二等獎

從直徑數公分的小漩渦，到直徑可達10公尺的巨型海漩；由F1~F5級的龍捲風到輕重度颱風，大自然中有各種渦流。不久之前還有雙眼颱風（杜鵑颱風）經過台灣，颱風出現雙眼時其行進路徑常有不尋常的擺動，行進方向忽而偏北，忽而偏南，擺動的頻率比一般颱風來得頻繁，又其結構紮實，對流旺盛，常造成莫大的災害。研究這個主題主要的目的是嘗試探討此雙渦流運動的起因、其運動方式和可能的控制方法。

1. Purpose of the research Characterization of bacterial and viral diversity of brine Tyro using molecular methods of identification. 2. Procedures For bacteria: 1. Amplification or multiplication of 16S rRNA gene (one of the most conservative gene) by polymerase chain reaction (PCR). 2. Agarose gel electrophoresis and purification of PCR product 3. Ligation of purified PCR product into the vector pGEM-T 4. Transformation of plasmids containing an insert into competent cells E.coli XB1 5. Blue-white selection (we need white colonies, they contain the insert of interest) 6. Isolation of plasmids containing an insert of interest 7. Sequencing of inserts 8. Bioinformatics analysis: matching homologues from GeneBank database, construction of phylogenetic trees, statistical analysis. For viruses: The same methods were used for gp23 gene, which code a major head protein of T-even bacteriophages; to amplify gp23 gene a special set of primers was used, along with a standard cloning protocol described above. 3. Data 1) Two libraries of clones were obtained during analysis: lake Tyro (24 operational taxonomic units (OTUs), 10 classes) and sea water (6 OTUs, 2 classes of eubacteria). 2) The most abundant classes were: gamma-, delta-, epsilon- Proteobacteria, which is in agreement with previous reports about bacteria in brines of Mediterranean Sea. 3) The number of clones was not sufficient to obtain stable estimates of diversity, the analysis require additional data. 4) The diversity of bacteria was unexpectedly high in brine but not in the seawater, due to higher and more diverse ion composition. 5) Most of the detected bacteria in the deep-sea lake belonged to the previously undescribed (18,75%) bacteria or had unusual metabolism (43,75%). 4. Conclusions The analysis demonstrated unexpectedly high diversity of halophilic bacteria inhabiting Tyro lake. Most of bacteria presented in brine water had unique and uncommon characteristics based on information about its closest relatives. Therefore, the deep-sea hypersaline lakes of Mediterranean Sea have great potential for further investigations. Preliminary results of diversity of viruses of Tyro lake were obtained during analysis, more complete description is coming soon.

我們試著尋找所需最小的城堡個數以看守整個a × b × c (a,b,c ? N) 的長方體。所謂城堡是一種棋子，當放置城堡的位置是(x, y, z) ，則(x, y,t)、(x,t, z)、(t, y, z) (t 是任何不超出邊界的正整數)是這個城堡可以看守的格子。我們用這些城堡來完全看守長方體，試著找出其最小值。在2005 年我們猜測了a = b = c 、a = b c 、a > b > c 的上界，而在2006 年時完成了a = b = c 、a = b c 的大部分情況的證明，少數不能解決的部份也提供了不錯的上界。目前我們在a = b = c 、a = b c 的情況幾乎完全解決，目前正在向a > b > c 的部份發展。A generalized searching method of finding the minimum number of castle which can oversee all over the rectangular box, defined as a × b× c (a,b,c ? N) , is presented. The castle here is defined as one kind of chess. The castle positioned as (x, y, z) can direct the lattice points of (x, y,t) 、(x,t, z) 、(t, y, z) (t is the positive integer and smaller than the box size). These castles we use here is to oversee the rectangular box and to help us to find the minimum number. In 2005, we got the upper bound of overseeing the rectangular box in the conditions of a = b = c、a = b c、a > b > c , while in 2006 we complete the proofs of the minimum number of castles based on the conditions of a = b = c 、a = b c . The further work we want to attain is to complete the case of a > b > c.

本研究運用兩套方法，成功的化簡、篩選眾多結構；配合繪圖檢驗，證明了六邊形共有20種對稱拼貼圖結構。透過本研究，在適當軟體的支援下，使用者可快速且精準的設計出富有創意的密貼圖樣；所有的圖形結構亦可被更加廣泛運用。運用本研究理論與結果，我們撰寫了一Visual Basic程式，可供使用者快速方便判別任意的六邊形磁磚是否可對稱拼貼；最後，我們將研究結果應用於相關立體圖形，如：環面(Torus)、圓柱曲面(Cylinders)及莫比紙圈(Mobius Strip)；運用前人的研究，再配合本研究結果，將可以有更廣泛的應用，如：阿基米德立體圖….等。

In this work, techniques to explore the capabilities of multi-walled carbon nanotubes\r (MWNTs) in sorting nanoparticles (NPs) were presented. A droplet of a solution comprising of quantum dots (QDs) with various sizes was deposited on an aligned array of intertwined MWNTs. Photoluminescence (PL) and fluorescence microscopy (FM) revealed that MWNTs were effective nano-sieves that could effectively sort out QDs with a size difference of ~ 2.1 nm.\r Cadmium Selenide/Zinc Sulfide (CdSe/ZnS)core-shell QDs and Cadmium Sulfide (CdS) QDs were used to explore whether chemical properties of NPs affect the sieving capability of MWNTs. Further investigation on the effects of micro-patterning on the sieving ability of MWNTs was also carried out.PL and FM results suggested that micro-patterning could aid in separation of QDs and thus improve sieving capability of MWNTs. With the above findings, QDs emitting different colors as a result of size difference could efficiently be assembled onto the MWNTs en route to three-dimensional architectures with controlled assembly of NPs.\r Together with controlled laser power to remove desired amounts of QDs decorated MWNTs, a multi-colored display could be achieved. Further experiments were also carried out to determine the feasibility of introducing MWNTs as filters for NPs. Dilute solutions containing NPs such as gold colloid was run through these MWNTs filters by gravity. Field emission scanning electron microscope (FESEM) images of the samples showed that MWNTs were successful in trapping the nanoparticles. Explorations into the length dependent effect of using MWNTs as filters, suggested that 300μm MWNTs are better nano-sieves compared to 50μm MWNTs.

本文主要研究以數學方法探究物理上的平衡問題，將物理與數學的代數、數論、組合及幾何做了緊密的結合，並導出幾個有趣的結果。文中得出n的因數結構與平衡多項式的關係，以及平衡多項式與平衡問題一般解的關係，並進一步探討其平衡的排序策略及個數。再則將平衡多項式引入複數平面，可以看到許多有趣的幾何性質，並進而回歸至物理的應用。

本研究主要著重在以三極式電化學測試探討不同有機酸燃料甲酸、草酸、檸檬酸與不同觸媒Pt/C、PtRu/C、PtPd/C 在陽極電極的氧化反應之研究。從CV 圖可得知，分子量較低的甲酸有較低的氧化電位。以CV 與LSV 圖可知，以較高的氧化電流區分，是以PtRu/C 為三種觸媒中最適合當陽極電極的；若以穩定度區分，則以PtPd/C 為最佳。我們挑選PtRu/C 此觸媒進行燃料電池放電性能測試，得到的電流不高，原因在於配置的甲酸溶液為1M，甲酸在PtRu/C 電極反應太快，質傳推動力不足，使得燃料供應不足，造成電位迅速下降。This main target of this study is using three-electrode cells to choose which Formic Acid, Oxalic Acid or Citric Acid and Pt/C, PtRu/C or PtPd/C are better for fuel cell. From CV test, Formic acid which structure is simple has the lowest oxidation potential. Combine CV with LSV, if we focus on current, PtRu/C is the best catalyst for fuel cell. But if we focus on Stability, PtPd/C has the best of them. We choose PtRu/C to do the cell performance test. The current density isn’t enough high, this is because the concentration of formic acid is just 1M. Oxidation reaction of formic acid on PtRu/C is very fast. Mass transfer driving isn’t enough for this high reaction rate, so the potential drop is very fast.