醬油為國民用活所不能缺乏之調味品，具有歷史淵源；周禮天官篇：「膳夫掌王饒、食醬百有二十甕。」史記；「通都大邑，醢醬千甕，此干乘三家。」1 今隨生活水準的日漸提高對調味料之選擇亦愈精細，不但要滿足色香味必要的物理條件外，尚需注軍營養素的質、量等化學醫療。據目前製造醬油後之醬渣，經分析結果；殘留蛋白質甚多棄之可惜。若作為飼料有過鹹才嫌。用於肥料，影響上壤pH 值。背時，曾使之灰化後，收回盒鹽。無論如何，在經濟價值上，殊堪可惜。若能改善製造方法，使蛋白質利用率折高，當可降低成本，增加生產。此為當前工商業所重視的問題。本研究即針對對問題，以不同方法製造醬油，再分析成品及醬渣中蛋白質的含量情形，以明瞭何種製造方法最為有利。

我一直在想，為什麼植物的美麗不能永恆呢？美麗的花朵，伴隨答淡雅的香氣，往往能美化環境，更能淨化人心，自小生長在鄉間的我，更能感受到這份來自花草的神奇力量，因此深深愛上這花草世界．但為何花朵的美麗總是短暫，為了想讓植物開花的時間長久，於是，我著手進行在自然科技雜誌及網路上搜尋相關的資料及訊息，但是找到的大多都是使生長速率變快的報告，卻找不到使生長速率變慢的報告。終於，曾經有人運用圓周運動的原理，而成功的使動物的生長速率變慢，於是，我針對直線運動及圓周運動分別依速度快及速度慢來分成四組，以及一組靜止狀態的綠豆，將五組實驗後的數據相互作比較，結果發現，除了陽光、水、空氣、土壤、養分及本身具有的胚胎外，在不同的運動狀態下也會影響到植物的生長速率 ·I was thinking about the reason why the beauty of plants couldn’t last forever. The beauty of flowers that accompanied with sweet-smelling could beautify the landscapes and purify our heart. I felt strongly about the magic power of the plant because I lived in the country in my childhood. Therefore, I loved plants deeply. Why was the beauty of flowers transient? As a result. I started to search for the related data and information on science and technology magazines and Internet. Most of the reports increase the growth rate of plants, but I cou1dn find the reports about slowing down the growth rate.At last, someone had successfully used the principle of circumference movement to slow down the growth rate of animals. Therefore, I focused on linear and circumference movement and divided them into four groups and one group of green beans with still state. I compared the data of five groups, and found that different movement affected the growth rate of plants m addition to sun, water, air, soil, and embryo.

(一)我們的化學課本第三冊第十四章第一節實驗14-1中，要我們”用定量的方怯來電解時，所生成物質的重量與電量間的關係，進而求得法拉第常數及離子的氧化數。實驗過程必須經過 L 配製電解液（ CuSO45H20 及 AgNO3）, 2.試裝電路，調整電阻器使安培計指在 0.1A 上，3.取下陰極片（ cu , Ag )。依次用稀硫酸、蒸餾水、乙醇及丙酮清洗。4.夾取洗淨之陰極片在烘箱內烘乾。5.夾取乾燥之陰極片分別”用天平精確稱重”，並紀錄之。6.掛陰極片於電解槽內，接通電路，”電解約 l 小時” 其時間之調整電阻器，保持 0.1A。7.1小時後夾取 1 陰極片依次用蒸餾水、乙醇及丙銅洗淨，且要以不可將晶體烘失。8.再入烘箱乾燥。 9.再用天平精確稱重，紀錄下來。10.依據實驗數據，計算法拉第常數及離子的液化數。以上是課本上的指導手續，我們也曾照著做過，不過做一次前後需要兩小時。由於第一次做這樣複雜的實驗，一切都是亂糟糟的。最後計算完畢，其誤差之大，實在叫我們臉紅，自信心完全喪失了！(二)我們的物理課木第一冊第二章第四節中，曾要我們自製微量天平。我們也按照課本做了，而且很好用。如果能把微最天平用在上述的化學實驗中，不僅可以節省時間，而且也因為是用微量天平來測量，結果一定比較準確。經過老師的同意和指導，我們就幹起來了。

Purpose of the Research:\r 1) To determine whether a poor understanding and inability of Grade 7 and 8 learners to apply the BODMAS principle in mathematics, influences scores obtained in a mathematics test.\r 2) To determine whether scores obtained in the given mathematics test can be improved with a BODMAS learning tool.\r Procedures:\r 1. Get the educators opinion on mathematics in schools. Send a total of 50 questionnaires to four schools.\r 2. Determine what percentage of a mathematical test/examination requires the application of BODMAS\r 3. Do a pre-test at two schools, a total of 370 grade 7 and 8 learners.\r 4. Design a BODMAS learning tool and verify it with three educators.\r 5. Implement the tool at the two schools.\r 6. Do a post-test at the two schools.\r 7. Get all the educators who were at the implementation session to evaluate the session.\r 8. Investigate two other schools, by sending 270 pre-tests to those two schools, to determine whether applying the BODMAS principle correctly is also a problem for learners in those schools.\r 9. Implement the BODMAS learning tool into the intermediate phase syllabus.\r Data:\r 1. Of the 41 educators in the sample, 52% think the standard of maths in their schools is average.\r 2. 38.9% of a grade 8 mathematics examination paper and 46% of grade 8 mathematics tests contains questions that are BODMAS related.\r 3. The learners achieved an overall average of 22.57% in the pre-test\r 4. The educators evaluated the BODMAS learning tool as very good as it is.\r 5. Learners and educators enjoyed the implementation session of the BODMAS learning tool.\r 6. In the post test learners did much better, the overall average increased by 21.00% to 43.57%.\r 7. Educators were positive about the way in which the tool was explained.\r 8. The learners in the other two schools also struggled with applying the BODMAS principle.\r 9. A second pilot study is being done in four primary schools by the Department of Education for the implementation in the Free State mathematics 2013 syllabus. \r Conclusion:\r My hypothesis is supported. \r 1) A poor understanding and inability of Grade 7 and 8 learners to apply the BODMAS principle in mathematics, influenced scores obtained in a mathematics test.\r 2) Scores obtained in the given mathematics test were improved with a BODMAS learning tool.

本文由‘‘分數7/17是否能表示成兩個相異的埃及分數之和’’這個問題出發，藉由簡單數論的性質以及反證法，得到一個真分數可表示成兩個相異埃及分數之和的定理檢驗法(定理1)。有了這個基礎，我們進ㄧ步推廣定理1 的結果，做出了嶄新的結果(定理2、定理3) 。此定理分別可以用來檢驗真分數表示成三個、四個相異埃及分數之和的存在性; 至於將真分數表示為5 項、6 項….k 項相異埃及分數之和的部分尚在嘗試。利用定理1、2，我們寫了兩個Matlab 軟體工具的電腦程式，使得我們可以檢驗任意真分數是否可以表示成兩項及三項的和，並可把所有的解列出來; 最後我們研究的是一個有關埃及分數的猜想(Erdos-Strauss Conjecture)問題，當分子為4，且分母為4k、4k+2、4k+3 時，猜想皆成立。對於分母為4k+1 而言，當k 為3r+1、3r+2 猜想亦成立，k=3r 且r 為奇數時也是成立的，因此目前需解決的問題只剩分母為24t+1 的情況了。值得一提的是，我們用Matlab 的程式檢驗出當分母為1014 至1014 +240000 之內的正整數時，猜想都是成立的，這已經超越了已知文獻的結果。This paper begins with the question: ‘‘Is 7/17 able to be the sum of two different Egyptian fractions?’’ to discuss the problem of Egyptian fractions. According to the complete division properties and the counter-evidence method, we get a back-check theorem which is about a true fraction can be the sum of two different Egyptian fractions (see theorem 1). Using the same method we obtain a new back-check theorem that is a fraction can be the sum of three or four different Egyptian fractions (thereom2, thereom3). Similarly, we can follow the same procedure to get the rule that a fraction can be the sum of five or six …or even more different Egyptian fractions. By the theorem1 and 2, we propose two programs written vie the Matlab software to examine that any true fraction can be the sum of two items and three items or not. Finally we focus on the Erdos-Straus Conjecture, which related about true fractions can be divided by three different Egyptian fractions. The conjecture is when the denominator is 4k, 4k+2, or 4k+3, the problem mentioned above can be solved. As for the denominator is 4k+1, then the conjecture also can be solved, as k equals to 3r+1 or 3r+2. Also, k being 3r and r is an odd number, the conjecture is satisfied. As for the case of r equals to even number, the problem has not been solved. But it is worth to mention here that we use Matlab software to examine the conjecture is agreeable as the denominator is between 1014to 1014+ 240000. This is beyond the results from the literatures.

根據我們找到的資料，視覺是植食性昆蟲覓食的重要工具。資料指出：果蠅的視覺對於 380nm（紫外光）、420nm（靛色）、500nm（綠色）這三種光線的波長較為敏感，又由於市售黏蠅板皆為黃色，因此，我們就針對果蠅視覺的辨色記憶、顏色偏好、不同色光的趨光性做探討，發現：一、辨色記憶：由實驗結果，我們認為果蠅應能記憶顏色，如此可間接證明果蠅能夠分辨顏色，果蠅可能是有彩色視覺的。二、顏色偏好：利用五種顏色的黏蠅板，發現在黑色背景下，亮度最高、反射波長範圍介於 500nm 至 700nm 而從 580nm 又趨於平穩的高反射率的黃色黏板最為果蠅所偏好的。由此顯示：背景、亮度、反射波長皆可能影響果蠅的顏色偏好。三、在不同色光的趨光性方面：果蠅對於不同波長的色光並不具有特殊喜好。原因可能為實驗所使用的 LED 燈泡波長涵蓋範圍太少，另一個原因則是，果蠅的趨光行為影響實驗結果。綜合實驗結果，我們認為：以植物為食的果蠅，對於不同的顏色，可能有能力區別並加以記憶，如此彩色視覺在果蠅的生理機能與行為上，可能佔有重要的地位。

本研究比較2003~2005 年，冬季及夏季西經168 度之「海平面溫度異常」對「緯度」的分布圖，結果呈現在赤道附近的變動較小，在高緯度地區的變動較大，為更精確的描述此變動，將每日高緯度地區的變動以「標準差」及「最大振幅」數量化，發現在南、北半球不論2003、2004或2005 年，每7~12 天南、北半球的「冬夏季海平面溫度異常」的變動變大，上述變化在北半球較為明顯，在南半球較不規則。 與2005 年冬季1 月31 日~3月17 日的北半球地面天氣圖進行分析比對發現，溫度的變動和極地天氣系統的形成關係密切，推測原因和冬季時極地為永夜，地面空氣溫度受到兩個跟月球有關的熱源影響較大，其一為海流和極地間每日有接近2 次的潮汐交替運動，其二為月球反射日光後投射到極地時，極地大規模的冰對月光的反照，對極地微弱的加熱作用。 針對2005 年6 月1 日~7月22 日之地面天氣圖作分析，結果發現夏季緯度的溫度變異和高中低緯度天氣系統的改變關係密切，推測此時和月球對海水的吸引使地表(特別在海陸邊界)的溫度，週期性的重新分配，或對大氣應也會造成週期性的質量分配有關。 以農曆為主重製溫度的變動圖並進行比對發現，無論2003、2004或2005 年，在月相為朔及望時常出現低值。此分析結果顯示，接近朔望時，高緯度海平面溫度有較穩定且變動較小的情形。而從天氣圖、農曆標準差綜合，所得結論為地月運動應和地球上高緯度天氣系統存在某種相關性。 ;Our topic is about how the moon phase variation influences the high-latitude weather system. This study analyzes the sea surface temperature anomalies (SSTAs), along 168°W in winters and summers from 2003 to 2005. The results show that the SSTAs varied relatively small around the equator and relatively large in high-latitude regions. So we next analyze the high-latitude SSTAs by the standard deviations, the maximum amplitudes, and the north surface weather graphs. After analyzing, the result shows that the SSTAs rise for every 7 to 12 days. Moreover, they relate to the winter high-latitude weather system very much while relating to the summer medium-and-low latitude weather system a lot. We think it’s because in winter eternal night, the sunlight won’t shine on the arctic zone easily. Other heat sources may become important: (1) the tidal movements between the ocean and the arctic zone. (2) The heat radiation of the moonlight and the moonlight reflection by the polar ice shields. But in summer, the moonlight effect becomes extremely small. The tidal force becomes the bigger influence factor: (1) the tidal attraction may distribute the temperature of the border between seas and land periodically. (2) It may cause the periodic atmosphere mass distribution. Additionally, after repeating the same experiment according to the Chinese lunar calendar, we found near full-moon and new-moon time, the SSTAs are more stable. Probably because of without the moonlight, the movements of rip-tides occur and help stabilize the polar weather conditions. In conclusion, the relative movement of the moon to Earth is likely providing a crucial heat source which will affect the high-latitude climate, and the heat source size probably influences the weather system cycle.

The starting point of this experiment is to study the structure of soap-film. By changing the height of the triangular prisms, cuboids and pentagonal prisms, I observed the patterns set by the soap within the frameworks. It is surprised that when the proportion of prism is in a specific range, the phase in the middle of the structure will overturn 90 degree and then transmitted into another kind of balance pattern. I named this process “phase transition”. According to the experiment ,we can conclude the change of film patterns within variable prisms are all applied to this regular cycle:： We know the soap films are forever attempting to minimize their energy. It stands to reason that surface tension tend to set up the film in its minimal surface. From the point of Mathematic, each structure should have only one single balance pattern, which is set up on the base of Fermat point and this pattern should stand to the minimize of it’s energy. However, we discovered that in some specific cases, one structure can allowed two kinds of balance films-patterns to exist. In these cases, any small vibration can cause the happening of “phase transition”. To sum up, I presume some structures have two different types of balance film-patterns: one of which stands to the local minimum (in this condition the pattern’s surface area isn’t the smallest); the other stands to the absolute minimum (in this condition the pattern’s surface area is the smallest). There is an energy valley separate local minimum from absolute minimum. The second pattern (local minimum) will appear when the structure is blocked from attaining its absolute minimum, but surface intention is not powerful enough to support the film jumping over the energy valley. In this condition, if we works on the structure (such as blowing), which would provide the film of energy to cross the valley, and then phase transition take place. Vice versa, we can also force the film to jump from absolute minimum to local minimum and phase transition will occur as well. In a word, phase transition can happen in each two way, which connects the two types of balance pattern. This report lays stress to find out the condition of phase transition. We also analyze the structure of soap-film by its included angles and surface area in hope to go deep into the science of soap-film. 我們實驗的出發點在於研究泡膜的立體結構。藉由改變正立方柱的高，觀察其平衡薄膜形式，意外的發現當正立方柱的邊長比在某個範圍時，泡膜結構中央會瞬間90 度翻轉，形成另一種平衡型式，我們將這個過程命名為面轉變(Phase Transition)。為了進一步了解面轉變發生的相關因素，我們設計了一連串的實驗，針對正三角柱、正四角柱、正五角柱、正六角柱發生面轉變的時機和條件分析討論。此外，我們還分析了泡膜結構中膜與膜夾角的特性、最小表面積和表面能之間的相關性，對於泡膜的立體結構做了一系列深入的探討。

有一天，放學之後留下來和老師一起練習打羽毛球，正當打得盡興時，天色已漸漸昏暗，突然間老師打了一個遠高球過來，赫然發現有一群蚊子在頭上飛舞著，阻礙了我叩殺此球，結果使我揮了空，心有不甘，決定找出原因來，為何蚊子只愛我，不愛老師呢？

以前，我們觀察落地生根營養繁殖的過程時，對它「為什麼落地才生根？從何處生根？會開花？結果嗎？」感到好奇與疑惑。課後跑去請教老師，老師很高興地說：「既然你們有這種求知的精神，何不動手去研究呢？」於是我們一行四人，請老師帶隊，踏上了「奇妙的落地生根」之旅。

對4 × 4 方格表中計數問題的二個解題方法(1..解方程式的方法， 2.分割圖形的方法)作分析和研究後，首先我推廣分割圖形的方法來証明 : “好的n × n 方格表” 存在若且惟若n 為偶數。同時証明這種“好的n × n 方格表”內所有n2 個數的總和f(n) 為n(n+2)/4。當討論一般的n×m 方格表時，發現分割圖形的方法盲點，無法繼續推廣來証明。再經過深入分析與推廣解方程式的方法，藉由n×m 變數方格表，我們終於找到構造所有“好的n × m方格表”的方法。同時計算“好的n × m 方格表” (n≦m)內所有mn 個數的總和f(n,m), n≦7和証明好的nxm 方格表會有2(n+1)行一個循環的現象。We first studied two solution methods (1.solving equations,2.dissecting diagrams.) for calculations on 4x4 checkboard. Using the method of dissecting diagrams, we proved that``good nxn checkboard'' exists if and only if n is even. Furthermore, the sum f(n) of those n2 numbers in a ``good'' nxn checkboard is equal to n(n+2)/4.In studying the more general nx m checkboards, we found that the method of dissecting diagrams does not work, However, by extending the method of solving equations, and by considering nx m variable checkboards, we obtained a way of obtaining all ``good nxm checkboards.'' By way of computing the sum f(n,m) (n≦7) of those mn numbers in a ``good nxm checkboards,'' periodicity in every 2(n+1) rows is observed.

在能源日漸耗竭的今日，開發環保新能源是重要的課題。本研究中使用的藻類電池，係藉著藻類照光會行光合作用而發電。藻類可以吸收空氣中的二氧化碳，因此更符合「節能減碳」的概念，藻類電池又被稱為「活的太陽能電池」。從研究結果發現製作藻類電池時，以藍綠藻與小球藻的組合為最佳，其中藍綠藻擔任負極，而小球藻擔任正極。藻類電池在光照強的環境，有較佳的發電效率，而且添加營養劑在藻類電池中，不僅可以提高發電率並可以延長藻類的生命。在不同色光的照射中，藍光與紅光對於刺激藻類電池發電效率最佳；綠光則是最差。藻類電池也可以進行串聯，藉此提高電壓與電功率。我們期待藻類電池在未來可以成為一種新的能源。