鈣池調控鈣離子內流(store-operated calcium entry, SOCE)是非興奮性細胞中最主要的鈣離子通道。當內質網缺乏鈣離子時，位在內質網上的STIM1(Stromal interaction molecule 1)便會改變構型與在細胞膜上的ORAI1(Calcium relaease-activated calcium channel protein1)接合，激活SOCE的路徑。近來的研究顯示，粒線體會影響SOCE的活性。已知平均有5%-20%的粒線體藉由連繫蛋白與內質網相連。又已知內職網在缺乏鈣離子時會移動至細胞膜附近，故我們認為粒線體有很大的機率藉由連繫蛋白與內質網一同移動至細胞膜並透過吸收鈣離子的機制來調控SOCE的活性。 在使細胞表現特定螢光蛋白的前提下，我們透過活體細胞攝影來觀察特定對象(粒線體、粒線體內鈣離子)的動態變化。 從實驗結果中我們發現：當SOCE被激活後，粒線體會移動至SOCE發生處且較靠近STIM1。又絕大部分移動至SOCE發生處的粒線體同時也會吸收鈣離子。 過去的研究已證實，當粒線體與內質網之間缺乏鈣離子時，SOCE的活性會降低，且當粒線體內膜的主要鈣離子通道MCU(Mitochondria calcium uniporter)缺乏時，亦會導致相同的結果。又從我們的實驗可知當SOCE被激活時，粒線體會移動至SOCE發生處並吸收鈣離子。綜合上述，我們可以推論以下機制，當細胞內的SOCE被激活時，粒線體會藉由連繫蛋白與內質網一同移動至SOCE發生處，同時以吸收鈣離子的方式來調控SOCE的活性以及細胞內的鈣離子濃度。

梅氏長海膽屬於棘皮動物，身上布滿短且較粗棘刺，居住在潮間帶偏低潮帶的石洞內，整年都能見到，數量穩定。 牠們屬於被動防禦生物，被碰觸到時會將棘刺往碰觸地方集中，側面棘刺會頂住石洞洞壁，使自己牢牢固定在洞內，難以被撼動。 透過3D石洞模型實驗，在可選擇情況下，牠們會待在大小適中石洞，且深度必須可以掩藏自己，如果石洞有內凹或有遮蔽，都可以讓海膽待得更久，而狹長型石洞則是牠們最喜愛的石洞。 透過野外長期調查，梅氏長海膽確實會慢慢經營石洞，若不得已換了洞，還可以利用棘刺長短來符合石洞大小，牠們也可以長達數個月甚至數年不出洞，只要時間夠久，最終都會將石洞經營成狹長形，而這也就是潮間帶主要的海膽石洞型態。

透過「七個正方形之謎」的深入探討，我們除了破解其謎題外，更進一步去探討「點」和「正方形」的關係，最後透過歸納和整理，找到了正方形數量的公式。 ∑k=1n(n-k+1)2×k=(n×(n+1)2 ×(n+2))/12 利用這個研究結果，我們更進一步去設計有趣的「287幻方謎題」以及「兒童四角棋」，希望能做為未來學習平面幾何正方形的補充教材！

The present research has as main objective to degrade the post-cured photopolymer of the stereolithography 3D printer resin using Galleria mellonella larvae. It is necessary to consider that the use of materials from 3D printers tends to increase considerably and in approximately seven years about 10% of everything that will be produced in the world will come from this type of printing. Considering also that the increase in population growth and technological development are directly linked to the increase of solid waste on the planet, in particular to polymeric materials, there is a need to degrade and give an adequate end to waste, avoiding a notorious accumulation along the time. For this purpose, Galleria mellonella larvae will be used because of it's comprovated capacity to degrade polyethylene, to find out if it is capable of biodegrading the post-cured resin of the printer. To carry out the research, compositional tests were done in partnership with the SENAI Institute for Innovation in Polymer Engineering, located in São Leopoldo, Rio Grande do Sul, and the creation of the larvae and degradation of the photopolymer will be carried out in partnership with the University Federal University of Health Sciences of Porto Alegre (UFCSPA). The data analysis will be based on the crystallinity determination tests by differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and attenuated total reflectance spectroscopy (ATR) that will also be applied in the larvae feces after contact with the polymer to assess for degradation. As a result of the compositional tests, the ATR showed predominantly characteristic absorptions of acrylic resin; in the TGA test, the loss of mass described in the test is related to the loss of mass of organic material, mainly polymer. Finally, in the DSC test a thermal event was observed in the heating of the sample, with peaks at 125 ° C (Tpm), characteristic of fusion, and a thermal event in the cooling of the sample, in 112 ° C (Tpc), characteristic of crystallization. Based on the analysis of the results obtained, it is possible to infer that most of the composition of the photopolymer is acrylic resin, widely used in stereolithography 3D printers. The research has the future objective of isolating the substance into the larvae responsible for degradation so that it can be degraded on industrial scales. The research started in March 2020 and is still under development due to the COVID-19 pandemic, which compromised the planned tests.

本研究將至多8維的超立方體(hypercube)Qn最小控制集(minimum dominating set)MDS(Qn)建構方式一般化，並藉由同構(isomorphic)的分類討論提出的建構模式之唯一性與否。由文獻得出的各超立方體最小控制集大小γ(Qn)以及已知的控制集形式，並從控制集重複控制的次數R(MDS(Qn ))，我們得出Qn的平方圖中最小控制集形成的子圖Qn2 [MDS(Qn )]可能的連通分量(component)數，最後透過Qn層狀圖(layered graph)中各層控制點數的運算，篩選得出可行的建構方式。 研究得出MDS(Q1 )、MDS(Q2)、MDS(Q3)、MDS(Q5)、MDS(Q7)只有一種同構；MDS(Q4)、MDS(Q6)有兩種同構，同時我們發現MDS(Q5)與MDS(Q6)構造上的關聯；Q8的情況較為複雜，我們先是證明了γ(Q8 )=32，並討論MDS(Q8)與MDS(Q7)構造上的關聯，提出了建構MDS(Q8)之方式。

本研究是參考光合作用對葉片的影響而有了行動的方向，我們知道光合作用的產物是葡萄糖，並轉化為澱粉的形式儲存能量。我們以鋁箔紙覆蓋在受光不同天數的葉片上，校園植物材料的選擇則盡量以嫩葉、 少毛狀物、較柔軟、角質層薄之葉片為主，藉由加水加熱的方式，再以酒精隔水加熱褪去葉綠素的干擾後，以碘液測試葉片所含之澱粉的多寡所產生的圖樣變化。最終將經碘液處理後的葉片樣本，測試在不同酸鹼及溫度等環境下，對於「碘－澱粉錯合物」的影響，並在當中選取對葉片最適合的酸鹼性及最良好的保存溫度，藉以改善植物進行光合作用實驗所呈現的結果。

本研究旨在建置可以「自動偵測土壤缺水的裝置」，我們利用簡單的電路設計，以LED燈作為指示燈，以其明暗提醒澆水時機，幫助人們更正確的判斷澆水時機，讓植栽所處環境乾、溼適宜，更適合生長。因此，我們先採用電阻法探討各式土壤的含水性質，測量土壤的飽和含水量，結果發現混合土（培養土、砂質壤土體積比2：1）的飽和含水量最佳，達31.7%且水分滲入的速度也相當快。以我們設計的「自動偵測土壤缺水的裝置」來對室內容積1600毫升的混合土（培養土、砂質壤土體積比1：1）盆栽進行澆水，每年可節省的水量約為9.8公升，對室外容積1600毫升的混合土盆栽進行澆水，每年可節省的水量更達22.8公升，省水效果相當驚人。

多邊形及中心多邊形自守數是鮮有人研究的課題，將廣為人知的「(中心)多邊形數」與「自守數」綜合起來，形成相當有趣的幾何與數論結合課題。 歷史文獻中僅提出六邊形與中心六邊形(s=6)自守數的想法，亦僅做了不完整的探究：1987年特里格(Trigg, C.)只尋找到小於10000的六邊形自守數，而2003年皮寇弗(Clifford A. Pickover)也只列出八位數以內的六邊形自守數及不完整的數列。 本研究首先討論s=3,4,5,6的情形，透過Bezout's identity確立各位數數量，並利用尾數重複出現的性質，找出各多邊形及中心多邊形自守數衍生的方法；再根據各判別條件，整理出 邊形自守數間的包含關係，以及中心s邊形自守數間的交集。

Cycling is a very popular mode of transport as well as a famous sport around the world. Many people enjoy this sport either professionally or recreationally. Cycling in the UK alone has grown up to 200% since lockdown in 2020. (Chandler, 2020) Cyclists make use of a broad selection of products to enhance their performance. Those products range from wireless gear shifting, advanced geometry, smart suspension. This project is aimed to indicate the importance of tire pressure and to introduce a product which will be able to adjust tire pressure while cycling. This product will give cyclist an advantage on different terrains as well as eliminate some common problems amongst cyclists. Flat tires are one of these problems. It occurs commonly amongst cyclists and can happen due to a variety of reasons. Another problem is wrongly inflated tires. This causes unnecessary loss in a cyclist’s power and speeds due to the high rolling resistance between the tires and the surface. This then results in losing time whether racing or commuting. In an article published in 2014 in Velonews.com, Lennard Zinn states: “Whether on tarmac or singletrack, a tire with lower rolling resistance reduces the power required to move forward while also providing a better quality ride. The tire absorbs small bumps by not transferring them into the bicycle and rider, resulting in a smoother ride, faster speeds, and better cornering." (Zinn, 2014) Taking this in consideration it becomes clear that it is important to develop a system which is able to control tire pressure.

從圖形分層遞降觀點找硬幣排列與方塊堆疊的遞迴關係式，可用流程圖找方法數。 一、將n個硬幣排成k列排法Bk(n) 種，共A(n)種 (一) 找出B1(n)=1, B2(n)=[n-1/2], B3(n) 。 (二) 從圖形解釋Bk(n)=Bk(n-k)+Bk-1(n-k) ： (三) Bk(n)拆為k-1列的關係式： Bk(n)=Bk-1(n-k)+Bk-1(n-2k)+…+Bk-1(n-tk) 二、將n個硬幣遞減排成k列排法Qk(n)種，共P(n)種 (一) 找出 Q1(n)=1, Q2(n)=[n/2], Q3(n)。 (二) 從圖形解釋Qk(n)=Qk(n-k)+Qk-1(n-1) ： (三) Qk(n)拆為k-1列關係式：Qk(n)=Qk-1(n-1)+Qk-1(n-1-k)+...+Qk-1(n-1-(t-1)k) 三、將n個方塊堆成k柱排法Tk(n)種，共S(n)種 (一) T1(n)=1, T2(n)=[n-1/2] 。 (二) 從圖形解釋Tk(n)=Tk(n-k)+Tk-1(n-k)+Tk-2(n-k)+...+Tk-t+1(n-k)，每柱取走1個： 最低柱為大於1層時，剩n-k個堆成k柱，排法Tk(n-k)種 最低柱為1層且有t-1柱，剩n-k個堆成k-t+1柱，排法Tk-t+1(n-k) (三) Tk(n)降為少於k柱關係式 Tk(n)=[Tk-1(n-k)+Tk-2(n-k)+...+Tk-t+1(n-k)]+[Tk-1(n-2k)+Tk-2(n-2k)+...+Tk-t+1(n-2k)]+...+[Tk-1(n-rk)+Tk-2(n-rk)+...+Tk-t+1(n-rk)] (四) 新發現S(n)數列。

研究科學玩具「nanodots」與數學曲線「懸鍊線」(Catenary)的關係，並更進一步思考nanodots的多寡與最終形成曲線的逼近程度是否有正向的關聯。