常我們遇到形如 x+2y+3z≦10 的不等式，而欲求其非負整數解的組數時，我們習慣的解法是：令 z=0 得x+2y≦10，共有( 0 ,0 , 0 ) , ( l , 0 , 0 ) , ( 2 , 0 , o )，…… 及 ( 2 , 4 , 0 ) , ( 0 , 5 , 0 )等 36 組非負整數解。 z = 1 得 x +2y≦7 ，共有( 0 , 0 , 1 ) , ( l , 0 , l ) , ( 2 , 0 , l )，…… 及 ( 0 , 3 , l ) , ( l , 3 , l ）等20組非負整數解。z= 2 得 x + 2y≦4 ，共有（ 0 , 0 , 2 ) , ( l , 0 , 2 ) , ( 2 , 0 , 2 ) ， …… 及 ( 2 , l , 2 ) , ( 0 , 2 , 2 ）等 9 組非負整數解。z = 3得 x + 2y≦l ，共有（ 0 , 0 , 3 ）及（ 1 , 0 , 3）等 2 組非負整數解。故合計有 36 + 20 + 9 + 2 = 67組非負整數解，這種解法主要是利用平面z = 0 ，…，z = 3 來逐點截取合適的解，它的精神由下圖（在坐標平面IR 2上）可以明白的表示出來，因此我們稱這種解法為“逐點截取法”。但是，一但n=1000 ，甚至更大，或是一般自然數 n ，如何用逐點截取法一點一點去取？顯然，它是繁瑣得令人厭煩！於是我們幾位同好就著手研究這個問題，希望能從中得到一個較為簡便的方法，下面就是我們的研究過程，請各位老師、先進指導。

1. Purpose of the research :\r One of the greatest challenges for 21st century society is to meet the growing energy demand for transportation, heating and industrial processes. U.S. and Brazil are currently converting corn starch and sugarcane juice into ethanol; however, these are edible products. To stop global warming and poverty, we tried to determine to develop new pretreatment method to produce biofuel using non-edible parts of agricultural products.\r 2. Procedures :\r For our research purpose, we conducted ‘Preparation of Rice straw - Powder’, ‘Pretreatment Method of Rice Straw and Statistical Optimization Using Response Surface Methodology’, ‘Enzymatic Hydrolysis for Saccharification of Pre-treated Rice Straw’, ‘Analyses of Pretreatment Efficiency and Production of Glucose and Xylose Using HPLC & TLC’, ‘Ethanol Fermentation and Recovery’, ‘Strain Improvement for Pichia’.\r 3. Data :\r For the first time, rice straw was pretreated in a novel manner using hypochlorite-hydrogen peroxide (Ox-B) solution. The optimum pretreatment condition was analyzed by response surface methodology and the pretreated rice straw was hydrolyzed using two kinds of enzymes. Following hydrolysis, Saccharomyces cerevisiae and Pichia stipitis were inoculated for ethanol production. The optimum condition was 60 min pretreatment using Ox-B solution containing 0.6% hypochlorite and 25% hydrogen peroxide for 1 g rice straw in 240 ml total reaction volume. The Ox-B solution treatment was an essential step for efficient hemicelluloase hydrolysis. Under these conditions, 406.8 mg glucose and 224.0 mg xylose were obtained from 1 g rice straw. The structural change of rice straw after pretreatment and enzyme hydrolysis was examined by scanning electron microscopy. With the 10% initial sugar concentration, the final ethanol concentration was about 3.46%, which is 90.5 % of stoichiometric and fermentation efficiency yield.\r 4. Conclusions :\r Rice straw was pretreated in a novel mean by using an Ox-B solution broadly used in potable water treatment. Pretreatment modified the structures of lignocelluloses. The Ox-B solution treatment was an essential step for efficient hemicelluloase hydrolysis. Pretreatment modified the structures of cell wall. Further optimization studies of the fermentation process and strain improvement research (for derepressed mutant) are in progress. In the future, I hope to see cultivators to move by the ethanol produced from rice straw and agricultural wastes.

The ASSOR is a device that allow to perform the sterilization function in hospital areas, the most important sectors of the hospital where it is required to implement this type of systems are the operating rooms, intensive cares, baby care, pathology, etc. The principle of the present project is a system that enables or either disables a valve that allows the fluid of the product, antiseptic or sterilizing, inside the room to be sterilized. The main application of this system is, after the manual cleansing of the room, in a control board, the procedure is turned on. The ASSOR consists, in general, of an electro valve that controls the fluid of the antiseptic into the room, a fan system, the electronic control circuit for the application of the product and electronic circuit to have a synchronized control of the system, and finally the product application in the target room.

由4x3的方塊中，在缺一方格下計算總方格數的挑戰為起點，我試著探討在缺塊n x n的正方形中總方格數和 任取一個位置方格(x,y) 或 任取出二個橫向位置方格[(x,y),(x,y+1)]、縱向位置方格[(x,y),(x+1,y)] 後之規律性及函數的關係，如下圖所示。並定義在未缺塊的正方形中，總方格數為C(n)，且C(n)=Σk2。 研究結果顯示，其函數式經由二種規律性 (A)一般性及 (B)遞迴性 求得，結果如下: 一、 任取一個位置方格(x,y)之總方格數二、 任取二個橫向位置方格 [(x,y),(x,y+1)] 或 縱向位置方格[(x,y),(x+1,y)] 之總方格數

台灣汽機車密度居世界之冠。汽機車排放之直接與間接形成懸浮微粒與臭氧，為都會區空氣主要污染物，並危害民眾健康，相關議題亦是全球關注的焦點。在法令規範未達一定成效時，戴口罩為保護呼吸道簡易的方式。口罩款式甚多，民眾認知甚少。本研究利用手持式粒子計數器、掃描式氣動粒徑分析儀與分光光度計等儀器，量測各式口罩對懸浮微粒與臭氧的攔截效率。結果得知機車廢氣之懸浮微粒主要粒徑落於「最易穿透粒徑」範圍，粒子不易攔截又易深入肺泡造成傷害。研究發現熔噴不織布層為口罩高攔截效率之關鍵因素，清洗後，短期效率無明顯下降，但因結構破壞仍需更換，藉此我們組合出高效率且可替換內層的布口罩。本研究結果可做為民眾選擇口罩之依據。

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。

牛奶的糖份主要是乳糖（(lactose），乳糖分子較大，不能直接被小腸吸收，必須分解成較小次單位分子的葡萄糖和半乳糖。 分解乳糖成為葡萄糖和半乳糖，需要酵素乳糖脢(lactase)，乳糖脢的形成，必須由乳糖脢基因作轉譯和轉錄後的蛋白質，再結合一些小單位物質，組成乳糖脢。 此題答案不是B和C的原因是，那些不能消化牛奶的人缺乏乳糖脢，而導致無法分解乳糖，不是因為缺乏分解乳蛋白的酵素或基因。某些人天生缺乏乳糖脢基因或缺乏乳糖梅，而導致無法分解乳糖，這樣的人喝牛奶後通常會有腹瀉、噁心、腹部絞痛的情形，而這種症狀稱為乳糖不耐症。

本實驗為製備「第三代光敏染料太陽能電池」之最佳化，並研究出「奈米級光敏染料太陽能漆」。比較七種花青素染料對於太陽能漆之影響，加入同樣具有光電效應的不同形狀奈米銀粒子，藉由照射各種光源與改變照射時間的長短，測定其電壓、電流並計算其轉換率。研究所得到的「奈米級光敏染料太陽能漆」，比較其正、負極條件不同之影響，所得到的實驗轉換率可高達1.43×10-2%。

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.

筆者將K?Cr?O?置於明膠溶液中煮沸，加入AgNO?水溶液，使之造成空間震盪反應。產生Liesegang ring。並且在研究空間震盪的過程中，筆者在研究過程中同時發展出一個程式，可以完成空間震盪實驗完成之後，由其震盪條紋的時空關係，得知ksp與擴散係數。或者可以在已知ksp和擴散係數的條件之下，預測出空間震盪實驗完成時的情形。We put K?Cr?O? into glutin, boiling it. After it concretizes, add AgNO? aqua into the glutin of K?Cr?O?. It is made to be space oscillation reaction with the Liesegang rings. And when we research for the process of space oscillation, we develop a program which can know the Ksp or diffusing coefficient after finising an experiment in Lablratory. Or we can predict the statement after the experiment on the condition of the Ksp and diffusing coefficient.

鋅銅電池是最古老的一種電池，這種電池在課本中僅用來說明電池的基本原理，它本身卻不能像鉛電池或乾電池那樣，能夠拿來做為各種電器的電源，例如使電燈發亮使馬達轉動等等。原因是鋅銅電池的太弱了，不到一般實用電池的千分之一。 正因為像鋅銅電池這一類的伏特電池不具實用性，所以科學家後來又發明了鉛電池及乾電池等比較優良的電池。我們很好奇的想知道，如果對鋅銅電池加以改進，是不是也能讓它像乾電池那樣優良，拿來做為實用性的電源，以點亮燈泡或推動馬達？

我們這整個實驗中的所有小實驗，都有自己的理由和為什麼要進行實驗的原因，不過到底是什麼原因讓我們開始進行這個實驗呢？ 原來是電視廣告，“茶樹油洗潔精的廣告”，一滴就靈：那個一滴就靈的現象讓我們全班印象深刻，一小滴的洗潔精竟然有哪麼大的力量，把整盤的油膩給拉到盤子的邊邊；小學生巧連智正好也進行著水面上的油彩實驗，所以我們決定要求好好的研究一下這些奇特的現象，經過了二個月的實驗，發現用牛奶來當作實驗樣本很容易觀察，又用色素滴在牛奶上來觀察運動的方向，就像是拔河比賽一樣，所以我們的實驗報告的題目就叫做“牛奶上的拔河遊戲”，其實就是研究表面張力。