聚丙烯酸(PAA)是尿布中吸水成份，我們利用其結構上的羧基螯合Ag＋，並成功以甲醛將Ag＋還原成奈米銀。但我們意外發現螯合Ag＋的PAA白色粉末在沒有其他還原劑存在下也會漸漸變成黃色，與「利用甲醛還原製得的奈米銀」顏色十分相似。本實驗即揭開此粉末變色真相，希望能在不使用額外還原劑下，直接以PAA將螯合的Ag＋製成奈米銀，不僅具環保與實用價值，更能使奈米銀製程朝向綠色化學。我們透過水溶性聚丙烯酸鈉(SPA)在均相中進行變色機制探討及影響變因的研究，找出有利的反應條件，再應用於PAA。研究證實PAA能將螯合的Ag＋同步還原成奈米銀，反應機制與檸檬酸鈉作用模式相似，而提升濃度、溫度或照光有利於反應，酸性條件則不利，照各種色光也有所差異。

在拋物線上置掛正三角形看似簡單，其實不然。本篇文章研究在二次函數的各種不同情況下，可做正三角形的分佈以及其個數。 1. 在一條拋物線上時，最多只能作正三角形。 4. 在三條對稱軸相等的拋物線和共頂點開口大小不同之拋物線上，本篇文章證明一定能找出正三角形落在它們之上。但由於最多有四個分界點，要解四次方乘組過於繁複，於是本篇文章對分界點作了一些估計，找出了分界點的極限值。 5. 本篇文章證明了對於給定的正n 邊形，存在一1 元n-1 次方程式可以通過它所有頂點。 Building a regular triangle on a parabolic curve looks easy . In fact , it doesn’t . This Article researches regular triangles distributions and its numbers in different conditions. 1. On one parabolic curve can only build regular triangles , squares and other regular polygons can’t be built. 4. For three parabolic curves which has same symmetrical axis or three concurrent parabolic curves, we prove that it can build at least one regular triangle on them .But because it can have at most 4 boundary points, to solve quartic equation is to complicated. So we do some estimation of boundary points, and find out some limits. 5. This Article prove that for given regular polygons , there exists a one dimension n-1 orders equation can pass all its apexes.

近在台灣新發現的筆筒樹萎凋病，造成大量筆筒樹(Cyathea lepifera)枯萎死亡，對於此疾病的防治已成亟需解決的問題。先前的研究中，已確認病原菌為新屬真菌並命名為Ophiodiaporthe cyatheae sp. nov.。本研究則在於以生物交互作用方式進行防治，尋找拮抗菌，針對特性實際應用。 研究中因實驗素材與操作方法的差異分為細菌與真菌類拮抗菌兩大主軸，且皆成功自土壤中各分離出數種有應用潛力的拮抗菌。細菌方面，尋獲並經鑑定為Burkholderia gladioli，對於病原菌有良好抑制效果，然由於此菌本身安全性有疑慮，實用上仍有待商榷。真菌方面，拮抗菌以超寄生方式與快速的生長能力制伏了病原菌，期待透過比較消除病原菌的速度，篩選出其中最強大適切的拮抗菌種，運用於實際田間病殘株處理。

跳舞草(Desmodium gyrans) 屬多年生木本豆科植物，其特殊之處在於小葉會對外界的聲音有所感應。本實驗以訊號產生器固定聲音強度，發出2、4、6、8、10 KHz不同聲頻之聲波刺激跳舞草，並以每5秒為單位紀錄小葉擺動角度之變化，分析其擺動週期、擺動幅度等不同的變化。實驗結果為跳舞草小葉之擺動週期與擺動振幅是隨著聲音頻率的增加而呈現sin函數變化之圖形。Desmodium gyrans (Leguminosae) is a perennial woody plant. Acoustic waves can stimulate stipules and cause to oscillation. This experiment used the coroma to immobilize strength, emitted the frequency of 2, 4, 6, 8, 10 KHz acoustic wave to stimulate stipules and recorded the changes of oscillation angle every five seconds. We calculated the oscillation cycle、oscillation span, and analyzed experiment data. The most importance result is that the experiment graphs of oscillation angle and oscillation span with different frequency of acoustic waves display sin function metamorphic diagram.

令Sn 為{1,2,…,n}任意排列所成的集合，π ? Sn 為其中的一個元素，我們記π = (π(1), π(2),…, π(n))。今給定π ? Sn ，若對所有i,1? i ? n，都有π (π (i)) = i 時，我們稱π 為involution。假設π ? Sn ，並給定σ ? Sm (m ? n)，當π 中任取m 項，其大小關係的順序都和σ 不同，我們稱π 避開σ，或稱π 是一個σ-avoiding 排列。在這篇報告中，我們主要分析了2143-avoiding involution，1234-avoiding involution，和3412-avoiding involution 中的一些統計量，給出了十數個結果與幾個猜想。Let Sn be the set of permutations on {1,2,…,n} and π ? Sn be an element in Sn. Denote π as π = (π(1), π(2),…, π(n)). We say that π is an involution if π(π(i)) = i for every i, 1? i ? n. Given π ? Sn and σ ? Sm (m ? n) , we say that π avoids σ (or π is an σ-avoiding permutation) if π does not contain any m-term subsequence in the order of σ. In this paper, we discuss some classic statistics on 2143-avoiding involutions, 1234-avoiding involutions and 3412-avoiding involutions. We get many new results in this field and give some interesting conjectures.

這是一系列關於水蒸氣冷凝為極細微小水珠的長程實驗。其中可以分為下列三個階段：第一階段是基礎實驗。將水氣導入至潔淨的光滑表面上(蓋玻片)，觀察水珠冷凝的機制。第二階段是在外加磁場及電場作用下，將水氣導入至潔淨的光滑表面（蓋玻片），觀察水珠冷凝的機制。這部分的實驗推翻了一般「水分子是電中性，在電場或磁場中不受影響 」的刻板觀念！實驗所呈現出來的冷凝水珠，不但有明確的自我組成模式( Self assembly pattern)。並且發現：電場會增速凝結水珠的成長(Aggregation)，而磁場則會抑制凝結水珠的成長。第三階段是將水蒸氣導引至超聲波的環境中：我們先將超聲波訊號產生器(變頻、定頻)面向於載台旁，再讓水氣導入至潔淨的光滑表面上(蓋玻片)，觀察冷凝水珠的機制。當使用固定頻率超聲波波源，我們發現：在超聲波場中水珠的成長會受到抑制，且成長速率會隨著頻率的升高而逐漸減小。第一階段與第二階段的實驗結果與討論已分別發表於2004 年及2005 年的台灣國際科學展覽報告中，本作品將詳述第三階段。 This experiment explores the basic nature of the condensation of water vapor into droplets on the surfaces of cover glasses. This condensation occurs because of the difference in temperature between the water vapor and the cover glass. The condensation process is observed under a microscope. The growth of the droplets can be described as: nucleation, aggregation (piling up) and coalescence. The growth is irrelevant to surfaces or environments. It is found that the temperature difference of moist air over the cover glass do not affect the nucleation size of the droplets in simple plain surroundings; while the change of flow rate does. In general, the coalescence is speeded up at higher temperatures. Furthermore, the effects of electric fields 、magnetic fields and ultrasonic waves are also studied. It can be observed that the size of water droplets become smaller and grow more uniformly under magnetic fields or imposed ultrasonic waves; also, the aggregation rate is decreased by imposed magnetic fields or ultrasonic waves, and it is increased by imposed electric fields. These effects of magnetic fields 、electric fields and imposed ultrasonic waves might be related to the flow conditions and the vibration of surrounding air in the system. This experiment provides the first step in the understanding of the formation of water droplets and their self assembly mechanism in different environment.

給定下面範例：\r 058823529411764705882 +235294117647058823532\r =0588235294117647058823529411764705882353，\r 其等式結果與質數17 的倒數結果(1/17)有某種關聯(卻沒有一個決定性的證據)，意即\r 1/17=0.0588235294117647=\r 0.058823529411764705882352941176470588235294117647...... ( Len(17) =16 )\r \r 曾經在下列網站上發現過幾組數字(挑戰試題)，引起我們極大的興趣。\r http://www.domino.research.ibm.com/Comm/wwwr_pondernsf/challenges/March2000.html\r http://www.math.smsu.edu/~les/POW08_96.html\r \r \r The two examples that I have are 0588 2+23532=05882353 and 058823529411764705882+23529411764705882353 2=0588235294117647058823529411764705882353 These were found by the Canadian professor Alf van der Poorten, and he gave a talk on these identities in December at the west coast number theory conference. He was unspecific as to exactly where these identities were coming from, but they are connected with reciprocals of primes:1/17 = 0.0588235294117647= 0.058823529411764705882352941176470588235294117647 ΛΛ ( Len(17) = 16 ) Though not mentioning how to obtain these equations, Prof. Poorten demonstrated the relationship between the above examples and the reciprocal of the prime numbers 17 (1/17 ) without a definitive proof.

The purpose of the study was to develop and create a semi-automatic multi-purpose sorting and counting machine of standard articles. Currently, there is a problem of equipping industrial enterprises as well as small trade companies and large retailers with computing sorting machines of standard products of a certain shape. We would like to fill this missing link up with a simple, compact and inexpensive device. Procedures The proposed research consisted of a consistent design of a virtual model of the device and its electronic-mechanical implementation. The virtual model is simulated by a computer program "SolidWorks" object, which graphically shows the operation of the future device. In the development of the computing sorting device standard electronic devices and their associated software have been used. The created simplified real model demonstrates the basic principles and characteristics of the proposed device. Data As an example for the implementation of the concept device a computing device for sorting coins, in circulation in Russia has been created. As a basic principle of sorting objects by their geometric and weight characteristics were used. It is important that the device is focused on the correct form of the objects of sorting (balls, rings, coins, regular polyhedrons, screws, nuts, etc). To confirm the effectiveness of the computing device of this type of sorting, a series of tests of counting of objects manually have been carried out . The effectiveness of the device is determined by comparing the time characteristics of manual and automatic sorting. Findings and conclusions As a result of research and work performed, we have concluded that: 1) The proposed device can be used in various industries. (for example, while sorting ball bearings.) 2) Such a computing sorting device may find it's application in various commercial enterprises: to assist cashiers in retail ATMs. 3) Can be used in payment terminals. 4) 4) After a certain modernization of the device it can be used for money encashment.

完全圖Kn是指一個圖中有n個點，且任意一個點都跟其它的點有邊相連。兩個圖G和H的卡氏乘積G□H的點集V(G□H)＝{(g,h)| g∈V(G),h∈V(H)}，兩個點(g1,h1)和(g2,h2)有邊相連若且為若g1=g2 且h1~h2，或g1~g2且h1=h2。 三個完全圖Ka、Kb、Kc 的立方乘積是指Ka□Kb□Kc。一個圖G中的一點v所連的其它點稱為這個點v的鄰居，也就是N(v)={x | x~v}。一個點集S中的所有點的鄰居的聯集稱為這個點集的鄰居，也就是N(S)=∪v∈S N(v)。如果一個點集S和它的鄰居N(S)包含了一個圖G的所有的點，也就是S∪N(S)＝V(G)稱這個點集S是這個圖G的一個控制集。我們把圖G的所有控制集中點數最少的稱為最小控制集，並定最小控制集的點數為最小控制數γ(G)，也就是γ(G)＝min { | S |, S是G的控制}。 本文的目的在於研究完全圖立方乘積的最小控制，也就是要給γ(Ka□Kb□Kc)一個上界。特別當 a = b = c = n時，γ(Ka□Kb□Kc) = 。 A complete graph Kn is a graph with n vertices, which any vertex is adjacency to every other vertices. The Cartesian product of two graph G and H which is denoted G□H is define as follow: the vertex set V(G□H)＝{(g,h)| g∈V(G),h∈V(H)}，and two vertices (g1,h1) and (g2,h2) is adjacent if and only if g1=g2 and h1~h2 or g1~g2 and h1=h2. The Cartesian product of three complete graph Ka,Kb,Kc is Ka□Kb□Kc,which is the same with (Ka□Kb)□Kc. In a graph G, the neighbor of a vertex v N(v) is the set of the vertices adjacent to the vertex v, that is N(v)={x | x~v}。 The neighbor of a vertex set S is N(S), which is the union of the neighbors of vertex v over S, that is N(S)=∪v∈SN(v). For a graph G, if a vertex set S unions its neighbor N(S) equal to the vertex set of G, that is S∪N(S)＝V(G), we say that S is a dominating set of G. The domination number of a graph G will be denoted as γ(G), which is the minimum size of all dominating set of G.. We give an upper bound to γ(Ka□Kb□Kc). And when a=b=c, γ(Ka□Kb□Kc) ≦

利用化學合成法合成出聚苯胺及MEH-PPV，經過一連串的製程作出高分子\r 發光二極體（PLED），再用I-V 儀量測。實驗中以聚苯胺及MEH-PPV 的薄膜厚\r 度為變因，進行實驗。設定I-V 的電壓值為10V，量測樣品通路上的電流。一開\r 始電壓在跑時，量到的電流都為0A，所得到的圖形為一水平直線；當電壓到達\r 一個值時會向上爬升，但爬到一個階段後圖形呈現鉛直掉落至電流為0A，圖形\r 又恢復成水平直線。過程中看到了薄膜厚度對樣品確實有影響，又鋁電極的厚度\r 不能承受過大的電壓，電壓一大，樣品馬上就燒壞了。\r Abstract：\r Using Chemiccal polymerize PANI and MEH-PPV make through a series\r Polymer light emitting diode（PLED）Produce.then using I-V meter surveies. PANI\r and MEH-PPV change of thick proces.Experiment design I-V volt for meter\r conduction of current of sample .The voltage moving.First meter current is obtaining\r the figure is horizontal when voltage increase to a special value , but increase a while ,\r the current will fall down to zero volt. Figure will go to horizontal that sample will\r change .Thick is different,and aluminum cathode can not suffer too much\r voltage .otherwise will burn.