Quantum Rings are defined to be polygons with sides all of the same unit length that are connected with a fixed positive or negative angle. In the research, the number of Quantum Rings corresponding to a given number of sides and a fixed angle will be discussed. Quantum Rings could be expressed by many sequences which would involve the theory of partitions and ways to eliminate the many to one nature of the sequences in order to evaluate the upper and lower bound. Besides estimating the upper and lower bound, a lot of the qualities of the Quantum Rings under certain circumstances will be mentioned.「能量環」為許多單位長度的線段以定角首尾相接，並且最後接回原點的多邊形。本研究將要探討對於給定邊長個數與相接角度的「能量環」的個數。「能量環」可以被表示成許多種數列的形式。在數列的運算中會牽涉到許多數字分割的理論與排列組合的排除重複以求得能量環個數的上下界。除了定量的求算出上下界以外，報告中也定性的歸納出許多給予特殊條件的能量環的性質。

This project aimed to create a simple model of coin sorter with cheaper price, electricity saving using recycled materials for use in place of manual separation and compatible to the automatic coin sorters commercially available in the market. The principle applied in inventing this device was the gravity force that pushed coins to fall through its upper compartment to the lower part via a slope that determines the coin path as well as the speed of the coins. The upper part of the box was designed to control the rate of the descending coins and transported the coins to the separation section in single file order to prevent jamming. The lower part of the box consisted of the coin sorting mechanism which conveyed the coins to their assigned compartment according to coin diameters. The box could separate three kinds of Thai coins, 1,5 and 10 baht, with 95-98 % accuracy. The efficiency was in the range 150-250 coins per minute with highest accuracy at 150 coins per minute. The box was made from acrylics. The designed box can separate coins faster than manual sorting although not with as high efficiency as automatic machines which can sort up to 500 coins per minutes. At the present stage, it can not count the number of coins. However, it can be built at cheaper cost, does not require electricity or electronic devices and is suitable for small and medium size business. We aim to improve the box to give higher accuracy with coin counting ability.

創意發想：在學習三角函數的三角測量應用時，由於立體感並非十分容易在平面中呈現，使得解題過程並相當困難。我們希望能透過程式，實際模擬出所看到的樣子，將有利於解決這方面的問題。學習美術者也需要了解一點透視的立體概念，皆可以透過程式來模擬。作品特色：我們的精神主要在於以高中的數學及物理為基礎，來研究其中的方法。除了研究3D 繪圖之基本原理，並著重於如何以程式實作，以達到高繪圖效能。預期效果：1. 讓電腦繪出有立體感(近大遠小)的圖形。2. 可以由不同位置及角度觀察物體。3. 讓立體影像具有光及影的效果。“想像您坐了一部直升機從1 樓向上到達頂端，觀看101 大樓有何不同的景象?!”Motive ：In learning the technique of triangulation, it is hard to show 3D coordinates on 2D graphics so that this kind of math problems is difficult to solve. We hope that we can simulate the 3D surroundings by programming to provide references in dealing the problems. In addition, painting learners also need the simulation to realize the concept of one-point perspective. Feature ：1. We do all the research based on mathematics and physics techniques learned in high school. 2. We not only figure out the method to draw 3D pictures but put some emphasis on how to use programming to run the method. Objective： 1. Let the computer draw 3D pictures, that is, the object looks big when near and small when far. 2. Making it possible to observe the object from different positions and angles. 3. Making the 3D pictures with lighting and shading effect. “Imagine how the sight would change while you are taking a ride on a helicopter from the ground to the top of Taipei 101.”\r

BCH (Bnip-2 and Cdc42GAP homology) domains are a novel class of protein-interacting domains. First identified in BNIP2 and in Cdc42GAP, a GTPaseactivating-protein (GAP), canonical BCH domains play important and varied roles in the control of cell morphology and apoptosis induction, amongst others. However, this domain is currently classified under lipid-interacting sec14 domains due to low sequence identity (~20%). Given this intriguing similarity, the relationship between BCH and sec14 domains is worth further study. As BCH/sec14 domains are closely associated with cell signaling and human disease, characterization of these domains and the elucidation of their functional diversity could better aid our understanding of their cellular functions and disease pathogenesis.

1. Purpose of the research Because we live in a famous winter sport region in Switzerland, we have been confronted with the problematic of avalanches since we were born. In winter 2011/2012 alone, 179 people were involved in an avalanche accident, of whom 25 died. The most important device for searching and rescuing a buried person is the avalanche transceiver. It creates an electromagnetic field, which can be used to locate a buried person with another transceiver. The most important factor while searching is time: After 30 min. the chance of survival of a buried person has dropped to 40%. Considering the fact that people often make mistakes when they are put under such a big stress, valuable time gets lost. This is where our project comes into play. With an automation of the searching process a fast and reliable search should be achieved. The aim we agreed on for this paper is to develop a prototype of a robot that can find an avalanche transceiver automatically and reliably. To study and optimize the functionality of our robot more easily, our tests have only been performed on flat ground. 2. Procedures The components of an avalanche transceiver with only one transmitting antenna are used as a receiver. With the help of this receiver, the signal of a transmitting avalanche transceiver was analysed. Furthermore, the results were used to evaluate the most suitable search technique. Our robot is based on the “RP6” robot system, which is programmable in the C-language. The signal of the receiver is modified in a way which allows the robot to read it. Based on the results of the signal analysis, a search algorithm is developed. In the final tests the robot was examined as to its functionality and efficiency. Therefore, the robot was positioned at randomly chosen starting points to locate the transmitting device. 3. Data The transmitter could be located correctly in every test. The starting points were successfully located up to 11 m from the transmitter. The search ending points were found at a maximum range of 0.5 m from the correct position. 4. Conclusions In view of the results, the aim of developing an automatic localisation of an avalanche transceiver on flat ground as a prototype is seen as fulfilled. Outside the specified range, the transmitter can only be located unreliably. This is due to the fact that outside that range the signal differential in different directions is too small to be processed by the robot. Our prototype was tested under ideal conditions. Certainly, our robot is still some way from being ready for use in an actual avalanche. Many different questions have not been answered yet or have come up during this project, for example: ‘How should the robot should be applied on uneven terrain?’ or: ‘How should it deal with several buried people at once (multiple transmitted signals)?’ Two aspects of our prototype, the low weight and the low construction costs, however, are particularly favourable.

思考公車車門開關時在地面上掃過的區域形狀與面積時，發現其中變動的直線為過定點與座標軸圍成三角形面積最小的直線，我們很好奇，這類圍成最小面積的直線更進一步的包絡現象，所以就動手去嘗試做研究。\r \r The research is done out of the curiosity we had when we pondered over the area and the shape a bus door sweeps on the floor when it opens or closes, and thus to discover the graph of the varying line which forms the smallest area so that we attempt to do research on such envelopment phenomena.

在國中理化中提到，紅、藍、綠三原色光，吸收、混合後可以合成其他顏色的光。但實際上，單波長光的顏色；以及課本實驗中，藍光照在綠色片上所呈現的顏色偏差（藍綠色，非黑色），便無法以此理論解釋。因此本研究計畫藉由 SP20 分光光度計能在可見光範圍偵測樣品對各波長光線吸收度的功能。捨棄光的三原色過於簡化的說法，以實際測量各有色樣品（濾光片、化學藥品、噴墨印表機墨水、實際列印投影片）所得吸收度曲線圖，重新解釋顏色的呈現。了解顏色是人類對光的感覺，而不是光本身的性質。並在完成對彩色噴墨列印樣品吸收度的基本測試後，設計以印表機、軟體、墨水顏色、濃度深淺為變因、交互搭配的 334組實驗，比較印出成品的最大吸收度比例與原先在電腦中設定顏色濃淡比例的偏差值，找出最能真實列印出顏色濃淡的組合，實驗結果顯示：印表機方面：HP 670C、Epson Photo EX表現最佳。軟體方面：CorelDRAW，Photoshop，Photoimpact 表現平分秋色。

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.

An orbital angular momentum (OAM) sorter concept was designed for high-speed data transfer. The OAM of a light beam known as an optical vortex can exist in one of an infinite number of states and may be used to carry information. The augmented alphabet of states carries the potential to increase date transfer speeds over conventional binary (0 and 1) methods. A vortex generator, or OAM encoder , was constructed from a slit cover slip functioning as an adjustable spiral phase plate, and a vortex analyzer, or OAM measurer, was created using a transparent print of a computer-generated hologram. The two components were then incorporated in an OAM sorter concept that that employs a novel combinatoric method for sorting data. The vortex generator and analyzer created were inexpensive simpli-fications of previous devices and have the potential to increase the alphabet of transmission states several thousand times over binary methods if implemented in the OAM sorter concept.

The reason for making this project was with the intention to help the blind persons. A lot of people with vision problems don’t have the resources available to acquire equipment or programs that make it easier for them to use a computer to write, to communicate etc... Being aware of this problem we took the liberty of researching at a community center that helps the blind persons in Tijuana Baja California, Mexico. We found that they had a type writer (Perkins) with only 6 keys that symbolized Braille. They also had a normal keyboard that had the Braille code over each key, but it is complicated to learn because of its many keys. Due to our research our intention was to design a system that respect the Braille symbols of the Perkins type writer and translated them to the common alphabet. We believe that this project will help many people especially the blind, with writing books, letters, articles, etc. So they can be integrated to activities and jobs reserved, until now, for people with the sight sense. My project also has 8 keys, when the person press a key combination the PC emits the sound of the letter. And when a word is completed the PC reproduce the whole word on the speaker. When the entire paragraph is completed there is an option to reproduce it. It has also other functions as erase everything, back space, etc. All these with the 8 keys. To control the system I used the parallel port of a PC, with a control program made in Visual Basic. Currently there are systems for the blind but are very expensive, they have a cost of approximately $900.00 US dollars, which is a high price to pay for some people. My project has a cost of $70.00 US dollars thus making it easy for a person who has a computer to be able to buy this keyboard. This project is being use in the “Blind Persons Training Center” of Tijuana city. They helped us to develop it, giving some ideas to improve it.

The project is a simple traffic light which operate two by two type. The new ideas in this project are :1- Digital counter for car signal.2- Digital counter for side walkers. 3- Auto traffic detector.4- Red light crosser detector. Digital counters. The signals counting the whole period the the junction do in each cycle. The counter starting counting from 16 sec. down to zero and each side walk counter is vise versa with it is main counter. The time is changeable between 1-99 seconds. Also there are four square lights fitted with the main counter to illuminate the colors. Auto Traffic detector. There are three sets of switches in front of each traffic light to detect if the road is clear for the cars to enter the next road. Red light crosser detector. After the signal become red this system will operate to detect any car try to cross the red light by the car cutting the switch two times.

By comparing eight different epoch images of the crab nebula taken through 1942 to 2004, we have calculated the expansion velocity of 27 optical bubble features and 60 filaments. The mean expansion velocity of bubble features and filaments is 0.173 arcsec/yr and 0.15 arcsec/yr, respectively. We also estimated the maximum radial velocity of the expansion by analyzing the emission spectrum of the nebula. The maximum radial velocity is 1385.5 km/s. Combining these measurements indicates that the crab nebular is approximately 5870 light year away. In addition, if we assume that the nebula has been expanding at a constant rate, our expansion velocity projected backward indicates the mean date of the supernova event as A.D 1124, more than 70 yrs later than the accepted date of 1054. The result confirms the well-known acceleration in the crab's expansion. Although we have analyzed eight images with a 62 yr baseline, the acceleration still can't be derived from this study. 透過量測由1942年到2004年之間八張不同年代的蟹狀星雲中爆炸後殘骸的位置變化，可以計算出蟹狀星雲爆發的擴張速度。本研究選定了27個包狀物和60個纖狀物，計算出的擴張速度分別為0.173 arcsec/yr.和0.150 arcsec/yr。再透過分析蟹狀星雲的光譜所計算出的徑向速度（radial velocity）為1385.5 km/yr，進而推得蟹狀星雲的距離分別為5430光年和6370光年，平均值為5870光年。 另外，如果假設擴張速度是等速運動，那麼把求得的擴張速度倒推出的爆發日期是在西元1124年，這比中國紀錄中超新星爆發的1054年晚了70年。這顯示出蟹狀星雲的確非等速擴張而是有加速度的狀態，才會造成以等速倒推發生日期時，晚了70年。雖然本研究中分析了相差62年之久的八張影像，仍然無法分析出星雲的擴張的加速度情形。