When you draw a wet finger around the edge of a half filled wine glass, a sweet musical sound comes forth. The pitch of this sound is directly correlated to the amount of liquid in the glass- the higher the height of the liquid is, the lower the frequency is. It means that the shorter the air column in the glass is, the lower the frequency is. This phenomenon differs from the variance in pitch in a wind instrument. In a wind instrument such as a flute, the shorter the air column in its chamber is, the higher the resulting pitches are. In order to study the wine glass phenomenon, we used a piezoelectric crystal loudspeaker connected to an oscilloscope. We recorded the resulting data by using a digital video recorder to capture the images of the waveform of sound, and than analyzed the waveform by using the computer. Our conclusions are as follows: 1. The frequency of sound thus produced was the same whether we draw our finger around the rim, or we strike the glass rim. The higher the height of the liquid is, the lower the frequency is. But the frequencies vary when we strike the glass and when we blow on the edge. 2. When we used a glass without liquid in it, the frequency emitted when we drew our finger around the edge, this frequency varied inversely as the cube root of their weights. 3. In a glass with liquid, the emitted frequency did not have any correlation to the weight of the contents. By taking two identically filled glasses and placing in each a solid object of the same size but different weight, we were able to see that there was no change in the frequency emitted between the two glasses as long as the height of the liquid remained constant. 4. According to “The Flying Circus of Physics”, if we tap the side of a glass of beer, because of the air bubbles in the beer, the frequency emitted will be lower than that from a glass of pure water. This is according to the book, because the speed of sound is lower in air than in water, therefore the speed of sound in an air-water mixture would be lower than in pure water. The resonant frequencies of the mixture will also be lower. However, in our experiment, we discovered that\r when the glass contained air bubbles, the frequency emitted higher. Our explanation is that the sound emitted since the rim of the glass oscillated transversely, the frequency depends only on the retard of the rim and that the frequency is independent of the speed of sound. The intention of this research is to clarify the many misconceptions of this interesting phenomenon.以溼的手指在玻璃酒杯邊緣摩擦，會有悅耳的聲音，而且頻率會隨著內裝液體減少（空氣柱變長）而變高，這種變化與管樂器隨空氣柱的變長而音調變低不同，為了研究它的原因，我們利用壓電晶片喇叭連接到示波器上，並且利用數位錄影機錄下示波器上的訊號，再以電腦分析出瞬間的頻率，結果發現：一、摩玻璃杯與敲玻璃杯，杯所發出之頻率相同，都是所裝液體愈多發出之頻率愈低。但敲玻璃管與吹玻璃管所發出之頻率不同。二、不裝液體之高腳杯，摩擦時所發出之頻率與重量之立方根成反比。（與鐘相同）\r 三、裝液體之高腳杯發出之頻率，不再與總重量有關，而是與液體之高度有關，保持液體高度不變，即使在杯子中央加入不同重量之固體，杯子振動頻率還是不變。若改裝不同密度之液體，則密度愈大頻率愈低。四、在“The Flying Circus of Physics”書中提到輕敲裝有啤酒之杯時，會因杯中含有氣泡而聽到較低之音調，書中解釋是”空氣中之音速低於水中之音速，混有空氣之水中音速變低，其共振頻率也會降低。”但我們的實驗結果是有氣泡時頻率反而高。我們的解釋是杯子所發出之聲音是由於杯面之振動也就是杯壁的橫向振盪，振盪頻率與液體對杯壁之阻尼有關，但與液中聲速無關，密度愈大之液體阻尼愈大。有氣泡時接觸杯壁之液體變少，阻尼較少所以頻率高。希望本研究能使大多數人對這有趣之現象不再有誤解。

人類目前廣泛的應用奈米鑽石，奈米鑽石粒子極為微小因此很容易進入生物體內，對於生物體所產生的影響為本次的研究對象：奈米鑽石、奈米磁性粒子之生物毒性與其在生物體的分布。\r 加入奈米鑽石、奈米磁性粒子之後綠豆發芽數減少。發芽的綠豆中加入不同量的奈米鑽石、奈米磁性粒子，發現濃度越高生長速度越慢。在綠豆吸收奈米鑽石、奈米磁性粒子後，在根、莖、葉細胞內都有發現奈米鑽石、奈米磁性粒子。在麵包蟲的研究中發現，在0.25克濃度下，有些微的影響，而在0.75克和1克之影響甚大。在人類胎盤滋養層細胞中，發現加入奈米鑽石800微克以上對其有毒性。在細胞的分布，可發現細胞質及細胞核中都有奈米鑽石，當細胞內太多或作用太久時，會出現細胞凋亡的現象，此時奈米鑽石會大量聚集在細胞核，這可能是造成細胞死亡的原因之一。本研究意外發現在細胞分裂時，奈米鑽石只分布在細胞核周圍的細胞質，但是在赤道板及染色體上並沒有。

二元根樹是資訊科學上最重要的結構之一，因此其結構的探討就很有價值。在這個研究中，我們探討二元根樹上反鏈(Antichain)，鏈(Chain),獨立集(Independent set)計數。在每一個子題之下，我們求出計算反鏈，鏈，獨立集的方法。之後我們求出極值(包括最大跟最小值)，並且討論該極值之下所有可能的樹形。此外，我們並討論要列出二元根樹上這些資料(反鏈，鏈，獨立集)所需的演算法。In this paper we enumerate the number of antichains, chains, and independent sets of a binary tree of size n. After that we focus on the extreme values (maximal/minimal). we calculate the extreme values and discuss the possible graphs of trees when achieving these extreme values. Moreover, we offer algorithms for listing all the objects in each extreme case.

這個專題研究的目的是要發展出一套簡單可靠的方法和廉價自製的器材，在地面上即能有效估測大氣層的厚度。我們小組研究光學中雷氏(Rayleigh)散射的原理，針對空氣分子對光線散射作用和特定方向之偏極效應，利用一已知散射長度之路徑，測量其偏極光的強度，同時比對由大氣層散射而來，在同一偏極面上的散射光強度，即能估算大氣層的厚度，方法簡單新穎，自製器材經實際測量和改進，有發展和推廣的價值。\r The main idea of the experiment is to set a system in order to effectively estimate the thickness of the atmosphere. On the theory of “Rayleigh Scattering” (small air molecules sizing about 10-4μm), we developed an equipment that has two tubes. The tubes lead the scattered lights from two paths. One is called “air light” scattered in the ground air, and the other “sky light” is scattered in the sky and reflected by a beam splitter. The two paths are on the same plane; the scattered lights are perpendicular to the direction of sunlight and 100% polarized. We could adjust and measure the distance “d” of the air light path. We simultaneously observe and compare the intensity of the lights from the two paths with the electronic instrument made by ourselves. By using the known distance “d” and the reflection “x” of the beam splitter, we can calculate the thickness of the atmosphere. The experiment is simple, novel and easy to do in an extensive field at school. Researchers don’t have to use a bloom, radar or satellite to discover the atmosphere, but you could use a simple equipment to observe the features of it.

中文摘要：\r 化學實驗中，常常會使用到各種具有揮發性的有機溶劑，如醇類、酸類、醛類及酮類等。\r 當吸入過量的揮發性有機溶劑時，將會對人體造成嚴重的傷害，故使用時格外需要留意。有\r 鑑於此，我們開始著手研究如何偵測氣相中的有機氣體分子。\r 本研究中，我們利用聚苯胺薄膜吸附氣體分子的特性並結合對質量變化極靈敏的石英晶\r 體微天平，自行設計了一套簡單、藥品用量少且不需昂貴儀器的實驗系統。藉由此系統，我\r 們有效的針對各種揮發性有機溶劑進行偵測，並進一步地探討不同氣體分子對於聚苯胺薄膜\r 的吸附現象。\r \r 英文摘要：\r Students usually use volatile organic solvent in laboratorys such as alcohols, carboxylic acids,\r aldehydes, ketones, etc. It will injure our body when we breathe in too much volatile organic\r solvent. For this purpose, we begin to study how to detect volatile organic compound in air.\r In this work, we combine polyaniline membrane which can adsorb gas molecules and quartz\r crystal microbalance which is highly sensitive to mass changes to design a simple and inexpensive\r system which needs only little chemicals. With this system, we can effectively detect different\r volatile organic compounds. Furthermore, we can also study the adsorption of polyaniline\r membrance for different volatile organic compounds.

我們從日常生活中的酒瓶填塞問題，延伸出圓在相守條件下產生的衍生圖面\r 積極值及相守圓排法等問題，研究過程中我們發現以下的結果：\r 一、 我們可以利用較少個相守圓的排法，以繁殖或增加的方式排出較多個相守圓\r 的衍生圖。\r 二、 當相守圓數量為2個、4個及6個時，相守圓以對角線排列，且衍生圖為正方形\r 時，面積會產生最大值。而當相守圓數量為3 個及5 個時，衍生圖面積最大\r 值會出現在相守圓排成波浪形時，但其夾角並非特殊角。\r 三、當相守圓數量為2個至6個時，相守圓以直線排列，衍生圖面積會產生最小值。\r 四、透過不同層數、個數的研究得知：當相守圓的數量為11個或14個以上時，存\r 在正三角形排法小於直線排法的情形 。而相守圓個數在10個以下時，直線排\r 法面積都叫正三角形排法小。\r 五、我們可以用質單元分割的方式討論更多圓數時，相守圓間的排列方式，使得\r 生多元間的排列變為數字間的加法排列，可以大大降低討論情形的複雜度。\r 六、我們可以用密度的概念，搭配質單元分割的方式，得到不同圓數時，以不同\r 衍生多元搭配波浪形法形成之衍生圖密度最小值。\r 七、我們可以算幾及柯西不等式來驗證特定類型的衍生圖面積極值，也可以列出\r 面積函數來分析不同類型的衍生圖面積極值。

我們使用陽極氧化鋁(AAO)模板來製備銅及其氧化物的奈米線。以硫酸銅和乳酸配製電鍍液，利用氫氧化鈉水溶液(NaOH)將其pH 值調整到12，供以不同電壓，可電鍍出銅及氧化亞銅奈米線。在較高電壓下可製備出銅奈米線，而在較低電壓下可製成氧化亞銅奈米線，若使用中間電壓則能製得銅及氧化亞銅的混合態。利用x 光繞射分析儀(XRD)來分析其結晶構造、使用場發射掃描式電子顯微鏡(SEM)以得知其表面形貌。電鍍出的奈米線直徑約60 nm。奈米線的長度可藉由調整電鍍時間或電壓來控制。在製作IC 內部導線方面，銅奈米線深具開發潛能；在提升太陽能電池的轉換效率、製作可見光光觸媒方面，氧化亞銅奈米線極具前瞻性。We electrodeposited copper and cuprous oxide (Cu2O) nanowires with anodic aluminum oxide (AAO) templates. Both Cu and Cu2O nanowires could be prepared with an alkaline cupric lactate solution, which was adjusted to pH 12 using a 6 M NaOH, when supplied with different electrolytic voltages. Cu nanowires could be prepared when a higher voltage was supplied, and Cu2O nanowires could be prepared with a lower voltage. A mixture of Cu and Cu2O nanowires could be prepared with a supply of a voltage in between. X-ray diffraction (XRD) is used to determine the phase composition, and scanning electron microscopy (SEM) is employed to characterize the morphology of the nanowires. The length of nanowires can be controlled by adjusting the time spent on electrodeposition and the voltage supplied. The resultant diameter of the nanowires was about 60 nm. Cu nanowires are promising materials for making the conductive wires in IC, and Cu2O nanowires hold great promise for improving the conversion efficiency of solar cells and manufacturing visible-light photocatalyst.

在模式植物──阿拉伯芥（Arabidopsis thaliana）中，AtYAK1（Arabidopsis thaliana Yak1-related protein kinase）是目前發現唯一屬於DYRK（Dual specificity Yak1-Related protein Kinase）的蛋白激?。雖然之前研究已證明，不同物種之DYRKs 和細胞的生長與發育過程有關。然而，其在植物中的生理功能卻尚未被明確地研究報導過。在先前的研究中，為瞭解AtYAK1 在阿拉伯芥內作用之位置，前人選取AtYAK1 基因ATG 上游約2.5 kb 的序列（Upstream Element, 2.5KUSE）建構至一含有GUS（β-glucuronidase）報告基因的質體中，並轉形至阿拉伯芥，進行GUS 組織染色分析。但在初步結果中，並沒有在轉殖株觀察到明顯的GUS 表現。進一步分析，我們發現在2.5KUSE 序列末端約0.5 kb 的5’非轉譯區（5’untranslated region, 5’UTR）中，有四組開放讀序框（Upstream Open Reading Frame, uORF）。有趣的是，許多研究也顯示，uORFs 會影響轉譯過程中的再起始（re-initiation）作用而調控該基因的表現。另一方面，前人亦透過構築好的2KUSE 轉殖株（即不含有5’UTR）進行上述GUS 實驗。結果發現，此2KUSE 轉殖株的GUS 表現非常顯著。本實驗即要瞭解AtYAK1 的uORFs 是否也會影響其蛋白質的合成。首先，我們以點突變的方式將四組uORFs 中之ATG 換成TTG，目的為構築不含有uORFs 之5’UTR（mutated uORFs, ΔuORFs）。在進行原生質體短暫表現分析法（protoplast transient assay）及GUS 組織染色分析後，將結果與含有uORFs 的結果作比較：當缺乏uORFs 後，其3’端報告基因的表現量確實比原來顯著。綜合以上，我們認為此uORFs 對於AtYAK1 蛋白質之表現佔有相當重要的影響地位。最後，我們對5’非轉譯區是否存在開放讀序框進行阿拉伯芥全基因組分析，相關結果亦於本研究報告中分析討論。AtYAK1（Arabidopsis thaliana Yak1-related protein kinase）is the first DYRK（Dual specificity Yak1-Related protein Kinase ） family member identified in the model plant ─ Arabidopsis thaliana and exists as one copy gene in Arabidopsis. Previous studies showed that many eukaryotic DYRKs are involved in regulating the growth and development of cells. However, the study of AtYAK1 in Arabidopsis is lacking to date. In order to understand where AtYAK1 expresses and functions in plants, a 2.5 kb fragment which is located upstream from the major ATG of AtYAK1（termed Upstream Element, 2.5KUSE）was previously constructed to drive the expression of a reporter gene, GUS（β-glucuronidase）, in transgenic Arabidopsis. Much to our surprise, no GUS expression signal could be detected in such transgenic plants. When further analyses were performed, we found that there are four upstream open reading frames （uORFs） in the 5’untranslated region ( 5’UTR ) within the 2.5KUSE. Many studies indicating that the uORFs can regulate the translation of downstream ORF encoding the major gene product through the procedure of translation re-initiation. This action represents a mode of translational regulation for gene expression. Indeed, GUS activity could be readily detected in transgenic plants expression 2KUSE::GUS, a construct lacking the 5’UTR of AtYAK1. In this study, I have tried to elucidate whether the uORFs of AtYAK1 can regulate the translation of the downstream major ORF. First, in order to construct a 5’UTR fragment of which uORFs have been mutated（ΔuORFs）, we apply site-directed mutagenesis to substitute ATG with TTG for the four uORFs and examine the expression of GUS driven by this mutated 2.5KUSE. After analyzing the results in both Arabidopsis protoplast transient assay and transgenic Arabidopsis, stronger expression of reporter genes in both systems were observed when the four uORFs were mutated. We have also confirmed that, in transient expression system, the increase of reporter gene activity was not due to the excess accumulation of the corresponding mRNAs. Rather, it is the four uORFs which play an important role in negatively regulating the translation of AtYAK1, possibly via inhibiting the translation re-initiation of major ORF. A genome-wide examination of uORFs in all Arabidopsis genes was also performed to assess the possible contribution of uORF in regulating gene expression.

本實驗在探討，當金奈米粒子和植物中的葉綠素產生鍵結作用力時，能量轉移的結果是否能幫助葉綠素激發電子。經由兩者混合後光譜的變化,發現兩者之間發生能量轉移。為探討此轉移現象和濃度的關係，我們將大小不同的金奈米和不同毫升數的葉綠素作用，並將其結果和金奈米與葉綠素的吸收強度和作比較，使用正規化的計算方法算出比值，由此看出兩者之間能量轉移的效率。當金顆粒約大於30nm時，正規化的數值隨的葉綠素濃度的增加而變大；而當金奈米顆粒約小於30nm時，則隨著葉綠素的增加而變小。Much attention is currently focused on chromophoric molecules because they can not only mimic natural antenna systems but also exhibit unique optical and physical properties. Chlorophyll , produced by extracting from green leaves, has electrostatic interactions with Au nanoparticles through carboxyl groups. Herein, we report the charge transfer between chlorophyll and Au nanoparticles using UV-vis electronic absorption spectroscopy. The efficiency of charge transfer from chlorophyll to Au nanoparticles was estimated by the normalization of Q-ban absorption intensity. From the observation of absorption intensity versus concentration of chlorophyll curves, we find that the efficiency of charge transfer is increased while the size of Au-particle is larger than 30nm, but decreased while the size smaller than 30nm.

傑克船長和他的海盜們掠奪到許多箱珍寶，每箱含有數量不等的金幣及鑽石。船員們深怕傑克船長又出什麼陰謀，一致同意讓船長任選一半的箱子拿走。\r 當然，傑克不知道金幣和鑽石的價格比，為了保證可以得到一半的利益，傑克希望他拿到的金幣和鑽石都各占一半。傑克的願望會實現嗎？\r 這個問題已用高等數學證明其解，而本研究利用初等數學的方法，除證明傑克需取的最少箱子數外，同時也能更快速的算出取法。\r 類似的結果可應用至分配災區物資等情形，或任何無法轉移、獨立的資源，如各式專長的人才、多功能的機械等，期望可對更有效的分配做出貢獻。