我們研究的問題源自於〝棋盤上的蛇〞(Snakes on a chessboard) ，是由教授Richard Stanley所提出。問題如下：在 棋盤形格子上，蛇由任意一格出發，但蛇的走法只能往右→，往上↑，或停住。若此蛇已停住，將由另一條蛇來走，且不同蛇走過的格子不可重疊。證明：將 棋盤形格子完全覆蓋的總方法數為費氏(Fibonacci)數列某些項的乘積。 我們以〝生成格〞概念來解決問題，藉由生成格建立二維棋盤形格子〝蛇填充數〞與費氏關係，並試圖拓展三維空間棋盤情形，在過程中發現藉由〝生成矩陣〞可以組成空間棋盤的〝生成格〞，並以此解決p×q×r的空間棋盤問題。 2022年9月，在網站The On-Line Encyclopedia of Integer Sequences上發現由教授 Greg Dresden及其學生Aarnav Gogri提出的數列，與我們2022年3月於高雄市發表的科展作品中的一組數列完全對應，甚而對此數列的原問題Tiling a Hexagonal Strip with Triangles and Diamonds，我們的作品還能做進一步延伸探討。

在先前的研究中，特定的格點多邊形如正方形與直角三角形曾經被探討過。任意格點多邊形性質被歸類於資訊研究，目的為用程式估計當範圍很廣或邊數很多時格點多邊形性質的數值解。 先前研究中，作者已針對格點多邊形的性質進行初步的探討，本研究進一步補足先前研究的缺陷：用數學化的方式探討格點多邊形的邊數最大值。研究當中探討的多邊形包含凹多邊形及凸多邊形，研究者改良先前研究中的「迂迴作圖法」，提出新的「對稱作圖法」，以「定義基本構形、先作短邊、再作中間」的順序，確保必定可在特定範圍內建構出符合最大邊數解的格點多邊形；並以數學歸納法證明當矩形範圍短邊為12單位以上時，必存在格點數與邊數相等的格點多邊形，達成重要的突破。 本研究推導出格點多邊形的邊數最大值如下式。運用本研究的結果，將有助於在有限區域或空間中依照特定規律設計最大路徑，例如遊樂場迷宮、駕訓班車道、或積體電路設計。 S(n,m)={█(4 {if n=1∨m=1}@3n+1 {if n=2∨m=2}@24 {if m=n=4}@(n+1)(m+1) {otherwise})┤

In this project, we created a function integrated onto a Lingao Chassis that allows the robot to use Slam and Gmapping to successfully navigate its way to the most convenient destination for the user, while avoiding any obstacles on the way, improving the default Gmapping errors.

2023年9月數學雜誌《Crux Mathematicorum》刊登有趣的三角形內心的幾何問題，我們先證明了原命題的長度性質，再創新刻劃出有趣的面積不變量。隨後將內心推廣到旁心、垂心與外心的建構，並且證明僅此四心的建構下才有長度與面積不變量。值得一提的是，除了前述的定量項目外，我們也發現四種建構下的三線共點之定性性質，同時刻劃四種建構的關聯性是漂亮的等角結構，這是本研究亮點。推廣到多邊形，我們發現本質的幾何結構為截線的角平分線性質（內心與旁心的結合），從而將此問題轉換成一般性問題，並給出了豐富的等長、等角、等面積之性質，以及連線多邊形恆為圓外切多邊形。

Electricity has become an essential part of modern life, powering homes, businesses, and industries. However, the misuse of electricity or malfunctioning electrical systems can lead to hazardous situations such as electrical fires, shocks, and significant energy wastage. This project focuses on creating a Comprehensive Electrical Security System to protect users and properties from the risks associated with electricity. The system is designed to prevent electrical malfunctions, ensure safety in various scenarios, and monitor energy consumption effectively. It integrates a variety of sensors and safety mechanisms to detect dangers and take preemptive action

Aim: The aim of this study is to make a disease-predicting model trained on data from weather stations and API using machine learning that gives the farmer the ability to predict crop diseases before they set in, allowing them to take timely preventative measures and reduce wastage. Materials and Methods: In this study the Internet of Things (IoT) sensors throughout agricultural fields of potato crops in Jafferabad, Depalpur Punjab. The sensors collect real-time data on environmental conditions, such as precipitation, air temperature, relative humidity, wind speed, and direction, Dew Point, VPD, and the Delta T values, to identify subtle disease indicators and patterns within the environmental data. Our novel machine-learning program makes use of the data collected by the weather station and analyses them. Results: Using the data, one predictive statistical method using Python 3.8.0 was created which uses the data from the weather station which can predict diseases before they set in.

In Brazil, approximately sixty million people suffer from or acquire some type of disease daily. However, the average time for blood count diagnoses, used to identify many of these diseases, remains very lengthy. This can lead to the worsening of conditions and delays in care, as well as a decrease in the patients’ quality of life. Moreover, in some cases, the waiting period can result in irreversible situations and even the death of the affected individuals. In this landscape, technological tools such as artificial intelligence software can help reduce the time taken for diagnostic reporting. In light of this, the project involves developing software to assist in the analysis of blood counts and optimize medical diagnoses. For this purpose, the methodology was divided into three stages. In the first, titled ”Medical Standardization”, a survey of the standard variables related to diseases that can be identified with the help of blood counts was conducted. Among the findings, diabetes, anemia, leukemia, dengue, polycythemia, tuberculosis, leprosy, meningitis, chlamydia, schistosomiasis, spotted fever, and malaria were the main diseases detected. Furthermore, hemoglobin, leukocytes, platelets, glucose, cholesterol, ions, and hormones were the key findings concerning the primary blood indicative factors for the mentioned diseases. In the second phase, the theoretical and practical foundations of the software were developed, based on artificial neural networks. In Python, regression models were also crafted to check the feasibility of the analyses. Finally, the last stage consisted of testing with real datasets, based on 1,227 anonymized blood counts. Among the artificial intelligence algorithm models tested, Support Vector (0.02) and Multiple Linear (0.61) had the lowest performances, while Polynomial (0.97), Random Forest (1.0), and Decision Tree (1.0) showed the best results. Given that the Random Forest and Decision Tree regression models achieved an accuracy of 1.0, while the Polynomial model scored 0.97, Support Vector 0.02, and Multiple Linear Regression 0.61, it is concluded that the blood count analysis system, with Python tools like regression, proved to be highly efficient. The closer the R² value is to 1.0, the better the programming fits the model, ensuring accurate analyses. Aside from that, in order to expand the number of analysis possible to do be done we decided to use a second tool called ”classification”, with which we made a bigger dataset to be used as a model to identify blood related diseases and the behavior of complex and diverse diseases. With that in mind, we performed a second evaluation of the models by doing an accuracy test, scored 87 percentage points and with a confusion matrix. With those results, we verified that the high performance of the tests indicates that Artificial Intelligence can be avaunt-guard to the elaboration of more efficient medical diagnosis, improving people’s lives quality and, overall, lowering the number of deaths in our country.

本研究結合奈米合成技術與生物醫學， 利用表沒食子兒茶素沒食子酸酯 (Epigallocatechin gallate, EGCG) 作為載體 調控摻雜Cu2+/Cu3+與 Fe2+/Fe3+之含量 並以π-π交互作用力附載缺氧性抗癌藥物替拉扎明 (Tirapazamine, TPZ) 成功製備出多功能金屬多酚配位奈米顆粒簡稱為EFeCuTPZ。 材料經紫外-可見光譜 (UV-vis)，、動態光散射 (DLS) 及掃描式電子顯微鏡 (SEM) 確認其粒徑大小、形貌學與穩定性。利用808 nm和671 nm雷射分析其光熱轉換效率 評估光熱療法效果，。在腫瘤微酸性環境下， EFeCuTPZ可利用高濃度之H2O2行芬頓反應 (Fenton Reaction) 產生高活性之氫氧自由基 (•OH)， 展現化學動力療法 (Chemo dynamic-therapy, CDT)，。同時， 藉由材料中的Cu²⁺與腫瘤環境中的穀胱甘肽 (Glutathione, GSH)反應減少高活性物質 (Reactive oxygen species, ROS) 的消耗 增強CDT之療效。酸性條件下 TPZ顯著釋放 有助於腫瘤治療。 另外， 細胞實驗顯示EFeCuTPZ具有高生物相容性與治療效果， 成功開發出具CDT，、CT及PTT功能之奈米複合材料 為醫學新興藥物材料提供可能性。

The country of Nepal, although beautiful, is facing many challenges due to its geography, lying between the towering Himalayas and the vast plains of Terai. The narrow mountain roads, prone to landslides and poor infrastructure, often result in frequent accidents. This situation is worsened by the delayed emergency response, as accidents are often reported much later than the time they occur. In the past ten years, over 15 major bus accidents have killed hundreds of people, and in 2024 alone, more than 80 deaths were reported. In response, the "Third Life" project was developed to improve emergency response time and save lives.The project has two main components: first, a device equipped with GSM (Global System for Mobile Communications), a GPS module (Global Positioning System), a gyroscopic sensor, and a microcontroller to detect accidents in real-time within seconds of the incident. Second, once an accident is detected, live coordinates are sent directly to emergency services and police stations for immediate assistance.This project is not only vital for Nepal but also for countries with similar terrain and infrastructure challenges. The "Third Life" project aims to save many lives that are lost due to delayed reporting, ensuring quicker emergency responses.A tragic example of this was the 2024 Trishuli bus accident, where many lives were lost when the bus plunged into the river. To date, the bus has not been recovered. Our project aims to create a waterproof device that, when connected to a satellite, will send live coordinates to emergency services, ensuring 100% reliability. This device could help locate the bus, which is still missing, within seconds.Ultimately, this initiative offers more than just safety it restores peace of mind and hope for the families of victims, providing them with a chance for a better future despite the tragedy.

Safe CrossWalk (SCW) is an innovative solution designed to enhance pedestrian safety at crosswalks, addressing the alarming issue of 270,000 pedestrian fatalities worldwide each year. By integrating advanced sensors, artificial intelligence, and real-time communication, SCW creates safer and more efficient urban environments. The system comprises three key components: SCW Strisce, a smart crosswalk device that detects pedestrian movement; SCW Car, a vehicle-integrated system that alerts drivers; and SCW AI, which processes data to optimize traffic flow and safety measures. SCW offers a proactive approach to reducing accidents through detection, alerts, and data-driven optimization. The solution not only improves safety but also supports urban planning by providing valuable insights into pedestrian and vehicle behavior. SCW aligns with the growing demand for AI-driven technologies in Smart Cities, presenting a scalable and cost-effective model for implementation. By fostering collaboration with municipalities and insurance companies, Safe CrossWalk aims to transform urban mobility, saving lives and creating smarter, safer cities.

Wibrazz is a wearable communication tool that allows the teacher, the therapist, the parent to communicate information to the child remotely using the device. Haptic (vibrationbased) feedback is becoming increasingly important in everyday life. A vibrating device that transmits information through clothing can help people with disabilities who have no or limited sensory use to live an integrated life in society without barriers.