This project aimed to study the motion which occurred from the end point on the circumference of the outermost circle by moving the center on the circumference of a preceding circle and the center of an innermost circle at origin. According to the study, when angular velocity was changed, it caused the different of loci. Based on the above information, finding the locus of the point on circumference of n-th circle that formed by moving the center of any radius circles on circumference of preceding set of circles was studied to get general equation. A set of circle and locus were created with GSP program. First, set the same radius circles on the X-axis with the first circle at origin, then found the relationship that occurred from the characteristics of locus. The result showed that if the ratios of angular velocity are 1:1:1, 2:2:2, 3:3:3, ..., …, n:n:n or 1:2:3, 2:4:6, 3:6:9, …,nw1:nw2:nw3, the characteristics of locus will be the same, while the others will be different. Finally, the equation of locus was found as follow: (x,y) = { ..........see in abstract...........} when .........see in abstract........... Where ri is the radius of i-th circle, zeta i is an angle between the radius of i-th circle and X-axis, wi is the angular velocity, t is elapsed time and alpha i is a starting angle between the radius of i-th circle and X-axis.

延續2020年視錯覺研究，我們想要探討視覺神經細胞接受不同亮度對立顏色刺激後是否會有不同活化程度，影響視錯覺？另外也想探討不同對立配色的赫曼方格中線條寬度的閾值是否有差異？我們設計網頁版程式，改變赫曼方格線條顏色的亮度和寬度，以正常受試者為對照組，色盲受試者為實驗組，探討視錐細胞的變異是否影響視錯覺的產生。我們以顏色拮抗理論定義對立配色的赫曼方格，以標準化情境進行實驗。在線條亮度的結果中，黑白配色的赫曼方格圖案中線條與方格對比度越大，視錯覺產生的效果越明顯。兩群受試者在綠紅、紅綠、藍黃這三組配色，線條亮度範圍呈現兩極化的趨勢，可能原因為色盲因錐狀細胞變異，需要較高亮度的對比顏色刺激才容易讓神經細胞有活化程度上的差異，造成視錯覺出現。在改變線條寬度的結果中，發現藍黃的赫曼方格閾值與明顯值最大，黑白次之，綠紅最小，可能與細胞感受野大小有關，且線條寬度超過感受野的閾值，視錯覺就無法產生。兩群受試者的線條寬度閾值差異，可能與色錐細胞變異有關。綜合以上結果，顯示視網膜色錐細胞與神經節細胞的作用，對視錯覺形成扮演一定角色。在消費行為問卷結果中，我們發現格子衣服若是顏色對比度大、線條較細的圖案設計，消費者的滿意程度較低，這原因可能與視錯覺產生影響衣服視覺效果。

本研究以AI虛擬試衣系統(Virtual Try-on)為主題，透過深度學習技術，並結合幾何匹配模型，開發出試衣系統，可將使用者上傳的照片，模擬成穿著新衣的模樣。 首先，以深度學習模型將人物原始圖片取出骨架節點，並生成人體遮罩以及保留人物頭部，再結合以上三種資訊合成為高維特徵圖。接著將目標替換衣物生成出依照人體姿態扭曲後的衣物圖片。最後於Virtual Try-on模型中將人體高維特徵圖與扭曲衣物作為輸入，並經過深度學習網路合成出穿著目標衣物之人體圖像。本研究結果發現，人物站姿單純，且雙手緊貼身側，以及拍攝角度為正面、衣服款式為短袖、背景色彩對比度較高與衣服圖案單純的原始圖片，可得到較好的合成結果。

本文企圖將公認的剛性△區分為軟和硬△，軟硬△定義如下:「若給定△的每一內角都不存在比分角線能多切一點點的塞瓦線，則此△被稱為硬△，否則為軟△。」文中推出兩項主要結論，(一) 若等腰△的頂角角度在36度及771/7度之間則為硬△，否則為軟△。(二) 一般△(非等腰△)三內角角度若都在45度及75度之間則為硬△，否則為軟△。明顯看得出來，任何鈍角及直角△都是軟△，只有部分銳角△才有機會是硬△。文章最艱難的部分是在18種擺放方式中，將僅存的七種成功擺放方式的臨界點都找出來，藉著臨界點的位置條件將∠B最大及最小範圍和∠A角度的關係式導出，作為可否多切一點點的依據，∠B的最大值和最小值曲線兩者之間空隙表示在定值∠A下，∠B取角的容許範圍，其越大越容易舉例。在七個可成功塞入的臨界點擺放圖的尺規作圖中，有幾個非常困難，文中利用圓錐曲線幫忙定位，簡化作圖難度。

太陽能是地球上最豐富的能源。我們這裡研究的光催化劑主要用於進行重要的化學反應，例如利用陽光進行污染物降解和製氫。光催化劑的靈敏度取決於半導體材料的組成。在這項研究中，提出了一種氧化錫和氧化鎢的錫（II）光催化劑（SnO-WO3或SnO2 / WO3）與p-n結半導體材料結合。我們發現重要的事實是，含有少量SnO2和WO3的光催化劑展示了敏感的光催化活性。使用光纖的掃描電化學顯微鏡（SECM）快速篩選SnO2-WO3光催化劑陣列以進行有效的光電化學反應，我們使用小於10％的SnO2量摻雜WO3。然後在0V vs.Ag/AgCl的條件下，我們發現在紫外線和可見光照射下，組合物中3:97 SnO2 / WO3的微小比例能夠顯示出最高的光電流。利用第一原理(DFT)計算，我們得到了接近費米能中SnO2的帶隙約為1.40 eV。我們認為這種小的帶隙和費米能級附近的態密度（DOS）分布是SnO2對n型WO3敏感的原因。

睡蓮蚜是一種生活在水域環境的蚜蟲，而本研究證實：此種蚜蟲對水源和水中浮萍具有偏好性，並在水中具有勝過陸生黑豆蚜和玉米蚜的求生能力和登陸能力。睡蓮蚜的這些能力源自其異於其他蚜蟲的構造：較輕的質量和較長的腳使其能夠憑藉表面張力於水上站立和移動，並且在登岸時可以產生物理中的Cheerios Effect快速吸附陸地，水中生活的機動性因而極高。另外，睡蓮蚜的腳有彎曲的特徵，加強Cheerios Effect 的效應，加強登岸能力。睡蓮蚜的腹面氣孔亦有朝兩側生長的現象，以適應水上腹面經常碰觸水面的生活。

921地震震波對高11-15層大樓產生重大危害。本研究以模型模擬11層大樓建築物，頂樓設置水塔配合陽台天花板設置水撲滿的雙阻尼消能系統設計，探討不同震度震波在雙阻尼系統減震成效。模擬之設備利用3D列印機自製水撲滿、不同形式網狀隔間液體阻尼零件，自製地震模擬器以電流調整器控制怠速馬達，進行模擬不同震度下高樓產生擺動與震盪之狀態與特性。 實驗發現單一阻尼消能元件的減震阻尼效能較差，雙阻尼消能系統可提升39％至58％減震阻尼效能。其中雙阻尼消能系統若有網狀隔間，水波擾動震盪越明顯，阻尼效能提升 6％至14％。11層大樓於頂樓設置平行器壁網狀隔間正方形水塔，並配合在第9至11層樓處，設置隔間距離較短網狀隔間水撲滿，二者水位設定六分滿，此液體雙阻尼減震消能系統，可抑制模擬震度5至7級震波對大樓產生的順向波動共振與大樓結構體的自主扭轉共振。

Commercially available bandages such as hydrocolloid are neither biodegradable nor anti-bacterial. Chitin is known to be the second most naturally available polysaccharide which could be transformed to chitosan which is known to be anti-bacterial (Hasan, 2018) (Chao, 2019) and haemostatic (Okamoto, 2003) (Hu, 2018). Chitosan can be further converted to hydrogel which is bio-degradable and has good water absorbance. Anti-bacterial crab bio-bandages and crab bio-dressings should be bio-degradable as it took 42 days and a month for complete bio-degradation respectively, so they should be better than commercial bandages such as Nexcare Hydrocolloid as the disposal of anti-bacterial crab bio-bandages with bio-dressings would no longer pose burden to landfilling or threat to our environment. Anti-bacterial crab bio-bandages with bio-dressings are anti-bacterial with degree of deacetylation of DD% (measured using FTIR Spectrum II) 82.6% (due to the presence of chitosan) even without the application of other anti-bacterial agents and hence can provide complete protection of wounds from skin and soft tissues infections and haemostatic (due to the presence of chitosan). After testing and certification based on IS997:2004 and BS EN 13726-1, they should meet many requirements specified. Anti-bacterial crab bio-bandages should be eligible for marketing. Some results were as follows: 1.4 Anti-bacterial effect of crab hydrogels and roasted crab hydrogels Pure chitosan, crab chitosan, crab hydrogels and roasted crab hydrogels showed significant anti-bacterial effect. NO oral bacterial colonies were present in drinking water with crab hydrogels. Thus crab hydrogels could serve as effective anti-bacterial wound dressings. 1.6 Basing on IS997:2004 standard, the load per unit of area of anti-bacterial bio-bandages was 342g/m2 which met the minimum requirement of 36g/m2, the anti-bacterial bio-bandages had stronger tension strength (>20N both in dry and wet conditions) than commercial hydrocolloid. (2.7N dry 2.8N wet) which was comparable with that required (50-67N) and pH of about 7 which met the pH range of 4.5-8. 1.7 The FSA Free-Swell Absorbency of synthetic blood of crab hydrogel bio-dressings was 1.86g per 5cm x 5cm dressing which was much higher than that of commercial hydrocolloid (0.299g per 5cm x 5cm dressing) based on BS EN 13726-1.

在第 屆科展作品（中華民國第 屆中小學科學展覽會換心手術）有給定了一個新的名詞(頂心三角形)：平面上給定△ABC及一點D，分別以A、B、C三頂點為圓心，¯DA、¯DB、¯DC為半徑畫圓，三圓交於三點E、F、G，再以三交點E、F、G為頂點作△EFG，則新△EFG稱為△ABC在D點的頂心三角形，本篇作品主要探討原三角形與其頂心三角形邊長與面積比例關係，並試著利用這些關係求出頂心線以及其他相關性質。 在我們的作品中，我們求出頂心三角形的三邊長為2¯AD sin⁡∠ CAB、2¯BD sin⁡∠ ABC、2¯CD sin⁡∠ BCA，也就是說在原三角形為任意三角形，可以得出頂心三角形的邊長與原三角形之間的邊長關係，我們再進一步利用邊長關係求出頂心三角形對原三角形的面積以及面積比例。我們還發現，當D點在原三角形的外接圓上時，頂心三角形會退化為一直線，稱為頂心線，而此頂心線會通過原三角形的垂心是本篇作品最重要的發現。

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.