This project was inspired by a tournament call the International Young Physicist’ Tournament (IYPT). The problem could be broken into two aims: ‘Investigate the forces that cause a ball to levitate in a titled airstream’ and ‘optimize the system for the maximum angle of tilt that results in a supported ball’. The first stage of the investigation was research and learning. Two fluid mechanics courses online were used to build a basic of knowledge of the subject. Next a force diagram was created to model the forces acting on the ball. The diagram identified a force called the lift force that must be acting on the ball to be supported. There were three contending theories that could explain the lift force: The Bernoulli theory, the Coanda theory and the Magnus theory. A practical investigation was then instigated to differentiate between these three theories. Since the Magnus theory is only applicable if the ball is spinning in the airstream, this theory was isolated by changing the center of mass of the ball but keep everything else constant (this allowed control of how much the ball spun in the airstream). Changing the center of mass didn’t impact on the maximum angle of tilt at all, proving that the spinning of the ball isn’t producing a significant amount of lift, and therefore the Magnus theory couldn’t be a cause for lift. Because further testing couldn’t isolate the Coanda and Bernoulli theories, a solution was developed to explain why the two remaining theories might co-exist. Further testing methods have been designed to investigate this possibility in more depth. To meet the second aim of this project, an investigation was launched to see how parameters affected the maximum angle that the ball could be supported at. The parameters investigated were: Ball radius, ball mass, ball surface, air speed and airstream diameter. A lot of time was spent creating a reliable experimental method. The method could be used to support a ball in an air stream, slowly tilt the air stream, and then measure the angle of tilt the moment that the ball fell out. After experimentation, a table was created to describe how the listed parameters affect the maximum angle of tilt that a ball can be supported at. Explanations were proposed for why each parameter affected this angle. Future experiments have been devised to build a deeper understanding of the effects of a wider range of parameters.

本文是利用整數分拆及排容原理研究以1x2 矩形鋪mxn 矩形的排法邏輯及總排法數，並進一步探討下列兩種情況：雙邊不含缺陷線及至少有一缺陷線的排法數。\r Based on the Apart of Number and the Inclusion- Exclution principle, this research intends to analyze the logic and final result of permutation by laying an 1x2 rectangle over an mxn rectangle. From the analysis, this study will go further to explore the possible permutation in the following two situations : when there is no fault line on both sides and when at least one fault line exists.\r

此研究以設計自動化發票對獎的系統（Award-checking System,簡稱ACS）為目標。架設網路攝影機拍攝發票上的數字，經由自製的二值化演算法、雜訊處理以及字元切割方法，將數字逐一取出，擷取影像中特徵向量，經過訓練完成的「支持向量機」模組判讀影像中的數字，進而對獎。其中為了達到自動化對獎的效果，以微控制器操控機械手臂翻取發票，與電腦端使用遠端程序呼叫的通訊協定，進行系統整合。 實驗後得知於此系統上，以顏色為依據的二值化方法之正確率為Otsu（最大類間方差法）演算法的2.88倍；且自製的光學數字字符識別（Optical Digital Character Recognition, 簡稱ODCR）較一般OCR(Optical Character Recognition)程式高出約18%的正確率。

本研究係使⽤快速傅⽴葉轉換對⾦屬圓板撞擊產⽣的⾳頻進⾏分析，並搭配⾃製的運算叢集，來實現使材料辨識系統。本研究為分析⾦屬圓版與其相關之物理量對⾳頻的影響，吾⼈透過 Journal of Sounds and Vibrations 中的⼀篇 “The Influence Of Poisson’s Ratio On The Natural Frequencies Of Free Circular Plates”之公式，配合⼤量實驗做為數據轉換的基礎，找出⾦屬的Ψ值，如鋁為0.15762、鐵為0.28921、銅為0.36213，最後將之整合，並提出以機器學習的⽅式優化材料辨識系統，⼤⼤提⾼本研究之未來發展性。

由於塑膠不能在自然情況下順利分解，所以我們在塑膠中添加其他成分使塑膠可以較易分解。我們選定常見的塑膠—熱塑性的耐綸-66。在聚合物的製作過程中添加葡萄糖、澱粉、洋菜粉末以及甲基纖維素，並觀察加入添加物的塑膠在結構上是否有變化？其塑膠在線型時之張力是否有增強？耐酸鹼性是否有變化？由實驗結果我們可以得知含有甲基纖維素之耐綸-66 所能承受之張力強度最高，且其彈性係數也比無添加物之耐綸-66 高出近2 倍；而含可溶性澱粉之耐綸-66 所能承受之張力最小，且彈性係數也最低。此外，進行生物分解的實驗可發現，含洋菜粉末的耐綸-66 分解的速率最快。使用400 倍的光學顯微鏡可發現含有洋菜粉末的耐綸-66 表面與其他耐綸-66 複合材料差異較大，值得進一步研究。;Because plastic cannot be decomposed naturally by itself, therefore, additives needed to be added to facile the decomposing process. Let us choose one common material: thermoformed Nylon 66. During the formation process, add the following additives: glucose powder, methyl cellulose, soluble starch and agar powder. Observe whether adding additives would allow changes to occur structurally, or would the elasticity be improved when exist in a linear state, or even it would form a better pH resistance property. Most importantly, observe whether the decomposing rate has increased or not. According to the experiments, when Nylon 66 contains methyl cellulose, it can sustain the highest tension. Its coefficient of elasticity is 2 times as large as the original one. In terms of the data, we can also observe that when Nylon 66 contains soluble starch, it has the lowest ability to sustain tension. Besides, it has the lowest coefficient of elasticity. And when Nylon 66 contains glucose, it has the highest rate in the process of decomposing. As we look at the surface of polymers under 400 diameters, we can observe that the Nylon 66 with agar powder has some filiferous substance. But we have not confirmed what the matter is. As to decomposing rate, we found that when Nylon 66 contains additives, it could accelerate its decomposing rate. And the one with agar powder has the highest rate of decomposing.

Modern capacitive touch input and proximity sensing technologies are rigid and limited to flat substrates making it impossible to apply them onto objects with irregular geometries like textiles or car handles. Furthermore, the high cost restricts the applications to small surfaces and cannot be scaled up to be applied on large surfaces such as walls. Therefore, a paint-on scheme would broaden the applications of capacitive touch input and proximity sensing devices. Paintable capacitive sensors are an emerging technology hindered by the high cost and lackluster properties of conductive paints. Existing conductive paints utilize expensive filler materials such as silver and gold to achieve high conductivity but suffer from low surface area. High surface area is critical for capacitive proximity sensors to detect objects from far distances and for overall sensitivity. Carbonaceous alternatives using micronized graphite exhibit low conductivity, require high loadings and most disintegrate when in contact with water. Multilayer graphene nanoplatelets are investigated for their high conductivity, high surface area, low cost, flexibility and eco friendliness. A waterproof acrylic latex is combined with multilayer graphene and dispersed via bath sonication. The optimal time of sonication and optimal graphene loading is determined through systematic testing. An Arduino Uno is loaded with a CapSense library and the graphene based paint is utilized as the interface to sense both touch and proximity.

這個研究起源於一個平分圓的問題：在平面上2n +1個點(n∈N)，其中任三點不共線，任四點不共圓，任取三點可以畫出唯一的圓，若一半的點在圓內，一半的點在圓外，則此圓為平分圓，Federico Ardila 教授在America Monthly 111 期[2]中發表了一篇論文，證明平分圓的個數為n2個。我們研究的目的是：如果將圓改成拋物線，則平分拋物線的個數是否為一定值? 若為定值，則為多少個? 我們的研究題目是：平面上2n +1個在正常位置上的點(n∈N)，平分拋物線的個數為何? 我們將研究的主要結果分述如下： 一、證明在平面上2n +1個點(n∈N)，平分拋物線個數為定值。 二、證明在平面上2n +1個點(n∈N)，平分拋物線個數為n2個。 接著推廣至：若平分拋物線改成(a ∨ b)拋物線，則個數為何? 我們將研究的主要結果分述如下： 一、證明在平面上2n +1個點(n∈N)，(a ∨ b)拋物線個數為定值。 二、證明在平面上2n +1個點(n∈N)，(a ∨ b)拋物線個數為2(ab + a + b +1)個。 This study originated from a question of “The Number of Halving Circles＂: Setting 2n +1 points in the plane is in general position if no three of the points are collinear and no four are concyclic. We call a circle halving with respect to those 2n +1 points if it has three points of those 2n +1 points on its circumference, n −1 points in its interior, and n −1 in its exterior. Then we call this circle “Halving Circle.＂ Professor Federico Ardila issued a paper in the America Monthly 111 [2]. The goal of that paper is to prove the following fact: any set of 2n +1 points in general position in the plane has exactly n2 halving circles. The purpose we make the study of is: If we turn circles into parabolas, how many Halving Parabolas are there? The title we make the study of is: Setting 2n +1 points in the plane (n∈N) , how many Halving Parabolas are there? We show our main effect below: 1. Proving that 2n +1 points in the plane (n∈N) , the number of Halving Parabolas is constant. 2. Proving that 2n +1 points in the plane (n∈N) , the number of Halving Parabolas is n2 . Spread: If we turn Halving Parabolas into (a ∨ b) Parabolas, how many (a ∨ b) Parabolas are there? We show our main effect below: 1. Proving that 2n +1 points in the plane (n∈N) , the number of (a ∨ b) Parabolas is constant. 2. Proving that 2n +1 points in the plane (n∈N) , the number of (a ∨ b) Parabolas is 2(ab + a + b +1) .

The purpose: To study the basaltic prisms to understand their formation. Tasks: To study chemical and mineral composition, textures and density of basalts of central and peripheral parts of prisms, to reveal the possible difference as a consequence of the formation of Benard sells. Basalt prisms have 6-5-4-face shape with a diameter 10 -50 cm and height of 30-40m. They are divided by transverse fracture in blocks of 20-50 cm. Prismatic jointing of basalts widespread throughout the world. There are many theories about its origin. We decided to collect data to identify the most appropriate of these. We suppose that if the hypothesis about the role of Benard cells is correct then the properties of basalt in the central and peripheral parts of the prisms must be different. If we consider the center of the prism as the center of the cell, where the hot matter rise, spreading out to the periphery and lower in the peripheral part, it is likely that the density of basalt forming in the center must be lower than at the periphery and later crystallization should lead to a slightly more acidic basalt in the middle. We determined the density of basalts of different parts of prisms. And the density of central part basalts was equal to 2.502g/sm3 and of peripheral part basalts was equal to 2.907g/sm3. X-ray fluorescence analysis showed that basalt of central part contain 12,91% Si and of peripheral part only 10,17%. Basalt of central part is depleted of Fe, Mn, Ti, Mg compared with of peripheral. We investigated samples and thin sections of basalts under the microscope MIN-8. For basalts of peripheral part flow texture expressed by the orientation of the microlites are characteristic. In the central part flow texture are poorly expressed but we can see many phenocrysts. Our data reveal a significant and expected difference between the basalts of central and peripheral parts of prism, that are the evidences in favor of the hypothesis about the role of Benard cells in the formation of basalt prismatic jointing.

Dye-sensitized solar cells (DSSCs) have cheaper and easier means of fabrication compared to the currently used solar cells, which are mostly silicon-based, so DSSCs are developed for a prospect of solar energy accounting for a higher percentage in the world’s total energy production, which is currently 0.1%. However, compared to their inorganic counterparts, their efficiencies are low, and the search for a dye that will maximize the potential of DSSCs is still ongoing. The aim of this study is to be able to evaluate the absorption range in the solar spectrum of dyes extracted from Basella alba leaves and Bixin orellana seeds, and of dyes resulting from the mixture of both extracts, using UV-Vis Spectrophotometer, with the objective of increasing the absorption; to be able to fabricate functional DSSCs from the individual and mixed dyes; and to be able to evaluate the different conversion efficiencies of the DSSCs of the individual and mixed dyes using Linear Sweep Voltammetry, with the aim of increasing the conversion efficiency due to a wider absorption range. B. alba leaves and B. orellana seeds were extracted using soxhlet extraction. The clean extracts were mixed in different proportions, and were characterized using UV-Vis Spectrophotometer. The two individual dyes together with two proportions of the mixed B. alba:B. orellana dyes, 1:1 and 2:1, were then incorporated into DSSCs. In the fabrication of DSSCs, twelve plates of Fluorine doped tin oxide were coated with titanium dioxide (TiO2) using spray pyrolysis. They were sintered and scraped, and were afterwards immersed in the four dyes for four days. Platinum plates were placed on top, and iodine-triiodide couple electrolyte was introduced via capillary action. The sealed DSSCs were subjected to Linear Sweep Voltammetry under dark and illuminated conditions, using a sun simulator. Results from the UV-Vis spectrophotometry showed that mixing the dyes had increased the absorption range of the individual dyes, although not superpositionally, and that the 2:1 mixed dye has the most potential. Being incorporated into DSSCs, the dyes, including the mixed ones, have successfully converted solar energy into electrical energy, as shown by the significance in conversion efficiencies under dark and illuminated conditions. However, despite the increase in the absorption range, neither of the mixed dyes have shown a higher conversion efficiency than the individual ones, which can be accounted for a possible weaker interaction between the two dyes and the TiO2, resulting to lower efficiencies. The study has been able to obtain and characterize dyes from B. orellana seeds and B. alba leaves and has been able to incorporate the dyes into DSSCs. With the wider absorption range of the mixed dyes, the study has been able to confirm the possibility of the dyes to maximize the potential of DSSCs, as shown by the successful conversion of solar energy into electrical energy of all fabricated DSSCs, including those of mixed dyes. If the possible problem with the dye-dye as well as the dye-TiO2 interactions could be solved, the possibility of much higher conversion efficiencies could be expected.

中文摘要 植物體在生長發育的過程中，有許多必要的營養素，一旦缺乏這些營養素，植物的生長 狀況會產生問題，不但會抑制植物生長，植物對外界的免疫力也會跟著下降。在台灣，水稻 不僅是台灣人賴以維生的糧食，更是台灣人引以為傲的作物。但台灣高溫多濕的海島型氣候， 適合多種稻作病害的發生，紋枯病及白葉枯病就是危害台灣稻作主要兩種病害。這些病原菌 的感染直接限制了該土地中植物的生長和生物的存活，間接的影響人類的生活。 本研究中，以水稻為實驗對象，我們主要探討六種水稻生長所必須的營養素：鈣、鎂、 鐵、鉀、氮、磷和水稻之間的關係。我們將水稻種植在缺乏某種特定元素的培養基中，觀察 其生長的異狀，以便於得知某特定元素對於水稻生長發育的影響為何。之後，再將缺乏各種 營養素的水稻及營養素供應正常的水稻，分別感染白葉枯病病原細菌及紋枯病病原菌，觀察 受感染的水稻之損傷程度，並檢測受感染植株中過氧化氫酵素活性的變化，試著歸納出其防 禦機制和營養素之間的關係，期望對其防禦機制能有進一步的了解。 英文摘要(Abstract)\r When plants grow up, there’s a lot of necessary nutrition. Once plants lack of this nutrition, some problems will occur. It can cause plant growth retardation and decrease the immune ability to the surroundings. Rice is a main cereal in Taiwan, and we are all proud of it. However, rice is frequently attacked by many pathogens , such as Xanthomonas oryzae pv. oryzae and Thanatephorus cucumeris. The infection directly limits plant growth and survive of organisms, but also indirectly effect life of human. In this research, we study the effect of nutrition deficiency such as nitrogen , phosphorus, potassium, iron , magnesium and calcium deficiency. First , we cultivate the crops on the media which lacks of some specific nutrition. After intensive observes on the plants, we can slightly discover the relationship between these nutrition and the plants. After the plants are infected by the pathogens (X. oryzae pv. oryzae and T. cucumeris) in two weeks, we record the spread of the lesion size resulted from the infection. The changes of Peroxidase activity after infection are also studied. We hope we can get a deeper understand about the immune system of rice.

The aim was to determine whether there is an amount of gyroscopic force that keeps a bicycle wheel upright and stable. Two hypotheses were used, the first being as the mass of a wheel increases so does the force required to tilt the wheel by thirty degrees and the second that as the speed at which the wheel is spun increases so does the force required to tilt the wheel.

我們想要了解過號看診等候的相關問題，在此研究中，我們先利用手繪 圖及電腦驗證找出「分段法則Ⅰ」，進而導出遲到情形與過號需等候人數的函數關係。 利用方格「走最短路徑」的方法，將到診情形轉為方格走最短路徑圖，找出「分段法則Ⅱ」，求遲到者插號位置及新的看診序號，並由等待數列，求過號需等候人數。 在一個獨立插號作業中，要找出到診可能情形方法數，我們將Catalan數列的條件加以變化，在一個 的方格內，向右走 單位長，向上走1單位長， ，證明其一路領先的方法數為 。 最後將取號碼單機器運用在候診上，並利用等候理論(Queueing theory)，做不同插號規則的比較。