全國中小學科展

未代表出國作品

梯型的分割與調和數列

Refer to Figure 1. Suppose ABCD is a trapezoid and . Passing the intersection M of and we construct a parallel line intersecting and at E and F, respectively. We obtain that , and then we can generalize the result. 如(圖一),若ABCD為梯形且,過 和交點M 分別作平行線交、 於E 、F ,可得 的關係,再加以推廣。

大自然的奧妙~土壤自我淨化能力

大氣圈、水圈與土壤圈是構成自然環境的三大領域,三者之間相互的影響,原本這些空間都具有極大的包容力,亦所謂「自淨能力」,許多的物質進入其中皆會被氧化分解或稀釋而消失於無形。近年來由於工業發展、人口增加,產生大量的廢棄物,長期、密集且迅速的堆積於環境中,使得天然的自淨能力無法應付而失去功能,造成嚴重的後果。就土壤而言,雖有較佳的自淨能力,但是一受污染,除了嚴重破壞土壤品質之外,同時也會直接或間接污染水源 (如:地下水)及空氣,對動植物造成危害,並且難以回復,實不容忽視。本實驗探討:一、土壤淨化能力是否受到不同地區、不同土壤性質的影響。二、同樣的土壤,對不同的污染物(色素、肥料、重金屬)淨化能力強弱的影響。實驗結果顯示大肚山土壤過濾溶液中的色素、磷、及重金屬中的鉻、鎳、銅的能力較中寮及大甲土壤強,只有氮與鉀的過濾能力較大甲土壤差,所以這次實驗中大肚山土壤有最好的污染淨化能力。實驗結果將來也許可以應用於土壤處理場址之適宜性評估。The air, water and soil are three parts of the nature. They affect each other. In fact, they have the "self-purity ability" - they can disassemble many polluted thing by this kind of self-purity ability. These years, because the industry development and the population explosion make lots of waste, the self-purity ability cannot do its best. The soil has better self-purity ability, but if it is polluted, it will not only pollute the water (ex: underground water) and the air, but also damage the animals and plants. We cannot ignore the serious result. This experiment will discuss:1. If the soil self-purity ability is affected by different area and different soil specificity? 2. The different purified results according to the different pollutant (ex: color, fertilizer and heavy metal) in the same soil. Results showed that Da-Du-San soil had strong ability then Chung-Liao and Da-Cha soil in filtrated color, phosphor, chromium, nickel and copper in the solution, but had weak ability then Da-Cha soil in filtrated nitrogen and potassium. Therefore, Da-Du-San soil had the beast pollution-purity ability in this experiment. In the future, results may be applied to the suitability evoluation of the soil treatment place.

天然植物色素與人工染料敏化之太陽能電池

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.

自由基VS抗氧化物

自由基會產生在神經系統、免疫系統、血液循環系統等等,進而影響到人體各器官的運作,甚至於近年來許多醫生學者提出自由基病理:自由基是百病之源。本次實驗筆者挑選葡萄子、維生素C、綠茶來抑制清氧自由基(OH.)所採用的方法是將10%雙氧水製入注射筒並加亞鐵離子催化,,使其與抗氧化物反應,由於雙氧水分解會產生氫氣自由基與氧氣,因此筆者用倍率放大器(OPA)放大生成氧氣造成的電壓,並用Data Studio測量記錄,最後可由氧氣體積對電壓的趨勢圖看出抑制氫氣自由基的效果;Free radicals will be produced in our nerves system blood circulation immunization system etc. and they able to influene the operaion for our organs many medical scholars have even come up with "free radical pathology"-free radicals are sourse of all he diseases in recent years.In this study, I chose rape stone vitaminC and green tea to restrain hydroxide radicals(OH.) Here is summary of the experimental process. First,I put 10%hydrogen peroxide into an injector and then added ferrous ion to hydrogen peroxide to catalyze it. Second I let it reaact with the sample. Because hydrogen peroxide can produce hydroxide radicals and oxygen, I used the mutiplier(OPA) to amplify the pressure caused with the prducion of oxygen, measuring and recording resuls by the software"Data Studio"Finally, we can tell which antioxidant is more effective in restraining hydrode radicals from volume-voltage gragh.

大富翁中的密秘—機率

記得小時候常玩大富翁,在走步數之前常要由擲骰子來決定。又在上國中之後學到了有關機率的問題,所以讓我想起此事,想藉由此次的科展對大富翁內的機率做一番徹底的研究與了解。

廢紙漿發酵產氫之探究

氫氣在燃燒後只會產生水而不產生溫室氣體之二氧化碳,可謂一種潔淨能源。 生質能源是屬於碳中性(Carbon neutral)型之利用方式,因此本研究著眼於如何建構一個操作簡便的共代謝系統,將生質料源從微生物之發酵反應中釋放氫氣出來。 實驗的主要方法是利用好氧性的Bacillus thermoamylovorans 與厭氧性的Clostridium butyricum 共培養分解廢紙漿以生產氫氣。廢紙漿是混合的基質,內富含纖維素、並含一些油墨及少許雜質。利用Bacillus thermoamylovorans 是好氧菌,同時也能將廢紙漿中的纖維素轉換成還原醣的特性,將原本有氧的環境轉換成絕對厭氧的環境,並將廢紙漿中的纖維素轉化成Clostridium butyricum 可以利用的還原醣。如此一來,原本不利於Clostridium butyricum 生長的環境,卻能透過簡單的共培養方式創造出有利於Clostridium butyricum 生長的環境並產生氫氣。除此之外,我們也對不同碳源、不同的植菌量、不同的氧氣量,比較其產氫能力差異,發現增加氧氣量可以提升最後的產氫量大約2.7 倍。 ;Our major goal is to develop a cost-effective biohydrogen production system by the co-culturing of Bacillus thermoamylovorans and Clostridium butyricum. The aerobic Bacillus thermoamylovorans will consume oxygen and converse waste paper pulp into reductant-sugar and the anaerobic Clostridium butyricum will generate hydrogen after oxygen is consumed. With the increase of aeration, the aerobic Bacillus thermoamylovorans growsappropriately leading to more biohydrogen production. However, in enhanced aeration condition, the Bacillus thermoamylovorans will consume sugars that can offer for the Clostridium butyricum. So we can conclude that the control of oxygen is the key point for the system to operate.

缺一格也可以─骨牌排列順序數量之探討

在一次偶然的機會中,我們在科學月刊上讀到一篇探討骨牌排列 (Domino Tiling) 問題的文章。文中骨牌排列問題看似單純,但其中卻有許多有趣的性質,因此,我們想對此進行更深入的研究。\r 我們將1x2的骨牌填入特別的方格中,考慮填入的順序並計算其排列情形的數量。由定義的兩個模型SDT(Standard Dominos Tableau) 與「缺一格」的GDT(Good Dominos Tableau) 為基礎,嘗試尋找它們之間的關連性,藉由對應(bijection)的方法,得知在高度的限制為奇數的情況下,SDT與GDT的數量相同,並且,兩者之間的結構有密切關聯。\r 除此之外,在這個研究中,針對SDT在高度不超過三排時,我們建構出了骨牌排列情形與我們架構的「廣義Motkzin路徑」的對應操作流程。接著,我們嘗試探討一般化的SDT與此結果的關聯性,由對應過程的想法,架構出高維度的「廣義Motkzin路徑」,並推測此路徑與SDT之間有緊密的相關性!

酒精對斑馬魚胚胎眼睛發育的影響

長期以來,臨床研究發現會影響人類胚胎的正常發育,造成胚胎畸形、成長遲緩等現象,稱為胎兒酒精症候群(fetal alcohol syndrome),但是其病理機制仍不清楚。最近的研究發現斑馬魚胚胎對於酒精有非常靈敏的反應,出現明顯的發育異常現象,例如心臟膨大、眼睛縮小、骨頭變形等現象,與人類胎兒酒精症候群相似,顯示斑馬魚非常適合作為研究胎兒酒精症候群的模式動物。在本實驗中,我們針對酒精影響視網膜神經發育的現象進行探討,並且也利用基因晶片篩選出胚胎發育時期受酒精影的的基因轉錄子,藉以了解酒雞造成胚胎畸形發育的機制。實驗結果顯示在眼睛發育過程中,1.5% 酒精浸泡會抑制視網膜神經細胞的分層(Lamination),而進一步利用RNA定位雜交的方式以眼睛的標示基因rx1、pax6b、six3b、alpha-crystallin、rho、neuroD、huC觀察他們的表現,發現酒精會減少視網膜神經細胞的分化,造成眼睛發育的缺陷。在基因晶片的分析中,我們發現酒精處理會抑制許多控制眼睛發育的基因調控子的表現,包括了crx、rybp、irx4a、optx2、rx1、brn3b1 與 vsx1等,此外約有16%的眼睛相關基因液受到酒精的抑制,遠高於其他基因受抑制的比例,顯示眼睛是酒精傷害最嚴重的區域之一。我們從實驗結果得知酒精並未對胚胎發育初期眼睛的發育造成明顯的影響,但是隨後由於控制細胞分化的幾個重要基因受到酒精抑制作用,造成視網膜神經細胞的分化停止,引起眼睛的異常發育的情況。It was known that prenatal alcohol exposure may cause serious birth defects and developmental disabilities. The molecular mechanism of this fetal alcohol syndrome still remains unclear. Here we used zebrafish embryo as a model to investigate the toxic effect of alcohol in retinal development. The histochemical analysis revealed that the cell lamination was prohibited by alcohol incubation. It appears that the retinal cell differentiation was inhibited. As revealed by whole mount RNA in situ hybridization, it appears that the transcription of a number of retinal-related regulatory genes, including rx1, pax6b, six3b, alpha-crystallin, rho, neuroD and huC, were all inhibited in zebrafish embryo by alcohol exposure. The transcriptional profile of alcohol-exposed embryos was also compared with normal embryos by microarray analysis at different stages. It appears that 16% of retinal-related genes were all repressed by 1.5% alcohol incubation, including several retina-related transcriptional factors, including crx, rybp, irx4a, optx2, rx1, brn3b1and vsx1. Our results suggest that alcohol did not interfere the early development of the eye, but has inhibited the final cell differentiation of retina cells. This study helps us understand the molecular mechanism of alcohol-mediated retinal malformation.

調幅超聲波解調高指向可聽音之研究

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.

可調式車刀架

在車床上車刀高度需使用墊片校正中心,螺紋刀太高或太低會造成牙角變大,不同的加工又需更換刀具再校正,費時、費力不合成本效率。我們設計出「無調式車刀架」,目的就是取代墊片的繁雜性,可以精準的將刀具對準中心,並隨意更換刀具。