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.

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.

Previously, I studied the acute effects of a common broadleaf herbicide, Killex (by Montsano) and a pesticide, Spidercide (by Wilson), on cytoplasmic streaming in detached leaves from the pond weed, Elodea canadensis. I found that Killex, active ingredient 2-4D, an auxin analog, applied at the recommended dose decreased the rate of cytoplasmic streaming by 64% over a 20 minute observational period. The Spidercide, active ingredient d-trans allethrin, a Na+ channel activator, stopped cytoplasmic streaming after a 5 minute exposure and no recovery was observed during the 20 minute observational period.

我們的研究重心是設計簡便的裝置來檢測生活周邊的用水 · 利用生物對於環境污染的生理特徵、活動力、忍受極限 … 等變化，作觀察、實驗之後，將紀錄結果分析、做成表格，進而形成明確、簡易的指標，以供給一般人更容易的了解用水的品質。本實驗不必使用昂貴的儀器來檢測河水與用水，成本低廉的水生生物為本實驗的最佳選擇 · 可於任何地點完成，作為大及化的檢測方法，本實驗參考水樣急性檢測方法一水蚤靜水式，以水蚤在不同眾屬離子、酸鹼值溶液中的實驗結果，用以做為分析水質的標準，佐證我們生活圈附近的水質現況。Our point of study is design the simple and convenient device to measure the water with peripheral life. Utilize the living beings to the physiological characteristic , energy of the environmental pollution, stand limit. Wait for and change, after making observation , experiment. noting down the result will be analysed , make into the form , and then form the clear , simple and easy index , in order to supply common people with the quality of easier understanding water. This experiment needn’t use the expensive instrument to measure river and water . the best choice of the experiment that the cost is based on living beings cheap aquatically. Can finish in any place , as the popular detection method. This experiment consults the acute detection method of water sample — Water flea’s quiet ability of swimming. with the experimental result in different metal and ion sour soda value solution of water flea, use the standard taking making as water quality of analysis, prove the present situation of water quality of adjacent place of our life range.

震盪反應有許多種反應類型，至今已被完整探討，但對於震盪反應之催化系統，卻鮮少有文獻提及，本研究小組偶然發現，醇類對於震盪反應具有明顯的催化作用，本文嘗試探討各級簡單的醇類對於震盪反應影響，並透過活化能的改變了解醇類在催化過程中所扮演的角色。The many types of BZ oscillation reaction have already been thoroughly discussed. However, little mention has been made in literature regarding the catalysis system of the reaction. The researchers have accidentally found that alcohols exert an obvious effect on the oscillation reaction. The study attempts to discuss the different influences that various kinds of alcohols have on the oscillation reaction and to understand the role alcohols play in the catalytic process through the change of activation energy.

Mathematics and music are two poles of human culture. Listening to music we get into the magic world of sounds. Solving problems we are immersed in strict space of numbers and we do not reflect that the world of sounds and space of numbers have been adjoining with each other for a long time. Interrelation of mathematics and music is one of the vital topics. It hasn’t been completely opened and investigated up to now. This is the point why it draws attention of a lot of scientists and mathematicians to itself. This is the point why it draws attention of a lot of scientists and mathematicians to itself. Having considered the value of these two sciences, it seems to us that they are completely non-comparable. In fact can there be a similarity between mathematics – the queen of all sciences, a symbol of wisdom and music – the most abstract kind of art? But if you peer deeply into it you can notice that the worlds of sounds and space of numbers have been adjoining with each other for a long time. In the work I will try to establish the connection between mathematics and music and to find their common elements, to analyze pieces of music with the help of laws and concepts of mathematics to find a secret of mastery of musicians using mathematics and also to investigate the connection of music with mathematics with the “research part”. They are my own calculations and researches which are an integral part of the work. The connection of mathematic and music is caused both historically and internally in spite of the fact that mathematics is the most abstract of sciences and music is the most abstract kind of art. V. Shafutinskiy, I. Matvienko, m. Fadeev, K. Miladze, Dominik the Joker – modern composers of the XXI century – have used the golden proportion only in 4% of their pieces of music and more often in romances or children’s songs. I have revealed this fact after investigating their pieces of music of different genres. However there is a question: why does modern music attracts all of us more but the classics is being forgotten? Investigating connection between mathematics and music I had come to the conclusion that the more deeply the piece of music gives in to the mathematical analysis, to research and submits to any mathematical laws, the more harmonious and fine its sounding is, the more it excites human soul. Besides I am convinced that many important, interesting and entertaining things have not been opened in this field. We can safely continue our research of these things. I think that I have managed to lift a veil over mathematics in music, to find something common for apparently incompatible science and art. In due time English mathematician D. Silvestre called music as mathematics of feelings, and mathematics – as music of intellect. He expressed hope that each of them should receive the end from the part of the other one. In the future he expected the occurrence of a person in which Beethoven and Gauss’ greatness would unite. Terms ‘science’ and ‘art’ practically didn’t differ during far times of antiquity. And though roads of mathematics and music have gone away since then music is penetrated with mathematics and mathematics is full of poetry and music!

高分子發光二極體為導電高分子之熱門研究課題，因其有低成本、製程簡易、可大面積化之優點為無機高分子發光二極體所缺乏，所以受到學術界與工業界之注目。由於高分子發光二極體其有廣視角、高答應速度、低驅動電壓、可製成撓曲式元件等特質，極具成為下一世代顯示器之潛力。高分子聚苯胺為高分子發光材料中，具有低驅動電壓與高發光效率之優點，故本研究將之選為電洞傳遞層材料。但唯一缺點就是不易溶於溶劑中，所以在實驗驗中有安排質子酸摻雜的步驟，就是為了要改變高分子的電性、磁性、光學性質或結構，同時導電度也隨之增加。本研究以ITO基板改質及無電極電鍍為研究主軸，以此來增加其之性能。改質ITO基板目的，是希望使得ITO陽極表面平坦化且可促使電洞注入，進而增加發光層材料附著力與阻隔電子直接導入陽極之特性，故可增加元件之發光亮度。而使用無電極電鍍法，因為其不須通電就能進行電鍍的反應，行成的薄膜也很均勻。所以採用無電極電鍍法，來完成電鍍的步驟。The polymer light emitting diodes is one of the most important study projects in the field of the conducting polymer due to the low production costs、 simple production process、great surface products that the organic light emitting diodes can not achieved. The purpose of this study is try to utilize the polyaniline as the electric hole transfer layer, and the MEH-PPV as the light emitting layer. The disadvantages of the polyaniline are the low solubility in solvents that was improved by doping proton acids. The performance of the indium-tin oxide was improved by the self-assembling method that made the surface of the ITO became more smooth to help the electric hole injection of electrions. And the aluminum cathode was produced by the electrode less plating.

Skin cancer, including basal cell and squamous cell skin carcinoma, is known to\r be the most common cancer type. Skin cancer is thought to make up half of all known\r cancers. Over one million non-melanoma skin cancers (NMSC) are reported every year. \r Approximately 300,000 of these cases are squamous cell carcinoma (SCC). It is\r estimated that about 2,000 people die from NMSC each year. Of the two skin cancer\r types, SCC tends to be the more clinically aggressive and likely to spread and invade,\r typically by way of blood or lymphatic vessels. Understanding the signaling pathways\r in SCC cells that regulate invasion will be important for developing improved cancer\r treatments. The signal transducer and activator of transcription 3 (Stat3) protein is a\r central regulator of numerous cellular activities, including proliferation, survival, and\r motility. Stat3 also has enhanced activity in many cancers, including skin SCC. This\r study shows that Stat3 regulates several invasive properties in a human skin SCC cell culture model.\r HGF (hepatocyte growth factor)- induced cell schattering was assessed for\r SRB12-p9 cells (p9WT), a human skin SCC cell line, along with SRB12-p9 cells\r engineered to have reduced Stat3 activity. Next, a cell viability-based adhesion assay\r was performed with these cells. Finally, severe combined immunodeficient (SCID)\r mice were injected subcutaneously with P9WT and S3DN cells and tumors were\r measured twice weekly. Extracted tumors were analyzed by immunohistochemistry and Western blotting for expression of the invasion related enzyme, MMP-2 and MMP-9.\r The suppression of Stat3 activity in S3DN cell lines resulted in reduced motility,\r greater adhesion, and a less invasive phenotype in SCID mice. Immunohistochemistry and Western blotting indicated higher levels of MMPs in the P9WT cells with\r expression localization towards the outer perimeter of the tumors. This data suggests\r that Stat3 plays a role in skin SCC invasion and better understanding of Stat3 function\r could lead to improved treatment and prevention of the disease.

1. Purpose of research \r To investigate the feasibility of using municipal cellulosic wastes as feedstock for production of biochar in pyrolysis, the effects of metal catalysts in pyrolysis, and the applicability of the produced biochar as a fertilizer\r 2. Procedures \r A. Investigation into the characteristics of (metal catalyzed) pyrolysis of various cellulosic wastes \r 1. The cellulosic waste (and catalyst) was weighed and put into a boiling tube. The tube was stopped with a plastic bung with holes. A plastic tube and a thermocouple were inserted through the holes. The other end of the plastic tube was submerged. \r 2. A Bunsen flame was used to pyrolyse cellulosic waste. Temperature and time of reaction were recorded. Gas produced was collected underwater. Biochar and bio-oil were obtained and weighed. \r B. Evaluation of adsorptive capabilities of different materials \r 1. Blue light absorbances of KH2PO4 solutions (mixed with vanadate-molybdate reagent to form yellow solutions) at different concentrations were found and an absorbance-concentration curve was established. \r 2. 5g of each material being evaluated was sandwiched between two pieces of filter paper before being put into a suction funnel. KH2PO4 solution was poured into the funnels. The setups were left overnight and filtrates were collected. \r 3. Collected filtrates were mixed with vanadate-molybdate reagent. Concentration of phosphates in each filtrate was found by the curve.\r 3. Data \r I. Highest percentage conversion from waste to biochar: 94.1% (paper towel, iron wool) \r II. Highest sequestration rate of carbon: 98.6% (paper towel, zinc) \r III. Lowest pyrolysis temperature: 162°C (paper towel, copper) \r IV. Best catalyst in terms of speed of biochar production: copper (+47.7%) \r V. Highest speeds of biochar production (w/ and w/o catalyst): 46.4g/hr (paper towel, copper) and 27.7g/hr (sawdust) \r VI. Adsorptions of KH2PO4: 14.4% (biochar from sawdust)/ 9.02% (sawdust)\r 4. Conclusions \r The pyrolysis of cellulosic waste to biochar was achievable at school laboratory conditions, with satisfactory results in carbon sequestration, production speed and percentage conversion. \r Under catalysis by various metals, the production of either biochar or pyrolytic gas and oil can be optimized, providing a low-cost way to derive fuel and sequestration-ready carbon, both crucial as answers to looming crises. The use of copper greatly speeds up pyrolysis and lowers the pyrolysis temperature, further increasing the economic potential of the process. \r Biochar is also an effective means to soil management, as shown in field and laboratory experiments. Its adsorption capability far exceeds that of untreated cellulosic waste, retaining nutrients to be taken by plants instead of leaching away. It was also shown to improve fruit yield and induce ripeness in tomato, making it obvious that biochar is also a viable fertilizer. \r All in all, metal-catalyzed biochar production from municipal cellulosic waste and the subsequent use of biochar as fertilizer have the benefits of: low feedstock cost, low energy cost, fast production, carbon sequestration, soil management and waste recycling. It is a remedy to some of the most persistent and serious global problems: food and energy crisis, water pollution, excessive greenhouse effect alongside waste treatment.

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.

1.Purpose of the research We observed frequent application of chemical pesticides and herbicides at the pear orchards near our school. Our concerning questions are the influences of agricultural chemicals on soil ecosystem which may be slowly deteriorating. There are many other orchards where the farmers are practicing environmentally-friendly agriculture using organic fertilizers such as composed manure instead of sycnthetic fertilizers. The purpose of this research is to examine chemical and mocrobiological quality of the orchard soil. We report biological control of pear disease using antagonistic microorganisms and suggest improvement of soil quality as a result of nature friendly agricultural practice. 2.Procedures and Data Two orchards were selected: Conventional fertilizers and chemical pesticide application farm; Environmentally friendly farm using organic plant manure and biological control of disease. Several different aspects of soil micro-flora, indicator microorganisms, physiological characteristics of pear fruit, residues of synthetic chemicals in the soil, soil chemical properties were examined. We could observe that use of organic manure and biological control agents for disease control by indigenous microorganisms improved biological and chemical quality of the orchard soil. Results are summarized as follow: A. Microbial diversity could be observed in organic farming orchard soil. Among 42 fungal genus, 7 species of penicillium including P. decumns, 3 Alternaria species, 4 Fusarium species including Fusarium graminearum, 6 Aspergillus species including Aspergillus niger were identified. In case of bacteria, 59 samples were isolated and 17 genus including Cystophaga johsonae were identified. B. Beneficial indigenous bacteria having several biological functions were isolated: Enterobacter intermedium produces organic acid therefore this bacterium can solubilize insoluble phosphate. Several Pseudomonas species were isolated. These bacteria produce iron chelating compound under iron limited environments and can control plant disease. Interestingly, we could find indigenous biocontrol agent Hypocrea vinosa which can effectively control black star disease on pear surface. C. We have formulated ten different microbial-pesticides using several combinations of indigeous microorganisms such as Hypocrea vinosa, Trichoderma atroviride, Rhizopus microsporus etc. These microbial-pesticides could inhibit 100% of black star disease on pear surface which showed similar inhibition effect as commercial pesticides indicate that these microbial-pesticides may replace synthetic chemicals in the near furture. 3.Conclusions Our research demonstrates the eco-friendly organic farming system could improve soil eco-system of pear orchard, where no synthetic fertilizers and pesticides are applied. As a result of manure application, the soil chemical properties are more stable and microbiological flora was more diverse. Use of microbial and bio-pesticide resulted in strong inhibition of black-star disease incidence on pear surface. We suggest that eco-friendly farming systems are needed to diminish environmental pollution in soil and water caused by frequent and abundant use of agricultural chemicals.

Phosphodiestarase of subtype PDE IVb inhibitors are considered as perspective drugs for the treatment of the central nervous system disorders (depression, Alzheimer’s disease, Parkinson’s disease). Pyrrolizidinone Glaxo-1, proposed by GlaxoSmithKline, is a highly potent PDE IVb inhibitor (IC50 = 63 nM), then conventional phosphodiesterase inhibitors Ro-20-1724, Rolipram and Cilomilast. However the activity of the Glaxo-1 was studied on a racemic sample, since the asymmetric approach to its synthesis has not been developed. Therefore the purpose of this research was the development of an efficient synthetic scheme enabling enantioselective excess to both (-)- and (+)-Glaxo-1, which can be than subjected to biological studies. \r The key stage in proposed asymmetric synthesis (-)- and (+)-Glaxo-1 is stereoselective [4+2]-cycloaddition of the nitroolefin to an optically activity vinyl ethers, derived from (-)- or (+)-trans-2-phenylcyclohexanols. The resulting chiral cyclic nitronates are transformed into a functionalized cyclic oxime ethers using tandem sylilation-nucleophilic substitution procedure. Reduction and decarboxylation of these products lead to optically pure Glaxo-1 and the regeneration of chiral 2-phenylcyclohexanols (91%). \r Thus both enantiomers (+) and (-)-Glaxo-1 were obtained selectively in average yield 12% from isovaniline and nitroethane. The study of biological profiles of each enantiomer of Glaxo-1 will be conducted in near future.