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.

本研究主要目的是以黃色小鴨的參觀風潮與商品特質，探討高中生對療癒系物品的偏好為何。黃色小鴨在全球形成一股風潮，許多人認為參觀黃色小鴨有紓壓的功能，也有人認為買小鴨玩偶陪伴自己，有療癒心情的效果，因此，本研究的主軸分別從「黃色小鴨的參觀活動」與「療癒系商品(HSP)特質」兩個大面向進行探討分析，釐清高中生對黃色小鴨療癒系物品(RDRP)的偏好為何。本研究對象為臺灣南部地區的高中生共254位，以「療癒商品與相關活動感受問卷」進行施測，分析結果顯示：(1) 對於療癒商品，女生喜好與購買意願均大於男生，其中又以「仿生造形型」類型最受歡迎；(2) HSP以「規律動作型」、「擬生命行為型」，而RDRP以「仿生造形型」、「手觸摸型」較能藉由放鬆及平衡情緒，達到療癒效果；(3) HSP與RDRP均以「聲控及感音型」較能藉由轉移情緖及產生驚喜，達到療癒效果。

題目緣由是數學奧林匹亞預選題的其中一題組合問題，題目探討在2^m×2^m的棋盤中(m∈N)先分割出對角線上的2^m一單位正方形，之後將剩下兩塊狀似等腰直角三角形的棋盤分割為若干個不重疊的矩形，求此棋盤被分割出的所有矩形周長和最小值。本文將原命題推廣至nn×n棋盤與m×n棋盤的情況，在2^m×2^m中達到周長最小值的矩形分割方式十分直觀，但證明過程中直接構造函數2x〖log〗_2 x以及利用琴生不等式等方法不甚直觀，於是我們在n×n部分的最後給出了另解，並說明原題為其特殊情況。 n×n的部分沿用原題之方法定義了十字分割，我們證明了利用完全十字分割可達到最小值，為4n(m+3)-2^(m+3) (其中2^m≤n

這份研究所探討的主題源自於1976年USAMO第一大題：將一4×7矩形方格表的每格塗色黑色或白色，欲使所有能構成矩形頂點的四個方格皆不全為同色。試證明其塗色必定失敗、或給出滿足的塗色方式。此研究從上述題目延伸，增加可填入的顏色數量、改變方格表的長寬，甚至將方格表改為三角格子表。研究過程主要運用鴿籠原理、組合數量之計算及柯西不等式來分析。我們已幾乎完整討論完矩形方格表中填入2色、3色，及三角格子表中填入2色的所有情況；並且對於矩形方格表，我們找到了一條判別式，可以判斷一般化的某情況下塗色是否必定失敗，但有部分必定塗色失敗的情況無法由此判別式判斷，需藉由其他方式討論。此外，我們也嘗試從滿足的塗色方式中找尋規律並建立構造的規則。

沙烏地阿拉伯 is the largest oil exporter in the world. 64,000,000 tons of sulfur oxides are produced every year through the combustion of organic sulfur compounds in the oil industry. This leads to several environmentally serious problems, including air pollution. This research provides a novel strategy to utilize natural-based Graphene Oxide (GO) as a support for ruthenium (Ru/GO) to functionalize as a green catalyst for hydrodesulfurization. Physical activation of camel bone samples was carried out by carbonizing them at 500oC to produce camel bone charcoal. Modified hammer’s method was employed for GO production, followed by doping of ruthenium in a simple synthesis step. The prepared catalyst has been characterized by XRD, SEM and EDX techniques. Thiophene and 3-methylthiophene were used as model compounds in the hydrodesulfurization process. The catalytic reactions were carried out at atmospheric pressure in a continuous up-flow fixed-bed quartz reactor. The composition of the sulfur containing gaseous products was analyzed by gas chromatography. The product distribution achieved for thiophene was 3-6% butadiene and 76-77% butane. And for 3-methylthiophene, it was 32.3% of pentaned 1-pentene and 2-pentene and the selectivity percentage was 45%. Ru/GO has been found to be an excellent catalyst of thiophene and 3- methylthiophene hydrodesulfurization and is a considerable improvement when compared to the commercially available catalysts. The prepared catalyst shall potentially lead to the reduction of sulfur pollution in the future. The positive effect on the environment could be substantial.

本研究旨在探討轎車四輪關係。藉由車體結構的限制:左右互相平行，其距離為輪寬w，後輪沿車身延長輪距d，會碰到當時刻的前輪位置，以此做為發想，發展出前推後、後推前、左推右及右推左四種推論方式，最後得到結論。 研究最後將結論應用於許多方面，如應用於刑事鑑定方面，此外亦將程式寫於MATLAB以利修改跑跑卡丁車只留下了後輪軌跡之程式不足。

低頭族發生『假性近視』、『脊椎側彎』甚至『黃斑部病變』等健康問題有越來越多的趨勢，邊走邊玩發生的意外也越來越多，因此，我們針對低頭族的健康與安全開發本作品。一、 健康方面： 撰寫「背景執行程式」，此程式完全不影響使用者玩遊戲、上網…等等，使用30分鐘後，透過「加速度感測器」檢測使用者必須做的手臂運動，完成後才可繼續使用手機，藉此『休息一下眼睛與僵化的手臂』。透過「環境光感測器」調整螢幕亮度，不讓螢幕光太強而造成眼睛更容易損傷。二、 安全方面： 「加速度感測器」與「陀螺儀」辨識出使用者邊走邊使用手機，就跳出提醒視窗暫時中斷使用者使用手機，使用者或許就會停下腳步或是抬起頭來恢復對環境的觀察能力以避免意外發生，按下「確定鈕」後，就可繼續使用。

本研究以希爾伯特－黃轉換 (Hilbert Huang Transform, HHT)，來分析311日本海嘯對台灣各港的水位變動影響。利用HHT將各港驗潮站資料分解成數個本質模態函數 (Intrinsic Mode Functions, IMF)，從中找出天文潮和海嘯影響的IMF。將主要的天文潮及趨勢線濾除後，可清楚看出海嘯影響水位的成份，進而分析各港口海嘯波抵達時間、振幅大小和主要頻率等。由 IMF 中可發現海嘯波來臨前海水水位退潮及急升狀況。此外，東部各港呈現出較為明顯的地震前導波(P波)所引起的高頻震盪波，與地震發生時間、P波傳遞速度、海水傳遞延遲及各港水位抬升時間都大致吻合，但較海嘯波到達時間大幅提前。上述研究結果，對瞭解海嘯波特性，將有所助益。

Even as a child, I was fascinated by the colors in nature, such as rainbows, butterflies and flowers. This fascination developed into curiosity with age, and as my school studies developed, I became particularly interested in the scientific aspects of the origin and development of colors. I wanted to answer the question: How are the different colors of the butterfly wings related to the nanostructures of scales and pigments? The color on the butterfly wings results either from the pigmentation (chemical color) or from the structure (physical color) of the wing scales. Colors such as yellow, black, red and brown are mainly created by pigments. The interaction of light and structures in and on the surface of butterfly wings, often the size of the wavelength of the light, results in physical colors. These colors are usually bright and dependent on the viewing angle (unlike chemical pigments that spread light diffusely). The colors produced here are usually golden, green, purple and blue. But, where do these colors come from and why do certain species dazzle more than others? To get to the heart of the matter, I identified two key questions: • How are the different colors of the butterfly wings related to the nanostructures of scales and to the pigments? • Using the nanostructure, can you find out the wavelength of the reflected light? In this work, I focus on the structural colors of butterflies and study the physics behind them. This includes parachuting in areas such as diffraction gratings, scattering of light, interference in thin films, and multilayer interference. In order to experience the greatest possible diversity, I selected butterflies from different species for the measurements. Using the spectrometer, I measured the light reflected from butterflies. High-resolution microscopes such as the laser microscope and the scanning electron microscope gave me the opportunity to study the detailed nanostructures of the wing. In addition, I was able to analyze and evaluate my results using existing physical models and MATLAB simulations (Maxwell equations).

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.