本試驗利用一般家庭常用之香辛料，如：蔥、青蒜、分蔥、芹菜、洋蔥、芫荽、辣椒、羅勒、薑、檸檬、蒜頭 等十一種香辛料植物以一般家用徒手操作之研磨器研磨得原汁，本試驗選取三種不同分類屬性之蟲體結構，進行防除試驗；（1）紋白蝶幼蟲（屬”鱗翅目”昆蟲）、（2）黃斑粗喙椿象（屬”半翅目”昆蟲）及（3）玉米蚜蟲（屬”同翅目”昆蟲）之蟲體上進行驅殺蟲試驗。試驗分三階段進行：第一階段 原汁噴灑試驗：以原汁噴灑蟲體，觀察其對蟲體之影響。發現辣椒、蒜頭、薑香辛液，對此試驗之三種蟲皆有驅殺功用。其於蔥、青蒜、分蔥、芹菜、洋蔥、芫荽、羅勒、檸檬等，對此試驗之三種蟲則無有效之結果；蟲體噴灑香辛液後，呈現嚴重不正常之活動情形，如：蟲體自動呈現腹部反轉朝上，後肢微微抽動扭曲或蟲體靜止活動，並可確定為死亡。由觀察得知，辣椒、蒜頭、薑具直接性觸殺劑（高濃度原汁施用一次，即可殺死蟲體）或殘效性觸殺劑之殺蟲功能（低濃度施用多次後，累積劑量才可致死）。第二階段 稀釋液噴灑試驗：為節省成本之考量，針對第一階段所得知試驗結果，選取辣椒、蒜頭、薑等三種香辛料進行稀釋液殺蟲試驗。結果發現，如：水：辣椒（體積比）1：2、水：蒜頭（體積比）第三階段 田間試驗：為確實印證香辛液於田間使用之可行性，此階段試驗根據前兩階段之試驗結果，施行於田間之結球甘藍葉面之紋白蝶幼蟲蟲體，可獲致有效驅殺蟲體之效果，證明本試驗於實際運用之可行性。本試驗以尋求簡易、方便、安全之家庭園藝用驅殺蟲液為目的，適合推廣應用為一般家庭小面積之園藝栽培，其具操作簡便之特性，並可達確保人體食用及居家安全之效用。

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.

有一天我們聽到工友黃伯伯口中唸唸有詞:「怎麼去年才過了，今年又長出來了，真有夠煩」，於是我們就近一看原來是菟絲子，之前上自然課時老師曾提過幾種生態殺手的植物，菟絲子就是其中之一，它會去吸收旁邊植物的養份，吸完之後，它又會到別的植物上吸取養分，拔也拔不完，到底是為什麼菟絲子有這麼強的繁植力，試著做各種實驗來探討菟絲子繁植力強大的來源。

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.

在上一屆科展中對地圖筆的褪色原理已有初步的了解，為了對產品能有更統整性的分析。因此，針對這個題目作更深入的研究和探討。此次研究的重點在於酚?、百里酚?及硝基酚對於各種材質的運用，試著找出有別於酸鹼指示的新方法。可自己製造顯示筆、消失筆，更可以創造出各種不同顏色的地圖筆。

本研究觀察平原菟絲子自種子萌芽至成株各階段的形態特徵，研究成株及小苗對十種校園植物的喜好性。根據成功大學廖國?教授2005 年的報告，平原菟絲子的寄生無專一性，但是平原菟絲子有無偏好的寄主？其偏好的寄主有何種生理及形態特徵？研究結果顯示，平原菟絲子四季皆可以開花結果，最適合生長的溫度為23~25℃。完成生活史約需3 個月，一年會有四次果熟期及果熟植株乾枯期。在無寄主的情形下，平原菟絲子的小苗成長最多至13 公分，最長可活20 天；其斷莖及小苗對寄主的喜好性相同，對有氣味、葉綠素含較多及角質層較薄的寄主，形成的吸器多於不具備以上性狀的寄主。平原菟絲子對於不同的寄主，形成的吸器顯微構造也不相同，顯示平原菟絲子對不同的寄主有不同的適應。

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!

南投溪頭米堤飯店在2001 年因土石流受創，產險公司以「土石流即是山崩」為由拒絕理賠。歷經5 年的訴訟後，2007 年1 月台灣高等法院認定，土石流屬保險契約中所規範的「洪水」，並非「山崩」，判決產險公司應給付賠償金。土石流究竟是洪水？是山崩？主要因素便是土石流發生的水文因子。本文藉由博愛村的現場調查及文獻探討先作初步資料分析（preliminary analysis），了解到地文因子(physiographical factor)是土石流發生的充分條件，非必要條件；一般僅考慮雨量因子，把地文因子看作常數（忽略地文因子受水文因子歷程(course)影響），簡單易懂，但在安全與經濟考量上有待討論。使用類神經網路對已發生過的土石流事件計算土石流發生臨界曲線，並使用模糊理論計算松鶴地區其受水文因子影響的土石流發生臨界曲線，這樣的模式，考慮似乎比較周到。由「米堤飯店」的例證，更說明土石流發生的水文因子的必要性。Lemidi hotel, Xitou, Nantou because mudflows and landslides and was wounded in 2001. The Insurance Company refused to settle a claim on the position on “A landside is a debris flow”. After the lawsuit which was going through 5 years. In January, 2007, the High Court of Taiwan asserted that the adversity in the 2001 belongs to “the flood” in the norm of the insurance agreement. As the norm of the insurance agreement said, the debris flows in the land is the flood, not the “landslide”. The High Court of Taiwan judged that the Insurance Company should compensate the Lemidi Hotel. Is debris low a landslide or a flood? The main cause is the Hydrology in the happening of a debris flow. We did preliminary analysis of forms by on-the-spot investigation on Song-Ho Village and reference discussing. We realized that physiographical factor is an abundant condition for a happening of a debris flow, not the essential condition. Generally, people only consider rainfall factor. And they consider physiographical factor as not as constant (neglect the influence of hydrology factor to physiographical factor). We can understand easily in that way. Therefore, in the aspect of security and economy, there is much doubt that is needed to be discussed. People who use neural network method to calculate the curve of the debris flow happening , and used fuzzy theory to calculate the curve of the debris flow happening which is influenced by the hydrology in Song-Ho Village. In that way, we may consider more thoughtful. From the example of the Lemidi Hotel in Nantou, we can prove that how necessary the hydrology factor in the debris flow is.

物體在流體中受到的阻力(Drag force) F=1/2CρAV^2（C 是常數，和物體的形狀有關，ρ是空氣密度，A 是垂直投影面積的大小，V 是速度）。但是我們在實驗室中檢驗降落傘的阻力，得到的結果並不是和垂直投影面積成正比，而是和降落傘面所包住的空氣體積大小成正比。進一步，我們發現體積的高度太高也不好，它存在一個最佳高度，此一高度和底面的邊長有關。此外，我們把降落傘頂端開一小洞並製作兩層的降落傘，希望增加降落傘下降的穩定度和阻力，得到很奇特的結果。希望我們的研究能夠對想要自製降落傘的人，提供氣流流動的基礎認知。

彈性物質受外力拉伸時，溫度會升高；反之，當彈性物質由拉伸狀態縮放回去時，溫度會下降，並且降溫溫差會比原本的升溫溫差來得大。對此現象，我們仿造氣體動力論的模型做解釋：溫度是一個宏觀的物理量，其根本為分子運動動能的表現，橡皮筋未拉伸前是一個三維系統，而拉伸後長度變長、截面積變小，使橡皮筋接近一維系統，然而在拉伸的過程中我們並未提供動能的變化，因此原本分布在三個維度上的能量現在集中在一個維度上，造成等效的溫度上升現象；反之，將橡皮筋放開使其恢復原長時，將使橡皮筋恢復成三維系統，能量重新分配在三個維度上，造成收縮後的溫度比拉伸時溫度低的現象。本實驗檢驗橡皮筋溫度上升與拉伸速率、拉伸長度的關係，並且檢驗拉伸時溫度上升倍率及下降時溫度下降倍率之間的關係，同時針對整個溫度變化過程做詳細的分析說明。

本研究主要是探討輪盤遊戲之破解，遊戲規則是從攤販設計好的遊戲輪盤中，玩家先選擇順時針or逆時針旋轉，再從一副撲克牌任意抽兩張撲克牌相加，得到的數字為N，再從轉盤上N處按照選擇好的方向轉動(N-1)步，最後停留的數字所對應的獎品歸玩家所有。研究結果發現：一、不論順時針或逆時針轉，最終轉到的數字只有1和奇數二種結果和找出此種結果的原因。二、找出輪盤的終點數公式。三、減少輪盤數字數時，同樣找出終點數公式和終點數公式的一般式。四、設計出新規則，用機率來讓遊戲更有趣。本研究與小六數學「怎樣解題」相關。

數學刊物從勾股定理談起以長方體的架構，長x、寬y、高z，對角線w 的概念去討論x2 + y2+ z 2= w2的畢氏數解，本文發現他遺漏了非常多組解。本文作者改以廣義的畢氏定理從平面幾何的概念找出所有畢氏數解。 傳統的畢氏定理只能在直角△上才能使用，本文探討一種廣義的畢氏定理，它適用於任何一種△(包括銳角△、鈍角△、直角△)，這種創新的廣義畢氏定理的靈感來自於直角△中的母子定理所使用的直角△，這種子△和原直角△的三邊依序垂直，銳角△和鈍角△中仍然存在著這種依序和原三角形三邊垂直的子△，文章中透過借用直角△推導畢氏定理相同手法去推導銳角△及鈍角△的畢氏定理，這樣的廣義的畢氏定理型如x2 + y2+ z 2 = a2 ，(其中a 代表△任一邊的長，x 和z 落在另兩邊上，而y 長的線段和a 長的線段平行)。在廣義的畢氏定理條件下，本文探討了正△、等腰△、直角△、銳角△、鈍角△的畢氏數，並找出了那些被遺漏的解，接著解開了四元二次不定方程x2 + y2+ z2= w2的所有畢氏數解。