拖線溜點
原題目是環球城市盃中，一個圖論的問題。而題目提供了一個證明，是證 明此種連線都是偶數的圖形，一定會在三的倍數邊形成立。在經過一番思考過 後，我們希望能將原本的偶數連線性質加以驗證，並確定奇存在性。此時，我們 也不禁聯想到：奇數是否也有所特別的性質。因此，我們也向奇數連線做研究。 就在平面得到了部分結論的同時，我們想到這個問題是否可以推廣至三維 空間。然而在推至三維空間的過程中，我們又聯想到，另一種平面：球面。在球 面上放點，能否也找到一些不同的性質。因此，我們分別從平面、球面、立體圖 下手。 基本上，探討平面和立體問題的方法，是以土法煉鋼的方式來求出結果。 然而這種圖論的問題，不可能嘗試到無限多點的情形。因此，我們是著找出一個 關鍵的key，那就是結合性質和外接合性質。以這兩種方法，我們可以將一個簡 單的基本圖形，推向無限多點和無限多邊的情況。 接下來，還有討論一些特殊狀況，例如： deg v＝3n+1，探討其結果。 最後得到的結論是： 1、平面偶圖成立的條件為：此多邊形為三倍數邊形， 而且除了內 部一、二、四點以外， 其他點數都可以成為偶圖。 2、平面奇圖成立的條件為：奇數邊形的情形下，除了三點以外，其 他的內部奇數點的都可以成為奇圖。偶數情形下， 除了四 點以外， 其他的內部奇數點的都可以成為偶圖。 3、三角形平面圖，d eg n 皆為m 成立的條件：2＜ m＜ 6( m? N ) 4、三角形內外任意點d eg 皆為3n ( n ? N )的成立條件： 三角形內部4 x+1 個點( x ? N )。 5、三角形內外任意點d eg 皆為3n+1 ( n ? N )的成立條件： 三角形內部3 x 個點( x ? N )。 6、立體偶圖n 頂點(n＞4)面體的成立條件為： 內部點數為5m+ n- 3、5m+ n- 1、5m+ n、5m+ n +1、5m+ n +3。(m 為大於或等於零的整數) 7、立體奇圖四面體的成立條件為： 內部點數為偶數皆存在。 The original problem is a question of Graph Theory in IMTOT ,which provides\r a proof that proving the figure which its linking-line number is even ,should also be\r contented in the triple-sides figure. After profound consideration ,we try to make sure\r the existence of the properties the we mentioned above. Meanwhile ,it also occurs to\r us that whether the properties would be contented ,in the figure which its linking-line\r number is odd. So we make our way to it. Additionally ,three-dimensional and\r spherical figures are part of our research as well.\r Basically ,we discuss the problem in two-dimensional and three-dimensional\r aspects with the simplest method .However ,it is impossible to discuss the problem in\r unlimited dots .Hence , we are going to find a “key” to solve this problem .As a\r result ,we can find a simple basic-picture , and expand to infinite-multiple lateral\r pictures.\r Next step ,we also discussed some special situations , for example: for each\r point v , deg v=3n+1.\r At last the conclusion is following:\r 1、The conditions of linking-line number is even: triple-sides. And the amount of\r points inside the figure is without 1,2,and 3.\r 2、The conditions of linking-line number is odd: In the odd-sides figure , all number\r of the points inside the figure can be content without 3 point. In the even-sides\r figure , all number of the points inside the figure can be content without 4 point.\r 3、In a triangle , each point’s deg is the same number m: 2
會逆轉的石頭－RattleBack 逆旋現象
具有長短兩軸的對稱性剛體，譬如半橢球，在施加適當質量配重後，給予其Z 軸方向的 初角速度，將會逐漸上下震盪、搖擺，而後改變原先的角速度方向，朝相反的方向逆轉回來。 此現象稱為「逆旋現象」，本研究分析關於配重、質心距離與表面摩擦係數等因素的影響，利 用光點投影方式判讀其軌跡，並建立數學模型以驗證物理原理。研究發現，動摩擦垂直長軸 的分力所造成的力矩，將會導致逆旋的發生，並且，對本研究的剛體模型而言，加以20g 配 重，與長軸夾45°距質心5.5cm 且動摩擦系數為0.1227 時，逆轉角度有最大值。當長短兩軸 的震盪頻率相近時，甚至會發生兩軸能量的耦合現象，而有不只一次的逆旋。 The phenomenon was found for rigid bodies with long and short symmetrical axes, such as half-ellipsoids. We add extra masses ( Δm ) to a stone of the shape of half-ellipsoid and then give it an initial angular velocity ( 0 ω ) to make it spin. While the stone spins, the two symmetric axes start oscillating up and down. Then, remarkably, the spin of the stone slows down while the amplitude of oscillation increases until the direction of angular velocity reverses. This process is called “Rattle Back Spin-Reversed Phenomenon.” Our study involves the effect of several parameters on the above phenomenon, such as the shape of the stone, the added mass, and the friction between the stone and the table surface. We try to build a physical model to explain the spin-reversed phenomenon which can be recorded by tracing the motion of the stone with optical means. According to our study, the shape of the stone and the distribution of the added mass played crucial roles. The torque generated by kinetic friction along the long axis also helps the spin to reverse. Furthermore, in our experiment, we record a maximum reverse angle with following settings: two sets of 10 grams of mass are symmetrically added to the flat side of half-ellipsoid, in the distance of 5.5 cm to the C.M. of stone and an included 45 degrees angle with a long axis. And the most surprising finding is that when the oscillation frequencies of two symmetric axes are close to each other, the spin of the stone can reverse twice.
ELECTRONIC STUDENT-TEACHER POLL ATTANDANCE SYSTEM
Our goal is to make roll call systems at schools technological. While Rolling Call system is getting technological capacities some useful outcomes occur as well like; To remove the cost for class books by abolishing the class books used for roll call To eliminate mistakes with the usage of class book .(The numbers written incorrectly) To save again a large amount of waste paper( The short messages will be send to the parents instead of mailing the letters to the their adresses once a week about their students' absance.) To improve communication among school and parents ,by this way to prevent various kinds of problems arising from absenteeism. To make teachers school boards more efficently and motivated besides their affairs will get easier as well. To save time of school managers(They have no Works like saving the absenteeisms into e-school network because everything including all the absenteeism info will be carried into the system automatically) To save time of each lesson the teachers will not loose time for the roll call ,so they will be able to devote their time to their students and training. -Technological polling mechanism will contribute to education, this contribution will make all the students and teachers happy because all the teachers carry concern whether their curriculum will be finished or not through this system recording all the rests of teachers because of illnesses and some national celebrations.
Prototype Educational resources for teaching basic pneumatic
The didactic prototype for the teaching of the pneumatic Basic is designed, so teachers can instruct knowledgement of pneumatics focused to identification, handling and application of its elements based on constructivist theory in which the student learns making, working on projects and in a collaborative way. This implies that his presentation should include the basic elements to be used in this study area, as well as allowing that the student can interact with it, still easy to use, and take them by the teacher into his area of education, which can be a classroom, room, Auditorium, workshop, lab, and even training courses to the industry, the only thing that requires is compressed air (2 to 4 bars). As well as, to create a secure environment for the user when this is manipulating. Its construction based on a compact, lightweight and ergonomic, structure to ensure that it can be transported without difficulty. Also that must comply with the minimum essential to enable the student to acquire competencies in the curriculum which consider the identification, handling and application of pneumatic elements; IE has the following 2 directional valves 3/2 NC, 1 directional valve 3/2 NC-operated with a knob, 2 valves 3/2 pneumatic drive, a 5/2 valve NC NC of stable pneumatic drive, 1 valve of simultaneity or function, and 1 valve selector or function, or double effect with pressure regulator piston1 piston of double effect, 1 piston for simple effect, 1 valve 3/2 NC with motorized drive and roller.
Recycled PET bottles for vacuum packaging
Vacuum packaging is a packaging technique intended to extend the shelf life of food via the removal of air from an enclosed package prior to sealing. This process limits the growth of aerobic bacteria or fungi due to oxygen deprivation. In this work, we present a novel do-it-yourself vacuum packaging device using the exchange of water and air between two bottles to continuously generate a vacuum-suction effect. The sizes of bottle and vacuum bag were investigated for its impact on the vacuum generation in a plastic bag containing smoked fish sausages. Large commercial 3.1-litre PET bottle generated more vacuum than the smaller ones. An equilibrated vacuum pressure of a smaller plastic bag was lower than that of a larger size. With 3.1-litre PET bottles, the vacuum pressure for 3”x5”, 5”x8” and 6”x9” bags was equilibrated at 8, 10, 18 mmHg, respectively. Sausages packaged by our device last for 14 days when they were kept in -20oC refrigerator, which was comparable to those packed by the commercial vacuum packaging system for household use. This project demonstrates an application of simple science in a real life situation as well as a promotion of environmental protection idea as the electricity is not used in the vacuum generation process and the disposed plastic bottles can be reused.
Research the efficiency of the fog-catching nets
Islands far from lands use the underground or surface water as the water for living. The population of the islands is growing fast and the amount of water usage is increasing year after year. However, the amount of water usage is limited, so that people who live in islands have trouble using water. To compensate this problem, underground water is drawn from deeper underground sites. If this matter occurs continuously, sea-level may rise and then we cannot use underground water. Seawater desalination is a way to solve the water shortage, but it requires a lot of energy. It is difficult for island far away from lands to supply a lot of energy. It is considered the eco-friendly way to minimize the use of energy on the island. In order to solve the problem of water shortage on the island, it is considered fog that on the island occur frequently. It is an attempt to create water from fog, but it is a lack of research of efficiency of fog-catching nets to create water from fog. In this research, I have studied the efficiency of the fog-catching nets, a way to increase the efficiency, the amount of water that is created on the island, usage of discarded fishing net for fog-catching nets. Through this research, I found a kind of fog which can be changed into water and the difference in efficiency due to the difference in the size of the mesh size of the fog-catching nets, wind direction, wind speed, water absorption capacity of thread of fog-catching nets, installation direction of fog-catching nets, a way of installation of fog-catching nets. Also I found fog-catching nets of discarded fishing nets on the island and the possibility of usage for everyday life that the amount of water are created for a day or a month during dry season on the island.