Abstract (一)、 In our study, we discuss a m×n chess and any beginning square p finding a directed path of chessman from p moving to an end square in which the chessman moves to adjacent squares including only three directions which are right move, up move and diagonal left down move. A m×n chess is ruled into m columns and n rows creating the number of (m×n) squares (二)、 A chess directed path moves from any beginning square to end square in a m×n chess and every other square is visited just once. In the view of the beginning squares, the chess paths are solvable paths in a mxn chess and the corresponding squares are solutions. (三)、 First, we find out that some beginning squares are located in a special area with no any solvable directed paths. We define the special area be no-solution area. (四)、 According the 3-color theorem, we determine more than two thirds of no-solution area. (五)、 Then, we derive properties of reversibility and symmetry in solvable paths. i.e. A solvable path exist another solvable path by reversibility and symmetry respectively. (六)、 Utilizing the generalization of no-solution area which is extended from the concept of no-solution area provides judgment for the next moves effectively. The judgment is defined as effective move principle. (七)、 Furthermore, using the other theorem called rules of shift Hamiltonian path gets augment solutions. (八)、 According to the effective move principle finding a number of solvable directed paths, use the reversibility and rules of shift Hamiltonian paths to get augment solutions. Finally, utilize symmetry to find out all solvable paths in the m×n chess. (一)、研究規則：在m×n 的格子中，任取一格A 當作「起點格」，在起點格上放一顆棋子，只能往「上」、往「右」、往「左下」的方向移動。(二)、定義：若棋子從「起點格」，按照上述規則能不重複的通過所有m×n 格子到達某一「終點格」，則對於「起點格」而言，此移動路徑稱為m×n 的「有解路徑」，其任4一「終點格」稱為「起點格」的「路徑解」。(三)、我們先研究出「基本無解區」。(四)、根據遊戲規則我們利用三種顏色將n × n 方格塗滿，並判斷出大部分的「無解起點格」。(五)、利用遊戲規則得到兩重要性質：(1)[可逆性性質] (2) [對稱性性質](六)、利用「廣義基本無解區」，當作我們[有效移動]的判斷，讓「有解路徑」快速的找出。(七)、利用本研究所稱的「平移哈式鏈」，得到[擴充解]。(八)、根據[有效移動]求出部分「路徑解」，再利用[可逆性性質]、 [擴充解] ，最後利用[對稱性性質]完成所有「路徑解」的尋找。

本研究先挑選出適合槌染的植物，探討如何清楚敲出植物外形，接著用不同的助染劑及媒染劑，進行槌染後顯色情形及固色效果的比較，再將研究結果應用在生活中。 研究結果發現，是否使用助染劑，對於顯色效果及固色情形，並無明顯差異。先槌染後媒染的方式，以鹽水、鐵鏽水、稻草灰水媒染後，綠色植物多呈綠色，僅有些微深淺的不同；以醋水媒染，植物顏色偏淡；以石灰水媒染，植物顏色變深，部分從綠色明顯轉為褐色。搓洗後，有使用媒染劑固色效果較佳。先媒染後槌染的方式，在不水洗的狀態下，較能保留植物鮮豔的顏色。彩葉草先媒後染，顏色有不同的變化，適合植物槌染，以鹽水及醋水媒染，褪色明顯。將槌染加以美化後，可以製作生活中許多實用小物。

The purpose of this study is to set up a quick, easy and economical way to evaluate the ability of different concentration of various antibiotics to penetrate biofilm and establish the antimicrobial susceptibility patterns of various antibiotics. The susceptibility of five antibiotics upon sessile cultures of Bacillus subtlis ATCC 6633, Escherichia coli XL, Pseudomonas aeruginosa ATCC 27853, Staphylococcus aureus ATCC 29213 and Sarcina lutea ATCC 9341 were measured ATCC 27853, and S. aureus ATCC 29213 proved to be very difficult to eradicate, with only Gentamicin proving to effective at achievable drug concentrations, but the S. lutea ATCC 9341 biofilm was the most susceptible to the Penicillin. The results demonstrated that for biofilms of the same organisms, several hundred to thousand times the concentration of a certain antibiotic were often required for the antibiotic to be effect, while other antibiotics were found to be effective at the MICs. The concentration of antibiotic to penetrate the biofilm is proportional to the thickness of biofilm. Indeed, our research have already indicated that the use of MIC values to indicate antibiotics effectiveness is misleading, because MIC values can not represent the actual effect of anticbiotics on microbiologicals that have developed biofilm. The antimicrobial susceptibility patterns of antibiotics to various bacterial biofilm are different. The susceptibility of the mixed biofilm depends on the physical and biological change of biofilm. Our biofilm device offers a new technology for the rational evaluation of antibiotics effective against microbial biofilms and for the screening of new effective antibiotic drugs.此研究之目的是要建立一套操作簡便、快速且費用低廉之生物膜厚度產生方法，藉此探討不同生物膜厚度對抗生素抗菌之影響，進而完成抗生素對生物模之抗菌圖譜。本實驗將測試五種抗生素Bacillus subtilis ATCC6633，Escherichia coli XL，Pseudomonas aeruginosa ATCC27853，Staphylococcus aureus ATCC29213和Sarcina lutea ATCC9341之抗菌圖譜。試驗結果顯示Gentamicin對前四株試菌有較佳之穿透力，對S.lutea ATCC 9341則是Penicillin。實驗結果證明最小抑制濃度值確實無法實際有效地表達對已形成生物膜菌體之抗菌效果，要完全去除生物膜之抗生素濃度是為最小抑制濃度之數百倍到數千倍，而且抗生素用藥濃度隨著生物膜厚度增加而成比例增加。不同抗生素對不同菌株生物膜有不同之抗菌圖譜，混合菌株生物膜是否會促進或抑制抗生素之穿透力，端視其生物膜結構有無改變。本實驗方法可以做為一種快速檢定抗生素對細菌生物膜敏感性之新技術，同時亦可有效地篩選新的抗生素藥物對生物膜的抗菌效應。

本研究利用偏振片、量角器為刻度盤、雷射光為光源，及照度計為偵測器，組裝一個簡易且可靠的旋光度計。我們利用單位時間旋光度的變化量當作反應速率，來測量蔗糖的水解速率，同時求出蔗糖水解反應的反應級數、速率常數(k)。利用糖類的旋光度具有加成性之特性，找出不同混合比例時的旋光度，追蹤實際蔗糖水解的每個狀態，找出最後平衡狀態，同時將蔗糖水解平衡結果顯示，旋光度與濃度有線性關係，而蔗糖水解反應對蔗糖而言為一級反應。接著，我們在蔗糖水溶液中加入不同種類的酸，探討催化劑的種類與蔗糖水解反應速率的關係。 In this research, in order to measure the optical rotation accurately without expensive equipments or complex process, we assembled a polarimeter by ourselves. With simple materials which can be found in ordinary senior high school laboratories, including a calibrated scale, a simple Luxmeter, a laser as the photo source, and other side devices. The Polarimeter ended up operating fluently and accurately. We put the laser under a tube, which has two pieces of polar screens on the top of it and on the bottom of it, ,and put a luxmeter just above the tube. When we slowly rotate the polar screen on the top, the figure shown on the luxmeter changes. By numerical analysis, we can get information about the hydrolysis of polarized substance. Secondary, we measured the optical rotation of glucose, fructose, malt sugar, galactose, and sucrose to get their specific rotation. Then we measured the optical rotation of sucrose every five minutes. By doing this, we could keep track of the hydrolysis rate of sucrose, figure out the order of reaction, and the rate constant (k) and the equilibrium constant (K). Thirdly, we used different kinds of acids into sucrose solution as the catalyst, and observed the effect. The result showed that hydrochloric acid is a better catalyst to this reaction than sulfuric acid and nitric acid. The polarimeter of this research can be used in science education of junior and senior high school. By teaching students to assemble and operate the self-made polarimeter, students can know better about optical rotation and polarized substance. Also, the interest in this experiement will add to students’ motivation to do science research.

p53 蛋白是一種轉錄調控因子，其在抑制癌症的形成扮演很重要的角色。已知的報告顯示它能影響下游特定蛋白表現進而調控細胞週期或促使細胞進行凋亡作用。如此作用機制對於可能癌化的細胞在生物體造成傷害之前能被先行消滅，因此正常的p53 蛋白存在與否，對癌症的產生有很大的影響。 根據上述結果，我們想分析不同表現量的p53 是否對於致癌藥劑-EtBr所引發的癌化細胞有所影響。所以我們設計實驗，將具有正常表現量p53 蛋白的老鼠(p53+/+)與僅能表現少量p53 蛋白的老鼠(p53+/-)，均塗以等劑量之致癌藥劑EtBr於其大腿皮膚上，觀察其致癌情形的差異。實驗結果發現 : 在塗EtBr 的14 隻p53+/-老鼠中，有3 隻出現了組織病變的症狀，包括脾臟腫大，淋巴組織長出腫瘤，而其他對照組(一)塗EtBr 的p53+/+老鼠，(二)不塗EtBr 的p53+/+老鼠或(三)不塗EtBr 的p53+/-老鼠都沒有產生異常的症狀。因此根據上述實驗結果進行推論，發現經EtBr 的刺激後，p53+/-的老鼠的確較其他的老鼠更容易得到癌化細胞。;p53 is a transcription factor that plays an important role in suppression of tumorgenesis. Previous reports showed it regulates cell cycle and enhances cell apoptosis by effecting specific proteins expression. By this way, the problematic tumor cell can be deleted to protect organism from tumor damage. According above conclusion, we are interested to know whether p53 plays a role involved the carcinogens-EtBr induced tumorgenesis. We compared the differences of tumorgenesis between mice express normal (p53+/+) or low (p53+/-) expression level of p53 proteins when they are smeared equal amount of EtBr on skin of thigh. In here, our results show three of fourteen p53+/- mice had pathological changes, containing spleen enlargement and lymphoma. However, other three comparisons, smear p53+/+ mice with EtBr (1), without EtBr (2) or p53+/- without EtBr(3), are normal. Therefore, We suggest that p53+/- mice are easily to obtain tumor than p53+/+ mice after EtBr treatment.

專題課時，利用20根義大利麵及有限的膠帶與棉繩搭高塔挑戰失敗，引發了我們對在有限資源下，如何搭出堅固高塔的好奇心。本研究利用自然課的教具完成簡易裝置，測試了幾種市售麵條的彈性與彎曲強度，挑出適合的義大利麵條進行棉花糖挑戰。接著使用圓竹棒代替義大利麵進行結構的實驗，再配合自製的剪力測量裝置進行研究，探討三角形長邊的重疊方式對剪力與耐重力的影響，並發現剪力與耐重力最大的重疊方式與加強三角柱的直立柱中間點可以加強耐重力。最後，運用研究結果與文獻資料，成功將20根義大利麵高塔由原本22公分高提升到97公分高，高度增加了四倍多。

可聽聲有向四周擴散繞射特性，而超聲波具有指向性，改以超聲波載送可聽音訊號後，其載波與旁頻帶均在超聲波範圍，實驗中人耳卻可聽到高度指向性聲音，且調幅解調後的可聽聲衰減率比純超聲波來的低。那為什麼超聲波會解調可聽音？我們以非線性的數學轉換概念，成功以數學推導解釋實驗中所聽到的可聽聲，是由旁頻經由非線性轉換而來的。為了證實空氣中的超聲波有非線性現象，以發射40KHz單頻訊號，除了接收到40KHz訊號外還可接收80KHz訊號，而80KHz訊號振幅，會隨著發射強度而遞增，也會隨著傳輸距離增加至穩定狀態，這所我們從文獻中的非線性理論所吻合。接下來進行調幅超聲波實驗，我們經理論計算旁頻帶強度為頻率響應與調變率乘積的一半，而解調可聽聲的強度為調變率、頻率響應與非線性係數三者乘積，我們也由實驗數據證實理論計算結果，在實驗中，換能器在40KHz有最佳的頻率響應，其非線性係數與所載送可聽聲頻率高低約略成正相關，並且與換能器距離遞增而越遠而增加。此外在提高高指向可聽音輸出功率方面，除製作專屬的放大器、運用方波取代正弦波來載波、配合陣列換能器輸出；在改善音質方面，利用等化器調整訊源頻譜分佈，降低低頻振幅，增強高頻振幅，讓各頻率的原始訊號都能有適當的調變，達到最佳音質。The audible sound has the characteristics of spreading and diffracting. And ultrasonic is directive. We modulate sound into ultrasonic signal. The carrier and sideband are ultrasonic frequency bands. But in the experiment, human can hear highly directive sound. In terms of attenuation rate, AM demodulation sound is lower than pure ultrasonic wave. Why can human hear the directive sound? By using the nonlinear mathematical transform, we managed to explain the audible sound which is transformed from sideband with nonlinear effect in the experiment. In order to confirm that nonlinear phenomena in the air ultrasonic, we launch 40KHz single tone ultrasonic signal. Besides the 40KHz signal, we also received 80KHz signal. The amplitude of 80KHz signal will increase with the emission intensity, and also with the transmission distance to increase its stability. These are consistent with nonlinear theory in the literature. Next we began AM ultrasonic experiment. We calculated the sideband intensity that is the product of frequency response and modulation index. The demodulation sound intensity is the product of modulation index, frequency response, and nonlinear coefficient. We also proved the calculated consequence through the experiment. In the experiment, the ultrasonic transducer has a best frequency response in 40KHz. The nonlinear coefficient has positive correlation with the modulation frequency, and increases transmission distance. To boost the power of directive audible sound, we made an amplifier, using square wave to replace sine wave of carrier, and in conjunction with array transducer output. To improve the sound quality, We use the spectrum-Equalizer to adjust the frequency distribution of the origin signal. The EQ reduces the low-frequency amplitude, and boost high-frequency amplitude, which enables every frequency of the original signal to be properly modulated, achieving the best sound quality.

本實驗以吸附染料之二氧化鈦奈米結構電極層為承載基材的太陽能電池為研究對象，旨在增進其光電轉換效率，促使染料有效地吸收光能後造成電荷分離，再經由二氧化鈦傳導帶向外傳出而形成電流，即所謂染料敏化太陽能電池。實驗主軸共分三：1、合成染料N3：觀察吸附度與浸泡時間之關係，發現在18~20 小時電池有最佳吸附；改變電解液濃度，求得最佳電解液濃度範圍；酸化二氧化鈦極板。2、天然植物色素：改變溶劑，得出高極性之丙酮對電池最佳；酸、鹼化植物色素；觀察電池隨著光照時間增加，性質趨於穩定。3、混合色素與染料：此實驗旨在印證不同吸能範圍之染料在極板混合浸泡後，電池吸能帶是否有疊加、擴充的效果，並觀察分開浸泡與混合色素一起浸泡之不同效應，量測IPCE 以玆比較。實驗結果可知，確實對於電池吸光範圍有所增加，且分開浸泡之效果較好。This experiment is mainly about the phtosensitization of Ti02 solar cell, aiming at improving the energy conversion efficiency, promoting the electric charge to separate from TiO2 and spread out through after the dye absorbs light. That is so-called dye-sensitized solar cell. The experiment mainly divides into three parts: 1. Ruthenium(II): Observing the connection between adsorption and dipped-time, find out that solar cell has best to adsorb in 18 to 20 hours; change the concentration of electrolyte; acidification TiO2. 2. Photosynthetic pigments: Change solvent, and get the conclusion that pigment has better adsorption in high polar solvents such as acetone; acidification/basification pigments; observe the changing of energy conversion efficiency while the illumination time increases. 3. Mixed the dye and pigment: This experiment is aim at proofing that the absorption spectrum of soaked-TiO2 may mix after dipped in different dye and pigment. Furthermore, we compares the differences between TiO2 dipped in one mix solution and dipped in several solutions separately, measure its IPCE. According to the experiment, the spectrum of soaked-TiO2 is certainly larger, and dipping in solution separately has better effect to the battery.

自從九二一集集大地震以後，中、小學對於防震教育是更加的重視，一次又一次的防震演習\r 還不夠，還讓學生到地震演練室去體會更逼真的地震實境。在地震演練室的下面就有一個六\r 軸動感平台，六軸動感平台的運作是各軸的伸縮長度不同而模擬地震的，而用彈簧製成的震\r 動台也可以達到模擬地震的效果，去做一些關於地震的研究實驗。地震有各種不同的震動方\r 式，多半是垂直的上下移動或是水平移動，不同的地震對於相同的建築物的影響也有所不同；\r 而地面上有各式各樣的建築物，有的高有的低，所以相同的地震對於不同的建築物的影響也\r 會有差別。\r Since the disastrous Earthquake 921 happened three years ago, the primary schools and junior high\r schools have stressed on the anti-earthquake education and training. Except for the anti-earthquake\r drills they take the students to an earthquake show room to experience more realistic earthquakes.\r Beneath the earthquake show room there’s a 6 degree of freedom Steward platform. The platform\r simulates the earthquakes by varying the length of the 6 axis. We also designed a platform by springs to\r simulate the earthquakes. There’re several types of earthquakes mostly horizontal or vertical .\r Different earthquakes have different effects on the same buildings. Earthquakes of the same amplitude\r will have different effects on different buildings.

本實驗用了業務用排風扇，並加上整流段，使氣流更加平穩、集中。裝上自製調速器以控制風速，並且改良出微型風速計，以測試棒球上下的氣流流速。棒球部分，則利用家裡面常會用到的圓形保鮮盒，改裝成測試架。此測試架可同時測到水平力、垂直力及阻力，不儘大大地突破過去的測試限制，更可以任意改變旋轉的角度及轉速，以及不同的旋轉軌跡。如此，幾乎所有的變化球都可以模擬出來，也可藉此找出新種的變化球。為了分析打擊時機，我們利用了電腦軟體(威力導演)，將打者的打擊影片進行連續的分析，以求得球路判斷點，最後利用電腦做0.01秒為間隔的力量分段分析，使數據更加精確，更有助於棒球軌跡的完整呈現。最後，再透過升力係數、阻力係數和自旋比的關係圖，發現高轉速下與馬格努斯經驗公式相違背的部分。