聞音起舞一 聲音對跳舞草小葉擺動之影響
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.
可表為兩個平方數和的一種特定型式的數及其性質推廣研究~「Concatenating Squa
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.
二次函數上正三角形建構之研究及探討
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.
什麼尚「氫」--談燃料電池之放氫探討
氫是一種非常理想的能源。不僅效率極高，且不會造成環境污染。空氣中的含量極少，常用的電解水方式又效果不彰。我們利用Ag、Ru、Cu 、C-CuPu、C 等數種電極，與H2SO4、 H3PO4 、HNO3 電解液，分別在10V 雙電極與-0.8V 三電極下做電解水實驗，研究何種電極與何種電解液能得到最多的氫氣量。在低電壓下找出最好的電極，液與太陽能電池結合，成為電池中的一部份，讓發電效果更好，以利未來燃料電池H is a kind of great power.It is not only effective,but also no environment pollution .Owing to the H in the air is very little,so it is not easy to take .Addition to,we often to take it by electro liquid,but the electrolysis effect is not ideal. Except Ag、Ru、Cu、C-CuPt、C and so on ,in theH2SO4、 H3PO4 、HNO3 electro liquid,we have a experiment in the 10V dual electrode and -0.8V triple electrode to study which electrode and which electro liquid to get the most of H.Under the low voltage,we can fund the best electrode.It is easy to bind with solar energy battery,andit can be a part of battery.Besides, it makes the generator effect better,and it is convenient to make the fuel cell commercialize in the future.
由嘉義地區的氣象資料來探討二十四節氣與聖嬰現象
二十四節氣是中國古代對氣象觀測的智慧結晶，由於近幾年來聖\r 嬰與反聖嬰現象的影響，在透過嘉義氣象觀測站的協助之下，利用\r Excel 進行簡易的雨量和氣溫統計，並配合中央氣象局發布的環流型\r 態和農業災害，來探討二十四節氣在嘉義地區的適用性。\r 以陽曆來區分節氣，每年會誤差6 小時，加上四年一閏，剛好彌\r 補差距，農曆則需19 年。至於聖嬰現象對嘉義地區則呈現涼夏和暖\r 冬，但在反聖嬰現象中則變為加強四季之特性，即是熱夏與寒冬。兩\r 者都造成雨量集中夏秋兩季，形成冬春乾旱。至於二十四節氣則是以\r 夏、秋的氣溫和雨量相關的諺語較適合嘉義地區。\r Abstract\r The 24 Solar Terms, is the achievement of weather observation from\r ancient China. Because of the effects from El Nina and La Nina these\r years, we proceed simple statistics of rainfall and temperature by using\r Excel and the assistance from Chia-yi Weather Station. We adopt the\r Circulation Type and the damage of agriculture from Central Weather\r Bureau, to discuss if the 24 Solar Terms for in Chia-yi area.\r To divide the 24 Solar Terms according to the solar calendar, there’ll\r be a six –hour gap every year. The gap could be made up every four years.\r But with the lunar calendar, it takes nineteen years to offset. The El Nina\r shows cool summer and warm winter in Chia-yi area, but the La Nina\r emphasizes the characteristics of the four seasons. It shows hot summer\r and cold winter. Both of them rain mostly in summer and fall, and cause\r the drought in winter and spring. The saying of the 24 Solar Terms is\r suitable for the temperature and the rainfall during summer and fall in\r Chia-yi area.
完全圖立方乘積之最小控制
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) ≦