George Sicherman discovered that it is possible to take a couple of 6-sided dice re-labeling them with different positive integers (1,2,2,3,3,4) and (1,3,4,5,6,8) having the same probability distribution as rolling a standard pair of 6-sided dice. Such unique pair of dice is calling Sicherman dice. The secret behind the Sicherman dice can be studied by combining the powerful mathematical tool “Generating functions” with the symbolic manipulation software “Derive 6”, The same procedure may be applied to studying the possibility of the generalized Sicherman dice along the consideration of :\r (1) Adding more dice. (2) Changing the number of faces. To this end, we introduce the concept of the Sicherman Bound. For a given integer n, the number of n-sided Sicherman dice is finite. We computed manually such numbers for n?50 based on the method of “Elimination of negative terms”. Sicherman Dice 就是一對點數配置與正常骰子(6 面正立方體，點數為1到6)不同的骰子，它所拋擲出的每一種不同點數和(2,3,4...,12) 的機率恰好與一對正常的骰子相同。這種骰子是美國的Col. George Sicherman 所發現的。 Sicherman 更進一步指出：在不使用Sicherman Dice 的情形下，不可能找到一組大於或等於三顆的非正常骰子，它們拋擲出的每一種不同點數和的機率恰好與一組同數量的正常骰子相同。本研究的目標在於1. 尋求計算「Sicherman Dice 的組合和正常的骰子有相同的出現機率」的方法2. 證明Sicherman 結論的真偽及是否適用於其他正多面體(4 面/ 8 面/12 面/ 20面) 的標準骰子3. 修正Sicherman 的結論，並定義Sicherman 極限(Sicherman Limit)。在假設n面正多面體(n 為自然數， n ? 50 )存在的情形下，探討每一個正多面體的Sicherman 極限4. Sicherman Dice (Crazy Dice) 的延伸探討(1) 不同面數骰子的組合，是否可以找到面數組合相同，但點數配置不同的Crazy Dice( 如4 面與6 面的標準骰子組合，找到4 面與6 面的Crazy Dice)(2) 多個面數相同或不同骰子的組合，是否可以找到面數、個數及點數配置皆不同的Crazy Dice ( 如3 個4 面標準骰子組合， 找到2 個8 面的Crazy Dice)在研究的過程中，我發現以下的現象：(1) Sicherman Dice 的產生，是生成函數因式重新組合的結果(2) Sicherman Dice 是否存在，則視上述重新組合的結果是否有負項產生由於上述的觀察，我使用自行發展的「負項消去」法來檢驗Sicherman 結論的正確性及求得n 面正多面體其對應的Sicherman 極限。同時我也和Col. George Sicherman 取得聯繫， 討論當年他發現Sicherman Dice 的經過及其結論的限制條件，作為本研究未來發展的參考。

1. Purpose of the research to detect the dynamics of the change of moisture regime on the territories of Olekminsk area for the past 100 years.\r 2. Procedures for analysis we used as materials of observations on the testing areas of school of ecological control of our Center, so and of the meteorological station Jikimda situated on the territories of Olekminsk reserve, as literary sources. Time-series analysis was conducted as to following scheme: for period 1901 -1914, 1949-1958 and for period 1996 -2009.\r 3. Data The changes of the temperature of air and sediments for the period of instrumental observations from 1901 to 2009 were analyzed\r 4. Conclusions Climate is characterized with many parameters coming in radiation, the heat and aqueous balances of territory. The most simple and widely measured parameters are the temperature of air and the quantity of atmospheric condensation. Carried out researches and the analysis of received results let us make tentative conclusions:\r 1. Average amount of precipitation increased on 41% (with 229 mm during the period 1901-1914 till 390 mm for period 1998 - 2006)\r 2. The decrease of firm precipitation in cold period and increasing of fluid precipitation in warm period are noticed for 100 years.\r 3. The gross amount of days with precipitation grows from 135 days (period 1901 - 1914) till 160 days (for period 1996 - 2006). For period 1901 -1914 a month with the greatest quantity of days with precipitation is January. The middle quantity of days with precipitation in it composes 16 days. A month with the least quantity of days with precipitation is July. The middle quantity of days with precipitation in it composes 8 days for period 1996 -2006. We should note that though increasing of the quantity of days with precipitation is on the cold period of year, increasing of the value of precipitation arises at expense of warm months. This reflects well the annual motion of the force of precipitation as to studied periods, the force of precipitation grows, in the first case achieving maximum in August, into second - in July. The maximal significances of the force of the precipitation of second period exceed of such the first period almost in two times.\r 4. The disposition of meteorological phenomena shows the change of climate to moistness. There are more days with fog, snow-storm, the quantity of days with precipitation increases from more 1mm, so more and 5 mm and it’s noticed that the quantity of days at a speed of wind more 10 and 15m/sec increases.\r 5. The change of the precipitation amount, especially in warm period affects the level and the expense of water in the Lena River. Analyzing as to decades the statistics on stratum of flow as to stratum flow since 1930 till 2006 can be noted tendency increasing of stratum flow from 132.8 mm in 1930 till 289 mm in 2006. The significance of the annualized expense of water with 6370 in 1999 till 8710 m/sec in 2006 enlarge, the annualized level of water changes from 282 till 376 cm. It is according. The area of the movement of the significances of the indicators changes to their increasing in the course of the year for the last 10 years. Averaging their significance exceed the norm of 18%.\r In conclusion we want to note that global change of climate actually touches all of us and already has significant influence on natural environment and the life of people. In simple words warming - the increase of temperature - for the many areas of our north country might become a favorable change of the conditions of life. But the trouble is that the change of climate is much more complex process, and one of its main manifestations is the augmentation of the instability of climatic conditions, changes of flora and fauna, increasing of infectious diseases. This influences badly on natural ecosystems and complicates the life of people. Besides, too quick warming does not let natural ecosystems adapt themselves, and they can be destroyed. And at least now we shouldn’t wait doing nothing, it is necessary to take all efforts to try to reduce climate change effect.

本研究探討在給定範圍的面積下，以最省錢的方式用籬笆圍出最大的矩形土地，其中矩形的邊長為正整數，且矩形對邊使用相同單價之材質的籬笆，但相鄰邊使用不同單價之材質的籬笆。我們希望透過轉換，將單價不同的情況回歸到單價相同的情況，以便完整的解決這個問題。\r 藉由改變邊長，將 轉換成 ，使問題轉換成相鄰邊之單價相同的情況；但是經過運算找出的最佳解 轉換回 後卻不一定符合「整數邊長」的要求(即 和 不一定是整數)。為了解決這點，我們重新以不同的角度探討單價相同的情形，以找出整數的最佳解。\r 最後我們發現，若 和 切線斜率的差值大於或等於1，則 坐標愈近 的解愈佳，而在差值小於1的範圍內，我們提出一個檢驗法，可以找到整個問題的最佳解，同時讓此最佳解 轉換回 後仍符合「整數邊長」的要求，進而解決問題。

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.

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.

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.

The purpose of the research is to investigate the settling mode of the viscid micro-particle, such as the ones from the “Miso Soup”, in static liquid. We constructed the “constant temperature environment” by constant temperature trough and transparent glass trough. The data is gathered from pictures captured from DV and then analyzed by Media Player. We did a stability test prior to the start of the experiment and found the system with good stability. The results of the experiment are as followed: 1. The settling mode can be divided into four phases: (a) Initial accelerated phase (b) Maximum phase (c) Gradually decelerated phase (d) Stationary phase. 2. The lower the fluid concentration is in the fixed temperature: a. the faster its settling interfaces appears; and the deeper it becomes for the depth of its settling interface. b. the faster the maximum sedimentation rates of the settling interface becomes and the slower it appears. 3. At the fixed concentration, the higher temperature: a. has the bigger maximum sedimentation rates of the settling interface b. gets to the stationary phase sooner c. has shallower stationary settling interfaces d. the time when the settling interface appears is independent with the temperature 4. The shape of the container has no effect on the settling mode as the settling interface is always perpendicular to gravity field. 5. If we add salt into the liquid, the stationary settling interfaces of the result will be higher than non-added ones.本研究的目的在於探討味噌這樣的微小黏性顆粒，在靜止液體中的沈澱模式。運用恆溫槽與透明玻璃水槽所建構之恆溫環境透過數位攝影機，以電腦播放軟體於特定時間擷取畫面進行分析。在正式實驗前，進行了穩定性試驗，發現穩定性良好。實驗的結果發現：一、 沈降模式：可以分為四個時期，分別為（一）起始加速期（二）高峰期（三）逐漸穩定期（四）完全靜止期。二、 在固定溫度下，溶液濃度越低：(一) 出現沈降交界面的時間越短且穩定距離距液面越深。(二) 沈降面沈降速率最大值越大且出現的越晚。三、 在固定濃度下，溶液溫度越高：(一) 沈降面沈降速率最大值越大。(二) 沈降交界面完全靜止期出現的時間越短，也就是越快達到穩定。(三) 沈降交界面的穩定距離距液面越淺。(四) 沈降面沈降速率最大值出現的時間與溶液的溫度無關。四、 容器內部的形狀與沈降面的沈降行為並沒有影響，都是成與重力場垂直的水平線沈降。五、 添加食鹽之後最終穩定沈降面比同濃度同溫度的高了許多。表示添加了食鹽對於味噌溶液有阻止沈澱的效果。

自1930年代以來，考拉茲猜想(Collatz conjecture)一直是個未解之謎，其敘述如下：選定一個自然數，如果是偶數，則用2來除；如果是奇數，則乘以3再加1，經過有限次迭代，最後一定得到1。也就是說會得到1,4,2,1,4,2,…的數列，稱之為1-2-4循環。即使此猜想敘述簡單，卻是個橫跨世紀的難題，至近幾年才有一些證明方法出現。 其中一種證明考拉茲猜想的想法為證明所有不符合考拉茲猜想的狀況為假，而其中一種狀況為除了1-2-4循環還有其他組循環，即有些正整數在經過數次考拉茲猜想的計算後，會進入一組非1-2-4循環的循環。 因此，在此篇報告中我們透過討論每一個奇數在經由乘3再加1的計算後，所得到的偶數的2的冪次，再經由反證法證明除了1-2-4循環不會有其他組循環。

The feasibility of new design approach for dual-band antenna array using genetic algorithm is demonstrated in this study. In the past year, one dual-band printed-strip dipole antenna, which operates at 0.9/1.8 GHz, had been implemented in the laboratory and leads to a satisfactory performance. However, the antenna element is suitable for application at base-station rather than handset. Conventional antennas suitable for base-station application are arrays, which consist of antenna elements and at least one feed network. Feed networks for antenna arrays are usually designed to operate at single-band capability, and therefore, it requires two feed networks for a conventional dual-band antenna array. Nevertheless, a dual-band antenna array fed by signal feed network is feasible in our study. To begin with, a full-wave solver ID3D is applied to evaluate the impedance matrix of antenna array with eight elements. Then, the antenna array is modeled as a cascaded equivalent transmission line such that the genetic algorithm could network of dual-band antenna array and yields a seven-section design, which meets the specification of base-station antennas.在過去的一年裡，本人曾製作過具有雙頻效果的雙面印刷偶極天線，並得到不錯的量測結果。由於此天線單元於實際應用上適於基地台天線陣列之設計，所以本研究著眼於天線陣列的設計。傳統上天線陣列的結構包含了兩個部分，分別是天線單元以及饋入電路。目前基地台所使用的大多都是單頻天線陣列，在雙頻天線陣列部分，通常需要兩個饋入電路分別對不同頻帶作訊號的饋入；因此，我們希望能實現使用單一饋入電路製成雙頻天線陣列的想法。本研究中，我們利用之前所做出來的天線單元來合成陣列，並希望此陣列在0.9HGz和1.8GHz兩個頻段都能產生良好的共振效果。我們利用電磁模擬軟體IE3D估算具有八個天線單元的天線陣列阻抗陣列後，再將此天線陣列轉換成串接式等效傳輸線電路。借由基因演算法(genetic algorithm)對此電路做最佳化，我們可以求得饋入電路各段傳輸線的尺寸。由此研究發現，我們的方法應用於單一饋入電路之雙頻天線陣列的設計是可行的，而此電路的模擬結果亦符合基地台天線陣列的規格。

Because the electrolyte solution used in an alkaline battery is a concentrated KOH solution, the zinc electrode in such a battery undergoes both a charging reaction and a corrosive reaction with the alkaline solution. The corrosive reaction not only reduces the lifetime of the battery but also produces hydrogen, which can cause the battery to explode and burn. Most of the zinc alkaline batteries currently on the market use mercury plating on the zinc electrode to increase its resistance to corrosion. To reduce corrosion of the zinc electrode in an alkaline battery and to avoid the use of toxic mercury, this study aimed to design a device to measure the quantity of hydrogen gas produced during the charging of a zinc-silver battery. We plated the zinc electrode with the immersion electroless plating method, using several different kinds of low-polluting anticorrosive additives(metallic compounds such as lead, tin, and indium)instead of mercury. We also used the vacuum immersion electroless plating method and added zincate ion into electrolyte solution to reduce further the quantity of hydrogen produced. The results of the experiment revealed that either a 10:1 or 100:1 ratio of lead to tin under optimal conditions will yield much better results than mercury.鹼性電池中使用的電解質溶液為濃氫氧化鉀溶液，因此電池中的鋅極除了放電反應之外，也會與濃鹼溶液中發生腐蝕反應。鋅極的腐蝕作用不僅會降低電池放電壽命，而且所產生的氫氣更可能使電池發生爆裂燃燒的危險。目前市面上所售之含鋅鹼性電池，大多是用鋅極鍍「汞」作為鋅極抗腐蝕的方法。為了改善銀鋅鹼性電池中鋅極在放電時的腐蝕效應，以及減少其所產生的氫氣量，本實驗設計了一動態放電裝置，可用於檢測銀鋅電池的放電電壓、放電時間與鋅極腐蝕反應的氫氣生成量。本研究藉由浸鍍其他低污染性金屬溶液 (鉛、錫、銦的化合物)來取代不環保的鍍汞製程，並進一步設計抽真空的浸鍍裝置，以及電解質溶液採用含有ZnO22-的KOH溶液，有效的降低電池中氫氣生成量。最後綜合所有優良條件，以鋅極採用真空浸鍍(Pb:Sn)為(10:1)及(100:1)的條件，此舉非常有效地提高電池中鋅極抗腐蝕性。此項製程所使用的Pb、Sn污染性質遠遠低於目前工業上所使用的汞製程污染，而且製程成本也遠遠低於Hg製程成本。