永不妥協
本文籍由一套數學遊戲的必勝方法及其背後潛藏的數學原理，來作為研究目標。透過研究德國數學家E.Sperner 提出的方法所延伸的數學遊戲，來解決潘建強、邵慰慈兩位教授留下來沒有證完的遊戲結果[1]，並將遊戲增廣至三維空間的探討且得到如下的結論：
一、平面棋盤
(1)不可換色，先下者恆勝，其最快獲勝方法，為依所下位置的三角形衍生子圖周界走。
(2)可換色，獲勝規則由棋盤的總頂點數決定，若棋盤的總頂點數為奇數，先下者獲勝；若棋盤的總頂點數為偶數，則後下者獲勝。
二、空間棋盤
(3) 不可換色，先下者恆勝，而最佳下法，則是下在大四面體本身內部的某一點，且其最快獲勝方法為，依正四面體稜邊所下位置走。
This study is mainly about an invincible method of a mathematical game and its theory from which it is derived. We want to solve the problems left by Professor Poon, K.K and Professor Shiu，W.C. and meanwhile extend it into three dimensions through the method brought up by E. Sperner[1].
On two dimensional case, the first player will win the game forever on condition that these two players can't change their chesses colors at will. And the fastest way to win will be just putting the chesses that along the baby triangle boundaries. If both players can change their chesses colors randomly, count the chesses number before starting the game. It is calculated that if the number of the total chesses is odd, the first player will win the game in normal and logical circumstances. On the contrary, if the number of total chesses is even, the latter will win.
On three dimensional case, the first player will definitely win the game without allowing changing chesses colors. And the best strategy is putting chesses in the inner of the big tetrahedron; what’s more, going along the edge of the tetrahedron will be shortest way to win the game.
電梯問題
本研究主要是研究「電梯問題」： 令某棟建築內任兩層樓都至少有一部電梯連接的建築稱為全能建築，若某棟建築內有m部電梯，每部電梯停n層，f (m, n)為使這棟建築成為全能建築的最高層數。對於不同的m, n，f (m, n)的值為何？ 本研究一開始先以一些參考資料為基礎，試著整理出其中未完成的部份。接著，我們針對了一些個別的f (m, n)，具體求出其值。令某棟建築內任兩層樓都恰有一部電梯連接的建築稱為完美建築，我們引入了一個新的函數g (n, k)=m，得到了一個與完美建築有關的定理。另外，我們還利用一些構造方法，求出了所有g (3, k)的值。 在這次的研究中，我們成功運用了各種不同的構造手法，得到了一些相關的結果。至於是否能將這些構造方法運用在求出一般的f (m, n)之值？這是我們將繼續探究的課題。
Auto-control water consumption System
By saving water you are saving lives including yours. All of us know that water is an invaluable and priceless gift. We can’t dispense it. The consumption of water differentiate from one country to another, we may use over quantities of water, in other countries people are thirsty living under the limits of poverty .It’s very important for agriculture, industry even human animals and plants can’t live without water. But people are careless, they consume a huge quantities of water in shower, washing car, gardening…. So that we thought to make this brilliant project F.W.S (frugal water system). This system is connected with you mobile phone by an application that shows you your water consuming and makes you control it. It record in every minute your consumption. This control system helps us to preserve water for the future generation. Besides, it tells you the price that you will pay and warns you if you pass the quantity of water that you should consume in a defined period. So you can also save your water bill. So we have to make this project works to let every person know that he is doing squandering water. With this system we can save planet resources of water. Finally, the water is as precious as our lives and with frugal water system, we will be able to monitor and control our water consumption. Also be alerted in the event of a leak or flooding. This project helps us to preserve water, reduce and avoid over-consumption. So we have to stand together against water squandering by making this project works.
Construction of an Emergency Portable Dynamo Mobile Phone Charging Station by Means of a Hand-Crank Gear Mechanism/ Solar Panels
The researchers aim to construct an emergency mobile phone charging station that runs on renewable energy and will serve as a cost-efficient alternative to more traditional power banks. Circuit components include a 20V / 6W solar panel supplemented by a hand-crank gear mechanism integrated with a 6V / 1A lead-acid battery, a usb output and an adjustable switch-mode power supply (SMPS) to convert excess voltage into current. Initial voltage and current outputs were measured under varying resistances. It was determined that the set-up satisfied the minimum voltage and current requirement for charging a mobile phone (5V / 1A). A subsequent phone charging test was executed using a Samsung Galaxy J2 (3.85V Li-ion battery 7.70W, Charge Voltage: 4.4V / 2000mAh) wherein it charged on an average of 0.277% per minute for the solar panel and an average of 0.263% per minute for the hand crank gear mechanism. A Mann-Whitney U statistical test was conducted to determine if the charging rate of the charging station had a significant difference from a commercially available power bank’s. The calculated UA: (4) from the test was below the lower limit and the UB: (217) was above the upper limit which indicated that there was a significant difference between the charging rates. While the efficiency was lower than the commercial power bank’s, it can still be used as an alternative charging method especially during emergencies and disasters.