外觀數列
The Look and Say sequence is produced by describing the appearance of the previous row. For example, start with “1,” which can be described as “one 1,” and therefore the second row is “11,” which is "two 1s," making the third row “21,” the fourth row “1211,”and so on. The main goal of this study is to work out the exact formula for this sequence, which means given the row number n, we can know at once what the n-th row is without having to start from the first row and doing the look-and-say iteration for n-1 times. Some of the methods used include dividing groups, repetition and cracks. The formula we derived speeds up the calculation and gives us a better understanding of the look and say sequence.「外觀數列」為依照外觀產生下一列的數列，第一列為「1」，第二列描述第一列「1 個1」而為「11」，第三列則描述第二列「2 個1」而為「21」，第四列「1211」，依此類推。本研究針對外觀數列的各項數學性質作研究探討，並由此推導出外觀數列的一般式，即給定第n 列就可知道該列的內容。我們運用了分組、重複性以及裂縫的方法分析數列，最後得到了其一般式，此一般式有助於運算速度的加快以及我們對數列性質的了解。
『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.
將錯就錯的knuth 河內塔
在這篇報告中，我們探索了「將錯就錯的Knuth 河內塔問題」。傳統河內塔問題在電腦科學上佔有重要的地位，是一個極具內涵的模型。由於這個模型的深厚數學內涵，使其和巴斯卡三角形建立了緊密的連結，且利用這個緊密的數學連結，設計出復原任意起始狀態的良好演算法。Knuth 河內塔起因於數學家Knuth 在論文[3]中，描述傳統的河內塔問題時所發生的一次筆誤。在這個新的規則之下，我們意外發現Knuth 河內塔存在著一個和傳統河內塔平行的模型，此模型在電腦科學及數學上有著完全不同於傳統河內塔的內涵。我們的研究主要如下：(分別為內文中的四大段)(一) 結構分析。移動環所需要的次數，如何移動環並分析每一次動作所動的環，及每個環何時被動到並給出演算法。(二) 正整數的分割。所有的移動步驟將正整數做了一個新的分割(Partition)；此分割模k之後有良好的循環性質。(三) 費波那契真分數的排序。這個正整數的分割形成一張表，這張表恰好就是分子分母皆為費波那契真分數之排序。(四) 隨意亂排的Knuth 河內塔復原演算法。在Knuth 河內塔的規定下將起始狀態改變，找出良好的復原演算法，並分析。 In this project we study the "Knuth Hanoi Tower", which is motivated by a typo in a paper of Knuth. This inadvertently typo leads to a new rule of moving the discs on the Hanoi Tower (see introduction below for definition). Although seemingly similar to the traditional Hanoi-Tower problem, it turns out that under this rule the "Knuth Hanoi Tower" problem consists of amazing properties, and is totally different from the traditional one. Our study focuses on the following directions: (1) Structure analyzing: We analysis the sequences recording the disc moving and offer enumeration results and recurrsive/non-recurrsive algorithms. (2) Partition of N: The moving sequence forms a partition (a table) of N, which has an amazing congruence property. (3) The order of Fibonacci proper fraction: The row/column of the partition table is, even more amazing, exactly the order when sorting the Fibonacci proper fraction with fixed denominator/numerator. (4) The Restoration of an arbitrary initial state: We offer an efficient algorithm for restoring any initial state of discs. We hope that our study on the "Knuth Hanoi Tower" offers a simple, neat, and new example on the theory of Algorithm, Number theory and Combinatorics.
台北市內湖金面山區兩棲爬行動物資源調查之研究
本研究之目的主要為調查臺北市內湖金面山區附近兩棲、爬行動物之物種概況，建立內湖地區的兩棲爬行動物基本生態資料庫，期望藉此研究可推行高中科學教育研究的基礎，並可充實自然生態保育與愛護鄉土心靈教育的實際教材。 調查研究工作是由2003年4月開始，至2004年5月為止，十四個月期間，總計85次的夜間野外觀察，已確認記錄兩棲爬行動物的種類共計有37種(分屬2綱3目13科24屬)，蛙類：4科13種，蜥蜴類：4科9種，蛇類：4科13種，龜鱉類1科2種。 各物種總出現隻次方面，蛙類以拉都希氏蛙的1547隻次為最多，最少的是長腳赤蛙及斯文豪氏赤蛙，僅6隻次。蜥蜴類以黃口攀蜥的1995隻次最多，最少的為麗紋石龍子，僅4隻次；蛇類及龜鱉類以龜殼花最多，共計85隻次，而以梭德氏游蛇、大頭蛇、白梅花蛇、赤背松柏根、南蛇、盲蛇、食蛇龜及材棺龜等均只有1隻次為最少。 出現頻度方面，十四個月份中，蛙類的拉都希氏蛙及古氏赤蛙皆有出現，在85次的調查期間，則是以拉都希氏蛙的97.65％為最高，最少的為長腳赤蛙，只有3.53％；蜥蜴類的黃口攀蜥於十四個月份皆有出現，而在85次的調查期間，則有75次、97.65％最高出現頻度，麗紋石龍子於14個月份及85次的調查，出現頻度均是最低，各是21.43％及3.53％；蛇類及龜鱉類物種中，以龜殼花14個月及61次的出現記錄為最高，出現頻度分別是100％及71.76％；而食蛇龜及材棺龜均只有出現一個月及一次，故其出現頻度為7.14％及1.18％。 分佈廣度而言，於二十二個調查樣區中，蛙類以拉都希氏蛙的95.45％為最大，最小的為長腳赤蛙及斯文豪氏赤蛙的18.18％；蜥蜴類以黃口攀蜥的100％為最大，，最小的是無疣蜥虎的9.09％；蛇類則以龜殼花的86.36％為最大；龜鱉類物種皆僅4.55％的分佈廣度。 各樣區出現物種數方面，蛙類以Ａ區的11種為最多，蜥蜴類以二期校區的7種為最多，蛇類是以ＡＢ區的9種為多；各樣區中，則是以ＡＢ區所發現的兩棲爬行動物物種數最多，合計共有22種物種。 由研究結果得知，調查樣區內的兩棲爬行動物物種歧異度大，其中蛙類的優勢物種為：拉都希氏蛙，蜥蜴的優勢物種為：黃口攀蜥，而龜殼花則為蛇類的優勢物種。而環境溫度的變化，與調查樣區內兩棲爬行動物出現活動的總物種數有顯著之相關性。 ;The goal of this research paper is mainly to investigate Taipei city, Neihu District, nearby Jin-Mian mountain’s amphibious and reptiles for the establishment of the lake area amphibious and reptile basic ecology information bank. It is hoped that this research will provide a foundation to further promulgate the high school science education and research, and may enrich the natural ecology protection and education materials for the loving care of local environment. The investigation started from April, 2003 to May, 2004, or for 14 months period and amounted to 85 times of field observations at night. It was confirmed that there were 37 species of amphibious and reptile ( 2 classes 3 aria 13 families 24genus),amphibious species: 4 families 13 species, lizard: 4 families 9 species, snake: 4 families 13 species, turtle: 1 family 2 species. In regard to the number of times of appearances, amphibious species of Rana latouchii had the most appearances with 1,547 times, and the least appearances was the Rana longicrus and the Rana swinhoana with only 6 times; for the lizards, Japalura polygonata xanthostoma had the most appearances with 1,995 times, and the least appearances was Eumeces elegans with only 4 times; for the snake and turtle, Trimeresurus mucrosquamatus had the most appearances with 85 times; for the Amphiesma sauteri sauteri, Boiga kraepelini, Lycodon ruhstrati ruhstrati, Oligodon formosanus, Ptyas mucosus, Ramphotyphlops braminus , Cistoclemmys flavomarginatn and Mauremys mutica , each had appeared only 1 time. On the appearance frequency, within the 14 months, amphibious species Rana latouchii and Rana kuhlii, Rana latouchii appreared 97.65%, the highest within the 85 investigations period, and the least was the Rana longicrus with only 3.53%; lizard Japalura polygonata xanthostoma had appeared within these 14 months, but in 85 investigations period, their frequency was 75 times, or 97.65% at the highest frequency. Eumeces elegans there upon within the 14 months and 85 investigations, had the lowest frequency each at 21.43% and 3.53%; for the snake and the turtle species, Trimeresurus mucrosquamatus within the 14 months and 61 appearances had the highest frequency record at 100% and 71.76%; but Cistoclemmys flavomarginata and Mauremys mutica only appeared once in a month and, therefore its frequency was at 7.14% and 1.18%. For the distribution breadth, in 22 investigation sample areas, amphibious species take Rana latouchii of the amphibious kind had the biggest record at 95.45%, and the smallest was Rana longicrus and Rana swinhoana at 18.18%; for the lizards, Japalura polygonata xanthostoma was 100% as the biggest, and the smallest was Hemidactylus bowringii at 9.09%; for the snake, the Trimeresurus mucrosquamatus was at 86.36% as the biggest; the turtle species had only 4.55% distribution breadths. For the number of appearance in each area, amphibious species in area A had the most with 11 species, lizard of second period school area had the most with 7 species, the snake of area AB had the most with 9 species. In all other areas, the amphibious reptile species number in area AB had the most with 22 kind of species. From the results of the research, the biodiversity of amphibious and reptile species within the investigation areas is very high, Rana latouchi is the codominant of Frog; Japalura polygonata xanthostoma is the codominant of Lizard, and Trimeresurus mucrosquamatus is the codominant of Snake.
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.
一后多夫否？黑棘蟻(Polyrhachis dives)聚落生殖策略之研究
A vast amount of research has been conducted on various ant species such as Monomonum pharaonis, Formica rufa, and Lasius niger, demonstrating the coexistence of polygyny and monogyny colonies. In polygyny colony, the high heredity variability of filial generation could be expected, but what could the monogyny colony do to hold the high heredity variability in order to increase the fitness? I hope I can account the sex ratio in the colony of spiny weaver ants, Polyrhachis dives, and compare the different colony with different reproductive strategies. I also want to check by V8 that the colony can form a polygyny colony and virgin queens can mate with many males of the same colony in the artificial nest. The results suggest that in the colony of spiny weaver ants, the higher the number of the dealate queens, the lower the number of the male. In the monogyny colony, workers control the sex ratio. According to the observation, we can see the alate adult mate in the artificial nest, and multimating can be recorded for the first time. The following study was there for undertaken to examine what’s the aftereffect made by the Reproductive strategies of polygyny colony and monogyny colony.在多后聚落內，子代變異度高是可以預期的，但是單后聚落中，又如何維持遺傳的變異度以增加其對環境的適應力呢？我們希望能計算黑棘蟻聚落組成，比較不同生殖策略的聚落之各種性比，並且錄影證實黑棘蟻聚落可以為多后聚落並進行巢內自交。我們發現：黑棘蟻聚落內，蟻后數愈高，則雄蟻比例較低；單后聚落之性比決定於工蟻；而根據錄影觀察，聚落中的有翅生殖族可在人工蟻巢中完成交配，多次交配的現象首次被實地紀錄，並且佔所有交配新生蟻后的92.8%。本實驗可利用黑棘蟻來了解單后與多后聚落的生殖策略對其族群發展的影響。
「金」枝「玉」葉—金奈米與葉綠素的交互作用
本實驗在探討，當金奈米粒子和植物中的葉綠素產生鍵結作用力時，能量轉移的結果是否能幫助葉綠素激發電子。經由兩者混合後光譜的變化,發現兩者之間發生能量轉移。為探討此轉移現象和濃度的關係，我們將大小不同的金奈米和不同毫升數的葉綠素作用，並將其結果和金奈米與葉綠素的吸收強度和作比較，使用正規化的計算方法算出比值，由此看出兩者之間能量轉移的效率。當金顆粒約大於30nm時，正規化的數值隨的葉綠素濃度的增加而變大；而當金奈米顆粒約小於30nm時，則隨著葉綠素的增加而變小。Much attention is currently focused on chromophoric molecules because they can not only mimic natural antenna systems but also exhibit unique optical and physical properties. Chlorophyll , produced by extracting from green leaves, has electrostatic interactions with Au nanoparticles through carboxyl groups. Herein, we report the charge transfer between chlorophyll and Au nanoparticles using UV-vis electronic absorption spectroscopy. The efficiency of charge transfer from chlorophyll to Au nanoparticles was estimated by the normalization of Q-ban absorption intensity. From the observation of absorption intensity versus concentration of chlorophyll curves, we find that the efficiency of charge transfer is increased while the size of Au-particle is larger than 30nm, but decreased while the size smaller than 30nm.