未得獎作品

In any , we prove that there exist cycles which have any length between 3 and 3n and paths which have any length between their smallest distance and longest Hamiltonian paths in any two different nodes; for any two nodes, there exist varied Hamiltonian cycles, making the two nodes locate on any possible counterpart position(only limited by the distance between the two nodes). In , there are 2n internally-disjoint spanning cycles, and 2n-1 internally-disjoint spanning paths. Besides, we also prove has no more than 2n disjoint spanning paths, and calculate its wide diameter. 本報告證明在環狀網路 中，存在有長度3到 3n 的所有迴圈；任何相異兩點都有各種不同的長度的路徑:從最短的距離到最長的漢米頓路徑；取定任意兩點，存在有各種不同的漢米爾頓迴圈，使得兩點位於所有可能的相對位置上(僅被兩點之間的距離限制)。在 中，也具有2n 個彼此不相交、經過所有點的迴圈，以及2n-1 個彼此不相交、經過所有點的路徑。除此之外，也證明了，在兩相異點間，具有個數不超過2n 且互斥的路徑，且這些路徑經過所有點。我們也估算了它的寬直徑。

After reading “CKSH Communication 20 “, we are interested in Question 5 . We try to explain that in all the No. Crunches, whether we can put the numbers in the No. Crunches any certain position. We specify the question, according to the “Point Symmitry Homing” in mxn No. Crunches, to find the correlated characters of the rules. Finally, we find a “switch” – we can get the better way to rotate the numbers quickly by some programs.從「建中通訊解題」第20 期第5 題出發，本研究嘗試去解釋對所有的數字轉盤而言，是否能將其中的數字歸位到任意指定的位置？接下來將題目特殊化，藉由m× n 數字轉盤的「點對稱歸位」，尋找遊戲規則衍生出的相關性質。最後，利用研究出的性質找到一個「判斷式」可藉由程式設計，快速的找到較佳轉法。

在數位化的今日，由於網際網路的技術蓬勃發展，網際網路變得更容易使用及具高度的親和性，使得網際網路的使用逐年成長。隨著越來越多人依賴網路進行交易，也衍生了層出不窮的網路詐騙問題。其中，網路釣魚就是一項著名的詐騙技術：詐騙者透過偽裝成知名企業的網站，藉此騙取使用者的個人私密資料。在本研究中，我們提出了一套植基於彩色視覺密碼學原理的網站驗證機制，使用者可以透過此機制，直接利用人類視覺的方式來驗證所連上的網站是否有問題，並在此機制之下，設計出另一套管理使用者密碼的方式，進而方便使用者不必費心的去記憶密碼。 Recently, as networks technology flourishes, Internet becomes easier and friendlier to use, and makes the usage of Internet grow up year after year. With more and more people relying on online transactions, it leads to endless network fraud issues. Among them, phishing is a well-known fraud technology to disguise the famous business website to get user’s private information by cheating. Therefore, in this study, an effective scheme based on color visual cryptography is proposed to test and verify the website. Through the proposed mechanism, users can check whether there is a problem website by using human vision directly. Furthermore, the proposed scheme also provides another way to manage user’s password effectively.

As soon as a drop from the same liquid falls to the surface of the liquid, a crown emerges, which is followed by a Liquid Column shortly afterward. In order to measure the diameter of the short-lived crown and the height of the liquid column, we developed two incredible and useful devices for each one of that. After a series of experiments and discussion, we decided to adopt collision and oscillation to illuminate the phenomenon. And the details are in the reports. 液滴活泉：一種碰撞與振盪的交合，也是表面張力與黏滯力的拉鋸。碰撞的同時與 表面張力交柔展現皇冠；振盪的同時與黏滯力以圓形波動吞噬液滴。 望冠興嘆：激起的液體皇冠徑和隆起的液柱高猶如曇花一現，測量技術就簡單設備 而言是窮則思變的契機。 滴滴入扣：滴落小液滴如質點的碰撞，隨著液面的振盪，而終止於波心；滴落大液 滴如多個小液滴集體行動，如聖誕老公公灑落糖果般，爾後激盪擾動迴旋 不已。

本實驗希望發展簡易光降解有機物的裝置以降低分解一些實驗室中常見的有機廢液，實驗中採用Pyrex 玻璃取代昂貴的石英材質反應槽，使用空氣打氣機取代純氧氣的輸送，以TiO? 在分解甲基橙的水溶液中可測得反應速率為二級，利用二級反應速率推得甲基橙降解半生期約44.5小時。本實驗中並嘗試以不同的反應初濃度探討甲基橙降解效果，發現甲基橙在愈稀薄的溶液中，分解效果較佳。;We hope that the experiment can help us develop an equipment to reduce the common organic waste in some laboratories. We will use Pyrex glasses to replace the expansive quartz reactor and the air pump to increase air flow instead of pumping pure oxygen. The results show that our reaction equipment is good decomposition efficiency. The phtodegradation in methyl orange is second order reaction, and the half of livetime is 44.5 hour. We find that the photodegradative rate of the methyl orange is much effective in a thinner solution.

本實驗利用喇叭、鍍鉑黑電極、波型產生器、鎖相放大器、及sciworkshope750 介面卡組合一套系統，此系統可使偵測精密度大幅提升，使得花蓮港模型尺度變小(120×60×4cm)，因此可節省實驗的成本與時間。本實驗希望藉由模型的建立，感測系統的整合，傅立葉分析，使研究者可在各種模型條件下，獲得水波傳遞的相關物理量。鑒於花蓮港喇叭狀港池經實驗後證明容易造成港內共振，且不同的入射波頻率不同，所造成的共振現象及共振位置相當複?。本實驗為縮小模型，但卻可測出的共振頻率、衰退時間及振幅且非常明顯（精密度達3.0×10-4cm/mV）。首要課題是要在港內消除反射的波，在模型實驗中，測量有無加消波線及加不同材質 的線時波衰退時間的長短，得到衰退時間牽線消波者比實驗組減少為0.2－0.6 之間；振幅減少為0.03－0.89 之間，且越鬆散、分支越多、孔隙越大的物質消波狀況越佳，所以毛線效果最佳，棉線次之而尼龍繩最差。 This study utilizes the loudspeaker, the platinum-plated electrode, Sweep Function Generators, DSP Lock-in Amplifier, and the sciworkshope750 interface to construct our system. The system will enhance the great precision of detection, which diminishes the Hualien Harbor model yardstick to 120*60*4(cm). Thus we can save the cost and time of the experiments. We combine the setting-up of the model, the integration of the sensors and the Fast Fourier Transform (FFT) system so that the researchers can obtain the physics-related data when the water transmits ripples in various kinds of conditions. Seeing that the bell-shaped Hualien Harbor is apt to cause resonance in its basin, which is confirmed by our experiments later, our primary goal is to find a way to diminish the waves reflected in the harbor. With the diverse frequencies of incident waves, resultant resonance phenomena and positions are rather complicated. Our experiments are based on a miniature model, but the resonance frequency, the time of wave declining and the wave amplitude are easily measured, with the precision up to 3.0×10-4cm/mV. In another experiment, we add strings made of different materials that can subdue waves. Compared with the records without strings, the strings can reduce the time of wave declining by 0.2-0.6 and can reduce the amplitude by 0.03- 0.89. We have come to the conclusion that strings made of looser, more-branching and bigger-interstice material perform better in diminishing waves. Hence, the knitting wool has the best results, followed by the cotton threads and then the nylon ropes.

人類的脂肪幹細胞,取得容易,且來源不涉及倫理問題,是一種理想的城體細胞來源,目前已發現其可分化成骨細胞,軟骨細胞,脂肪細胞,等等,因此深具未來發展的潛力,將可應用於組織工程細胞治療上,而Chitosan(幾丁聚醣)則是一種具生物相容性,生物分解性且無生物毒性的材料,在生醫材料的領域一具相當發展性,在這個實驗中,我們將chitosan薄膜經過氬氣電漿處哩,並測量其與水的接觸角.發現電漿處理時間越長,接觸角越小,表示電漿處理有助於增加chotosan薄膜表面的親水性.細胞在經過電漿處理的薄膜上,其黏附情形一隨處理時間增長,黏著數目越多,且形態愈扁平,表示電漿處理過的chotosan表面有助於細胞的吸附.;Human Processed Lipoaspirate cells (hPLA) can be subtracted easily from lipoaspirate and the source of the cells does not violate the moral and ethic standard. Therefore, it is an ideal source of somatic stem cells. Recently, researches show that the hPLA cells have the ability to differentiate into osteoblast cells, chondrocytes cells, adipose cells, and skeletal muscle cells. In the future, they have great potential in tissue engineering or cell therapy. Chitosan is a biocompatible, biodegradable, and non-toxic material. It is also an advanced material to be used in the biomaterial field. In this study, we treated chitosan film with argon plasma and measured its contact angle with water. The contact angles decreased as the duration of plasma treatment on chitosan increased, indicating that plasma treatment has a positive influence on increasing the hydrophilicity of chitosan film surface. Moreover, the numbers of hPLA cells adhering to chitosan films increased and their morphology became flatter when the durations of plasma treatment on chitosan films prolonged. Hence, the result showed that plasma treatment on chitosan films also promoted the adhesion of hPLA cells on chitosan film surfaces.

編號1~mn 的mn 個物件已隨機置入m× n 階的矩陣中，另外有一行m 個空格的暫存區供物件暫存用。我們探討將這mn 個物件移至目標區並按照1,2,…, mn 的次序排列，所需的移動步數；每一步的移動中，只能移動每一行最頂層的物件到其他行(含暫存區)的最頂層或目標區。在這篇報告中，我們給出了一個適用於n ? m ?1時的移動方法，此方法在一般的情形下，所需的移動次數未必是最少；但是在最不利於移動的情形下，我們證明此方法所需的移動步數為最少。There are mn objects, numbered from 1 to mn, put on an m× n matrix randomly, and there is another column with m blank spaces for temporary storage purpose during moving. In each step of moving, we can only move the top object from one column to the top of another column or to the target pile. The total steps needed to move these mn objects to the target pile in increasing order from the bottom to the top is studied in this article. A general method for solving this problem when n ? m ?1 is given, and we prove that it provides an optimal solution in the worst cases. However, it may not always provide the minimal steps in all cases.

本實驗是利用二氧化矽分子篩保護奈米銀的方法，有別於市面上奈米銀產品大都以有機溶劑浸泡，且保護劑均是採取界面活性劑，該項產品浸在純水中除了不會改變溶液性質外，又能以分子篩特性讓奈米銀漸進式釋放而達到長效性效果。 針對棉衫吸附奈米銀實驗非常成功，經過十次以上洗滌且放置時間長達一個月以上，對於抗菌效果也有長效性的功能，為本次實驗重大突破。 The experiment is to use SiO2 molecular sieve protected nano Ag method , different from nano Ag popular product which is organic solvent-soak, and the protectant are all surfactant. This product will not change solvent’s proterty in pure water , beside , molecular sieve generally release nano Ag and achieve long-term effect . The experiment for cotton clothes adsorptive nano Ag is very successful , and achieve long-term effect in antibacterial property , that is the most significant .

西爾平斯基船帆(Sierpinski Gasket)與西爾平斯基掛毯(Sierpinski Carpet)都屬於碎形(fractals)圖形的一種，可以利用迭代運算系統IFS(Iterated Function Systems)碼來產生，代入迭代運算方程式後，經由多次的運算，可以得到重覆的圖形。本研究中，我將提出一些作法，找出西爾平斯基船帆與掛毯圖形其遞迴關係式，進而討論出其數位圖形之規律性及所涵蓋的內容與性質，著重在推廣西爾平斯基船帆與掛毯圖形的概念，將一段音樂曲取出，把它們看成反覆隨機迭代點，利用程式經由多次的插值運算，計算出各段音符。最後加入基因演算法來解決音符長短的問題，把製造好的音符染色體放置到交配池中，以隨機的方式在交配池中選取其中之一個染色體進行交配的動作，此二音符染色體會交換彼此的基因，產生下一代新的代表音符長短之染色體，應用於數位音樂創作，而衍生的西爾平斯基船帆與掛毯圖形新穎應用與創新的結果，希望能提供數位音樂創作的多樣性，更進而可以找出「好聽的音樂」與數學的直接關聯性。‘Sierpinski Gasket’ and ‘Sierpinski Carpet’ are two graphics that belong to fractals. They can be produced by IFS (Iterated Function Systems). By iterative computation of many times, we can obtain the similar graphics. In my research, there are some methods to generate Sierpinski Gasket, Sierpinski Carpet, and the iterative algorithms. In addition, I would discuss the regularity and the content as well as the properties of those digital patterns. At last, the advanced application of Sierpinski Gasket and Sierpinski Carpet to digital music pieces was presented. The program took a note of several measure of music as the beginning point, and made the IFS calculations for each new note in each measure. But there was no difference in beats if you just make the IFS iteration. So I changed the beats with genetic crossover method. In this research, the expression of the DNA to each beat of note was adopted. The same way, it took a note as a beginning point. And the system obtained the new DNA from the old notes for new ones randomly. That would make a piece of brand new music. What I want to do in this research is improve the multiformity of music and find what the relationship is of ‘good music’ and mathematical algorithms.