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，以真菌生長率、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。

方形盒盛透明液體，置放在冷源上方，液體發生熱擴散時，溫度由上往下逐漸下降，形成溫度梯度以及折射率梯度。雷射光照射和鉛直線成一定角度的玻棒透鏡，再穿過方形盒的透明液體時，在屏上形成斜直線，經一段時間的熱擴散後，變成曲線；曲線和斜直線的距離(h)，隨著時間(t)以及光線照射的位置(y)改變，作不同y的h-t圖可得知液體的熱擴散率狀況。 冷源的溫度0℃，分別用甘油和乙醇作待測液，得到的h-t圖，符合熱擴散推導出的h隨t改變的方程式；改用水當待測液，得到的h-t圖，就不符合熱擴散推導出的h隨t改變的方程式。改用-5℃的冷源，分別用水和氯化鈉水溶液作待測液，得到的h-t圖，不符合熱擴散推導出的h隨t改變的方程式。 用簡易的設備可以了解折射率梯度，溫度梯度，熱擴散率，以及液體的非線性熱擴散。

An isosceles set is a collection of points in which any subset of three points forms an isosceles triangle. We want to find the upper bound for the size of isosceles sets in any n-dimensional Euclidean space. Kido has already completed the study of isosceles sets in 3 and 4-dimensional space. We study the upper bound of spherical two-distance sets, a special type of isosceles sets, to help us find the upper bound of isosceles sets. More specifically, Musin’s Linear Programming technique on spherical two-distance sets could be used to study isosceles sets if a consistent relationship between isosceles sets and two-distance sets can be characterized. We offer a conjecture of this relationship. We also offer non-trivial lower bounds of isosceles sets in dimension 5 with 17 points and dimension 7 with 30 points as examples.

Technology is erratic. We never know what could be the next big thing. Nowadays, IoT (the internet of things) has taken over the market. Every technology created nowadays is somehow related to IoT. You should manage to connect the IoT technology with a robust area of hospitality. Catering customers' needs during peak hours at any restaurant or cafe could get overwhelmed with hectic tasks such as taking orders, fetching water, and ordering meals. We created a raw model to accommodate the limitations of the human mind. The technology-based IoT (Internet of things) can come in handy during hectic sessions. A Robot waiter is built from scratch using materials like Arduino (2), Gear DC motor (2), L298N motor driver (1), Ultrasonic sensor (2), IR sensor (2), Servo motor (4) HC-05 Bluetooth module. Desired orders are sent on a wireless network through the menu bar to the kitchen. Then, the robots transfer the food from the kitchen to the customers. The floor will be all white, while there will be a strip of black line to connect every sitting and the kitchen. For instance, if table number three is to be served, we click the number three in the app, which renders an obstacle in table 3. The motor barricades the robot, and the ultrasonic sensors sense it, and it stops. If anyone picks the plate, the ultrasonic sensor senses it, the blockage is removed, and the robot paces in the designated path. People visited the place more often to experience such stimuli. Using the robots attracted more customers and made the work very quick.

本作品研究星狀網路和完全網路，兩種不同結構的連結網路，使用點擴展運算結合成一個網路結構，並且在一定的容錯範圍內，保證存在漢米爾頓迴圈性質。漢米爾頓迴圈在連結網路的研究中相當重要，若存在此性質，則可以保證發送訊號時，能將訊號發送給連結網路上的每一個元件並接收，且不會重覆接收到訊號。我們使用圖形理論的方式，將星狀網路和完全網路，這兩種連結網路結構，分別抽象化成星狀圖和完全圖，網路中的元件抽象化為點，元件之間的連線，抽象化成邊。如果元件之間的連線故障，無法使用，則稱為壞邊。我們證明 n+1 維度星狀圖和 n 維度完全圖使用點擴展運算後，壞邊數量最多是 n-4 時，保證存在漢米爾頓迴圈。

Harmful microorganisms in food can cause deterioration of human health, poisoning and in some cases even death. Especially fresh meat and chicken products create a suitable environment for the growth of microorganisms in terms of the nutrients it contains, water activity and pH level. For this reason, detection of microorganisms in meat products is an important issue in terms of food safety and human health. In this project, it is aimed to detect live microorganisms in meat products, especially chicken meat, in a simple, non-destructive, non-contact and fast way using laser speckle method. Laser speckle images of healthy and stale chicken meat were taken, contrast parameter and correlation analysis of the obtained patterns were made. It was observed that the contrast parameter for staled chicken meat increased by approximately 3 times compared to fresh chicken. This increase provides an understanding of the difference between contaminated chicken and fresh chicken. Speckle density changes over time in relation to the movements of living microorganisms. Thus, the correlation in laser speckle density patterns taken from contaminated tissues is disrupted. In the measurements taken with photodiode, by analyzing the change of light intensity of the speckle patterns on fresh and contaminated tissues over time, the detection of microorganisms was made easier and more precisely without the need for image processing. The proposed measurement system is a new method that detects meat contamination with laser speckle imaging. It can be developed and made portable and can be used easily in homes. Since it is a simple, non-destructive and fast method, it can be used to determine the shelf life of meat in food distribution places and markets. In addition, it has the potential to be calibrated and used for other food products other than meat products. The system developed with this study is cheap and easy to use, and the laser speckle imaging method is used in a different field other than biomedical, contributing to the literature.

本研究利用海冰覆蓋面積的變化、北極震盪指數(Arctic Oscillation index, AOI)和南方震盪指數(Southern Oscillation index, SOI)的相關性，希望可以探討與聖嬰現象的關聯。 取用1950年到2020年的海冰覆蓋面積資料及195!年到2020年的SOI及AOI資料。我們將AOI和SOI做折線圖、X-Y圖，數據分成平常年、聖嬰前、聖嬰時、聖嬰後、反聖嬰前、反聖嬰時、反聖嬰後，試圖找出一些規則。利用區間分析來觀察區間範圍大小及上下界的數值隨不同事件發生的次序，探討各個事件的特徵。 聖嬰年時，區間縮小，反聖嬰年則區間略為放大且數值上升。最後將1997年聖嬰年的數據和區間做疊圖，並以2018年底到2020年的聖嬰轉反聖嬰來做驗證。若AOI的區間縮小、或海冰覆蓋面積下降後上升，表示可能是聖嬰現象要來的前兆。此外，本研究也發現，無法單獨區隔聖嬰年和反聖嬰年，兩者間會相互影響，應該要把聖嬰跟反聖嬰合併為一個氣候變化週期，才能做準確的預測。

Max Gold's project, titled “Solving Mathematical and Chemical Equations using Python”, is a website comprising of 4 main programmes: one to find the smallest possible combination of two chemical compounds or elements; a self-made parsing function to convert a chemical equation into a matrix, then using Gaussian-Jordan elimination to find coefficients for an equation; a programme to parse a mathematical expression and use that parsed expression in algebraic division of an algebraic dividend of nth degree polynomial by a divisor of 1st degree polynomial; finally, a programme to solve binomial equations for the power s∈Q. This website was originally made so that Max Gold could improve his programming skills for GCSE computer science but expanded to incorporate his passion for chemistry and maths and thus allow others to use these programmes to help them with their problems as well. A problem with many conventional calculator websites is their lack of specificity – they tend to be able to compute some functions but not all. These programmes are tailored to GCSE and A level maths and chemistry, meaning this website provides an outlet to compute specific topics of problems.

本文主要在探討平面幾何學中的兩個重要結果—三角形中的『Menelaus定理』與『Ceva定理』推廣到任意的『球面n邊形』的相對應結果，對於任意的球面n邊形，我們分別找到了『球面n邊形的Menelaus共線定理』與『球面n邊形的Ceva共點定理』的一般化結果。

This work is devoted to solving the problem of orientation in the space of visually impaired people. Working on the project, a new way of transmitting visual information through an acoustic channel was invented. In addition, was developed the device, which uses distance sensors to analyze the situation around a user. Thanks to the invented algorithm of transformation of the information about the position of the obstacle into the sound of a certain tone and intensity, this device allows the user to transmit subject-spatial information in real time. Currently, the device should use a facette locator made of 36 ultrasonic locators grouped in 12 sectors by the azimuth and 3 spatial cones by the angle. Data obtained in such a way is converted into its own note according to the following pattern : the angle of the place corresponds to octave, the azimuth corresponds to the note and the distance corresponds to the volume. The choice of the notes is not unambiguous. However, we used them for the reason that over the centuries, notes have had a felicitous way of layout on the frequency range and on the logarithmic scale. Therefore, the appearance of a new note in the total signal will not be muffled by a combination of other notes. Consequently, a blind person, moving around the room with the help of the tone and volume of the sound signals, will be able to assess the presence and location of all dangerous obstacles. After theoretical substantiation of the hypothesis and analysis of the available information, we started the production of prototypes of the devices that would implement the idea of transmitting information via the acoustic channel.

Max Gold's project, titled “Solving Mathematical and Chemical Equations using Python”, is a website comprising of 4 main programmes: one to find the smallest possible combination of two chemical compounds or elements; a self-made parsing function to convert a chemical equation into a matrix, then using Gaussian-Jordan elimination to find coefficients for an equation; a programme to parse a mathematical expression and use that parsed expression in algebraic division of an algebraic dividend of nth degree polynomial by a divisor of 1st degree polynomial; finally, a programme to solve binomial equations for the power s∈Q. This website was originally made so that Max Gold could improve his programming skills for GCSE computer science but expanded to incorporate his passion for chemistry and maths and thus allow others to use these programmes to help them with their problems as well. A problem with many conventional calculator websites is their lack of specificity – they tend to be able to compute some functions but not all. These programmes are tailored to GCSE and A level maths and chemistry, meaning this website provides an outlet to compute specific topics of problems.

This paper represents IOT Based Automatic Water Temperature Adjustor. IoT (Internet of Things) refers to the network of physical objects that are embedded with sensors, software, and other technologies for the purpose of connecting and exchanging data with other devices and systems over the internet. This system is for adjusting water temperature according to the possible surroundings such as home temperature, atmosphere temperature, etc. To solve problems like high water temperature while using, time-consuming waiting for water to heat and cool, high power consumption, and not satisfying water temperature this system offers the feature for automatically adjusting the temperature. Arduino, DHT11 (Temperature-Humidity Sensor), Bread Board, DS18B20 (Water Temperature Sensor), Jumper Wires, Resistor, I2C OLED, Water Heating Coil, Relay and LED are used for operating this system. The application of this system is very vast as it can be implemented in power plants, hospitals, mountain regions, local homes, and lodges. This system is time-saving, cost-efficient, easy to implement, provide automatic features, less power consumption, safety, and many more. Compared to other water geyser systems it has the feature of automatically detecting the environmental temperature and adjusting the temperature of the water accordingly. This system is still in its developing phase.