在generalized Petersen graph P(n,5)中的hyper Hamiltonian
Generalized Petersen graph P(n,k)，定義為n 為不小於2 的整數以及1≤ k ≤ n−1，有頂點{ u0, u1, . . . , un−1, v0 , v1 , . . . , vn−1 }，及路徑{ uiui+1 , uivi , vivi+k：1≤ i ≤ n−1 }。在 [2] 中，我們可以知道P(n,5) 是Hamiltonian 等價於當n≠11。
在這一篇報告中，我們證明當generalized Petersen graph P(n,5) 是hyper Hamiltonian（一種Hamiltonian graph 再去掉任何一點後，仍然是Hamiltonian graph）的充要條件是n 為不等於11 的奇數且n ≥ 7。
The generalized Petersen graph P(n,k), n ≥ 2 and 1≤ k ≤ n−1, has vertex-set { u0, u1, . . . , un−1, v0 , v1 , . . . , vn−1 } and edge-set { uiui+1 , uivi , vivi+k：1≤ i ≤ n−1 with subscripts reduced modulo n}. And we can know that P(n,5) is Hamiltonian if and only if n≠11 from [2].In this paper it is proved that generalized Petersen graph P(n,5) is Hyper Hamiltonian (A Hamiltonian graph can still be a Hamiltonian graph when any one of the nodes fault) if and only if n is odd and n≠11.
了解抗氧化的「旋」機-利用自製的旋光儀來探討旋光性與抗氧化成分之間的
In this research we derived heating effects on anti-oxidation by optical rotation analyses. A simple and accurate Polarimeter was devised with polar screens, laser, and photo resistor; the laser was used for light source, and the photo resistor for detection. Four kind of fruits, Hyloceeus polyrhizus, California plum, kiwi and tomato were experimented by heating them in boiling water and microwave oven. Their optical rotations versus time duration were calculated. Then we used ABTS/ the H2O2/HRP analysis system from Arnao's research to obtain the heating effects on anti-oxidation by calculating the vitamin C densities versus lag time. We found that there was a tendency of increased anti-oxidation at the beginning by heating, but decreased afterwards. Better oxidation was achieved by using microwave for Hyloceeus polyrhizus, by using boiling water for kiwi and tomato, and by using both methods for California plum. The same tendency was also found in the optical rotation analyses. Therefore we successfully developed a new method to measure the antioxidant activities by the optical rotation. We can also apply this method to simulate the fruit digestion process in the stomach, which let us understand further about anti-oxidation ( or optical rotation ) versus time. 本研究利用偏振片、雷射光為光源、光敏電阻為偵測器，組裝成一個簡易且精確的旋光度計。 我們利用此旋光度計對奇異果、火龍果、聖女蕃茄、加州李子四種水果以微波、水煮及油浴三種方式來處理，求出水果的旋光度與熱處理時間的關係。再藉由Arnao 研究的ABTS/ H2O2/HRP 分析系統，以不同濃度的維生素C與延遲時間畫圖作為標準曲線來測量總抗氧化活性，並比較熱處理後抗氧化活性的變化趨勢。 透過本研究可以了解不同熱處理方式對四種水果之抗氧化活性初期皆有增加的趨勢，但隨著時間增長則抗氧化活性降低。其中奇異果與聖女蕃茄用油浴，火龍果用微波處理，加州李子則是用任何熱處理方式均可得較佳的抗氧化活性，而熱處理後在旋光度測量上也有相同的趨勢。因為此兩種方法有一致的反應趨勢，所以證明我們成功地開發出一種可以利用旋光度來測定抗氧化的新方法。 最後，應用本方法進一步模擬水果在胃部裡的消化，讓我們更可以了解在整個消化的過程中抗氧化活性(旋光度)隨時間變化的情形。
丹尼爾寶寶的酗酒日記--酒精對斑馬魚胚胎頭骨與腦下垂體基因的影響
長期以來，臨床研究發現酒精會影響人類胚胎的正常發育，但是其分子機 制尚不清楚。在本研究中利用RNA 定位雜交的方式觀察酒精對於胚胎發育過程 中shh、sox9a、sox9b、col2a1、hand2 的影響，發現這些基因的表現均會受到酒 精的抑制。這項結果顯示在胚胎發育過程中，酒精透過對上述基因的影響，造成 神經脊細胞減少，細胞遷移異常，以及干擾軟骨細胞分化的現象，進而造成頭骨 發育的嚴重缺陷。此外，實驗中亦發現生長激素在腦下垂體的表現亦受到酒精抑 制。這項研究的結果成功地從基因的層次深入了解胎兒酒精中毒症候群造成頭骨 畸形及生長遲緩的病理機制。 It was known that prenatal alcohol exposure may cause serious birth defects and developmental disabilities. The molecular mechanism of this fetal alcohol syndrome still remains unclear. As revealed by whole mount RNA in situ hybridization, it was shown that expression of a number of craniofacial cartilage-related genes, including shh, sox9a, sox9b, col2a1 and hand2, were all inhibited in zebrafish embryo by alcohol exposure. It suggests that alcohol exposure may result in reducing neural crest cell production, interfering neural crest migration, preventing chondrogenesis and eventually cause craniofacial defects. In addition, the transcriptional profile of pituitary hormones were investigated by RNA in situ hybridization. It appears that only growth hormone, but not prolactin and thyroid stimulating hormone, was inhibited by alcohol exposure. The reduction of growth hormone transcription was also confirmed by real time PCR. It also appears that the expression of upstream transcription factor pit1 and downstream target gene igf1 remains unchanged. It suggests that the reduction of gh transcription is mediated by a PIT1-independent pathway. The transcriptional profile of alcohol-exposed embryo was investigated by gene microarray analysis. It appears that the expression profiles of a number of development, cellular signaling, cell growth and apoptosis related genes have be affected by 1.5% alcohol treatment. It was noted that a number of retinal-specific genes were all repressed significantly. It consists with histochemical observation that alcohol exposure results in loss lamination and disturbed differentiation. This study help us understanding the molecular mechanism of fetal alcohol syndrome.
分子篩與過氧化氫感測器
目前市面上缺乏簡單而精準的過氧化氫檢測法，我們參考Fenton Reaction 中，鐵離子對過氧化氫分解的催化模式，利用鐵、鈷、鎳、錳、鋅分子篩，測試他們催化過氧化氫分解反應的效率，從成本、毒性、活化能的多方考量下，選擇以分子篩來固定金屬催化離子，作為我們後續實驗的研究主軸。實驗的初步，我們選擇過氧化氫作為自由基，並著重於過氧化氫的分解反應。利用濃差電池的原理，設計出一套濃度檢測系統，由分子篩作為電極。鑒於粉末狀的分子篩容易流失，我們製備出陶土鐵分子篩，以陶土固定分子篩，並以此作為電極，搭配白金絲，透過能士特方程式，測出過氧化氫的濃度，且藉由電路調控放大倍率，可以直接控制檢測範圍。從實驗結果得知，鐵分子篩在處理過氧化氫的時候，不會有鐵離子溶出的現象，且其催化性在酸性液中可以維持，能不斷的使用，長時間來看，分子篩相當有經濟與環境保護上的價值。We attempted to provide a system for quickly determining the concentration of free radicals. The existing methods or techniques are inefficient or need expensive equipment, therefore, an inexpensive system is being sought for. As a preliminary study, we focused on the decomposition of hydrogen peroxide. Taking the Fenton reaction as reference, we designed a measuring system. This system includes a catalyst containing Fe or Pt ions for catalyzing hydrogen peroxide decomposition reaction. The Fe- and Pt-zeolite were prepared to hold Fe and Pt ions to avoid losing. Because the electrically induced potential would decrease with the decrease in the concentration of hydrogen peroxide, we could measure the concentration of hydrogen peroxide by monitoring the electrical potential. We determined the initial concentration of hydrogen peroxide in water from the initial electrical potential measured through the equation obtained from the calibration line. The practicability of this system has been assured after a series of experiments. We will further develop the technique for measuring other free radicals. We anticipate that this technique will be further developed for measuring other free radicals. Although there are several problems and limitations to be solved and conquered, one thing is for sure: this system is an environment-friendly and cost-effective facility for determining the concentration of free radicals in an aqueous solution.
大自然的飛行家--蝴蝶飛行之初部探討
本研究主要針對蝴蝶之飛行進行探討，研究中主要探討蝴蝶翅膀形狀、身體重量、翅膀面積、展弦比、拍翅頻率及環境溫度對飛行速率之影響，並利用自製之風洞裝置，觀察蝴蝶之翼翅運動，分析通過蝴蝶模型之氣流方向及相關氣動力。研究結果顯示：紋白蝶展翅約4.5~5 cm，平均展弦比(AR)為1.71 ± 0.12，身體重量約為0.06± 0.02 g，翅膀面積約0.0012 ± 0.0003 m2，當紋白蝶身體重量愈重，則翅膀面積愈大(R2=0.9586)。另外，紋白蝶身體重量愈重、展弦比愈小，則飛行速率亦愈快(R2=0.5559、R2=0.4726)。23℃時，紋白蝶飛行速率為1.01±0.24 m/s，當環境溫度愈高(5、16、23℃)，則飛行速率亦愈快(y=0.07x＋0.7733，R2=0.6967)。風洞實驗發現：蝴蝶會逆風而飛，當風洞的風愈強，蝴蝶翅膀拍動角度愈大，且快而持久，仰角也變大(45 度)；蝴蝶翼尖軌跡呈八字形，翼翅運動包含線性平移及旋轉；蝴蝶拍翅時，可在翅上方及前方產生低壓帶，在後方產生高壓帶，以利蝴蝶向前方飛行。另外，翅緣彎曲角度(上反角)愈大，蝴蝶模型之上升高度亦愈高，當上反角60°時，蝴蝶模型之上升高度最高(2.2±0.1cm)。This research approaches the flying ability of butterflies. Our research mainly discusses the weight, aspect –ratio of butterflies, frequency of flapping, and the shape, surface area of butterflies’ wings, and the connection between temperature and flying velocity. More over, we use the wind tunnel which was made by us to observe the movement of butterflies’ wings and analyzed the direction of airflow and aero-elastic which pass through the wind tunnel. Our research shows that Pieris canidia’s length of wings is about 4.5 to 5 cm. The average of aspect –ratio (AR) is 1.71±0.12 . Its weight is about 0.06±0.02 . And its surface area is about 0.0012±0.0003 m 2 . The heavier Pieris canidia is, the bigger its surface area will be (R2 =0.9586). In addition, the heavier it is, the smaller its aspect –ratio will be (R2 =0.5559, R2 =0.4726), and the swifter its flying velocity will be. When it is 23°C, the flying velocity of Pieris canidia is 1.01±0.24m/s. The hotter temperature is (5,16,23°C), the swifter it flies (y=0.07x+0.7733,R=0.6967). Accroding to the detect of the wind tunnel’s experiment , the butterflies will fly on luff. When the stronger the wind of the wind tunnel is, the larger the angles of wing’s flap are. And they are fast and lasting, the elevation also becomes larger (45°). The butterflies’ trochoids of wings mimic the word “eight”, and the movement of wingspan includes parallel movement of linearity and wheel. When butterflies flap, it will amount depression upon and in front of the wings, amounting the high pressure on the back so that butterflies can fly antrorsely. Furthermore, the larger the curvy angle of marginal wings (Dihedral) is, the higher the ascending height of model butterfly will be. When dihedral is 60°, the ascending height of model butterfly is the highest(2.2±0.1 ㎝).
當急驚風遇上「玻璃片」－以簡單原理研製便宜準確風速計
本專題研究之目的，在於運用簡單的原理自製出準確、廉價、適用於低風速範圍的風速計；方法是藉由將一連接轉軸的玻璃片迎風，探討迎風時，玻璃片偏轉夾角和風速之間的關係。實驗過程中同時發展出可以用馬達旋臂的裝置與v=rω的原理，產生穩定可計算風速的環境。研究結果發現：在低風速的環境下，θ 範圍小時玻璃片與地夾角和風速大略成正比的關係，所以我們可以得到近似式” v≒aθ+b”，參數(a,b)依玻璃片而定。另外θ 範圍大時，我們可以使用二次逼近曲線的方程式與內插法來作角度與風速的對應。藉由控制玻璃片的厚度、質量與形狀，我們可以製造出相對應風速範圍的風速計。The purpose of our research is to use easy theorems to make accurate and inexpensive anemometer which is available in low wind velocity. To make such anemometers, we made a piece of glass, which was connected to a axle, to face wind; then, we could figure out the corresponding relation between wind speed and the angle created by the original and the resulting positions of the piece of glass. While we were experimenting, we found that we could make a steady-wind-speed environment by using motors, sticks, and the theorem ”v=rω”. The research showed that the angle created by the original and the resulting positions of the piece of glass and wind speed are in direct proportion in low wind velocity in small θ range. Consequently, we\r can derive the formula ” v≒aθ+b” , for each piece of glass (a,b) can be different. In addition, when in bigger θ range, we can use quadratic approximate equation and interpolation to describe the corresponding relation between the angle and wind speed. By adjusting the thickness, mass , and the shape of the glass, we can make anemometers corresponding to different wind velocity ranges.
AtbZIPs 轉錄因子及其下游基因啟動子的特定序列之研究
Arabidopsis thaliana bZIPs（AtbZIPs）是一群影響層面相當廣泛的轉錄因子，一半以上的 AtbZIPs 基因表現受到光的調控，且近九成的分子機制尚未明瞭，因此探討 AtbZIPs 在植物光調控機制中所扮演的角色將是個有趣的課題。AtbZIP16 與 AtbZIP17 皆被推測會參與光的調控機制，然而迄今少有文獻針對這二個轉錄因子進行更多的研究。因此，我們想藉由細菌單雜合系統（Bacterial one hybrid system）的方法，找出能與 AtbZIP16 與 AtbZIP17轉錄因子結合的 DNA 序列，以瞭解此二轉錄因子調節下游基因表現的分子機制，並探討其在光訊息傳導途徑中所扮演的角色。針對 AtbZIP16 與 AtbZIP17，本實驗分別找到了 7 與10 種可能的結合序列。首先，經由資料庫比對分析，我們發現其序列上帶有的 motifs 功能，主要參與在光調控、環境逆境反應機制、組織發育、賀爾蒙調節、病原菌防禦、鈣離子訊息傳遞等方面，其中又以光調控佔最大的比例。再者，藉由將 motifs 的功能繪製成文氏圖，並與 HY5 （AtbZIP56）做比較，結果顯示，這三個轉錄因子雖同屬於 AtbZIP family，據推測皆受到光的調控，可能參與某些相似的生理調節過程，但都各自具備不同的功能，影響植物體的發育。如此的差異，表示他們有實質上的不同，值得我們更深入的研究。整體而言，本實驗結果除了說明 AtbZIPs 的功能確實廣泛之外，也顯示AtbZIP16 與AtbZIP17 是執行光訊號傳導很重要的調控因子。Arabidopsis thaliana bZIPs (AtbZIPs) is a group of transcription factors affecting a wide range of responses in Arabidopsis. The expression of more than half of the AtbZIPs is regulated by light, and the molecular mechanism for roughly 90% of these AtbZIPs remains unknown. Therefore, the roles AtbZIPs play in Arabidopsis light signal transduction is an interesting topic to pursue. AtbZIP16 and AtbZIP17 have been suggested to participate in the regulation mechanism mediated by light. However, only limited studies for these two transcription factors have been previously performed. For this reason, we intended to determine the DNA-binding sequences for AtbZIP16 and AtbZIP17 via the bacterial one hybrid system to reveal their target binding sites in the promoter region of their downstream genes and to speculate their possible biological function especially in light signal transduction pathway. We have identified 7 and 10 possible recognition sequences for AtbZIP16 and AtbZIP17, respectively. Using motif-finding programs analyses, we found the motifs identified are mainly involved in light and stress signaling, tissue development, hormone regulation, pathogen defense and Ca2+ signaling. Among these regulation pathways, sequences involved in light regulation owns the highest proportion. Furthermore, a Venn diagram was generated to compare functions of genes regulated by AtbZIP16, AtbZIP17 and HY5. Results revealed that, although these three transcription factors all belong to the AtbZIP family and are predicted to be regulated by some similar physiological regulation process (e.g. light), they still possess distict biological functions in plant development. Further studies are thus required to put these transcription factors into their shared and unique biological context. Taken together, the results of this experiment not only indicated light is a key regulation factor for AtbZIP16 and AtbZIP17, but also showed the function of AtbZIPs could be diverse.
Listen to Your Heart
a. Purpose of the Research Nowadays people are getting unhealthy, especially the heart. Since the outbreak of SARS, the Hong Kong citizens cared more about their health. In the past two decades, due to the technological advancement, many medical instruments that were used by doctors are now available to the public. One of the examples is the sphygmomanometer used for measuring blood pressure. On the other hand, very few heart monitoring devices are developed for public use. As a result, there is a need that such heart monitors should be available to the public. b. The device Our device is a modified stethoscope, which electronic components are added to this common medical instrument. The device mainly consists of 3 parts: 1. The sensor: modified from ordinary stethoscope, which a condenser microphone is added to change the heart sounds into electrical signals 2. The signal processor: integrated circuits and resistor-capacitor couples, which the cost is much lower than digital electronic components, are used to amplify and filter the noise in the electrical signals. The processor is divided into 3 stages: - Preamplifier: Amplifies the electrical signals converted from heart sounds - Low pass filter: Filters the noise in the signal. The cut-off frequency is 600Hz, which most of the heart sounds are below 600Hz. - Power amplifier: Amplifies the filtered signals before outputting into computers or earphones. 3. The output devices: it can be a computer or an earphone. In a computer, the heart sounds can be converted into graphs, enabling precise graphical analysis. Since many abnormal heart conditions will alter the heart sounds, with the aid of computers and graphs, people can know whether their hearts are normal or not, and can seek for medical support before developing any critical situation. Moreover, abnormal heart sounds are more significant in graphs, so any heart problems can be discovered more easily. c. Data During an exhibition in Hong Kong, about 1000 people tried the device. Among them approximately 150 people were confirmed to have heart problems with abnormal heart sounds. Using our device, we discovered 109 of them. As a result, the accuracy of the device is about 72.6% d. Conclusion With the low cost of our device (~€9.80/US$12.80), everyone would be able to afford it. As a result, people can check their conditions of their hearts more frequently, and would be able to discover any early heart problems.