本研究源於 2016 年數學雜誌 Crux Mathematicorum 的一個三角形定性問題[1]，我們將這個問題進行推廣且創新探討其定量與定性性質。我們先討論任意三角形與任意凸四邊形、凹四邊形，分別針對不同連線情形下的兩個衍伸圖形的有向面積之和與有向面積之差進行完整討論，再巧妙利用平移不變性處理行列式級數和，最後給出一般化的不變量關係式與刻劃其幾何意義。此外，我們也特殊化探討其衍伸圖形恆為正三角形、正方形等有趣優美的定性性質。最後，系統性推廣到平面上任意封閉的凸四邊形、凹多邊形，先給出不同連線方式之間的重要輪換對稱性質，再分為奇多邊形與偶多邊形進行討論而得出任意連線構造的衍伸圖形之有向面積不變量的一般式。

In this project, we evaluate the effectiveness of Random Shuffling in the Cross Lingual Information Retrieval (CLIR) process. We extended the monolingual Word2Vec model to a multilingual one via the random shuffling process. We then evaluate the cross-lingual word embeddings (CLE) in terms of retrieving parallel sentences, whereby the query sentence is in a source language and the parallel sentence is in some targeted language. Our experiments on three language pairs showed that models trained on a randomly shuffled dataset outperforms randomly initialized word embeddings substantially despite its simplicity. We also explored Smart Shuffling, a more sophisticated CLIR technique which makes use of word alignment and bilingual dictionaries to guide the shuffling process, making preliminary comparisons between the two. Due to the complexity of the implementation and unavailability of open source codes, we defer experimental comparisons to future work.

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divisor of 1st degree polynomial; finally, a programme to solve binomial equations for the power s∈Q. This website was originally made so that Max Gold could improve his programming skills for GCSE computer science but expanded to incorporate his passion for chemistry and maths and thus allow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.

本研究的腦波辨識基於特徵提取，可應用於身分認證，具有不能被仿冒的優點。我們用低成本高便利性的腦波儀，自行撰寫程式讀取原始腦波，建立一致性的實驗程序。首先用腦波專心度的高低來控制智能車，再用腦波來測謊，有隱藏說謊行為時會觸發高電位腦波，在兩項前期研究後發現可用腦波特徵進行身分認證。三位受測者於不同日期提取10份腦波，每份腦波紀錄5120筆數據。接著我們反覆嘗試組合數十種統計函數進行特徵提取，找到兩項最佳特徵，達成將大量凌亂腦波資料降低維度又具有辨識力。我們腦波辨識分類方法使用近鄰演算法，測試程序用盲測交叉驗證法，辨識正確率百分百。最後我們用Arduino板來展示腦波辨識應用於腦波身分認證，資料庫中只要儲存每位受測者的腦波特徵值，就能在數秒內正確辨識說出受測者身分，顯示每個人腦波是不同的，而且能用特徵將其分辨出來。

Swimming pools are one of the transmission routes of superficial and cutaneous fungal infections. Maintenance of environmental hygiene in different parts of swimming pools is of great importance, especially the hygiene of water (1). The conventional fungal detection methods include direct smear preparation, culture, and pathological examinations. However, these methods are not fast enough or do not have sufficient sensitivity (2). Therefore, the present research introduces a novel method for detecting Aspergillus niger in pool water through creating optimal conditions for this fungus, which leads to the citric acid production by the fungus and pH changes of the related culture medium. Four experiments in 10 steps were performed to find the optimal conditions for fungal growth. According to our results, adding each of the variables sucrose, soy, and ferrous sulfate can lead to favorable results. Moreover, the shaker speed increase and fungal aeration are important. Also, we showed that soybean led to the best results compared to other variables. Considering the obtained results, including the shortened detection duration and cost-effectiveness, this method can be presented to the swimming pool owners and pathobiology laboratories as the method of choice for Aspergillus niger detection.

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.

Nowadays, cooling open spaces in hot seasons without using fossil fuels has gained a lot of attention. In this regard, natural air conditioning is a great method for conserving energy that can be used for reducing energy consumption and environmental pollution. Structures like windcatchers are used for natural air conditioning as a building component in warm climates since they are placed in the path of the wind and direct the wind to play a significant role in reducing the temperature. The main objective of the current study is to explore air conditioning in open spaces based on sustainable architecture. The current study reviews the relevant literature from credible journals, and it includes studies with relevant subjects published from 1851 to 2021. The findings show that implementing this design project can result in significant advances in terms of reducing humidity, removing dust and insects from the air, conserving energy, reducing the global temperature, using renewable energies, and producing conditioned air for the area

高斯光束(Gaussian beam)穿過透明液體時，對液體局部加熱，使液體有溫度梯度，伴隨著產生折射率梯度。葉綠素-a(Chlorophyll-a)乙醇溶液對紫光的熱吸收率為乙醇的數百萬倍，橄欖油的葉綠素-a含量很高，利用高斯光束照射橄欖油時，橄欖油吸收的大量的熱量產生折射率梯度，以及產生熱透鏡(Thermal lens)和自調相(Self-phase modulation)現象。 以雷射光照射橄欖油，由於熱透鏡現象使光束擴張成大亮點(半徑R)，由於自調相現象使光束在屏幕上產生繞射圖樣(繞射亮紋數目N)。圓柱筒裝橄欖油(液柱長度a)，用不同功率的雷射照射橄欖油，探討吸收的熱量對R和N的影響。另外使光束先經凸透鏡聚光再照射低熱吸收率的色素水溶液做對照比較。

目前水冷散熱系統普遍應用在電腦CPU降溫中，雖然水的「比熱容」比空氣及大部分介質都高，但因水冷散熱系統內冷卻液的熱量，最終仍靠風扇送到機殼外，故CPU之最低溫度仍存在一個臨界值。本研究旨在對於「一體式」與「分離式」電腦水冷散熱系統及「熱電致（製）冷晶片」（Thermoelectric Cooling Module）結合進行模組開發設計，將此兩類相關元件搭配結合，以突破傳統水冷式散熱所無法降達的溫度。本研究將「致（製）冷晶片」之致冷端及水冷系統作結合，利用致冷端作為吸收CPU主要熱量，結果發現：與單純只利用風扇將熱量帶走的方式相比，本研究所開發之『第一代』一體式散熱模組與『第二代』分離式散熱模組皆成功地將頂級CPU之工作溫度再壓低，使電腦工作效率維持在最佳範圍。

Due to having Asperger's syndrome, I want to make a pressure vest suitable for hot and humid climates like Asia to help reduce the daily anxiety of children and adults with autism, ADHD, sensory disorders, etc. To solve this problem, I first tried using a porous material. But after seeing a pressure vest in person, I found it to be useless. Therefore, I came up with the idea of creating an active airflow cooling system between the body and the pressure vest. To experiment, I wanted to make pressure vests. However, I found that a high-frequency TPU welding machine is required. Thus, I made models of pressure vests using airbags, water-resistant nylon, and quick-drying fabric. I also made models, which came from sandwich fabric. Through this research, I discovered that the sandwich fabric design has the best passive heat dissipation, and the combination of the sandwich fabric and the active airflow cooling system has the best active heat dissipation.

目的：在台灣，胰臟癌雖非癌症發生數最高，但85%為末期，五年存活率小於5%，有癌王之稱。如何早期偵測胰臟癌風險，一直是醫療上的重大議題。本研究運用時間矩陣搭配深度學習進行大量變數之胰臟癌風險偵測。 方法：健保資料庫收集國人疾病、用藥等結構化資料，可藉此反映每人健康狀態。將三年內診斷與藥物碼轉為時間矩陣，以卷積神經網路訓練，訓練組與測試組比例為9:1。 結果：共計案例組1095名及對照組10950名，訓練後測試組表現之AUROC(area under the receiver operating characteristiccurve)為0.937，六十歲以上及以下AUROC分別為0.846及0.897。 結論：結論：能將診斷、藥物、時間轉成矩陣，是以疾病軌跡預測胰臟癌風險，且能找到新特徵，未來搭配健康存摺，為低成本、快速、大量的胰臟癌數位快篩。

Currently, no method can completely eliminate the human immunodeficiency virus (HIV) in an infected person. HIV employs an accessory protein called Nef that forms a complex with cellular AP-1, preventing detection of HIV-infected cells. Lovastatin has been recently identified to inhibit the formation of said Nef-AP-1 complex, but its effective concentration is remarked to be far higher than other Nef inhibitors. This study aims to develop a modified lovastatin molecule exhibiting higher binding affinity to the HIV-1 Nef protein than lovastatin in silico. Modified lovastatin molecules based on the interaction map of lovastatin with Nef were modeled, and flexible ligand-flexible receptor docking to the Nef binding site was performed using AutoDock Vina. Residues within the Nef binding site identified by Liu et al. (2019) to be crucial (Glu-63, Val-66, Phe-68, Asp-108, Leu-112, Tyr-115) were set as flexible. Fragment-based drug design was utilized to append molecular fragments to lovastatin in order to maximize its interactions with said crucial residues. From the fragment-based approach, molecule F4 ((1S,3S)‐8‐{2‐[(2R,4R)‐4‐chloro‐6‐oxooxan‐2‐yl]ethyl}‐3‐(hydroxymethyl)‐7‐methyl‐1,2,3,4‐tetrahydronaphthalen‐1‐yl 4‐aminobenzoate) exhibited a binding affinity of -9.0 kcal/mole, and its estimated IC50 ranges between 0.25-0.51 μM which is at least 7.5 times lower than the reported IC50 of lovastatin from literature. This study presents insights on the key modifications to improve lovastatin as an HIV-1 Nef inhibitor and pertinent information about the Nef binding site for future drug development studies.