The temperature of the water was commonly higher and both of electrodes were oxidized during electrolysis by using alternating current, but the above happenings were only found at the positive electrode by using direct current. It can be explained by the principle of the microwave stove. The exchange of the current causes the water molecules to release heat. The strength and weakness of electrolytes, the length and width of the electrodes, and the frequency of the alternating current can affect the rate of electrolysis of water. Commonly speaking, the stronger the electrolyte is, the faster the rate of electrolysis will be. NaOH and HNO3 are strong electrolytes, but the amount of the gas is zero during electrolysis by using alternating current. Maybe both of electrolytes react with stainless-steel electrodes to form some kinds of protective layers to affect the conduction of current. When copper bars, carbon bars, and iron nails are used as electrodes, either the alternating current or direct current is used, the amount of the gas is very small. Maybe these electrodes react with oxygen produced during electrolysis to form oxidized layers to block the conduction of current. Long and wide electrodes produce more amount of the gas. The amount of the gas increases when the frequency of the alternating current increases. The longer the distance between electrodes is, the smaller the amount of the gas will be. The smaller the angle between electrodes is, the smaller the amount of the gas will be, too. When the number of multiple electrodes in parallel increases, the total amount of the gas almost increases. The amount of the gas is smaller at the farther electrode. The amount of the gas at the electrode at the same distance becomes smaller when the number of multiple electrodes in parallel increases. At the same voltage, the effective current of the alternating current is about 0.707 of that of direct current. So we can predict that the total amount of the gas elect rolyzed by alternating current must be about 0.707 of the total amount of the gas electrolyzed by direct current. When we used stainless-steel electrodes and the electrolyte- H2SO4, we found the ratio was about 0.4286. Maybe the system of the electrolysis of water doesn’t obey the ideal linear system of Ohm’s Law and some part of electrical energy is wasted by increasing the temperature of the water and the oxidization of electrodes. 交流電解普遍水溫較高且兩極都有被氧化現象，直流電解則只有正極有上述現象，可能是交流電有類似微波爐的原理，電流交替時造成水分子震盪發熱。電解質強弱、電極種類、電極長短粗細、交流電頻率會影響電解水速率：強電解質較快，但NaOH 、KNO3 雖是強電解質，在交流電解時，氣體產生量幾乎是零，這可能是他們與不銹鋼電極反應形成某種保護層而影響導電；以銅棒、碳棒、鐵釘為電極時，不管是交流電或直流電，氣體體積都很小，這可能是這些電極和產生的氧氣反應，形成氧化層阻礙了導電；長的和粗的電極氣體產生量較多；交流電頻率越大，則電解所產生的氣體量也隨之增加；電極之間的距離越大兩極的氣體體積越小；兩電極之間的角度越小，兩極的氣體體積越少；多重電極並聯的個數越多，總氣體體積約略越大，距離越遠的氣體體積越小，同距離的氣體體積隨並聯的個數越多氣體體積越小。在相同電壓下，交流電輸出的均方根電壓(電流)為直流電電壓(電流)的0.707 倍(1/√2)，所以推測交、直電解水的氣體總體積比值也應為0.707，但我們以不銹鋼為電極、H2SO4 為電解液下比值為0.4286，這可能是本電解水系統並非為遵守歐姆定律的理想線性系統，且電解水時部分電能被消耗在水溫的升高及電極的氧化上。

在嗜甲烷菌中，甲烷與甲醇間的轉化是由甲烷單氧化酵素來進行。目前已知有兩種型態\r 的甲烷單氧化酵素，一種是溶解型甲烷單氧化酵素，存在於較低銅離子濃度之水溶液環境中﹔\r 另外一種為微粒體甲烷單氧化酵素，鑲嵌在細胞內質膜上，表現於較高的銅離子濃度環境下。\r 除了本身的天然基質－甲烷之外，其他種類之簡單烷烯類化合物，甚至芳香族化合物，均可\r 作為此酵素催化的基質。其中，甲烷單氧化酵素將丙烯轉化成環氧丙烯與甲烷轉化成甲醇的\r 催化活性非常接近，因此丙烯普遍被用來作為酵素活性測量的基質。為了直接測量它們的活\r 性，我們設計出一種方法，可以讓我們直接利用氣相色層分析儀，來偵測細胞的催化反應過\r 程。基於異丁烷在甲烷單氧化酵素幾乎不存在任何活性，故我們將其作為內標準氣體，並藉\r 由丙烯在氣相色層分析儀中吸收訊號的遞減來偵測細胞的催化活性。在多樣性的動力學實驗\r 中，我們發現以sMMO 為催化酵素時，丙烯的轉化是依據一級動力學反應趨勢而減少。相對\r 的，以pMMO 為催化酵素時，丙烯的減少趨勢則是依據零級動力學反應模式進行。在比較完\r Pipes 緩衝液、上清液蛋白質及內質膜蛋白質溶液之丙烯吸附量測試結果後，我們發現內質膜\r 蛋白可吸附的丙烯分子相對於其它兩種溶液是最多的。依據Michaelis-Menten 動力學理論，\r 可得到以下結論﹕丙烯的轉化在sMMO 中是以基質受限的催化形式進行，而在pMMO 中則\r 已達到最佳的催化速率。\r \r In methanotrophs, the oxidation of methane to methanol is catalyzed by methane\r monooxygenase. There are two distinct forms of the enzyme associated with different gene\r products. One is the soluble methane monooxygenase (sMMO) expressed in the cytosolic portion\r of the cell and grown under copper-limiting growth conditions. The other enzyme is the\r particulate methane monooxygenase (pMMO), a membrane-associated protein that is expressed\r under high copper-to-biomass ratios. In addition to the natural substrates of methane gas,\r simple aliphatic alkanes, alkenes, or even aromatic compounds could be used as the substrates of\r the methane monooxygenase. In those gaseous simple alkenes and alkanes, propylene converted\r to propylene oxide by methane monooxygenase has been considered as popularly use for enzymatic\r activity determination because of its comparable activity to the methane gas. To measure the\r catalytic behavior of the methanotroph directly, we design a method to choose isobutane as the\r internal standard because of the negligible activity in the methane monooxygenase. The catalytic\r activity can be simply inferred from the decrease of the gaseous propylene signals in the GC\r chromatograms by generating the liquefied epoxides mediated by MMO within the methanotrophic\r bacteria. Under various kinetics measurements, when we incubate the methanotroph grown under\r copper-limiting concentrations, we observed the diminishment of propylene follow a first-order\r kinetic behavior with the over-expression of soluble methane monooxygenase. However, the\r growth of bacteria under 40 M presents the zero-order kinetic trend with the bulk expression of\r pMMO. After the quantification of the dissolved propylene in the deionized water, soluble\r proteins solution as well as membrane proteins solution, we observe the membrane proteins could\r adsorb more propylene molecules in comparison with the other solution mixtures. By considering\r Michaelis-Menten kinetics, we conclude the propylene conversion in sMMO is under substrate\r limiting catalysis whereas the pMMO has attended the optimized velocity of propylene conversion.

由人類活動造成的溫室效應可能導致地球溫度升高,聖嬰現象加劇等現象與災害,本文利用個氣候中心發展出的模式,推估台灣和東亞地區未來氣候變遷的情況,我們發現當大氣中的二氧化碳濃度增加為現在的1.9倍時,台灣地區的年平均溫度將升高0.85-2.50度C而東亞地區將會升高1.46-4.07度C,在同條件下個模式的平均推估量也顯示,台灣地區將每天增加0.10公厘的降水，而東亞地區每天將增加0.08公哩,我們希望這個研究結果可以做為其他相關研究的基礎,使大家提早因應未來氣候變遷所可能引發的種種變化;Greenhouse effect, incurred mainly by human activities may result in lots of phenomenon and damages such as the increasing of the world's average temperature and he aggravation f the "ElNino" effect. In this research, we simulate future metrological values by employing several simulation modes developed by different climate centers and predict future climate changes in Taiwan and East Asia area. We found that when the concentration of carbon dioxide exceeds 1.9 times than current value, the estimated range of the increased year-average temperature are0.85-2.5℃ and 1.46-4.07℃ for Taiwan and East Asia, respectively. Under the same condition, the ensemble mean reveals that the precipitation raises will be 0.1 and 0.08mm per day, for Taiwan and East Asia respectively. We hope our work can be the foundation of other related researches, and all the researches together can help for coping with possible damages caused by future climate changes.

此篇報告中,主要是在敘述以單晶片8051為主體,運用其所具有之功能,製作成此作品,稱為記數抽籤機,又稱抽籤機,根據本篇報告結果,可歸納出以下結果:1.本實驗能讓初學者對單晶片8051之特性與功能有更深的了解,以增進實驗與成品實作的能力。2.此作品以便利為原則,故其體積不大,重量輕攜帶方便。3.使用之元件普遍,價格便宜,在電子材料行均可買的到,成本低。4.依本品之功能,可用於學校讓老師進行抽問,也可用於其他有抽籤或抽獎活動之場合,公平又公正。;In the report, we take the single chip 8051 as a main body, making use of function to do the counting drawing lots machine, which are also called drawing lots machine. According to the resultof this report, conclusions are as followings: 1. With the experiment, the beginners egt deeper understanding about the characteristics and the finished products. 2. This machine is light and its volume is small, so it is easy and convenient to carry with. 3. The essential elements are common,cheap and can easily be bought in the store which is sellong electronic materials. 4. The drawing lots machine can be used at schools when teachers want to pick out some students to ask or it can be used for some drawing lots occasion as well. The outcome is just and fair.

一、目的：1.找出基隆沿岸是否受到塑膠微小物的污染，建立塑膠成分的簡易檢定法，3.分辨所發現塑膠微小物成分，4.試圖分析其污染源，並尋求減輕汙染方法。二、結果：本研究為首篇證實東北部海岸已遭受塑膠微小物污染之本土研究。我們想出了不用昂貴儀器的位之塑膠簡易成分判別法，發現海面漂浮的油渣含有塑膠微小物，還觀察到海岸生物（藤壺）由本來附生在岸邊的石頭上轉而附著於漂浮的塑膠垃圾及漁民和釣客所使用的浮標、漁網、浮桶等。三、為減少海岸的塑膠微小物污染，建議政府立法規定業者主義塑膠原料運送中產生的問題，並提倡垃圾分類，人民本身也應自我覺醒。Taiwan is an island, and the sea is very important for us. So in this study, we tried (1) to examine the small plastics (resin pellets and plastic fragments) pollution of the northeast coast, (2) to identify the components of unknown plastics by burning, soluability in organic solvents and relative weight but without using expensive instruments, and (3) to classify the small plastics we found and to find out where were they from. Our study is the first grassroot research proving that the northeast coast of Taiwan has been polluted by small plastics. We attempt to identify the components of unknown plastics without using expensive instruments. The present study discovers that there are many small plastics in the floating oil scum. The relation between the oil scum and small plastics needs more study. We finds marine life (bamacles) growing on floating small plastics. The ecological importance of this discovery needs more study. We also make suggestions for reducing the minute plastic pollution of the coasts: (1) the government should ask big companies to be more careful on the transport of plastic pellets, (2) people should be aware of the problems caused by small plastics.

在這篇研究報告中，我們討論的是一種方形集合圖形的數量。”多元方形鏈”約略在 60 年代被提出，衍生出一系列的問題和遊戲，例如熟知的電玩軟體 『 俄羅斯方塊 』 ，或是 『 益智積木 』 的遊戲，都是多元方形鏈的應用。在這些問題當中，最令人頭痛的難題就是 n 元方形鏈的圖形總數。為了解決這道難題，我們採用一種轉換方法將圖形轉換成序組，並且給出序組的性質，再據此寫成 C 語言的程式；反覆地修改程式以增進執行效率及速度，最後利用該程式成功地統計出圖形總數。 In this report, we discussed the amount of polyominoes, the graphs of a set of squares. “Polyominoes” has been brought up in 1960s, and later developed into a series of questions and games, such as a well-known video game — Tetrix, and the game of puzzle blocks. Both are the applications of polyominoes. Among those questions, the toughest one is the amount of n-polyominoes. To solve this problem, we used a method which transforms the graphs into sequences. By looking into the properties of those sequences, we obtain a set of rules that can be used to determine the quantity of n-polyomines. The rules are implemented into computer codes in C language with proper modifications made to speed up the efficiency of our algorithm. The computational results show that the amount has been successfully calculated.

相剋作用是指植物在代謝過程中釋放出有毒物質以抑制本身或鄰近植物種子萌發及植株發育生長的過程。一般認為，榕樹是具有相剋作用的常見植物，但很少見到相關的文獻探討。本實驗利用榕樹不同組織萃取液，以小白菜、結球白菜與阿拉伯芥作材料，探討該萃取液對上述植物發芽與生長之影響，結果顯示榕樹葉萃取液所造成之影響較顯著，不同榕樹組織的萃取液、不同濃度的萃取液對不同植物所產生的效果不盡相同，針對不同生長期的植物進行處理所造成的影響亦有差異。進一步以管柱層析法與高壓液相層析法（HPLC）分離葉萃取液，結果發現以正己烷和乙酸乙酯75：25為沖提液的條件下，於HPLC的層析圖中分離時間約8分時所流出的物質具最明顯的抑制作用。電泳剖面分析顯示處理與未處理間有些許蛋白質條帶差異，此變化蛋白可能與植物幼苗對該萃取液之耐受性有關。利用核酸微陣列(microarray)對榕樹萃取液處理之阿拉伯芥植物進行基因表現分析，發現榕樹萃取液對植物部分基因表現也有促進和抑制的情形，經由基因體與蛋白質體分析法可推論出一些受影響之相關基因。 Allelopathy was defined as a phenomenon which certain plant species, by secreting metabolites to the environment, can suppress the growth of themselves, seed germination and/or growth of other plants in the same habitats. Banyan （Ficus microcarpa L.f.） is a plant species in our campus likely to have allelopathy effect. However, documents describing such action on allelopathy were rare. In this study, we applied the crude tissue extracts including leaves, stems, roots of banyan onto the germinating seeds of Pai-Tsai （Brassica rapa L.ssp.chinensis（Rupr.（Olsson）））, Chinese cabbage （Brassica pekinensis Rupr.） and Arabidopsis（Arabidopsis thaliana, ecotype Columbia-0） to study the effects of such plant extract on the germination and seedling growth of other plants. It is found that allelopathic effects on seed germination vary among different tissues used for extract preparation. Different concentration of the extract also yield various degree of allelophathic effects. It is also noted that the application of extract onto the post-germinated sprouts has less effects on plant growth. The extract of leaves was subsequently chromatographed over silica gel using hexane/EtOH gradient solvent system and HPLC. The result showed that there was one fraction about 8 min in the chromatography of HPLC eluted with 25% EtOAc in hexane had the most inhibitory effect. SDS-PAGE analysis on the electrophoretic profiles of water soluble proteins has explored a different band pattern between the treated and non-treated sprouts. The observed band difference might provide a clue for exploring proteins which reacted differently upon the application of extract. DNA microarray analysis on the effect of banyan extract on Arabidopsis gene expression has also been employed to characterize genes responsive to the allelophathic treatment. Cross-comparison between the differential transcript and protein profiles will reveal key regulators in plants experiencing allelophathic condition. \r

溫差電池中若僅進行的反應，則其電池電壓與溫差成正比，且純粹是利用化學反應將熱能轉換成電能，我們稱之為「典型溫差電池」，由熱力學公式可推導出典型溫差電池的電動勢(ΔS = S(s)—S(aq)，S為絕對熵， n為得失電子數，1F = 96487 C )，且得到下列三項推論來說明溫差電池的特殊現象。 (1) 同一溫差電池，其電動勢與溫差成正比 (ε∝ ΔT)。(2) 不同的溫差電池，當溫差一定時，電壓ε 與ΔS 成正比，與得失電子數n 成反比。典型溫差電池中，電解液濃度越小，金屬離子濃度也愈小，會使得ΔS = (S(s)—S(aq))的絕對值變大，因此溫差電池的電壓也就愈大。(3) ΔS 值的正負決定電壓ε 的正負。Cu(NO3)2 及ZnSO4 溫差電池的ΔS 為正值，所以高溫杯為正極；AgNO3 溫差電池的ΔS 為負值，所以高溫杯為負極。因水溶液中陰、陽離子不能單獨存在，所以單一離子水溶液的絕對熵無法求得，但科學家把氫離子水溶液的標準絕對熵定為零，藉以求出其它離子的絕對熵，然而我們測得在一定溫差時典型溫差電池的電動勢ε，再查得金屬的標準絕對熵 S(s)，代入S(aq) = S(s) — nFε/ΔT，便可得到離子水溶液的絕對熵。Cu(NO3)2 溫差電池的電解液中若含有1M 或0.5M 的KNO3，電池電壓仍然與溫差成正比， 但卻可獲得較大的電流，我們稱此類溫差電池為「改良型溫差電池」。我們利用改良型溫差電池的原理，自製環保、節約能源、可重複使用的實用溫差電池，以PVC 水管當容器，上、下兩端開口用銅片封住當電極，管內裝海棉及0.125M Cu(NO3)與 1M KNO3 溶液，熱源加熱上層銅片形成溫差，當溫差維持在70℃，電壓約為70 mV，若串聯30 個實用溫差電池，電壓可達2 V 以上，就可以對鉛蓄電池充電。實用溫差電池的熱源可由回收冷氣機、工廠的廢熱，或直接利用太陽能來當熱源。 If the temperature difference cell only goes through the following reaction Then the potential created by the cell is proportional to the temperature difference, and such a reaction purely changes the thermal energy into electrical energy through chemical reaction, which we often name it “typical temperature difference cells”. We can come to the following formula for the typical temperature difference cells through a series of thermodynamic formula: ε= ΔT ． ΔS/ nF (ΔS = S(s)—S(aq), where S is the standard 3 entropy, and n is the number of electrons gained or lost, and 1F = 96487 C). We also provide the following three inferences to demonstrate the special phenomenon for the temperature difference cells: 1. Within the same temperature cell, the electromotive force (EMF) is proportional to the temperature difference. 2. When the temperature difference keeps constant, the electromotive force is proportional to the ΔS in different temperature cells, and is inversely proportional to the number of electrons gained or lost. Within the typical temperature difference cells, when the concentration of the electrolyte becomes more diluted, the concentration of the metal ions also proportionally become lower, which will make the absolute value of the following equation bigger, as a result, will make the electric potential of the temperature difference cells bigger: ΔS = (S(s)—S(aq)) 3. The value of ΔS decides the value of the electromotive force. The ΔS of the following temperature difference cells is positive value: Cu(NO3)2 and ZnSO4 . As a result, within the copper and zinc temperature difference cells, the higher temperature glass is the anode. On the other hand, the ΔS of the AgNO3 temperature difference cell is negative, which means that within the silver temperature difference cell, the higher temperature glass is the cathode. Meanwhile, because the cations and anions can not exist alone, therefore, it is not possible to find the standard entropy of the single ion solution. However, scientists define the standard entropy of the solution containing hydrogen ion to be zero, as a result, we only have to determine the electromotive force for a typical temperature difference cell, while keeping the temperature difference constant, followed by finding the standard entropy for the said metal S(s). Inserting it into the following equation to find the standard entropy for the ion solution. S(aq) = S(s) — nFε/ΔT If the electrolytes for the Cu(NO3)2 temperature difference cell contains 1M or 0.5M KNO3 , the electromotive force is still proportional to the temperature difference, and we can obtain bigger electric current. We call this kind of temperature difference cells “improved version of the typical temperature difference cells”. We try to make more environmental, energy saving, and recyclable temperature difference cell by applying the theory of the improved version of the typical temperature difference cells. We use PVC water pipe as the containers, both edges of the pipe sealed with copper metals, also work as the electrodes. Within the pipe filled with sponge and 0.125M Cu(NO3) and 1M KNO3 solution. The heat source keeps heating the upper copper metal to keep constant temperature difference. When the temperature difference is kept around 70℃, the electric potential is 70 mV. If we can connect 30 practical temperature difference cells in a series, the electric potential will reach 2V, which can then charge the lead rechargeable battery. The heat sources of the practical temperature difference cells can be supplied by the recycled air conditioners, heat waste from a factory, or directly comes from the solar power.

給定一個P∈(0,1),令k0=0, p0=p，定義k1為能使 的最小正整數k，而 ; 相同的，對於給定的kn-1, kn 為能使的最小正整數k, 。若存在kn 使得，則稱p∈ In; 若對於所有n 與kn ，，則稱p∈ I∞。如此區間(0,1)可分解成集合I1,I2,…,I∞。

密閉容器置入待測液，放入浮沉子，施加壓力，當浮沉子恰要沒入液中瞬間，因表面張力的總力達極大值且向上，外加壓力(p1)為極大值，浮沉子沒入液中；液面減壓，當浮沉子在液面正下方時，外加壓力 p2，量 p1、(p1- p2)，浮沉子的質量 m，外半徑 R，及玻璃管的體積 G V ，可求得液體表面張力。 液面再減壓，浮沉子恰要露出液面時，表面張力的總力達極大值且向下，外加壓力(p3)為極小值，量 p3、(p2- p3)，浮沈子的質量 m，外半徑 R及 G V ，應亦可求得表面張力；但實驗時浮沉子漂移到容器邊，並吸附在器壁上，因此發現浮沉子的”Cheerios effect”。 利用浮沉子和容器的相吸及相斥現象，可解釋西式早餐的小榖片放入牛奶中為何會漂移到碗緣，並支持 Vella在 2005 年 9 月份美國物理期刊(AJP)認為 Cheerios effect的成因除了由於接觸角不同外，浮力、重力、表面張力共同作用，使小榖片間有相吸、相斥現象。 The experiment apparatus is equipped with a Cartesian diver by using a glass tube with air trapped inside that floats or submerses in a closed vessel containing liquid. The external pressure may be varied with a syringe and measured with a water manometer. The maximum pressure P1 inside the vessel is measured when the diver is just about to sink, where the surface tension that acts on the diver is upward. Then the pressure P2 of the vessel is measured when the diver is just beneath the liquid surface, where no surface tension acts on the diver. Finally, the surface tension is calculated from P1, P2 and the radius of the diver, R. When the pressure inside the vessel is decreased, the diver will rise. As the diver is about to emerge from the liquid, we get the minimum pressure P3 inside the vessel, and the surface tension that acts on the diver is downward. By measuring P3, P2, and R, the magnitude of surface tension is found to be the same as above. When the diver is just about to sink into the liquid, it floats to the center of the vessel. When the diver is about to emerge from the liquid, it sticks to the wall of the vessel. This phenomenon is named the “Cheerios effect.” Our results again strongly support that the cause of the effect is due to the different contact angles between the diver and water, as well as the balance of gravity and surface tension in the case of the sinking diver, and the balance of buoyancy and surface tension in the case of rising diver as Vella claimed in his paper (AJP 73, 817 (2005)).