龍眼樹的枝葉漸漸枯萎了，從一枝蔓延到另一枝，又由這一棵傳到另一枝，範圍越來越廣，原來的盎然綠意，卻換成了淒零肅條，我們的心裏好生可惜和疑問？有時候也曾看到一些人，手拿竹竿兒繫著鐮刀，挨著一棵棵的樹，在割取那些長了瘤的枝條，然後像寶貝似的裝進了袋子。它到底是什麼東西？怎樣來的呢？會是它才使得樹枝枯的嗎？它會有什麼用途呢？

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.

We study the magic power of dark energy and dark matter by using theoretical derivation and numerical simulations. We found that: 1. The dark energy will gain kinetic energy from the moving dark matter through gravitational interaction. Due to the law of energy conservation, the motion of the dark matter will slow down and satisfy Ek(t)−Ek0 ∝ρDE1.92 t, where Ek(t) is the kinetic energy of the dark matter, Ek0 is its initial kinetic energy, ρDE is the energy density of the dark energy, and t is the time. 2. The formation history and the structure of galaxies will be different due to the existence of dark energy. The more the dark energy, the earlier the formation of the galaxy core. In addition, the kinetic energy Ek(R) as a function of R will be different if the ρDE is different. Thus we can observationally measure the Ek(R) of galaxies, compare it will our results here, and then deduce the ρDE in our universe. The results here can be applied to the observations in the near future. 我們藉由理論的推導，配合電腦模擬的手段，來探討宇宙中黑暗物質和黑暗能量的神祕力量。我們發現：一、黑暗能量會透過重力交互作用而從運動中的黑暗物質獲得力學能，而且因力學能守恆，致使黑暗物質的速率減慢，滿足 Ek(t)−Ek0 ∝ρDE1.92 t, 其中 Ek(t) 為黑暗物質的動能， Ek0 為其初始動能， ρDE 為黑暗能量的密度，t 為時間。二、星系的形成過程及結構，會因黑暗能量的存在而改變。黑暗能量越多時，星系的核心會越早形成。而且動能 Ek(R) 隨著至星系中心距離 R 的變化，會因 ρDE 的不同而不同，因此可以試圖量測宇宙中星系的 Ek(R) ，然後和這裡的結果比對，即可推導出宇宙中的 ρDE 。這些研究成果，將可直接應用在未來的觀測結果上。

在1940 年代，Bouwkamp 提出一系列有關如何將矩形切割成若干個正方形的研究報告，但是如何找出正方形個數最少的方法仍是長久以來懸而未決的問題。在本研究報告中，首先引進「四角切割」的方法，並結合輾轉相除法的概念，來研究矩形的切割問題。我們的方法能大幅度降低正方形的個數，也適合做為此問題的上界函數。有關如何在長方體中切割出正立方體的組合，我們也將輾轉相除法的概念延伸到三維空間，進而建立所切割出最少個正立體數的一個上界模式。此外，藉由四角切割概念的延伸，我們也發現這個上界亦可再予修正。In 1940’s, Bouwkamp proposed the study of dissecting squares from rectangles. Among the study, the problem of the least number of dissected squares has been open for decades. In this project, we first propose a corner dissection method, associated with the famous Euclidean algorithm. By reducing nearly three fourths of the number dissected by the primitive Euclidian algorithm, our method indeed establish a suitable upper bound of the minimal number of dissected squares from the given rectangles Meanwhile, the Euclidean algorithm has also been considered to dissect the cubes from cuboids. We analyze the fundamental properties of the method and establish a prototype of upper bound function for the minimal number of dissected cubes. Moreover, the method of corner dissection has also been implemented for some cuboids, which also exhibits the acceptable improvement being a suitable upper bound.

在浩瀚的海洋當中有一個神秘的百慕達三角洲，那麼在數學幾何當中是否也有神秘的三角形呢？ 在課堂上，數學老師提到拿破崙不只是軍事家而且也算是數學家，他在數學史上留了一個以自己為名的三角形定理，名為拿破崙三角形定理。當看到此圖形〈圖一〉，幾何當中有如此神秘的圖形，因而興起了對此圖形深入研究的慾望，也是讓我們自己對數學有更深入的了解。雖然它是簡單的幾個三角形與線段所組成的圖形，卻是個富含許多創意與深思的幾何圖形，讓我們不由自主的陷入其中。

近幾年來，果汁飲料盛行，且標榜著含有豐富的維生素 C。維他命 C 是我們生活中所必須攝取的營養素之一，同時也是人人皆知的美容聖品。但究竟這些果汁飲料是否真的與新鮮水果一樣含有維他命 C？而檸檬是不是維他命 C 含量最豐富的水果？以及維他命 C 會不會受溫度改變而被破壞呢？希望透過收集資料及進行實驗後，對各種水果及果汁類飲料中維他命 C 的含量有更深一層的認識。同時，也提供資料給需要攝取維他命 C 的人與常喝果汁飲料的人作為參考。

本研究主要探討電解液之帶電離子在磁場中的動力行為。為了觀察更細微的結果，共歷經三代裝置改良，第一代用五個電錶及探針測量徑向橫截面上五點的電壓，所測數值電壓有下降趨勢但不足以呈現細微部份的變化。第二代利用電壓感應線、搭配平移台及電腦，呈現連續性且經數位處理之結果，出現電壓升降的電荷堆積現象。第三代為了更精確，將裝置結構及器材上改良。觀察到在磁場作用下有旋轉現象，改變電極極性時，會有順逆時鐘方向的改變，且只有電解質液才會有旋轉。更可以使用帶電質點受到勞倫茲力F=q(VxB)理論解釋。且旋轉中的電解液比沒有旋轉時，析出的銅量少，反應溫度升高快，電解液內電壓分布因電荷堆積造成的高低起伏。經過改變磁場強度、電解液濃度，不銅價離子電解液，結果濃度大、磁場大、離子數較多者，呈現電壓分布圖快速變化，彎曲大。This thesis report is the study of combining the moving charged particles under the perpendicular magnetic field. By using the theory of moving and electrolysis, the electrolytic liquid will swirl through the particular arrangement of the horizontal cylinders enclosed in a circular enclosure container and strong magnet. Then, the researcher observes the force situation of the charge in the magnetic field and discusses the differences of the electrolysis effect, which is experimented under the different conditions, such as, in the magnetic field or no-magnetic field. Furthermore, the researchers discuss the conduction of voltage spreading and interfering when the moving electrons under different position of two electrodes and under the different interaction of electric field and the magnetic field. And the changing reason as follow: （1）the magnetic field strength. （2）the concentration of the electrolytic liquid. （3）electrolytic solution. When the experiment group compared with the comparison group, the result may provide fundamental understanding as follow：（1） The researchers can find out the charged particles rotating in the magnetic field. And it proved the moving condition when the moving electrons in the magnetic field. （2） This experiment can be used in judging the solution, which I electrolytes, or not. （3） This experiment also proved for Arrhenius’s ionic theory. （4） The researchers found out the quantity of Cuprun decrease, the rise in temperature and the reducing in voltage.

本研究探討符合環保又延長花期的方法，由預備實驗已知碳酸飲料能有效的延長切花花期，因此實驗設計分別探討碳酸飲料所含的單一成分對切花開花的影響，採用蒸餾水以及對花期有顯著延長作用的50%碳酸飲料溶液作為對照組，比較不同成分和不同濃度的溶液所獲得的結果。結果顯示碳酸飲料的成分中，適當濃度的檸檬酸與葡萄糖促進開花與花形，但凋謝率也高；而由檸檬酸和檸檬酸鈉形成之緩衝溶液，不但促進開花也延緩凋謝。 關於吸水率的研究發現，適當濃度的檸檬酸溶液、緩衝溶液以及修剪花梗基部等提高吸水率的處理方式，促進開花速度與花朵品質，但對延緩凋謝幫助不大；「摘除頂芽」較能有效延長花期，而一般所知摘除雄蕊阻止授粉的方式，對於穗狀花序的劍蘭並不適用。 綜合本研究結果，提供適當的碳水化合物，維持偏酸且pH值穩定的溶液，配合摘除頂芽，可以提高花瓣展開程度和延長花期。

紋白蝶的一生中，由卵→菜蟲→蟲蛹，再變化成蝶。蟲蛹期是最危險的時期，蛹不能爬也不能飛，一旦被天敵發現，就只能坐以待斃。因此蟲蛹在自然界要如何利用環境來躲避天敵，保護色就是它生存的保障。我們發現，蛹色都是由褐、灰、綠三色所組成的，有如阿兵哥的迷彩裝。蟲蛹本身會隨著光線明暗度與環境顏色而調整色彩的深淺和色系，讓天敵不易發現。而環境四周的顏色可以穿透蛹殼半透明的淺褐色，使得蛹色和環境顏色融合在一起。小蟲蛹在生存的競賽中所展現出的智慧，堪稱自然界的勇士。

民俗技藝中有一項童玩─「竹製的響螺」，經由在自然科學研習社的活動過程，我們發覺以底片盒所製成的的響螺，也具有相同的效果。進一步在實驗中了解到其頻率與多項因素有關，因此想藉由自行設計的工作平台進行頻譜數據量取，而從所得數據分析發現：一、響螺在垂直地面旋轉時並無法發出聲音，但當與地面不垂直時反而會發出聲音；由此可知，響螺是在不垂直地面的情況下與空氣有較劇烈摩擦進而在筒內產生共鳴。二、當響螺傾斜時，它的特徵頻率會隨著傾斜角增大而有先降低而後升高的現象發生，此與空氣摩擦程度有關。三、響螺之轉速愈快，特徵頻率會愈大，但增加到某一程度時其特徵頻率會回到較低之頻率。四、響螺的缺口如果加長或加寬皆會提高其特徵頻率。五、缺口厚度較薄會使特徵頻率降低，但會使響度加大。六、缺口受風邊如果是凸出則特徵頻率較低，反之凹陷時會較高七、響螺之材料與管子直徑皆不影響其特徵頻率。八、響螺管子愈長，其特徵頻率會愈低，反之則較高，但太短的共鳴管所產生之特徵頻率需修正為八分之一波長的共振。