2008年

This project aimed to create a simple model of coin sorter with cheaper price, electricity saving using recycled materials for use in place of manual separation and compatible to the automatic coin sorters commercially available in the market. The principle applied in inventing this device was the gravity force that pushed coins to fall through its upper compartment to the lower part via a slope that determines the coin path as well as the speed of the coins. The upper part of the box was designed to control the rate of the descending coins and transported the coins to the separation section in single file order to prevent jamming. The lower part of the box consisted of the coin sorting mechanism which conveyed the coins to their assigned compartment according to coin diameters. The box could separate three kinds of Thai coins, 1,5 and 10 baht, with 95-98 % accuracy. The efficiency was in the range 150-250 coins per minute with highest accuracy at 150 coins per minute. The box was made from acrylics. The designed box can separate coins faster than manual sorting although not with as high efficiency as automatic machines which can sort up to 500 coins per minutes. At the present stage, it can not count the number of coins. However, it can be built at cheaper cost, does not require electricity or electronic devices and is suitable for small and medium size business. We aim to improve the box to give higher accuracy with coin counting ability.

A documentary profile about an invention (a secure safe) Introduction: Firstly, we thank Allah, the Lord of all, and the Prophet Mohamed “peace be uponhim”. The importance of scientific innovations and inventions is demonstrated in the development of humanity fulfillment the requirements of modern life. In this respect, the presented innovation and thoughts have appeared in order to help the humanity. Within this context, the man or anyone needs to feel secure as far as his wealth and properties are concerned. Within this regards, the idea of creating (inventing) a secure safe appeared, and this will enhance the perspective of security, and confidence via making a secure safe. It has been stated in our Scared Quran “co-operate and help each other in the constructive and good works and don’t co-operate to do hostility and bad actions. Invention identity: Name of the invention: secure safe Components: sensor, mobile phone, battery, conductive means (wires)How does the invention work? Operating Process Firstly, when approaching or touching the safe body, the electric circuit attached to a sensor in the safe is closed and this will directly get the mobile phone ring. Therefore, the safe’s owner will realize that there is danger about his properties or the money included in the safe. The main objective of the invention: Adding further security to the private and public properties, and enabling the owner to watch or control his properties all time everywhere. Where this invention can be used: usage fields This invention will be used in the security domain as well as that of the economic. It can be employed and used instead of a lot of security persons. The future vision of the invention Its components can be integrated into one unit and therefore the usual size can be minimized. Further, it could be possible to add a camera to the invention to be used for additional purposes in several fields; e.g. cars, premises, house, etc.

在一個有障礙的平面上，給三個定點，我們探討連接此三點的最佳網絡。我們討論了諸如直線、射線、線段、圓、網格狀、三角形……等類的障礙，當網絡每穿越障礙一次，就必須付出代價，例如「拖延5 分鐘」。所以，設網絡穿越障礙的次數為y ，則網絡除了原本的總長度之外，還額外加入y 倍某固定數值的損耗。我們以費瑪點的各種性質及三角形不等式等方法為工具，就不同的穿越障礙次數綜合比較，而找出最佳網絡。在某些情況下，最佳網絡不是以費瑪點來連接三點，而是在障礙(如：直線)上找出符合某種與餘弦值相關特殊性質的點，以該點來連接三點，而此網絡可用GSP 軟體相當精確地作出。另外，我們也探討在考慮障礙造成損耗的情況下，兩點間的「實際距離」為何。 最後，我們考慮「混合障礙」問題。在此類問題中，除了前面所討論的障礙，還另加了如同「河流」的兩平行直線間區域之障礙，在這種障礙區域中，網絡的長度要乘以數倍來計算。我們發現，此類問題的最佳網絡也可用特定的正弦條件配合GSP 而相當精確地作出來。;Considering various kinds of obstacles in a plane, such as a line, a segment, a ray, a circle, a triangle or chessboard grids, which function like a red light, we research into the problem of finding the optimal network connecting three given points A, B, C in the plane amidst obstacles described above. Each time when the network crosses an obstacle, it will cause losses, such as five minute’s delay or a loss of one hundred dollars. Taking advantage of Fermat points, some basic inequalities concerning triangles and some special qualities about sine or cosine functions, we obtain the optimal networks in different situations. Besides, we consider what the “real distance” between two points is when there are obstacles in a plane. We also put another obstacle, including a line and a weighted region between two parallel lines, into consideration. In the region, like a river or a muddy ground in real life, the length of the network should be multiplied by a fixed time. Furthermore, we can use GSP to make the networks very accurately.

傳統的畢氏定理三元二次不定方程x² + y² = z²有一組漂亮的整數解為(m² - n²、2mn、m² + n² )；中國數學家嚴鎮軍、盛立人所著的從勾股定理談起一書中記載四元二次不定方程x² + y² + z² = w²的整數解為(mn、m² + mn、mn + n²、m²+ mn + n² )，這組解被我們發現有多處遺漏，本文以擴展的畢氏定理做基礎修正了他的整數解公式，並推廣取得N 元二次不定方程的整數解公式。 There is a beautiful integer solution formula for the Pythagorean theorem equation, x² + y² = z² , such as (m² - n² , 2mn ,m² + n² ). The “m＂ and “n＂ of the solution formula are integer number. A book written by two Chinese mathematicians, Yen Chen-chun and Sheng Li-jen who expanded the Pythagorean theorem equation to the four variables squares’ indeterminate equation, x² + y² + z² = w² . They claimed that they found its integer solution formula, such as (mn , m² + mn , mn + n² , m² + mn + n² ) for any integer “m＂ and “n＂. But we found it losses many solutions. This paper corrected their faults due to the expanded Pythagorean theorem built by ourselves. Further more, we derived a general formula of N variables squares’ indeterminate equation. Now, we can get integer solutions of the equation, (for all natural number “n＂) easily by choosing integers m1 , m2 , m3 ,……, mn−1 up to you.

本實驗使用奈米級二氧化鈦能經紫外線催化，分解空氣中的水分子產生自由基，攻擊膠原蛋白中碳與氫鍵結的部份，使膠原蛋白的分子量成功的從300000 減少至少到20000 以下。其次，利用紫外線波長或酸鹼值的變因之下，控制降解出來的分子量大小。利用此法可在4個小時內得到很好的降解效果，不僅可以節省反應所需的時間，所需的成本也比當今所使用的酵素降解法來得低。 其次，我們檢測降解完後膠原蛋白的活性，發現只要不照光超過2 小時，膠原蛋白所剩的活性還不錯。如此一來，我們就可以利用此法快速的製造出有用的膠原蛋白了。 ;In the experiment, we use the properties of TiO2 which can be catalyzed by UV rays and breaking the molecules of H2O and produce free radicals that can attack the bond between carbon and oxygen in collagen, degrading collagen's molecular weight from 300000 to at least below 20000. We also use different UV rays and pH to conduct the experiment, controlling the molecular weight by degradation. By using this technique, we can get good effect of degradation in 4 hours. It can not only cut back the reaction time, but also costs much lower than the way using enzyme to degrade collagen. Furthermore, after the degradation of collagen, we also carry out the experiment to make sure whether collagen is “alive” or not. We have got the result that collagen can still work if it is not shone under UV rays more than 2 hours. In this way, we can use the technique to produce useful collagen rapidly.

本研究主要探討蝌蚪之游泳運動特性，及游泳速度(V)與尾鰭長度(SL)、尾鰭高度(SH)、身體質量(M)、尾鰭擺動頻率(TBF)、擺動幅度(AMP)之關係，並分析蝌蚪游泳之體軸變化及流場變化。祈能了解蝌蚪之游泳運動特性，進而探討其適應環境之機制。研究結果顯示：黑眶蟾蜍蝌蚪體重(M)愈重，則鰭長、鰭高亦隨之生長，並呈現高度相關性(R2=0.9381、R2=0.9809)。另外，尾鰭生長時之長度增加較多。蝌蚪體重(M)與鰭長(SL)、鰭高(SH)之迴歸方程式(M=0.027SL＋0.342SH－0.078，R2＝0.9832)。黑眶蟾蜍蝌蚪之游泳速度，會隨著尾鰭擺動頻率之增加而提高。尾鰭長度愈短之蝌蚪，增加游泳速度時尾鰭擺動頻率增加較多。蝌蚪游泳速度(V)與鰭長(SL)、擺動頻率(TBF)之迴歸方程式(V=0.480TBF＋4.804SL－4.381，R2＝0.9110)。不同尾鰭長度蝌蚪之擺幅對體長之比率並無明顯變化，其擺動幅度(AMP)的範圍介於0.45(BL)至0.56(BL)之間。蝌蚪游泳時各部分體軸之擺動幅度自吻端開始(P=0)至P 為0.24 時逐漸遞減，且在P 為0.24 時呈現最小擺幅，但P 超過0.24 之後直至尾鰭部分卻又大幅遞增，其最大值出現在尾鰭末端(P=1)。蝌蚪游泳是以尾鰭快速向中心軸擺動，產生較大的前進動力，過了軸線則慢速擺動，以減少阻力。This investigation is to explore the swimming habits of tadpoles- the relationship between their swimming velocity, length and height of their tails, mass, the frequency at which their tails movement, and the amplitude of the tail’s movement, as well as analysis their body axes, and the flow distribution of the water, in order to understand how the swimming patterns of the tadpoles are affected by the changes in their environment. The results of this investigation have shown that as the mass of the tadpoles increases, both the length and the height of their tails also increase according to the R values of the tail increases according to the R values of 0.9381 and 0.9809. However, it is observed the length of the tail increases at a faster rate than its height during the tadpoles’s growth. The formula which models the regression relationship between the tadpole’s mass, tail length, and tail height are found to be (M=0.027SL+0.342SH-0.078,R=0.9832). It’s also noted that as the length of the tadpole’s tail decreases, the velocity and the frequency of the tail would increases (the length of the tail is inversely proportional to the tadpole’s velocity and tail frequency). The formula which models the regression relationship between the tadpole’s velocity, tail length and tail frequency is (V=0.480TBF+4.804SL-4.381,R=0.9110) The different frequency model by tails of different lengths do not appear to have an apparent relationship with the tail length, given that the amplitude is between 0.45(BL) and 0.56(BL). As the tadpole swims, the angle between its oscillating body axes decrease as the P values increases from 0 to 0.24, their force the angle is at a minimum whom the P is at 0.24.Yet when P exceeds 0.24 the angle would increase dramatically. The maximum value is observed when P=1.The tadpole’s swimming motion mainly relays on the rapid oscillations of the tail about the centre of mass (body axis)-producing a stronger driving force, and slowing down towards the end of each oscillation to minimise the friction forces acting on the tadpole, which in furn, decrease its velocity.

The main purpose of this experiment is to discuss the characteristics of iridescent colors of Taiwanese Euploea’s wings, inclusive of the relations between the colors of wings and squamas. According to the results from scanning electron microscope, we discovered that the iridescent colors had a close relation to nanostructure and arrangements of squamas. We inferred that both the nanostructure and the arrangements would influence the formation of iridescent colors and the basic colors on wings. In addition, the basic colors on wings are related to different types of scales. To compare with the diverse formations of different sorts of Taiwanese Euploea’s wings, we took SEM pictures of Elymnias hypermnestra as well, discovering that its iridescent colors had similar relation with scales. And there was the regulation that Elymnias hypermnestra had only one type of scales at iridescent area, and two different scales at not-iridescent area as well as Euploea’s. 本實驗目的為探討台灣地區紫斑蝶蝴蝶翅膀幻色的特性，以及翅膀幻色與鱗片的相關性。由結果得知，幻色實驗中利用掃描式電子顯微鏡發現紫斑蝶幻色的形成和其鱗片的細微結構與排列方式有密切相關。我們推論紫斑蝶的鱗片細微結構與排列皆會影響其幻色的形成，而顏色的不同則與不同類型的鱗片相關。除此之外，我們亦對同具幻色的紫蛇目碟進行拍照分析，發現其幻色亦與鱗片有相關性。紫蛇目蝶的幻色區具有單一種鱗片構成的規則性，非幻色區則有兩種鱗片，與紫斑蝶相同。

The project is a simple traffic light which operate two by two type. The new ideas in this project are :1- Digital counter for car signal.2- Digital counter for side walkers. 3- Auto traffic detector.4- Red light crosser detector. Digital counters. The signals counting the whole period the the junction do in each cycle. The counter starting counting from 16 sec. down to zero and each side walk counter is vise versa with it is main counter. The time is changeable between 1-99 seconds. Also there are four square lights fitted with the main counter to illuminate the colors. Auto Traffic detector. There are three sets of switches in front of each traffic light to detect if the road is clear for the cars to enter the next road. Red light crosser detector. After the signal become red this system will operate to detect any car try to cross the red light by the car cutting the switch two times.

格子點上的三角形表示這個三角形三頂點的座標皆是整數。本研究先探討用平面格子點可以連出哪些三角形的相似形，再推廣到可以連出哪些多邊形的相似形；接著再研究空間中的格子點可以連出哪些三角形及多邊形的相似形，並用研究的結果討論空間中的格子點可以連出哪些正多面體。推廣到四次空間的格子點時，運用一條數論中的恆等式，發現可以做出來的三角形種類(所有相似形為同一種)居然與空間中的格子點一樣，這是個非常神奇的結果。另外，運用四平方和定理可導出，在五維空間中就能夠將所有可能用格子點連出的三角形種類連出來，這也是另一項收穫。When a triangle is formed with grid points, this means the coordinates of the vertices are all integers. This research aims to find out what type of triangles can develop into symmetries with vertices that fall right on 3 grid points on a plane. The same process is further applied to polygons. Based on the results obtained, the researcher moves on to explore what type of triangles can develop into symmetries that can be formed with spatial grid points. By using an equation in number theory to expand the study to a 4-dimension space, it is formed that the kinds of triangles—their symmetries included—which can be formed with 4-dimension grid points can also be formed in a 3-dimension space. In addition, all the possible kinds of triangles which can be formed in a 6-dimension space or up can also be formed in a 5-dimension space.

本專題的目的是研究以任意實數 a1 、 a2 、 a3 為起始的M&m Sequences 之穩定性質。我們主要關心的問題是：(1) 是否任給定三數a1 、 a2 、 a3 為起始的M&m 數列皆會穩定？(2) 若上述的M&m 數列穩定，則其穩定的長度與a1 、 a2 、 a3的關係為何？(3) 其穩定的值與a1 、 a2 、 a3的關係為何？我們研究的主要步驟及結果如下︰1. 當1 2 3 a 1) 為起始的M&m 數列。3. 我們證明了下列性質：(1) 若M&m 數列中前n 項所成數列的中位數為n m ，則下式成立： (2) 當存在 k > 4 , k ? N ，使得 ?1 ?2 = k k m m 成立時，則此數列穩定，且穩定長度p 滿足：min{ | 4 } ?1 ?2 = > = k k p k k 且m m ，其中p 必為奇數。(3) { n m }為單調遞增且, 5 1 ? ? ? a m n n n4. 如果x ? 41.625，則{?x,1, x}為起始的M&m 數列，其對應的數列有相同的大小次序且此M&m 數列會穩定，穩定值為41.625，且穩定長度為73。5. 我們觀察發現：如果x 1). 3. We prove the following properties: (1) If the median of the former n numbers of the M&m sequence is n m , we obtain (2) There exist k > 4 , k ? N such that ?1 ?2 = k k m m , then the sequence is stable and the stable length min{ | 4 }?1 ?2 = > = k k p k k and m m , where p must be an odd number. (3) { n m } is monotone increasing and , 5 1 ? ? ? a m n n n . 4. Suppose x ? 41.625, then the all M&m Sequences beginning with –x , 1 , x are the same, and the sequences will be stable, the stable value is 41.625 and the stable length is 73. 5. By the computer experiments, we observe that if x is any positive real number less than 41.625, the M&m Sequence starting with –x, 1, x, will be also stable but does not appear to follow any clearly discernible pattern of behavior. However, the stable lengths are much variant and exist some unknown relation with point format of x. Moreover, we have the following properties: (1)If x is a node, then the stable value is x and the stable length equals to the index of median of the node + 2； (2)Near the branch of 41.625, the stable length is almost a constant except at the edge area，the stable length of (-x,1,x) as x around branch 1 is chaos； (3)If x near the node (K= 3, 5, 7, …, 67, 69), then the stable length is l(K)+K?1 where the positive integral l(K) is determined by Prop1 (see Table 6 and 7).