The project is devoted to the study of the Seymour’s Second Neighborhood conjecture by determining the properties of possible counterexamples to it. This problem has remained unsolved for more than 30 years, although there is some progress in its solution. The vector of the research is aimed at the analysis of possible counterexamples to the conjecture with the subsequent finding of some of their characteristic values. In addition, attention is focused on the generalized Seymour’s conjecture for vertex-weighted graphs. Combinatorial research methods and graph theory methods were used in the project. The author determines the values ​​of densities and diameters of possible counterexamples, considers separately directed graphs of diameter 3. The conditions under which specific graphs cannot be counterexamples to the Seymour’s conjecture with the minimum number or vertices are defined. The relationship between the Seymour’s conjecture and vertex-weighted Seymour’s conjecture is explained. It is proved that if there exists at least one counterexample, then there exist counterexamples with an arbitrary diameter not less than 3. Under the same condition, the existence of counterexamples with a density both close to 0 and close to 1 is also proved. The equivalence of the above two conjectures is substantiated in detail. It can be concluded that if the Seymour’s Second Neighborhood Conjecture is true for a directed graph of diameter 3, then it is true for any digraph, so that problem will be solved. Moreover, if the conjecture is true, then vertex-weighted version of this conjecture is true too. That is why a digraph of diameter 3 needs further research.

複雜蜃景(Fata Morgana)專指擁有多重影像的特殊上蜃景，形成於高緯度海面上，也是「飛行荷蘭人」的主要成因。本研究主要藉由探討介質折射率梯度變化與觀察者高度位置等變因，釐清複雜蜃景形成與觀察的最佳條件。藉由控制高濃度糖水溶液擴散形成的密度梯度，我們在六十公分的水缸中重建出形成複雜蜃景的環境，主要是因為糖水溶液中的折射率梯度遠大於海面上空氣的逆溫梯度所造成之折射率變化。為了進一步解析光在複雜折射率介質中之行進模式，我們以綠雷射光入射糖溶液，在側向以相機紀錄光的行進軌跡，分析探討其折射現象。我們同時利用相機觀察放置於水缸另一側的模型船，藉以觀察實際蜃景的形成與演化。本研究中我們另發展一套光軌跡的模擬程式，以協助實驗的進行與驗證實驗的成果。藉由實驗與理論模擬相互映證，充分探討複雜蜃景的成像與形成的最佳條件。

本研究旨在設計一個使用模式，以不切換中、英文輸入法打字的原則之下，能夠完整的自動辨識出一個包含中文（注音、嘸蝦米、倉頡）與英文完整句子。經實測結果，正確率達到94.23%以上。

The use of brine shrimp nauplii to test for the overall toxicity of sediment samples is proposed. Brine shrimp nauplii were cultured with different concentrations of heavy metals, including chromium (III), copper (II), nickel, lead and zinc, and organic pollutants, including triclosan, oxybenzone, octinoxate and bisphenol A. The brine shrimp nauplii were observed under a dissection microscope to determine the death rate. Results showed that brine shrimp nauplii are more sensitive to copper, cadmium, bisphenol A and oxybenzone. The LC50 (24h) are 55.5, 24.9, 5.6 and 2.7 ppm respectively. Zinc is likely to have synergistic toxic effect with nickel or lead. The synergistic toxic effects of other heavy metals and organic pollutants should be confirmed with further investigations. Brine shrimp nauplii were treated with extracts from sediment samples collected from the oyster culture zone of the Deep Bay, namely Pak Nei, Sha Kiu Tsuen and Hang Hau Tsuen. The sediment samples were extracted with neutral sodium acetate to dissolve the exchangeable heavy metal ions and some organic pollutants. The death rate of brine shrimp nauplii treated with the sediment extract of Hang Hau Tsuen was similar to 1 ppm PBA. It was also about 10 to 20% higher than that of the other two sites (Pak Nei and Sha Kiu Tsuen). Since Hang Hau Tsuen is closer to the residential area and Lau Fau Shan Seafood Market than the other two sites, its sediment sample is likely to have a higher level of environmental pollutants. The results suggest that brine shrimp nauplii may be used as a biomarker to monitor the environmental changes in the overall level of pollutants in sediment samples.

癌症是世界性的嚴重疾病，長年位居國人十大死因之首。而基因調控的失控是造成癌症的主要原因之一，由先前的文獻已知，微小核醣核酸let-7負向調控下游基因lin-41是調控細胞週期及癌症發展和預後的重要路徑。由於此調控路徑具有演化上的保守性，本研究以較易操作實驗的秀麗隱桿線蟲為生物模型，透過RNAi 的方式，降低特定基因的表現，觀察是否影響與let-7/LIN-41調控路徑相關的突變性狀，來推測該基因是否參與此路徑相關之細胞週期調控。 本研究中，我們發現以RNAi降低核糖核酸結合蛋白msi-1的表現量可抑制let -7(n2853) 突變種線蟲中因let-7功能缺失所造成的接縫細胞的重複分裂的突變性狀，並增強對下游基因col-19的活化調節。我們推論，降低msi-1表現量可以提升let-7路徑的功能。我們期望可以藉由研究msi-1如何調控此路徑的機制，更加了解MSI-1此一核糖核酸結合蛋白對於細胞週期的控制，並提供未來癌症標靶藥物的重要參考。

The project is devoted to the study of the Seymour’s Second Neighborhood conjecture by determining the properties of possible counterexamples to it. This problem has remained unsolved for more than 30 years, although there is some progress in its solution. The vector of the research is aimed at the analysis of possible counterexamples to the conjecture with the subsequent finding of some of their characteristic values. In addition, attention is focused on the generalized Seymour’s conjecture for vertex-weighted graphs. Combinatorial research methods and graph theory methods were used in the project. The author determines the values ​​of densities and diameters of possible counterexamples, considers separately directed graphs of diameter 3. The conditions under which specific graphs cannot be counterexamples to the Seymour’s conjecture with the minimum number or vertices are defined. The relationship between the Seymour’s conjecture and vertex-weighted Seymour’s conjecture is explained. It is proved that if there exists at least one counterexample, then there exist counterexamples with an arbitrary diameter not less than 3. Under the same condition, the existence of counterexamples with a density both close to 0 and close to 1 is also proved. The equivalence of the above two conjectures is substantiated in detail. It can be concluded that if the Seymour’s Second Neighborhood Conjecture is true for a directed graph of diameter 3, then it is true for any digraph, so that problem will be solved. Moreover, if the conjecture is true, then vertex-weighted version of this conjecture is true too. That is why a digraph of diameter 3 needs further research.

研究初期顯示增加儲存時間會降低花粉萌發率，並造成內源性酯類顯著降解。因此我們推測花粉萌發所需的能量可能由內源性酯類提供。先前研究發現雌蕊柱頭分泌物(SE)含有促進花粉萌發的因子，本研究探究 (1)花粉萌發過程中內部酯類組成變化；(2)找出SE如何影響酯類代謝進而促進花粉萌發。利用薄層色層分析法比較後發現極性酯於花粉萌發較中性酯重要，而SE主要加速了磷脂醯肌醇(PIs)、磷酯醯膽鹼(PCs)的降解與雙酸甘油酯(DAGs)的生成。利用LC-MS發現添加SE確實能加速PCs/PIs的降解及DAGs的生成，更能促進PAs的快速生成再降解。我們推測添加SE能夠促進PCs/PIs降解，PIs磷酸化成PIP2後經過PLC水解生成1,4,5-三磷酸酯(IP3)以及DAGs，IP3能促使粗糙內質網釋放內源性鈣離子，而DAGs磷酸化成磷酯酸(PAs)後促使膜上的鈣離子通道打開，讓外源性鈣離子進入花粉管內。而PCs在經過PLD水解後也能形成PAs讓鈣離子進入花粉管內。

本研究定義1967~2016年的極端寒流並將其分成1985前與1986後兩個時期，進行前後期寒流個案合成之綜觀環境場的比較，得知前後期確實有所不同，且以天為單位，後期寒流及非寒流差異較不明顯，推測需要更長時間尺度才能凸顯差異。再以臺北冬溫與世界冬季的溫度、風場做相關性分析，發現緯向風的蒙古地區，在前後期正相關性都相對明顯；經向風則是西伯利亞西部的負相關在前後期皆較明顯。因此，我們分別取蒙古緯向風及西伯利亞經向風以月為單位做不同季節延遲、同步及領先的迴歸分析，並發現與臺北冬溫相關性最高者，分別為蒙古冬季同步緯向風，及西伯利亞春季領先2經向風。最後為了驗證，再將此二風場1967~2016年的數據分為寒流、非寒流期間及全部數據進行比較，觀察同個月份在寒流及非寒流期間與平均值的差別，也探討這些差異與臺北冬溫三個月份間的差異有何異同，結果證實寒流及非寒流大多具有明顯不同。

全球貧血人口普遍，然許多人並不了解自身是否罹患貧血；長期患有貧血的病人，亦需定期抽血檢驗追蹤是否有貧血惡化達到需接受輸血的程度。研究顯示，結膜之顏色與貧血有絕對關係，結膜越白則貧血越嚴重，醫師也常使用結膜顏色推測是否有貧血情形。若能設計手機軟體自動分割結膜影像並分析其顏色，將有機會推測受試者是否罹患貧血。本研究收集22位無貧血者及8位貧血病人，並獲得其近期血紅素數值。以手機取得受試者之眼睛影像後，成功設計程式以深度學習完成結膜自動影像分割，對於分割影像以面積大小進行後期處理後，依其取得下眼瞼結膜之三原色平均，再利用kNN與SVM演算法判斷預測出該受試者是否具有貧血之症狀。本研究主要分為兩階段，其一為進行下眼瞼結膜分割模型訓練；其二為製作有無貧血之判斷模型。整合上述眼瞼分割模型(IoU=89.8%±0.02%)與貧血判斷模型(SVM以polynomial核函數測出 準確值93.3%±24.3%)後，可得貧血診斷準確率為80%。此結果代表AI技術有機會透過結膜影像，判斷被拍攝者是否有貧血情形，未來若能增加研究人數，將可設計網頁版或手機APP加以推測血紅素值，供大眾居家篩檢。

本研究可分為三個部分：第一部分利用指尖陀螺在不同角度(0-90度，指旋轉面與水平面之夾角)下進行轉動實驗。實驗結果顯示當角度越大，指尖陀螺的轉動時間越長;當角度為90度時有最長的轉動時間。轉動過程可分為高轉速區與低轉速區。前半部為高轉速區，其轉動頻率隨時間成指數衰減關係;後半段為線性區，其轉動頻率隨時間成線性衰減關係。在第二部分，我們將樹脂注入微型聚乙烯管進行離心實驗，結果顯示指尖陀螺與水平面角度為40度轉動時，可以達到最短的樹脂長度，亦即最好的分離效果。在第三部分，我們根據前述之實驗結果提出設計離心機的新概念，那就是：結合以下兩個要件1.試管轉動時應與轉動軸垂直與 2. 試管的轉動平面與水平面成40度時，此種離心設備相較於傳統離心機應可具有較高向心力(離心力)，可達更好的分離效果。