從參考資料[1]可知，將凸n+2邊形利用n-1條不相交的對角線剖分成n個三角形的圖形數量即為卡特蘭數Cn。而我利用不相交的對角線把n+2邊形剖分成數個多邊形和三角形的組合，並從此類的剖分圖形與三角剖分圖形之關聯，進而由卡特蘭數的一般式推導出此類剖分圖形數量的一般式。在本研究中可得，若到把n+2邊形剖分成一個k+2邊形和多個三角形的圖形數量是(2n-k+1 n+1) ；把n+2邊形剖分成一個k+2邊形、一個m+2邊形和多個三角形的圖形數量，當m≠k，數量為n+2/2(2n-k-m+2 n+2) ，當m=k時，數量為n+2/2(2n-2k+2 n+2) ；把n+2邊形剖分成一個k1+2邊形、一個k2+2邊形、一個k3+2邊形、和n-k1-k2-k3 個三角形的剖分圖形，當k1,k2,k3兩兩相異時，數量為(n+2)(n+3)(2n-k1-k2-k3+3 n+3) ；把n+2邊形剖分成一個K1+2邊形、一個K2+2邊形、一個K3+2邊形、一個K4+2邊形和n-K1-k2-k3-k4個三角形的剖分圖形當k1,k2,k3,k4兩兩相異，數量為(n+2)(n+3)(n+4)(2n-k1-k2-k3-k4+4 n=4)。並猜測若k1,k2,...,ki兩兩相異時，把n+2邊形剖分成一個k1+2邊形、一個k2+2邊形、…、一個ki+2邊形、和n-Σkj 個三角形的剖分圖形數量為(n+i)!/(n+1)!(2n-Σkj+i n+i) 。

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.

我們的研究是利用空氣盒子設計出一個裝置，用以觀察環境中懸浮微粒潮解膨脹現象。 我們觀察了由硝酸銨與硫酸銨各自以及不同比例與混合模式組成的懸浮微粒。純硝酸銨的潮解點不明顯，純硫酸銨有明顯的潮解點。內混合懸浮微粒有一個潮解點，並且出現3種類型的潮解行為，分別是偏向硝酸銨或硫酸銨以及過渡型，後者粒徑成長的比例會比前兩者來得高。外混合懸浮微粒有兩個潮解點，保留兩種成分各自的特性。 我們利用雨水觀察環境中懸浮微粒的潮解膨脹現象，將其與內混合懸浮微粒的潮解點與潮解行為做比較，來推估其成分與來源。確定我們的裝置能推估出主要的污染成分及來源。

小分子團水(water cluster)的製備及應用一直是科學界的挑戰。本實驗利用熱蒸鍍法，加熱金屬塊材成原子蒸氣，在氬氣環境配合液態氮溫度下冷凝收集，成功製備了平均粒徑10nm金、20nm銀、54nm銦、71nm錫、14nm鎳奈米顆粒。將定量的奈米顆粒滲入去離子水中，以超聲波分散顆粒團聚，再以波長530奈米的綠光照射，讀取拉曼散射譜圖，判定來自小分子團水的振盪強度，探討5種奈米顆粒對形成小分子團水的功效。我們驚訝的發現奈米銦藉表面電漿共振(surface plasma resonance)及表面電子氧化還原功效，弱化水分子團簇成大分子團的功效為奈米金的16倍，奈米錫為12倍，也均高效於奈米銀及奈米鎳。以奈米銦及奈米錫增益小分子團水後，對將癌細胞藥物、養分帶入細胞的功效明顯提升。

本研究在生物光伏電池(Bio-photovoltaics, BPV)的陽極添加能氧化含氮廢物放出電子的硝化菌，並在陰極添加能吸收電子還原硝酸鹽與硫酸鹽產生氮氣與硫化氫的厭氧菌，建立不需外部供給物質，能夠自我維持且不斷發電的微型生態圈(Boxed Micro-Biosphere, BMB)。實驗結果顯示在陽極加入硝化菌後，能使含小球藻與共生菌Sym1的BMB功率提升38倍至99.46±9.31μW · m-2，而在陰極加入厭氧菌能讓功率再提升至262.51±37.30 μW · m-2，且此電池截至目前為止已運轉超過4272小時，發電功率仍保有67.4%(176.98 μW · m-2)。若將Sym1與Sym2同時加入陽極則可使功率密度提高至463.19±25.50 (μW · m-2)，夜間功率可達白天的93.1%，但在野外實驗環境下一週內就失去發電能力。若將BMB中小球藻換成來自高溫與強酸環境的溫泉藻(H)，其野外平均功率為388.80±14.87 μW · m-2，夜間發電量為白天97.9%，其功率與壽命(目前尚在運作中)遠高於小球藻BMB。 未來我們將篩選能加強溫泉藻發電能力的共生菌使其更具實用性。

缺氧（Hypoxia）在癌症中，影響腫瘤微環境（Tumor microenvironment，TME）的重塑扮演重要的角色。原位癌細胞與欲轉移之遠端器官的微環境間，會透過細胞外囊泡（extracellular vesicles，EVs）進行細胞間相互作用，對於轉移前腫瘤微環境（Pre-metastatic niche，PMN）的形成和轉移過程至關重要。 本研究目的在闡明缺氧條件下，肺腺癌如何透過產生的外囊泡重塑肝臟轉移前微環境。結果顯示缺氧刺激肺癌產生的細胞外泌體（Exosome）增加了肝臟星狀細胞（hepatic stellate cell，HSC）活化和血管生成。由於缺氧肺癌所分泌的EVs含有CD151蛋白，促進HSC的活化和血管新生。缺氧肺癌所產生的Exosome增 加了HSC和內皮細胞中FAK（focal adhesion kinase）、Src（SRC proto-oncogene, non-receptor tyrosine kinase）和AKT（AKT serine/threonine kinase）通路的激活。 總結此實驗證實了缺氧腫瘤衍生的Exosomes，探討其中富含的CD151機制，活化了HSC與特別的訊息傳遞於細胞中，調節肝臟PMN的形成。因此CD151可作為肺腺癌轉移至肝臟的新治療靶點。

The research work is dedicated to analyzing the impact of disposable tableware and packages made from synthetic polymers on people and the environment, and the search for ecological alternatives to synthetic polymers used in their production. Various types of disposable tableware and packages, their composition, production technology, harmful effects on the human body, environmental pollution, processing and recycling were studied. The statistics of the use of disposable tableware and packages in Ukraine and the world as a whole, the places of their use were analyzed. Ecological alternatives to disposable tableware and packages made from various natural materials have been studied. A practical study of the use of organic waste and wastepaper for the production of ecological disposable dishes and packages was carried out.

The development of rapid and efficient synthetic approaches to the bioactive cyclic and polycyclic azaheterocycles is one of the most important challenges in organic synthesis. In this work effective and simple synthetic approaches to polysubstituted pyrrolidin-2-ones 2 and isoindolines 3 from donor-acceptor cyclopropanes 1, bearing the ester group as the one of acceptor substituents, and amines were developed. The γ- pyrrolidone based skeletons and isoindoline ring system is a constituent of many biologically active molecules, both natural and synthetic, and a key component of clinically relevant entities (Fig.1,2) [1,2]. The synthesis of pyrrolidin-2-ones 2 includes Lewis acid-catalyzed opening of the donor-acceptor cyclopropane with primary amines (anilines, benzylamines, etc.) to γ-amino esters, followed by in situ lactamization and dealkoxycarbonylation. The reaction has a broad scope of applicability; a variety of substituted anilines, benzylamines, and other primary amines as well as a wide diversity of donor-acceptor cyclopropanes bearing (hetero)aromatic or alkenyl donor groups and various acceptor substituents, can be involved in this transformation. In this process, donor-acceptor cyclopropanes react as 1,4-C,C-dielectrophiles, and amines as 1,1- dinucleophiles. The resulting di- and trisubstituted pyrrolidin-2-ones can be also used in subsequent chemistry to obtain various nitrogen-containing polycyclic compounds of interest to medicinal chemistry and pharmacology, such as benz[g]indolizidine derivatives. The synthesis of the substituted isoindolines 3 is based on the domino-reaction between donor-acceptor cyclopropanes, bearing in ortho-position of aromatic substituent a bromomethyl group, and different primary amines (e.g., anilines, benzylamines, cycloalkylamines) was developed. The reaction involves the generation of secondary amine followed by nucleophilic ring opening of cyclopropane with amino group. Moreover, this process provided a new practical method for the rapid synthesis of benzo[b]pyrrolizidinone 4 from readily available starting materials.

文獻指出若神經導管能針對不同組織調整適切軟硬度，將更有效協助神經再生，因此，了解胞外基質軟硬度對神經細胞的影響和其感知路徑非常重要。本研究以神經母細胞瘤Neuro-2a進行研究，分析不同軟硬度基質上N2a細胞面積、神經突長度。結果顯示分化後N2a細胞在100 KPa基質上面積大且神經突較長，說明N2a細胞能偵測基質軟硬度並進行生長調控。同時，advillin、paxillin、myosin IIa和pFAK等細胞骨架蛋白於細胞本體表現量在不同軟硬度基質上有所差異，但未與神經突長度相關。生長錐上細胞骨架蛋白表現量於不同軟硬度基質上具有差異，且與神經突長度趨勢吻合，說明神經細胞透過調控advillin和細胞骨架蛋白在生長錐上的表現量影響神經突生長長度。未分化N2a細胞轉染pAdvillin-IRES-hrGFP和pS1S3-HP-FLAG後長出神經突，且根據基質軟硬度生長情形不同，但轉染pS1S3-HP-FLAG長出的神經突長度較短，說明advillin的nucleation功能在神經突生長扮演重要角色。

許多長者常因吞嚥功能退化，飲食過程中易引發吸入性肺炎，或是患者手術後吞嚥功能暫時消失。目前台灣社會對這些狀況最易被接受的治療方式是從鼻腔放入一條直達胃部的軟管，俗稱鼻胃管。但是管子本身會造成人體不適，因此許多患者會將管子拔出。管子拔出相對舒適，但當再次將管子放回時，會使病患更加不適。且台灣步入高齡化社會，照護人員短缺，使鼻胃管脫落成為台灣醫療通報事件的榜首。 為了改善這問題，我們設計了一款照護輔助手環，藉由EMG Sensor 來偵測手指動作，搭配3組感應距離不同的RFID讀取器，來偵測手部與鼻胃管接頭距離。當系統認為患者有自拔危險時，便啟動約束裝置，由手環上方彈射出一塊彈性布將手掌全部包住，並同步發出警告聲響及手機訊息。本作品可以避免患者面臨二次插管的窘境，亦能減輕照護者及護理人員的負擔，是長照時代的重要幫手。