研究在一三角形上，要分配P、Q、R三點分別在頂點或三邊上(不可在同一邊，在同一邊則未能達到最好分工效率)，P、Q、R三點所負責的區域為「距離最近則劃分給誰」，要如何定位才能使P、Q、R三點負責的面積一樣大。我們先依序從正三角形、等腰三角形、等腰直角三角形、直角三角形以及特殊角度的順序做起。我們在交點上設幾個參數，找出重要交點作標，在計算的過程中用Mathematica找出參數解，最後再用多邊形面積公式計算區域面積找出解，並利用GSP作圖模擬。

This study completes an air vibration equation expressed wind speed slope and wind speed. First, preliminary experiments identified air vibrations when wind speed differences occurred over distance. Several air fans were connected in series and the rotational speed of the air fan was adjusted to vary the wind speed with distance. At this time, only certain pendulum oscillates during a particular wind speed slope. It was expected that the pendulum would shake because the frequency of the air due to the slope of the wind speed was equal to the natural frequency of the pendulum. In addition, relatively short pendulum swings in large wind speed slope, long pendulum swings in short wind speed slope. After calculating the natural frequency of the seasonal growth of fruit using the physical factors model, we experiment how resonant frequency was related with cone length, angular width, wind speed, velocity and secondary derivative. the actual experiment analyzed the natural frequency of the fruit and resonance from the air vibration as the linear function of the wind speed, velocity, and secondary derivative. The experiment determined that the pendulum of a specified number of frequencies resonated with a particular wind speed pattern. It is judged that the vibration of air is related to first derivative of wind speed depending on speed and distance. However, it is very difficult to express the flow of nonlinear fluids as a function of simple function, particularly the effects of air vibrations caused by wind speed second derivative, which appeared to be associated with forces. This is a task that needs to be solved through further research.

Visual impairment is a major global health problem. In 2017, WHO estimated that there were 253 million people worldwide with this ailment. According to the journal of the American Medical association, the prevalence of visual impairment in the Saudi population is 9.3%. Learning Braille by families of students with visual impairments remains a major obstacle, which precipitates several communication issues. Moreover, difficulties for the students themselves lie in learning braille with languages that include diacritical marks; consequently, affecting their academic progress. My main objective of this project is to help improving life quality of these individuals, and the focus is to advance their social productivity and adaptation. This was accomplished through creating a new simpler Arabic writing system using geometrical shapes. As a part of this project, fifteen participants with visual impairments were interviewed and tried this new writing system; two of them are adults between 25 and 40 years old while the rest are students from 9 to 17 years old. Additionally, 100 participants with visual impairments completed a survey. The data showed that students learned this system in two hours in comparison with students that mastered braille in a few months. This shows that this system is easier to learn and subsequently saves time and effort. The most important value added to this project is that diacritical marks were combined with the alphabet, thereby considerably reducing book sizes compared to Braille-written books. This project presents a novel system that helps people with visual impairments to increase their confidence and independence.

Saccharomyces cerevisiae 是常用來研究老化的模式生物。S. cerevisiae的壽命稱為replicative lifespan (RLS)，被定義為母細胞一生中可產生的子代總數。S. cerevisiae有一種缺少整套粒線體DNA的突變種，稱為petite。在這個研究中，我們利用附解剖針之複式顯微鏡測量年輕單倍體細胞和老單倍體細胞形成的合子、年輕單倍體petite細胞和老單倍體細胞形成的合子之RLS。此外，我們也使用ROS螢光探針DCFH-DA及DHE測量不同單倍體細胞的ROS含量。實驗結果顯示ROS本身並不足以降低合子的壽命。本研究可為人類生殖細胞影響受精卵的機制提供有用的資訊。

Pests can ruin every healthy tree’s crop within 10-15 days. This huge loss can only be detected at harvest season. If the pests have already got inside the fruits or the fruits had fallen down prior to the time of harvest. If pest-control is unconscious, 50-75% loss may occur. In Szabolcs-Szatmár-Bereg county the most common fruit production is apple. Codling moth can cause significant damage to the crops. Codling moths damage the apple directly and they are expected during the whole year. If there are signs of any nuisance we are not able to protect the crops anymore, because in this case they protect themselves from chemicals. The most important part of protection against pests is prevention. Protection can be successful thanks to insects killers and expert’s prognosis. Pheromone traps developed against wrong-doers are very practical. They are easy to use, but the problem is that the manufacturer has to check these traps repeatedly to find out about the infection, and when one has to spray the trees with the right chemicals.

本研究主要探討塔粉綠尺蛾食草選擇與其葉內真菌之關係。觀察培養四種植物（烏臼、鵝掌柴、白匏子與島榕）葉內真菌，以真菌生長、菌絲與孢子形態辨識真菌種類。當我們以烏臼葉內間座殼菌屬（Diaporthe sp.）真菌與不同植物放在一起時，幼蟲有取食原為非食草的白匏子葉片，而島榕則有嘗試啃食之現象；此外，飼養過程中我們發現取食烏臼的塔粉綠尺蛾幼蟲糞便較其他種幼蟲易長出真菌，進行幼蟲糞便與消化道真菌培養後，皆有與葉內真菌相似的菌體形態。我們推測烏臼、葉內真菌與塔粉綠尺蛾間的交互作用關係之一可能為：烏臼透過葉內真菌誘使塔粉綠尺蛾雌蛾前往產卵，經幼蟲食用葉片後所排出之糞便以作為葉內真菌傳播的媒介。

在種子萌發的階段，光會造成幼苗的形態變化，稱為光形態發生(photomorphogenesis)。然而microRNA (miRNA) 如何影響光形態發生，一直未被詳細探討。藉由次世代定序 (Next Generation Sequencing)之結果分析，得知阿拉伯芥 (Arabidopsis thaliana) 幼苗中，具有受光調控的miRNA。利用北方墨點法 (northern blotting) 及即時聚合酶鏈鎖反應 (Real-Time PCR) ，我們驗證了miRNA和其降解目標之相關性。在篩選過後選得miR396s和miR858s，作為後續研究的目標。下一步便是了解他們的功能。目前已經證明miRNA及對應目標基因的突變株確實會影響花青素、葉綠素累積，下胚軸延長及子葉發育。考量到miRNA有功能性的替代物 (functional redundancy) ，我們於是進行標的序列模擬(target mimicry) ，以削減miRNA之功能；也在建立大量表現上述miRNA之轉殖株，了解其與光形態發生之關聯。最終目標為解開miR396與miR858對光形態發生的調控機制。

A simple and cheap bubble film experiment system was constructed by us. Although it is simple, it can observe the phenomenon similar to those observed in the wind tunnel system or PIV system. But because of gravity, bubble film become a little more complex. We programed some codes to analyze the data and showed bubble thickness is proportional to the Reynolds number. The low frequency sound can make bubble film rotate. And we also study the wing’s attack angle, from 0 to 75 degree with interval of 15 degree, discovering the 15 degree is the best flying attack angle.

本研究是將梅齊裏亞克的砝碼問題( The Weight Problem of Bachet de Meziriac )，由等臂天平延伸至不等臂天平。 若i、k、m與n皆為正整數。首先在等臂天平中，討論k磅砝碼摔成i塊其解是否存在？是否有唯一解？並試圖找出通解的一般式。使用列舉的試誤法，之後設計視覺直觀的數學實驗程式，找出數學式，歸納出解的一般式。發現可以使用變形三進位的方法來決定符合解的砝碼。接著將等臂天平延伸到1:n不等臂天平。在1:n不等臂天平中，先找出所有解的組合，再找出最常出現幾組的不可稱解的最大可稱磅數、規律、性質與一般式。最後希望可以利用1:n不等臂天平的不可稱一般式推廣到m:n不等臂天平中。

鹵氧化鉍是第三代太陽能電池的材料，受到極高重視。鹵氧化鉍和g-C3N4皆為可見光光觸媒，將其彼此複合可增加其活性。研究利用水熱法 (hydrothermal method) 在高壓釜 (autoclave) 中合成三元鹵氧化鉍及其複合物 (BiOxCly/BiOmBrn/BiOpIq、BiOxCly/BiOmBrn/BiOpIq/g-C3N4)，成功做出鹵氧化鉍的一系列化合物，並檢測其特性。三元鹵氧化鉍及其複合物是可見光驅動之光觸媒，因此將其降解結晶紫染料(Crystal Violet, CV)來評估其活性。在pH值為1與4時觸媒樣品光生電子電洞的重組率較低，此對於降解效率有益。在沒有複合g-C3N4的情況，BC1B1I1-4-100-12樣品降解結晶紫的效率最為理想。而在pH值為10且有複合的情況，BC1B1I1-10-100-12-10wt%g-C3N4樣品降解結晶紫的效率最為理想，其光催化降解效率增為1.8倍。因此，複合光觸媒可增加降解效率，更有效處理紡織與染整等有機廢污水，大大減少廢污水的污染。

The 3D printer that we created is able to print objects out of concrete and is modular, so it can be assembled the way it is needed.

The cost of damage caused by hurricanes in 2017 is estimated to be over 200 billion dollars. Quick and accurate prediction of the path of a hurricane and its strength would be very valuable in alleviating these losses. Machine learning based prediction models, in contrast to models based on physics, have been developed successfully in many problem domains. A machine learning system infers the modeling function from a training dataset. This project developed machine learning based prediction models to forecast the path and strength of hurricanes in the North Atlantic basin. Feature analysis was performed on the HURDAT2 dataset, which contains paths and strengths of past hurricanes. Artificial Neural Networks (ANNs) and Generalized Linear Model (GLM) approaches such as Tikhonov regularization were investigated to develop nine hurricane prediction models. Prediction accuracy of these models was compared using a testing dataset, disjoint from the training dataset. The coefficient of determination and the mean squared error were used as performance metrics. Post-processing metrics, such as geodesic error in path prediction and the mean wind speed error, were also used to compare different models. TLS linear regression model performed the best of out the nine models for one and two time steps, while the ANNs made more accurate predictions for longer periods. All models predicted location and strength with greater than .95 coefficient of determination for up to two days. My models predicted hurricane path in under a second with accuracy comparable to that of current models.