The objectives of this investigation were to evaluate the growth conditions and the antioxidant activities of fermented black bean soy milk(BBSM) with Bifidobacterium longum B6 and 15708 cultured in four media, namely, ( BBSM ( 100%)+ 1% glucose ), ( BBSM (100%)), ( BBSM (50%) + milk (50%)), (milk (100%)) . These results indicated that; (1) both strains attained viable cell numbers about 7.19~9.53 log CFU/ml after 18 hrs of incubation and were in the order of ( milk (100%))＞( BBSM (50%) + milk (50%))＞ ( BBSM (100%) + 1% glucose)＞( BBSM (100%)), (2) both strains in ( BBSM (100%)) exhibited higher pH value ranging from 4.79 to 5.50 , but lower titratable acidity(%) ranging from 0.27% to 0.61% than the three other media after 48h of fermentation, (3) both strains displayed an even smaller tolerance to simulated gastric juice at pH = 2.0 for 3h, especially in ( BBSM(100%)), while in simulated gastric juice at pH =3.0 for 3h had higher tolerance , (4) both strains had high resistance ranging from 72.51% to 92.62% to 0.3% bile solution for 12h, (5) the reducing power of ( BBSM (100%)) was more excellent than that of ( milk (100%)), (6) the scavenging effect of yogurt (BBSM ( 100%) + 1% glucose) on DPPH radicals was significantly higher than that of ( milk (100%)), (7) In general, at ten- fold dilution the chelating effect on copper ions of these four un-fermented media except ( milk (100%)) was significantly higher than that of fermented media with B.longum B6 or 15708. 本研究是探討雙叉桿菌(Bifidobacterium longum B6及15708)在四種發酵基質(【黑豆奶(100%)+1%葡萄糖】、【黑豆奶(100%)】、【黑豆奶(50%)+牛奶(50%)】、【牛奶(100%)】)中的生長情形及抗氧化活性。結果顯示： (一) 兩株菌在四種培養基中的生長菌數大小順序如下：【牛奶(100%)】＞【黑豆奶(50%)+牛奶(50%)】＞【黑豆奶(100%)+1%葡萄糖】＞【黑豆奶(100%)】。 (二) 兩株菌在【黑豆奶(100%)】的pH值比較高於其他三種優酪乳，而最終發酵可滴定酸度比較低於其他三種優酪乳。(三) 兩株菌於pH2.0環境下，在【黑豆奶(100%)】優酪乳中耐酸性很低，而於pH3.0環境下卻有很高的耐酸性。(四) 兩株菌對0.3%膽鹽之耐受性均很高為72.52%~92.62%。(五) 在稀釋10倍的四種基質中，不論發酵前或發酵後的還原力皆以【黑豆奶(100%)】為最高，【牛奶(100%)】為最低。(六) 在濃度稀釋10倍時，【黑豆奶(100%)+1%葡萄糖】對DPPH‧自由基清除率明顯比【牛奶(100%)】高。(七) 在濃度稀釋10倍的四種優酪乳中，除【牛奶(100%)】外，發酵後比未發酵的銅離子螯合率明顯降低。

本研究以模擬實驗探討波浪在斜坡海灘上的行為。實驗在長1.8公尺、寬0.75公尺的透明水波槽中進行，以長0.90公尺、寬0.60公尺的木板在深水區產生單峰波向淺水區前進，同時以數位錄影機錄影後進行分析。結果發現單峰波由深水進入淺水，波速會變慢，但當波高對水深的比值增加到一定值時，波速隨水深變淺而變快，波高也變高。當比值繼續增加，波前方的水面形成垂直的水牆，接著波就碎了。如果坡度較緩，碎波點會離水岸線較遠，水牆維持的時間也較長。有趣的是，水波槽中的單峰波移動時，有蠕動現象，波寬會伸縮，波高會起伏，波速也會些微地忽快忽慢。 ;This study simulates the behavior of the wave on a sloping beach. Experiments are performed in a sloping wave tank. A paddle wave maker at the deeper end generates single crest waves. To analyze the wave height, speed and breaking point, a digital camera is used. The results show that when the wave moves toward the coast, the shallower the water is, the slower the wave moves. But when the ratio (wave-height/water-depth) exceeds a critical value, it turns out that when the water is shallower, the wave speed becomes faster and the wave height, higher. As the ratio keeps on increasing, the front part of wave becomes a vertical water-wall, and then breaks. If the slope is gentler, the breaking point will be farther from the coast and the water-wall will keep for a longer time. An interesting phenomenon is also found that a single crest wave squirms with slightly undulated changing of width, height, and speed while it propagates in the sloping wave tank.

By comparing eight different epoch images of the crab nebula taken through 1942 to 2004, we have calculated the expansion velocity of 27 optical bubble features and 60 filaments. The mean expansion velocity of bubble features and filaments is 0.173 arcsec/yr and 0.15 arcsec/yr, respectively. We also estimated the maximum radial velocity of the expansion by analyzing the emission spectrum of the nebula. The maximum radial velocity is 1385.5 km/s. Combining these measurements indicates that the crab nebular is approximately 5870 light year away. In addition, if we assume that the nebula has been expanding at a constant rate, our expansion velocity projected backward indicates the mean date of the supernova event as A.D 1124, more than 70 yrs later than the accepted date of 1054. The result confirms the well-known acceleration in the crab's expansion. Although we have analyzed eight images with a 62 yr baseline, the acceleration still can't be derived from this study. 透過量測由1942年到2004年之間八張不同年代的蟹狀星雲中爆炸後殘骸的位置變化，可以計算出蟹狀星雲爆發的擴張速度。本研究選定了27個包狀物和60個纖狀物，計算出的擴張速度分別為0.173 arcsec/yr.和0.150 arcsec/yr。再透過分析蟹狀星雲的光譜所計算出的徑向速度（radial velocity）為1385.5 km/yr，進而推得蟹狀星雲的距離分別為5430光年和6370光年，平均值為5870光年。 另外，如果假設擴張速度是等速運動，那麼把求得的擴張速度倒推出的爆發日期是在西元1124年，這比中國紀錄中超新星爆發的1054年晚了70年。這顯示出蟹狀星雲的確非等速擴張而是有加速度的狀態，才會造成以等速倒推發生日期時，晚了70年。雖然本研究中分析了相差62年之久的八張影像，仍然無法分析出星雲的擴張的加速度情形。

We understood the definition and meaning of spider number by reading〝Wonders of Numbers〞. It interested us so much. So, we took further step to study the situation of extreme value when the gap sometimes lie on the line and sometimes on the circle or even on both. That is to say, we explored the relation between spider number and the gap when the spider number is maximum or minimum. New research for the application of spider number involves several directions. First, we design a new game called〝Stepping Land Mine〞with the rule of spider number. Give you a net with several hidden gaps, trying to find the right positions of gaps. Second is the further result for a different type of net about regular n-polygon. Third is a tactic for a net with destroying of the strategy points. In this situation, the gaps amount on the circle and on the line are fixed. At the same time, consider the situation of circles and lines designing the tactic of placing the gaps to attain the maximum of the destructive effect. 在本文中我們定義一個蜘蛛網上的蜘蛛數，若在蜘蛛網中加入缺口後，會影響蜘蛛數的大小。我們探討蜘蛛網上的缺口，該如何分配才能夠得到蜘蛛數的極值(最大值及最小值)。先觀察一直線和圓上缺口如何放置蜘蛛數有極值，再探討許多條直線及圓上的情況，進而推展至許多同心圓及通過圓心的許多條放射線的缺口，該如何放置，蜘蛛數才會有極值發生。

由於結網性蜘蛛視覺不靈敏，如何在網上藉振動進行獵捕，這是長久以來頗令科學家困惑的難題，當周遭環境各種振源觸網時，首先會產生不同振盪，蜘蛛是否藉由這些振盪得知獵物資訊？如何迅速準確的定位？又有那些決策條件影響蜘蛛的捕獵行為？更特別的，為何蜘蛛在捕獵過程中會“扯網”？本研究以台灣最大型結網性蜘蛛－人面蜘蛛為研究對象，並設計出一套非接觸式的測量方法，就上述謎題作深入的探討後，成功的解開人面蜘蛛的捕獵機制。簡單來說，其機制分為兩大系統：(1)當獵物擾動不明顯，人面蜘蛛會立即扯網，藉有無產生阻尼振盪，以判斷有無獵物存在；在阻尼振盪產生時，蜘蛛將感知其中具有最大阻尼振盪之放射絲為獵物所在方向，而振盪週期長短，係蜘蛛用以判斷獵物遠近之有效因素。(2)當振源明顯時，蜘蛛直接判斷各種擾動的振幅大小、頻率高低、波形模式、振源質量輕重，決定是否啟動捕獵或逃離反應，並在反應前先行定位，亦即以步足腳勾偵測並比較各放射絲之振盪大小，以振盪最大之放射絲為獵物方向，其次藉由第二對步足之位移所產生之準光角，判斷獵物之遠近。蜘蛛正確的將獵物定位後，會以適當的速度往前衝，一口咬住獵物，以蛛絲重重包裹後，拖往網中央並進行吸食。 Giant wood spider, Nephila pilipes, is the biggest orb web spider in Taiwan. The mature N. pilipes may even grow to exceed 5 cm body length. While waiting for the prey, its giant body hangs quietly on the hub of the web. Owing to its ineffective vision and sense of smell, the spider depends almost on detecting the vibration signal of the struggling of web cause by the struggling prey. When various kinds of sources from the environment contact the web, they will generate various types of vibrations which cause the spider to judge whether they represent danger, prey, or irrelevant signals. Our results suggest that if the disturbance is obvious, through discriminating the amplitude and frequency of the vibration, the spider will make a decision whether to attack or escape immediately. Yet, before any decision is made, it will need to locate the source of vibration. For example, it will locate prey correctly by comparing the vibration transmitted from the radiating strings. The radiating strings that transmitted the largest vibration are where the prey is entangled. The displacement of the second pair of legs will generate a quasi visual angle which enables it to comprehend the distance of prey. When the vibration signal is obscure, it will jerk the radiating string immediately. After jerking it, if there is damping oscillation on the web, then the spider can judge the location of the prey. When there is damping oscillation, the radiating string that transmitted the greatest damping oscillation is where the prey is entangled. Furthermore, the frequency of damping oscillation helps the spider to judge the distance of the prey. After locating the prey correctly, N. pilipes approaches the prey fast, wraps it with silk then drags the prey to the hub to feed.\r

Our aim to attend this science fair is to design an instrument that can plat and measure the mass at the same time. In hope of designing a simple, accurate and convenient apparatus, we created an electronic circuit to display our original idea. In the process of constant improvements, we finally accomplished a “Super Mass Plating Gauge”, which can be easily and widely utilized in school teaching. The production of microbalance and the arrangement of electric circuit are the most significant parts in our research. The major components of the “Super Mass Plating Gauge” include a straw, metal clips and our creativity—the well-arranged electric circuit. The idea of microbalance originated from the Internet, but we advanced it by numerous experiments. First, we attached a steel cord to one side of the cathode in the electricity supplier. Next, we fixed the other side to the negative plate. And then, on the end of the negative plate, we tied a metal clip with the metal that will be plated. Eventually a new “plating gauge” was invented. By doing so, we could use this instrument to make our experiments. Our experimental goal is to research how different kinds of metal, time, electrode and voltage can affect the reduced mass on the cathode. We made use of such metal as copper, zinc and silver to carry out the experiments. In the end, by analyzing the results, we concluded a plating formula that can be applied to metal plating. 我們做此科展的目的，是要設計一個可以邊電鍍、邊測量質量的儀器，我們希望這個儀器是簡便、精確、且線路簡單，並且能推廣到教學的器材。經過我們不斷改良，終於完成了「便利質量電鍍器」 。 其中製作微量天秤和線路的配置方法，是本研究的重要部分。微量天秤的主要結構是吸管、鱷魚夾、及線路。微量天秤的構想，是參考以前的科展作品並加以改良，可精準測量到0.00010g，而裡面的線路，則是我們的創意（如圖一） 。只要把電源供應器的正極，接上左右任一鋼條，負極接到容器另一端，並加上一個鱷魚夾，夾上被鍍物，便是一個可邊電鍍，邊測量質量的儀器了！如此一來，我們就能以此儀器來作我們以下的實驗。 我們實驗目的在探討電鍍時不同金屬、不同時間、電極大小及電壓，對正極金屬片所減少質量的影響。 最後，我們推導出一個有關電鍍時正極金屬片質量變化量的實驗公式。為此，我們也要做許多次、許多種的實驗，來驗證我們的公式是否正確，並以我們所學的理論來推論。

跳舞草(Desmodium gyrans) 屬多年生木本豆科植物，其特殊之處在於小葉會對外界的聲音有所感應。本實驗以訊號產生器固定聲音強度，發出2、4、6、8、10 KHz不同聲頻之聲波刺激跳舞草，並以每5秒為單位紀錄小葉擺動角度之變化，分析其擺動週期、擺動幅度等不同的變化。實驗結果為跳舞草小葉之擺動週期與擺動振幅是隨著聲音頻率的增加而呈現sin函數變化之圖形。Desmodium gyrans (Leguminosae) is a perennial woody plant. Acoustic waves can stimulate stipules and cause to oscillation. This experiment used the coroma to immobilize strength, emitted the frequency of 2, 4, 6, 8, 10 KHz acoustic wave to stimulate stipules and recorded the changes of oscillation angle every five seconds. We calculated the oscillation cycle、oscillation span, and analyzed experiment data. The most importance result is that the experiment graphs of oscillation angle and oscillation span with different frequency of acoustic waves display sin function metamorphic diagram.

本研究主要分析氣象因子對於灰面鵟鷹春季過境八卦山區之影響。分析1994年至2004年灰面鵟鷹遷徙資料發現彰化八卦山區之微氣象與灰面鵟鷹族群遷徙波動性具有顯著的相關性，其中以日平均氣壓、日平均相對濕度、日平均風速及日平均風向等氣象因子分別對起鷹、落鷹之族群數影響最為明顯。而其遷徙週期之動態變化，明顯地集中於約16日內完成主要族群之遷移。不論是同一年度內之高峰期變化，或是高峰期與日期契合之相關性，顯示氣象因子為其遷徙影響的重要因子。然而，從各年度間的遷徙高峰期間的相關性分析結果得知，目前11年過境調查紀錄，應該無明顯的規律性動態變化模式，考量其他對於遷徙過程可能具有影響的因子，應有其他的環境或生物因素影響遷徙期間族群的波動性及週期性。對於建立其遷徙模式而言，可能需要更多且更詳盡的遷徙紀錄，以及配合遷徙過程的各過境點的氣象或其他因素合併分析，方能獲得更為明確的結果。The main purpose of this study is to find the effects of the meteorological factors on the dynamics of the migrating population observed at the Pakuashan area in spring for the gray faced buzzard. The migrating population dynamics observed at the Pakuashan area correlated significantly with the local meteorological factors noted from 1994 to 2004. The daily average atmospheric pressure, average relative humidity, average wind speed and wind direction had significant impact on the soaring and landing populations of the gray faced buzzard. Obviously the annual migrating dynamics observed at the study site was accomplished within 16 days. In addition, the similar variation pattern of the peak migrating populations in the same year as well as the consistency of the date of the peak population observed annually supports the hypothesis that the local meteorological factors have a great impact on the migrating behavior of the populations. However, the correlation analysis of the peak migrating populations among years indicated that little cyclic migrating pattern was found in the past 11 years’ observation records. Other biotic or abiotic factors might have influence on the periodicity and fluctuation of the migrating populations. In order to establish a precise population model to describe the migrating behavior of the gray faced buzzard, detailed records of the migration process and the analyses of the relationships among the meteorological data as well as other factors and the bird populations observed should be gathered and performed.

This research is mainly in observation with Caenorhabditis elegans ’s genetic mutation caused via nervous system abnormal character. In the study, I the sample have been cultivated purified and add some chemical material EMS to speed up C.elegans mutation. Then based on the character to further analysis what causeof gene deal with mutation and observe the effects in heredity. The research has two stages, on the first stage of study the mainly target is to both search and purify the mutation of C.elegans. The second stage is based on the exploration of mutation’s searching andpurifying. Because the certain mutation bodies aren’t easy to find out, the project is still on progress at the beginning of second stage, and we conclude some heredity special cases in preliminary of study. 這個實驗主要是觀察並針對線蟲因為基因的突變所產生的神經系統異常的變異性狀，在實驗中我先將樣品線蟲培養並純化至一定數量，並加入適當藥劑EMS造成其突變，經篩選並分析此性狀，進而找出造成其突變之基因，以及觀察此性狀對遺傳表現所造成的影響。 該計畫分成兩階段，第一階段的實驗重點是在突變株的搜尋以及純化上，第二階段則是在突變基因的探討上，由於特定突變株的搜尋並非容易，所以目前計畫只進展至第二階段的遺傳實驗初期，對於其遺傳特徵與突變形式上已有了初步的分析，但尚未定位出該基因的位置。

完全圖Kn是指一個圖中有n個點，且任意一個點都跟其它的點有邊相連。兩個圖G和H的卡氏乘積G□H的點集V(G□H)＝{(g,h)| g∈V(G),h∈V(H)}，兩個點(g1,h1)和(g2,h2)有邊相連若且為若g1=g2 且h1~h2，或g1~g2且h1=h2。 三個完全圖Ka、Kb、Kc 的立方乘積是指Ka□Kb□Kc。一個圖G中的一點v所連的其它點稱為這個點v的鄰居，也就是N(v)={x | x~v}。一個點集S中的所有點的鄰居的聯集稱為這個點集的鄰居，也就是N(S)=∪v∈S N(v)。如果一個點集S和它的鄰居N(S)包含了一個圖G的所有的點，也就是S∪N(S)＝V(G)稱這個點集S是這個圖G的一個控制集。我們把圖G的所有控制集中點數最少的稱為最小控制集，並定最小控制集的點數為最小控制數γ(G)，也就是γ(G)＝min { | S |, S是G的控制}。 本文的目的在於研究完全圖立方乘積的最小控制，也就是要給γ(Ka□Kb□Kc)一個上界。特別當 a = b = c = n時，γ(Ka□Kb□Kc) = 。 A complete graph Kn is a graph with n vertices, which any vertex is adjacency to every other vertices. The Cartesian product of two graph G and H which is denoted G□H is define as follow: the vertex set V(G□H)＝{(g,h)| g∈V(G),h∈V(H)}，and two vertices (g1,h1) and (g2,h2) is adjacent if and only if g1=g2 and h1~h2 or g1~g2 and h1=h2. The Cartesian product of three complete graph Ka,Kb,Kc is Ka□Kb□Kc,which is the same with (Ka□Kb)□Kc. In a graph G, the neighbor of a vertex v N(v) is the set of the vertices adjacent to the vertex v, that is N(v)={x | x~v}。 The neighbor of a vertex set S is N(S), which is the union of the neighbors of vertex v over S, that is N(S)=∪v∈SN(v). For a graph G, if a vertex set S unions its neighbor N(S) equal to the vertex set of G, that is S∪N(S)＝V(G), we say that S is a dominating set of G. The domination number of a graph G will be denoted as γ(G), which is the minimum size of all dominating set of G.. We give an upper bound to γ(Ka□Kb□Kc). And when a=b=c, γ(Ka□Kb□Kc) ≦