenic specific\r transcriptional factor (CBFA1). A plasmid containing ras-mutant (Ser 17 Asn) which\r can inactivate the expression of ERK was transfected into the HS-5 cells for studying\r the influence of oxidative stress on ras-mutated mesenchymal cells. Surprisingly,\r it was found that oxidative stress did not promote osteogenesis but it enhanced\r adipogenesis from the ras-mutated HS-5 cells. Further studies indicated that superoxide\r neither induced ERK activation nor CBFA1 expression, but it did enhance expression\r of adipogenic specific transcriptional factor (C/EBPα) and lipoprotein lipase in\r the ras-mutated mesenchvmal cells. Taken together, the study model to induce the\r bone cell differentiation from human mesenchymal stem cells may be employed to make\r bone cells for tissue engineering.