The water-supporting system of community should use high efficiency pumps to\r support water and set up a unique water tower for each floor. Since there are high and\r low period of water-consuming and the variety of water pressure, we have to set up a\r unique water tower for higher floors firstly.\r It help us through high peak period of water-consuming, or it turns on pressure-aid\r pumps to save energy.\r 社區供水系統應採高效率之幫浦高壓供水,分樓層設置專用水塔,在用水有高峰\r 及離峰時段,水壓有高低變化,優先順序供水給較高樓層的專用水塔,樓層專用水\r 塔容量必須足以渡過用水高峰時段之容量,否則就啟動輔助加壓幫浦,達到節約能\r 源之目的。

Generalized Petersen graph P(n,k)，定義為n 為不小於2 的整數以及1≤ k ≤ n−1，有頂點{ u0, u1, . . . , un−1, v0 , v1 , . . . , vn−1 }，及路徑{ uiui+1 , uivi , vivi+k：1≤ i ≤ n−1 }。在 [2] 中，我們可以知道P(n,5) 是Hamiltonian 等價於當n≠11。 在這一篇報告中，我們證明當generalized Petersen graph P(n,5) 是hyper Hamiltonian（一種Hamiltonian graph 再去掉任何一點後，仍然是Hamiltonian graph）的充要條件是n 為不等於11 的奇數且n ≥ 7。 The generalized Petersen graph P(n,k), n ≥ 2 and 1≤ k ≤ n−1, has vertex-set { u0, u1, . . . , un−1, v0 , v1 , . . . , vn−1 } and edge-set { uiui+1 , uivi , vivi+k：1≤ i ≤ n−1 with subscripts reduced modulo n}. And we can know that P(n,5) is Hamiltonian if and only if n≠11 from [2].In this paper it is proved that generalized Petersen graph P(n,5) is Hyper Hamiltonian (A Hamiltonian graph can still be a Hamiltonian graph when any one of the nodes fault) if and only if n is odd and n≠11.

地震波會以橫波和縱波的方式傳遞能量，學校的教學大樓中地下具有蓄水池者搖晃的持續性感覺比較短暫，於是利用彈簧波模擬地震波測試不同質量的台車接收到的能量會較空車為多。並利用自製模型測試不同容器形狀和水量的阻尼作用，結果發現搖擺時，時間球形＞錐形台≒方形台；球形台裝有不同水量時擺動時間裝滿裝滿時＞未裝水＞裝1500mL 時；平行移動時則是球形台裝水2000mL 後鉛錘移動距離最短。整個實驗過程中由於未裝滿水的模型內部重心改變不規律，而且模型內所裝的水量因為不規則擾動經吸收的能量轉換成水溫上升的熱能，因此導致擺動能量的消耗造成擺動時間縮短，如果新式大樓興建時考慮消防蓄水池和水塔的造型和裝水容量，應可以減少地震時的搖晃時間，降低心理的緊張和物體因震動而產生的移動傷害。Seismic wave can transmit energy with transverse and longitudinal wave. The shaking of these buildings with reservoirs underground in our school for a shorter time, so we use spring wave to simulate seismic wave, and test the proportion of transmissible energy received from different mass of objects. The energy gets from wave motion passing on is bigger when cars carrying capacity than empty cars. And we use homemade models to test damped effect of different forms and water. At last we discover the time is Sphere ＞ Taper ≒ Square while they swing with different amounts of water, the time it cost is Full ＞ Non ＞ 1500 mL. When they move horizontally, the plummet moved shortest, when the water of the sphere is 2000 mL. During the whole experiment, the center of gravity in the models, which are not full of water changes irregularly, and the water in the models can absorb heat energy from energy disturbing, so the swing of energy consuming makes the time of the swing shorter. If the fire controls reservoirs, the shapes and dress up water volume of the water towers, are taken into consideration, the duration of the shaking of earthquake will be shortened so that our fear and nervousness will be lessened, and the damage causer from the shaking will be reduced.

The definition of "Fermat Point" is that a dot, which lies in a triangle, has the minimum distance to the three apexes. In other words, "Fermat Point" has the minimum distance to three dots which are not on the same line. In the broad sense, then, in a N polygon, a dot which has the minimum distance to the N apexes could be named "Fermat Point." But what if we link up the N apexes and find out that they cannot make a convex polygon? The above is what we wish to fully discuss. Our inspiration comes from a paper on"Fermat Point." It just describes N convex polygon, so we think of putting the case to naturally polygon. The case may be that it is a concave polygon or part of the apexes which lies on the same line. We would not base our study on the conventional methods. Moreover, strictly defined, the repeated line segment will not be taken into account. That is, if the "Fermat Point" drops on the line with more than two dots on it, we just count the\r line segments except for the shorter line segments which were originally included in other studies. According to the theorem, our conclusions are as follows: 1. If N points lie on the same line segment, then the "Fermat Point"can be any point on the line segment. 2. If (N-1) points are on the same line segment, then the "Fermat Point" is on the point which two lines join together. One is that the line segment, and the other is the one which passes the remaining point and\r perpendicular to the first line segment. 3. Now there are (M+N) points. Among them, M points will make a M jog-polygon. The others all drop in the polygon. As the diagram shown beneath, we know that the "Fermat Point" drops on the point which two lines join together. The two lines must pass as many points as possible. 所謂的「費馬點」是指三角形內到三頂點距離和最小的點。換言之，「費馬點」就是到平面上不共線三點距離和最小的點。因此，我們可定義，廣義的「費馬點」即是n 多邊形內到各頂點距離和最小的點，亦即到平面上不共線n 點距離和最小的點，但若平面上n 點不能恰為n 多邊形的頂點呢？這就是我們所要討論的。由於我們的靈感來自一份關於「費馬點」的科展作品，所以我們想到，當平面上n 點不能恰為n 凸多邊形的頂點，甚或其中有一部分的點共線時，將不能以n邊形的方法來探討，但我們可以將之化為m 邊形內（n-m）個點來討論。而更重要的是，我\r 們增加了另一個限制，重複的線段將不被我們列入計算。亦即當所求點落在某一多點共線的線段上時，我們只計算該線段的總長，而不計其中重複的較短線段。根據這個原則，我們試行證明平面上三點、四點、五點及六點的可能情況，期望能從中找出足以推廣至平面上n 點的一般性。結果雖不完美，但我們總算差強人意的歸納出了下列結論：1.若n 點共線段，所求點可為所共線段上任一點。2.若（n-1）點共線段，則由該不共線點引一線與共線段垂直，其交點即為所求。3.若（n+m）個點中有m 個點為一m 多邊形的頂點，另外n 個點落在該m 多邊形內，則由兩個外頂點引直線盡可能通過最多點，該兩直線的交點即為所求。

This research primarily aims to observe how does the electric work, why does it work and the relationship between the surrounding circumstance and the repulsive torque. The electric whirl is made of an enameled wire bent into right angle with sharpened ends. When an AC high voltage is applied, the electric field intensity around the whirl ends is strong due to the small curvature radius of the ends. The molecules in air at both ends are ionized. This cause the phenomenon of point discharge. The positive and negative ions produced by alternating current forms AC ion wind, and produce a torque to make the whirl rotate. The object of this experiment is to observe the relationship between the surrounding circumstance and the torque repulsion. We design an apparatus to measure the angular velocity of the rotating whirl. We also calculated the kinetic energy of the whirl and the work done by the torque. The repulsive torque can be obtained by Work energy theorem. Result: (1)The angular velocity of the electric whirl is direct ratio to repulsive torque. When we want to find out the relationship between the manipulate reason and the repulsive torque, we can just compare the angular velocity with the manipulate reason. (2)The angular velocity of the electric whirl is only related to the peak voltage, and it does not make difference whether we apply AC high voltage and DC high voltage. (3)When the humidity is over 68%, the electric whirl cannot function normally. (4)Under the low-pressure circumstance, the electric whirl will rotate with glow discharge and the angular velocity will decrease to zero gradually.本實驗是探討電離轉輪的性質、原理與周圍環境的關係。「電離轉輪」為漆包線兩端折成直角並磨尖而成，接上交流高壓電源時，其尖端曲率半徑小，電場強度相對大，會游離尖端附近的空氣分子，產生尖端放電的現象，而交流電交替產生的正、負離子會形成交流離子風，並產生轉動力矩，使轉輪轉動。我們設計一個裝置，使其能偵測轉輪轉動的狀況，運用測得數據計算出轉動時的動能和作功狀況，套用功能定理便可求得轉輪通電時產生的斥力矩。實驗結果顯示(1)轉輪的角速度和尖端斥力矩成正相關，所以當我們想得知尖端斥力矩和實驗操縱變因的關係時，只要比較角速度和操縱變因就可以了，這簡化了原本繁複的計算和冗長的數據處理過程。(2)轉輪的角速度只和峰值電壓有關，和直流或交流沒有直接關係。(3)轉輪在超過溼度68%之後，就不會正常運作。(4)在低壓條件下，轉輪轉動時會伴隨淡紫色的輝光放電(glow discharge)現象，而抽氣塔中與轉輪尖端最接近的一點，也就是電場最強的一點，會和尖端同時產生光芒，相互輝映。

In recent years, sandstorms have seriously attacked Taiwan day by day. Combining with the observations of Central Weather Bureau and the satellite images of NASA, the study has been collected the data of suspension grain in decades. And the study hopes the sandstorms’ information could be observed in early period. Still it hopes to find out the possible transmission paths in the atmosphere. Then we know how to cope with sandstorms in early time. Sandstorms attack Taiwan frequently in alternation of the spring, the autumn, and the winter. Compared with thecharts of sandstorms and the satellite images, we could broadly aware hat the moving paths of sandstorms are related to the currents and the characteristics of the atmosphere. When El Nino happens, the times of sandstorms attacking Taiwan decrease, and that increase when La Lina happens. From the observation data of acid rain, when sandstorms attack Taiwan, acid rain would diminish. Combining actual Measures and satellite data in the future, maybe we can establish a prediction mechanism of sandstorms.近年來，大陸沙塵暴侵襲台灣的情況日趨嚴重影響。本研究中收集了近十年來懸浮顆粒資料，配合中央氣象局所觀測的資料與美國太空總署的衛星影像資料，希望能夠在早期觀測發現大陸地區沙塵暴訊息，和沙塵暴所帶至大氣中的懸浮顆粒可能傳輸的路徑期能早期應映。發生沙塵暴侵臺事件的季節，主要在秋冬及冬春兩季交替期間發生的次數為最多。由沙塵暴監測氣候圖表及美國太空總署的衛星影像進行綜合比對之後，可大致瞭解大陸沙塵可能的移動路徑與大氣環流及特徵有關。聖嬰現象（El Nino）發生時，侵襲臺灣的沙塵暴次數會減少。在「反聖嬰現象」（La Lina）發生時，侵襲臺灣的次數相對增加。由酸雨中得知大陸沙 塵暴侵襲台灣時，酸雨情況會減緩。未來結合實測及衛星資料或許我們可以預報大陸沙塵暴的侵襲。

利用陰極電弧蒸鍍各種薄膜，如：類鑽膜（DLC）、氮化鈦膜（TiN）、氮化鉻膜（CrN）、氮化鋁鈦膜（TiAlN）以及先披覆上一層氮化鋁鈦膜（TiAlN）再加上類鑽膜（DLC）的合成膜等。這些薄膜現在已經被廣泛的應用於各種刀具、模具的表面處理之中。本研究主要在探討高速鋼鍍上氮化鉻膜（CrN）之後，對於硬度、磨耗性質的改變，以及觀察氮化鉻膜（CrN）表面結構之組織。 在研究中我們運用陰極電弧蒸鍍系統蒸鍍氮化鉻薄膜，分析上運用SEM來觀察薄膜表面結構組織，以及運用洛氏微硬度機來觀察試片的硬度，另外還有使用磨耗試驗機來進行磨耗測試。以上這些測試總括來說都是在得知性質有無實際上的改變，而這些實際上的改變對於蒸鍍之後的模具或刀具都能夠大幅的提高使用的壽命。 We evaporated different kinds of thin films by using the anode of the electronic arc, such as DLC (Diamond-Like Carbon), TiN (Titanium Nitride), CrN (Chromium Nitride), TiAlN (Titanium Aluminum Nitride), and synthetic films of covering TiAlN and DLC. These thin films have been used widely in processing the surface of a variety of cutters and moulds. The purposes of this research were to investigate changes of hardness and abrasion and to observe the organization of the surface structure of CrN after High-speed steel evaporates CrN. In this study, we use the system of the anode of electronic arc to evaporate CrN. Besides, SEM is used to observe the organization of the surface structure of the thin films and Rockwell Micro-hardness Test Machine is used to investigate hardness of testing samples. Moreover, we use Abrasion Tester to test abrasion. These tests are taken to lead to a better understanding whether the quality really changed. These changes of evaporated moulds or cutters would extend their frequency of using.

一、若Mn×n(s)表示在n×n 的正方形棋盤中，排列s 顆棋子在方格內，且每一方格最多只能排1子，其中s 顆棋子的配置需滿足兩個條件：1. 並無任意4 子可以形成矩形框的4 個頂點。（此矩形框的邊需與棋盤的邊平行）2. 在沒有棋子的方格中，無法再加入棋子。二、若Vn×n×n(a1,……,an) 表示在n×n×n 的正方體棋盤中，每層的棋子個數分別為a1,……,an，且s= a1+……+an，其中s 顆棋子的配置需滿足兩個條件：1. 並無任意8 子可以形成長方體的8 個頂點。（此長方體的邊需與立體棋盤的邊平行）2. 在沒有棋子的方格中，無法再加入棋子。本研究即在Mn×n(s)與Vn×n×n(a1,……,an) , s= a1+……+an 中探討s 的最小值、最大值及變化情形，並分析其配置方法。之後推廣至長方形Mn×m(s)及長方體Vn×m×k(a1,……,ak) , s= a1+……+ak。最後根據其研究結果設計一個「避開矩形框棋」，並加以分析出致勝的策略。一．If Mn×n(s) indicates in the n×n square chessboard, we put s chesses to line in the square and each square only can put one chess. Then the station of s chesses must satisfy the following two conditions：1. No any 4 chesses can form the tops of the rectangular frame ( The sides of rectangular frame must be parallel to the sides of chessboard )2. If there’s no chess in the square, we can’t add any chess. 二．If Mn×n×n(a1,……,an) indicates in the n×n×n square chessboard, the chess number in each layer are a1,……,an and s= a1+……+an. The station of s chesses must satisfy the following two conditions： 1. No any 8 chesses can form eight tops of the rectangular cube ( The sides of rectangular cube must be parallel to the sides of cubic chessboard ) 2. If there’s no chess in the square, we can’t add any chess. This research try to explore the minimum, maximum and variation of s which in Mn×n(s) and Mn×n×n(a1,……,an), s= a1+……+an, and analyze its station. Then we will extend the research to rectangle Mn×m(s) and rectangular cube Vn×m×k(a1,……,ak), s= a1+……+ak. Finally, according to the result of research we wish can design one “avert rectangular frame chess“ and analyze the strategies to triumph.

The main purpose of this experiment is to discuss the characteristics of iridescent colors of Taiwanese Euploea’s wings, inclusive of the relations between the colors of wings and squamas. According to the results from scanning electron microscope, we discovered that the iridescent colors had a close relation to nanostructure and arrangements of squamas. We inferred that both the nanostructure and the arrangements would influence the formation of iridescent colors and the basic colors on wings. In addition, the basic colors on wings are related to different types of scales. To compare with the diverse formations of different sorts of Taiwanese Euploea’s wings, we took SEM pictures of Elymnias hypermnestra as well, discovering that its iridescent colors had similar relation with scales. And there was the regulation that Elymnias hypermnestra had only one type of scales at iridescent area, and two different scales at not-iridescent area as well as Euploea’s. 本實驗目的為探討台灣地區紫斑蝶蝴蝶翅膀幻色的特性，以及翅膀幻色與鱗片的相關性。由結果得知，幻色實驗中利用掃描式電子顯微鏡發現紫斑蝶幻色的形成和其鱗片的細微結構與排列方式有密切相關。我們推論紫斑蝶的鱗片細微結構與排列皆會影響其幻色的形成，而顏色的不同則與不同類型的鱗片相關。除此之外，我們亦對同具幻色的紫蛇目碟進行拍照分析，發現其幻色亦與鱗片有相關性。紫蛇目蝶的幻色區具有單一種鱗片構成的規則性，非幻色區則有兩種鱗片，與紫斑蝶相同。

本研究主要探討電解液之帶電離子在磁場中的動力行為。為了觀察更細微的結果，共歷經三代裝置改良，第一代用五個電錶及探針測量徑向橫截面上五點的電壓，所測數值電壓有下降趨勢但不足以呈現細微部份的變化。第二代利用電壓感應線、搭配平移台及電腦，呈現連續性且經數位處理之結果，出現電壓升降的電荷堆積現象。第三代為了更精確，將裝置結構及器材上改良。觀察到在磁場作用下有旋轉現象，改變電極極性時，會有順逆時鐘方向的改變，且只有電解質液才會有旋轉。更可以使用帶電質點受到勞倫茲力F=q(VxB)理論解釋。且旋轉中的電解液比沒有旋轉時，析出的銅量少，反應溫度升高快，電解液內電壓分布因電荷堆積造成的高低起伏。經過改變磁場強度、電解液濃度，不銅價離子電解液，結果濃度大、磁場大、離子數較多者，呈現電壓分布圖快速變化，彎曲大。This thesis report is the study of combining the moving charged particles under the perpendicular magnetic field. By using the theory of moving and electrolysis, the electrolytic liquid will swirl through the particular arrangement of the horizontal cylinders enclosed in a circular enclosure container and strong magnet. Then, the researcher observes the force situation of the charge in the magnetic field and discusses the differences of the electrolysis effect, which is experimented under the different conditions, such as, in the magnetic field or no-magnetic field. Furthermore, the researchers discuss the conduction of voltage spreading and interfering when the moving electrons under different position of two electrodes and under the different interaction of electric field and the magnetic field. And the changing reason as follow: （1）the magnetic field strength. （2）the concentration of the electrolytic liquid. （3）electrolytic solution. When the experiment group compared with the comparison group, the result may provide fundamental understanding as follow：（1） The researchers can find out the charged particles rotating in the magnetic field. And it proved the moving condition when the moving electrons in the magnetic field. （2） This experiment can be used in judging the solution, which I electrolytes, or not. （3） This experiment also proved for Arrhenius’s ionic theory. （4） The researchers found out the quantity of Cuprun decrease, the rise in temperature and the reducing in voltage.