全國中小學科展

2003年

關於二元根樹上的鏈、反鏈、獨立集的計數及極值

二元根樹是資訊科學上最重要的結構之一,因此其結構的探討就很有價值。在這個研究中,我們探討二元根樹上反鏈(Antichain),鏈(Chain),獨立集(Independent set)計數。在每一個子題之下,我們求出計算反鏈,鏈,獨立集的方法。之後我們求出極值(包括最大跟最小值),並且討論該極值之下所有可能的樹形。此外,我們並討論要列出二元根樹上這些資料(反鏈,鏈,獨立集)所需的演算法。In this paper we enumerate the number of antichains, chains, and independent sets of a binary tree of size n. After that we focus on the extreme values (maximal/minimal). we calculate the extreme values and discuss the possible graphs of trees when achieving these extreme values. Moreover, we offer algorithms for listing all the objects in each extreme case.

廣鹽性吳郭魚氯離子調節機制- - - NKCC在氯細胞中扮演之角色

本實驗中我們利用廣鹽性吳郭魚進行氯離子調節機制的研究,探討廣鹽性吳郭魚如何能在不同環境中維持體內氯離子恆定,進而適應生存環境。我門想要探討:『是否NKCC 這種蛋白質在淡水吳郭魚MR 細胞中扮演吸收 Cl- 的角色? 如果是,吳郭魚又如何藉NKCC 的調節適應環境中 Cl- 的變化呢?』我們利用細胞免疫螢光染色法、西方墨點法和共軛焦顯微鏡觀察分析NKCC 在不同 Cl- 濃度人工淡水馴養的吳郭魚MR 細胞上的表現量,結果發現 NKCC 分布於頂端細胞膜(又稱為細胞開口),及其附近的細胞質內;環境中 Na+ 濃度的差異對NKCC 在MR 細胞上的表現影響不大,但低 Cl- 環境馴養的吳郭魚,NKCC 表現量都高出其他組很多。顯示NKCC 參與了氯吸收的機制。另一個實驗中,我們將吳郭魚由淡水中轉移至海水以分析它們在適應海水的過程中NKCC 的表現變化。結果發現在馴養初期(16 小時內),圓點狀NKCC 仍然可以在MR 細胞的開口附近觀察到,但到了24 小時後,NKCC 在開口的表現就明顯減少甚至消失,取而代之的是轉移到底側邊細胞膜上的NKCC。此實驗證實了NKCC 這一個與Cl-運送相關的蛋白質,在廣鹽性吳郭魚氯離子調節中扮演了很重要的角色。 Euryhaline tilapia (Oreochromis mossambicus) is capable of maintaining internal ion constant ineither hypertonic or hypotonic environments (fresh water or seawater).MR cells in the gills of tilapia play critical role in absorbing Cl- from fresh water or pumping redundant Cl- from body fluid into seawater. Chloride transporter (NKCC) which distributed in basolateral membrane of MR cells is involved in Cl- secretion of seawater teleost. However, the mechanism of Cl- absorption in fresh water MR cells is still unclear. Whether NKCC is also involved in Cl- absorption and how do tilapia regulate Cl- absorption are the questions this study aim to answer. By using immunofluorescent staining, western blot, and confocal microscopy, the distribution and expression level of NKCC in fresh water MR cells were examined. We found that NKCC is distributed on the apical membrane of freshwater MR cells where is known to be the site for active Cl- absorption of MR cells. We compared the expression level of NKCC in MR cells from tilapia acclimated in high, normal, and low Cl- artificial water for 7 days. The results showed that NKCC is induced by ambient low Cl- , and in contrast suppressed by high Cl- water, indicating NKCC might be involved in Cl- absorption of freshwater MR cells and up-or down-regulated to maintain Cl- uptake constant. In addition, we also examine the expression pattern of NKCC in MR cells from tilapia transferred from fresh water to seawater. Confocal images show that apical expressed NKCC disappear gradually within 24h seawater acclimation and is substituted by basolateral expressed NKCC. This study provides a novel regulatory mechanism of NKCC in Cl- transporter of MR cells.

這不是群體防禦─反駁行為學家對魚群行為的高估

This study is to discuss the reason that interfere the fish schooling behavior " adult fish surround the young fish ". I use mathematic simulation, to observe the result when the fishes are stimulated, due to the body size , the speed of swimming , the difference of sensitivity will make different reaction. We predict the motion dots of fish when the hunter appears on the block paper, then analyzes the motion of adult fish and young fish in dot to determine if the result remind "adult fish surround the young fish "structure. The conclusion shown that natural reaction physiologically on fish will show "Adult fish surround the young fish "results, so, the factor that interfere the structure of fish group is not so called "group defense by ethnologist".本研究目的,在探討影響魚群「成魚圍繞著幼魚游」的行為。本研究是以數學模擬法,依觀察結果,設定魚在受到刺激後,因體型大小、游速的快慢、靈敏度的差異等,所產生的不同的反應。再在方格紙上模擬魚群在捕食者出現時,游開的動線。最後分析成魚幼魚的動線分布情形,是否仍是「成魚游在幼魚外圍」的魚群結構。研究結果發現,依魚類的生理條件所設定的條件下模擬,自然形成「成魚游在幼魚外圍」的魚群結構。所以,影響魚群結構的因素,的確不是行為學家所說的防禦行為。

台北市內湖區金面山地衣調查與空氣污染對地衣影響之探究

本研究工作自2001 年7 月至2002 年6 月止,在臺北市內湖區金面山進行地衣實地探勘採集調查,以位於臺北市內湖區之麗山高級中學之校園為中心點,範圍由校園金面山至學校前門所面對的港墘路與環山路口。應用「外部型態比較」,「切片觀察(徒手切片技術)」與「化學分析(薄層色層分析Thin Layer Chromatography, TLC)」等三種方法,鑑定所採集之地衣所屬種類,並探討空氣污染程度對金面山地衣類分佈狀況的影響。調查至2002年6月為止,本研究已發現生長於金面山區之數種地衣,其中殼狀地衣包含有:癩屑衣屬(Lepraria)、球粉衣屬(Spheophorus)、大孢衣屬(Megalospora)等三屬;屬於莖狀地衣的僅有石蕊屬(Cladonia);為葉狀地衣的則有:黃梅衣屬(Xanthoparmelia)、裸緣梅衣屬(Parmotrema)、梅衣屬(Parmelia)等三屬,合計共七個屬。本研究針對臺北市金面山區及麗山高級中學之校園附近市區道路地衣類分佈的情形做調查,結果發現行道樹上之附生地衣在較靠近山區的地方,於樹幹上的生長覆蓋面積才會有明顯增加的情形,又其中在市區道路上只發現殼狀地衣生長,而莖狀及葉狀地衣則出現於金面山頂附近,所以就此情況而言,除了金面山區外,市區已呈現地衣沙漠化之狀況,間接顯示,市區的空氣污染是相當嚴重的。本研究將所調查結果之各屬地衣類進行特徵描述與分佈地區之標定,以便於日後臺北市內湖區金面山地衣之鑑識及後續相關研究之進行。This research was carried out between July 2001 and June 2002 on the Jinmian Mountain in Neihu,\r Taipei City and consisted of an on-the-spot exploration and collection of lichen. The Taipei Municipal\r Lishan High School was the center of this research, and the researched territory consisted of the areas\r between the mountain at the back of the school (Jinmian Mountain) and the intersection between\r Gangcian Rd. and Huanshan Rd. in front of the school’s main gate. Comparison of external appearance,\r dissectional observation (manual breaking technique), and chemical analysis (Thin Layer\r Chromatography, TLC) were the research methods applied to determine the genus of the lichen and the\r influence of the degree of air pollution on the distribution of the lichen.\r By the end of the research in June 2002 the presence of three types of lichen on the Jinmian\r Mountain was observed: crustose lichen: Lepraria, Spheophorus, Megalospora; fruticose lichen: Cladonia;\r foliose lichen: Xanthoparmelia, Parmotrema, Parmelia. Seven different genus of lichen have been found.\r The research has been done on the distribution of these different genus of lichen in the area of the\r Jinmian Mountain and The Taipei Municipal Lishan High School: By observation the sidewalk trees\r near the mountain’s area, we found the covering area of the lichen on the sterns apparently increases,\r while on the trees in the city district, only crustose lichen grow. The fruticose and foliose lichen only\r grow near the top of the Jinmian Mountain. This impoverishment of the diversity of lichen in the city\r district might (indirectly) be an indicator of the considerable decline of air quality in the city. The\r outcomes of this research regarding the description and distribution of the lichens contribute to the\r knowledge on lichens in the Jingmian Mountain area in the Neihu District, and may raise the similar\r research in the future as well.

核醣核酸蛋白粒之K 蛋白基因表現及功能之研究

核糖核酸蛋白粒之K 蛋白具有多種功能,可參與在基因轉錄和蛋白質轉譯等過程。我們發現\r 一新奇的cDNA 較已報告的K 蛋白cDNA 少了72 個核?酸,分別命名為S 形與L 形。由基因\r 組DNA 的分析,S 形可能是經由替代剪接少了第8 個exon 所形成。以西方墨點法分析細胞中\r 的K 蛋白,亦證明有S 形存在,其表現量較少且多存在於細胞核中。為了探究兩種K 蛋白等\r 形的表現和功能,我們以PCR 偵測K 蛋白在不同組織與細胞株和人類乳腺腫瘤組織中的RNA\r 表現,結果顯示主要以L 形為主;我們並將S 形與L 形K 蛋白分別轉染至人類乳癌細胞株MCF7\r 中,以抗生素篩選出穩定表現K 蛋白之細胞株,生長速率分析顯示表現S 形之細胞株生長速\r 率較慢,其分子機轉仍有待研究。另外在比對K 蛋白之基因組DNA 時,除了在第九對色體\r 上有完整之K 蛋白基因組DNA,我們亦發現在第2、3、5 及11 對染色體上有類似K 蛋白基\r 因的序列,以cDNA 的形式存在,這些DNA 序列是否可以表現RNA 及其意義為何,目前尚\r 不清楚。Heterogeneous nuclear ribonucleoprotein K (hnRNP K) is a multifunctional protein known to be\r involved in the regulation of transcription, translation, nuclear transport and signal transduction. We\r have identified an alternative splicing transcript of hnRNP K lacking exon 8. This novel isoform\r (named S form compares to L form of full-length hnRNP K) encodes a protein that is 24 amino acids\r depletion between RNA binding KH1 and KH2 domain. To explore the functional roles of both isoforms,\r we detect their expression in several tissues (including liver, lung, kidney and heart), cell lines (MCF7,\r 293T, HeLa, NIH3T3, WEHI, P388D1) and specimens of human mammary gland tumor by RT- PCR.\r The results showed that L form was expressed in all samples, whereas S form was only expressed in cell\r lines. Using Western blotting analysis, we found that L form existed in both cytosol and nuclear\r fractions, and little amount of S form was detected in the nuclear extract. Furthermore, we construct the\r MCF7 cell lines that stably expressed S form or L form hnRNP K. Growth rate analysis indicates that\r the overexpression of S form of hnRNP K could decrease cell growth rate. The molecular mechanisms\r of growth inhibition by S form hnRNP K are to be further investigated. On the other hand, when we\r blast the human genomic genebank, we found except the chromosome 9 containing complete hnRNP K\r genomic DNA, there are near complete hnRNP K cDNA sequence appears in chromosome 2, 3, 5, and 11.\r The meaning of these sequences is unclear.

突變ras基因造成過度表現在骨髓間質幹細胞啟動氧自由基誘導細胞凋亡

特定基因的表現與不同氧自由基的產生,已知會影響細胞的生長和死亡。我\r 個人有興趣利用間質幹細胞體外培養擴充,以為筋骨組織再生的可能應用。因此\r 利用轉植(transfect)突變ras 基因(Glu61Leu)進入骨髓間質細胞株(HS-5 cells),來\r 控制ras 基因表現的高低,進而研究這些間質細胞隨著Ras 蛋白質表現的高低,\r 對氧自由基引導細胞生長與死亡之影響。結果發現ras 基因高度表現的間質細胞\r 生長減緩;相較於原生株平均減少62.4%。進一步研究其生長減少是否與細胞凋\r 亡有關,發現ras 基因高度表現的間質細胞凋亡確實比原生株高22.6%。探究其\r 凋亡原因,發現與caspase-3 有關但和粒腺體功能無關:因為caspase-3 有活化,\r 但是以粒腺體膜電位螢光追蹤劑JC-1 測得的膜電位卻沒有改變。追蹤ras 基因高\r 度表現的間質細胞其細胞內氧自由基的產量,發現Ras 高度表現株其細胞內氧自\r 由基明顯增加。當細胞外加入超氧根轉化酵素(SOD, 500 U/ml)去清除超氧根時,\r 對Ras 高度表現細胞的凋亡沒有影響;但是外加觸化酵素(catalase, 500u/ml)於培\r 養液中,卻可以抑制ras 基因高度表現的間質細胞內caspase-3 活化和細胞凋亡;\r 並且增加細胞生長循環促進分子Cyclin D1 的表現。從這些研究我們歸結出兩點\r 重要新發現: 1) ras 基因突變造成Ras 高度表現時,會促成細胞內特定氧自由基產\r 生,使得細胞生長減緩並進行細胞凋亡,只有特定抗氧化酵素(catalase)才能恢復\r 其異常; 2) Ras 蛋白高度表現而引導氧自由基產生的細胞凋亡與caspase-3 活化\r 有關,但與粒腺體功能無關。根據這些發現,未來我們或許可以朝調節特定氧化\r 還原反應或使用caspase-3 抑制劑去調控間質幹細胞的生長,以供筋骨組織再生\r 的應用。Certain gene’s expression as well as different species of oxygen radicals can\r affect cell growth and apoptosis. We are interested in amplifying mesenchymal\r progenitor cells for the application of musculoskeletal tissue regeneration. Thus, we\r transfected a mutant ras gene (61Glu/Leu) to change Ras protein expression in the\r mesenchymal progenitor cell line (HS-5 cells) and studied how ras expressing levels\r influenced intracellular oxygen radicals, and its relationship to cell growth and\r apoptosis. Results showed that Ras over-expressing HS-5 cells grew slower than those\r with wild type ras HS-5 cells and revealed a higher apoptosis rate. The higher\r apoptosis in Ras over-expressing cells was not related to mitochondrial dysfunction\r since mitochondrial membrane potential was normal as determined by flow\r cytometric analysis of JC-1 fluorescent staining assay. The higher apoptosis was\r related to higher caspase-3 activation. Further studies showed that Ras\r over-expressing HS-5 cells revealed a higher production of intracellular oxygen\r radicals in comparison to those with wild type ras HS-5 cells. Addition of catalase\r (500 u/ml) but not superoxide dismutase (SOD; 500 u/ml) specifically revived the cell\r growth associated with increase of cyclin D1 expression, but decrease of apoptosis\r associated with lower caspase-3 activation. Results from these studies demonstrated\r two important findings: 1) the ras gene over-expressing in a ras-mutant HS-5 cell line\r triggers a higher production of intracellular oxygen radicals resulting in higher cell\r apoptosis; and 2) the higher oxygen radicals related cell apoptosis is mediated by\r caspase-3 but not mitochondrial dysfunction. Based on these findings, we may\r propose to regulate mesenchymal progenitor cell growth for musculoskeletal tissue\r regeneration via modulation of redox reactions or caspase-3 inhibitors in the future.

環保水氣壓計

本研究利用波以耳定律為基礎,以理論計算推導的方式,模擬水氣壓計的操作模式,並 探討其校準模式與誤差來源。 以此設計出的水氣壓計有以下兩個特色: 1. 大氣壓力的變化與水氣壓計液面的變化為線性關係。 2. 可以得到比水銀氣壓計更佳的靈敏度。 而在水氣壓計的校準上分別探討了標準校準、壓力差校準、溫度校準與重力密度校準。 利用標準校準可以得到水氣壓計液面變化與大氣壓力變化的線性關係式。而溫度校準與密度 校準在儀器操作環境為定溫下則可併入標準校準。 This study based on Boyle's law imitates the operation model of water barometer and discusses its calibration and sources of error. The designed water barometer has two features: 1. The relationship between atmospheric pressure and the height changes of the surface of the water barometer is linear. 2. More sensitive than that of a mercury barometer. We also discuss standard calibration, pressure calibration, thermo calibration and gravidensity calibration. The linearity between atmospheric pressure and the height changes of the surface of the water barometer is known by standard calibration; thermo calibration and gravidensity calibration can be merged into standard calibration under constant temperature surroundings.

挑戰你的好眼力

想像一下,原來固定的一個黑色大正方形(以下我們簡稱S1)四個角經過較小之正方形(以下簡稱S2)遮蓋後旋轉,為什麼會有放大縮小的感覺呢?(圖一) 我們猜測這是因為未被遮蓋部分(以下簡稱S3)的面積改變了,所造成的結果。令S1的邊長為 r,S2的一個小正方形邊長為n,k=r-n,θ為旋轉角度,我們實際算出了旋轉角度θ對S3的面積函數,

『吸凍!』--再造保麗龍的第二個春天

中文摘要 本實驗先尋求將廢棄保麗龍磺酸化為陽離子交換樹脂(本實驗稱”保麗龍膠”)的方法。將保 麗龍依:丙酮溶解→硬化→打碎→與濃硫酸共煮三小時→浸於50%硫酸溶液中→沖洗→以水 浸泡的流程,即可達再造的目的;我們測得其磺酸化比例為62.5%。再利用「碘滴定法」(浸 泡式)與「相對電壓檢測法」(流動式),依次尋求保麗龍膠吸附金屬離子的最佳條件。其中「碘 滴定法」可有效測出銅離子濃度,但手續繁瑣;「相對電壓檢測法」最大的好處是知道保麗龍 膠何時吸附達飽和必須再生。 目前我們所知,要保麗龍膠達到吸附陽離子的最佳效能,其條件依次為:使用細粒的保 麗龍膠;低濃度的金屬離子溶液;質量愈大的保麗龍膠;低溫下較慢的金屬廢水流速及pH 值約為4.30 的銅離子廢水;鈉型的保麗龍膠吸附效能優於氫型。保麗龍膠對不同金屬離子亦 有吸附力,單位體積所含離子數愈少,初始的相對電壓會愈高;在相同莫耳濃度下,不同離 子的吸附力依次為Cr3+>Fe3+>Ni2+>Cu2+>Co2+;分次吸附確可將金屬離子完全去除;由 吸附等溫線觀察得知,可能保麗龍膠為多孔物質,導致500ppm 以下的吸附模式無法明確判 斷,1000ppm 以上則為物理吸附模式;保麗龍膠可以再生也可被覆在砂粒上達到不錯的吸附 效能;最後,我們將吸附過金屬離子的保麗龍廢膠與硫酸鈣、紙漿及些許的石灰(質量依序為 13 克、13 克、7 克、0.04 克)混合,可製成類似紙黏土,做成造型磁鐵,廢物利用十分有趣。 Abstract The Experiment will, first of all, explore the ways to sulfonate expandable polystyrene into cation ion exchange resin (called “polystyrene rubber” hereafter in the experiment). The procedures of treating expandable polystyrene are as follows: acetone dissolve→hardening→smashing→ boiling with sulfuric acid for three hours→immersing in 50% sulfuric acid solution→washing→ immersing in water so that we may reach the goal of reconstruction. We calculate the sulfonated rate to be 62.5%. Then we make use of “Iodine Titration”(immersion method) and “Opposite Voltage”(floating method) to seek for the best conditions of adsorption the metallic ion through polystyrene rubber. The former can effectively calculate the concentration of copper ion, but the procedures are quite complex. The greatest advantage of the “Opposite Voltage” method is that we may know when the adsorption of polystyrene rubber is saturated and should be regenerated. As far as we know at present, the conditions of obtaining the best effect that polystyrene may adsorb the cation ion are as follows: fine particles of polystyrene rubber; low concentration metallic solution; polystyrene rubber of which the mass is greater; at lower temperature, slower waste water flow speed and the copper ion waste water with pH 4.30; the adsorption effect of sodium type polystyrene rubber is better than the hydrogen type. Polystyrene rubber also has adsorption effect toward different metallic ion. The less ion per cubic contains, the higher the original opposite voltage. With the same mole concentration, different ion adsorption effects may range as follows: Cr3+>Fe3+>Ni2+>Cu2+>Co2+. The batch adsorption definitely may erase metallic ion completely. By observing the adsorption isotherm, possibly because the polystyrene rubber is a multi-apertured matter, we find that it is impossible to judge exactly the adsorption model of those metallic ion solutions of which the concentrations are below 500ppm. Those which are over 1,000ppm belong to physical adsorption models. Polystyrene may be regenerated and get an adsorption effect by coating sand particals. In the last analysis, we may make paper clay and magnets of different styles by mixing the adsorbed metallic ion polystyrene rubber with calcium sulfate, paper pulp and a little lime(the mass are respectively 13g, 13g, 7g, and 0.04g). The reuse of waste is really very interesting.

吸〝氣〞大法-QCM 對有機氣體之吸附與偵測

中文摘要:\r 化學實驗中,常常會使用到各種具有揮發性的有機溶劑,如醇類、酸類、醛類及酮類等。\r 當吸入過量的揮發性有機溶劑時,將會對人體造成嚴重的傷害,故使用時格外需要留意。有\r 鑑於此,我們開始著手研究如何偵測氣相中的有機氣體分子。\r 本研究中,我們利用聚苯胺薄膜吸附氣體分子的特性並結合對質量變化極靈敏的石英晶\r 體微天平,自行設計了一套簡單、藥品用量少且不需昂貴儀器的實驗系統。藉由此系統,我\r 們有效的針對各種揮發性有機溶劑進行偵測,並進一步地探討不同氣體分子對於聚苯胺薄膜\r 的吸附現象。\r \r 英文摘要:\r Students usually use volatile organic solvent in laboratorys such as alcohols, carboxylic acids,\r aldehydes, ketones, etc. It will injure our body when we breathe in too much volatile organic\r solvent. For this purpose, we begin to study how to detect volatile organic compound in air.\r In this work, we combine polyaniline membrane which can adsorb gas molecules and quartz\r crystal microbalance which is highly sensitive to mass changes to design a simple and inexpensive\r system which needs only little chemicals. With this system, we can effectively detect different\r volatile organic compounds. Furthermore, we can also study the adsorption of polyaniline\r membrance for different volatile organic compounds.