Substance losses, burns and injuries arising from various causes represent a constant problem encountered by homo sapiens throughout its existence. Rudimentary treatments, relatively effective and less effective, have left their mark on the way we perceive the presence and treatment of wounds caused by various factors. Searching through medical archives, we can trace the specific protocols for these medical conditions back to 2200 BC, when they were structured in three steps: 1) cleaning the skin lesion, 2) applying a dressing (from glue to various preparations) and 3 ) bandaging the skin lesion. Currently, the appearance of wounds on the skin is caused both by accidents in the performance of various activities and by certain diseases that manifest themselves through skin rashes or skin lesions. Their frequency is in the thousands, according to the latest statistics, affecting the majority of the population non-selectively. It is vital that skin lesions receive the necessary care and attention, commensurate with their severity. Being open wounds on the surface of the skin, it is essential that the treatment be meticulous and appropriate to their type, as skin lesions represent a threat to the patient's life. From infections to hydroelectrolytic imbalances specific to burns, the multitude of factors that influence healing highlight the need for a dressing that can be easily customized according to the specificity of the wound, the needs of the patient and that is affordable both from the point of view of production cost as well as its use, making death from skin lesions easily avoidable through an intelligent approach. One of the most complex biological processes and indispensable to humans is the healing of skin lesions. Healing involves a carefully regulated series of biochemical and cellular activities in tandem. Traditional therapies and substances of natural origin have been used to facilitate the regeneration process and accelerate the wound healing process, being applied with encouraging results. Despite the fact that these generally present a low cost, they can be more expensive than contemporary treatments and can be influenced by regional, seasonal factors, showing fluctuations from batch to batch, which could lead to unpredictable allergic reactions, side effects and inconsistent clinical findings. Currently, the standard of care for skin lesions is to clean the wound with antiseptic solutions to prevent infection, apply a dressing followed by bandaging to keep the dressing in place, and if necessary excision of the tissue that has become non-viable. In the case of diabetic ulcers, it is necessary to excise the tissue that has become non-viable and to maintain control over the level of glucose in the body.

破囊壺菌為海洋原生生物，因可產生DHA 而被廣泛使用於藻油生產。破囊壺菌可透過18srRNA 鑑種，不同菌株之產油量相差甚大。其產油途徑主要有 FAS 及 PUFAs 二條路徑， 含有 PUFAs 之菌種通常具有較高之產油率。前人依產油途徑將破囊壺菌分為三型 （I–III 型），然而各型基因組間之差異仍待研究。本研究透過生物資訊分析 8 個破囊壺菌基因組， 發現同型之破囊壺菌其產油相關基因 （PUFAs, Desaturase, Elongase 及 Citrate lyase）之存 在具有高度相關性，基因共線性分析也顯示其產油基因間具有高度同源性，然而同屬之破 囊壺菌不一定為同一型，顯示以 18s rRNA 鑑種可能不適用於破囊壺菌。此外，Citrate lyase 僅存在於第 II 及 III 型，顯示第 I 型破囊壺菌其 DHA 合成之碳源來自不同途徑。

本研究主要探討，有n位教授要在一個圓桌上舉行會議，其中每位教授都有自己的編號 (1~ n號)，同時圓桌的 n個位置上也有各自的名牌編號 (1 ~n 號) 以順時針擺放置圓桌上與教授們的編號對應。其中第一個進來的 1號教授坐到了圓桌上 k號位，此後的教授們亂序一個一個進入，若發現與自己編號相同的位置是空的，就直接入座；若與自己編號相同的位置被占走了，就以逆時針方向尋找空位，直到有空入座。在這樣的遊戲規則下，本研究探討了，有 n位教授，且 1號教授坐到 k號位，如何給定一組教授入場的順序，就能即刻的找出對應的坐法，以及計算坐錯人數的期望值和坐錯人數次數分佈表等等，後續再將遊戲規則改為，1號教授不限定為第一個入場的人，同樣的探討上述問題。

給定三種大小不同的正三角形，邊長由大至小分別為正整數a、b、c，在每種三角形皆需使用的情況下，去拼出邊長為正整數的正三角形。眾所周知，「找到所有可以被拼出的正三角形邊長。」這個問題是困難的，原因是正整數有無窮多個，且可行的拼法非常多種。故本文欲探討的問題為：「尋找a、b、c的條件，使得無法被拼出的正三角形之正整數邊長個數僅有有限個。」 我們估算無法被拼出的最大正整數邊長，並為所有大於此數的正整數邊長，分門別類地創建合適的拼法，解答了上述問題。

本研究的研究靈感來自於科學月刊，原題為在一個六面體中，有一隻螞蟻位於其中一個頂點並沿著邊行走，每當牠走到頂點時就會選擇一條邊繼續行走，且牠任何方向之機率皆相同，但不可走回頭路，求螞蟻回到出發點時經過邊數之期望值。本研究將題目延伸出了以下三個問題，得出結論後並證明。並得出了以下結果：簡單連通 圖，螞蟻從其中一頂點出發，且往任何方向之機率皆相同，無論螞蟻是否可以走回頭路，牠第一次回到出發點時經過邊數之期望值之通式。在 n 點連通路徑圖 Pn(n -path graph) 中，螞蟻從其中一點 vi出發，第一次走到另一點 vj時經過邊數之期望值通式。並找出了當 n 點循環圖 Cn (n-cycle graph)上有一隻螞蟻從其中一點 vi第一次走到另一點 vj時，經過邊數之期望值與兩點之距離的關係。

k距離集合是一個在離散幾何領域中被探討到的問題，也是我們在這篇文章中所想要研究的主題。我們將會先對平面中 4，5個點與三維中 5，6個點的二、三距離集合進行分類，然後再探討在三角形與正方形格子點上的 k 距離集合中點的個數與不同形狀的格子點之間的關聯性，並對這些 k距離集合中的點在 k值較小時進行統計與分析。而我們的研究目的為找出在不同格子點構造中 k 距離集合點的最大個數，並比較兩種構造的形狀以及效率差異。

受到地區限制，偏遠地區一直面臨著缺水和缺電的問題。有許多解決方案，其中一個被視為在乾燥地區收集水的有效方法是薄膜霧氣收集技術。這項研究受到自然界沙漠甲蟲的啟發。我們在不吸水的石墨烯/PVDF基底上使用仿生的幾丁聚醣陣列，幫助水滴在霧氣中凝結和滾動脫落，使水收集效率達到0.63LMH。此外，我們使用石墨烯和離子液體一起誘導PVDF晶型自組裝成具壓電性的β相，獲得最適化薄膜的電壓輸出可達到13V(±6.5V)。我們還對於薄膜進行同時取水和取電的可行性評估，結果顯示，在4m/s的霧氣風速下，水收集效率為0.74LMH，發電功率為99.2mW/m2。基於上述研究結果，我們證實了使用單一薄膜利用霧和風作為驅動力，可實現同時產生水和電，這對解決偏遠地區的缺水與缺電問題提供了新的解決方案。

Vitas is a combination of binaural beats (BB) with background white noise (ASMR) as accompanying music without reducing the quality of brain stimulation and is able to stimulate the left and right brain while synchronizing brain waves so that it can be used as a media for coping with stress for Gen Z students. To find out the effect Vitas in reducing stress levels, research was conducted on high school students belonging to Gen Z. This research aims to measure the stress index of students belonging to Gen Z, then find the effect of the combination of binaural beats (BB) and ASMR on students'stress levels, and finding the best audio combination to reduce stress levels as a coping mechanism. This research uses a quantitative approach with a quasi-experimental design using a one group pre-test-post-test design scheme. The sample in this study consisted of 105 students who were divided into seven treatment groups to listen to a combination of BB and ASMR with different bandwidths. Stress levels were measured using the DASS 42 stress section questionnaire which has been tested for reliability and validity. The results of the student stress index were 16.26 in the mild stress category. There was a significant difference between the negative group, the alpha + ASMR group and the positive group with a T-Paired test result of less than 0.05. Based on the results of the Post Hoc LSD test, it was found that the combination of binaural beats alpha (12hz) + ASMR was the best combination for reducing stress in students.These findings were developed into a digital therapy application product called "Vitas" as an alternative media for coping with stress for Gen Z.

人腦中約有一千億顆的神經細胞 (王希文，2018)，他們之間的突觸錯綜複雜，這些樹突與軸突皆連接到正確的位置，讓人不禁好奇這些突觸的連接機制。在經過文獻的查詢過後，才發現Dscam是控制大腦發育的蛋白質之一，Dscam使得細胞能夠進行細胞辨識，能夠使軸突及樹突在腦中進行特定的連結而不致於黏合。目前我們尚未知道，Dscam 會如何影響嗅覺區域中介神經細胞的生長及神經連結，本研究針對黃腹果蠅(Drosophilamelanogaster) 大腦中一小群被 GMR51C07-GAL4標定的嗅 覺區域中介神經元，觀察在正常情況、Dscam過度表現、Dscam表現量受抑制下，這群神經元的型態如何發生。

若使氣流流經轉動的有孔圓盤，將出乎意料產生明顯的聲音。一開始我們假設聲音之來源僅為氣流被圓盤切成一段段的疏密波，並以此基礎進行後續研究。但儘管已使用吸音棉等設備，且對錄下來的聲音傅立葉分析後，卻發現現象並非想像中的簡單。這當中仍有許多無法解釋的現象值得深入探討：包含基頻之相對振幅對比泛音顯得極小、還出現了馬達與氣閥以外的噪音等等。故隨後我們滾動式修正研究方法並尋找更多理論解釋和支持，譬如運用物理引擎 COMSOL 模擬、查詢各方面文獻及理論。 歷經此探究過程，我們最後觀察到顯著的一組諧波，其基頻等為洞數乘以轉動頻率，且第 n 個振幅隨著 n 增加逐漸遞減。我們基於《Siren Harmonics and a Pure Tone Siren 》 (E. A. Milne, R. H. Fowler, 1921）中提到的的諧波模型，加上利用 COMSOL 進行模擬，最後對所觀測的諧音序列提供定性定量解釋，以及證實其他的噪音乃風切現象所貢獻。