2008年

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.

My project explores the practicality of biodiesel. It researches the argument of food versus fuel, compares the energy efficiencies of petroleum diesel and biodiesel and studies the effect of temperature on biodiesel. To study the effect of temperature on biodiesel, I blended biodiesel with petroleum diesel. Biodiesel blends are represented by the letter B, and the percentage of biodiesel. I used B5, B10, B20, and B50 blends, as well as pure biodiesel. I then observed the reaction of the biodiesel blends with cold weather. My pure biodiesel and B50 blends gelled to an unusable point within 15 minutes outside at -20oC. The B20 blends didn’t gel until about a temperature of -20oC. I have concluded that the B20 blend would be best for the summer, and the B10 or B5 blends would be the best for winter in northern climates, where I live. Although the B10 blends gelled slightly around -30oC, this would only be a problem for northern climates. As I predicted, more energy is produced by biodiesel than is consumed in the production process. The process of making biodiesel uses 0.31 units of energy to get 1 unit of energy out. More energy (1.2 units) is used to produce petroleum diesel than is yielded (1 unit). Although B20 isn’t as energy efficient as B100, the energy factor is still only 0.98 units of energy in for every 1 unit of energy out. When I started this project I thought that Canada would have enough farmland to produce the canola needed to run the country on biodiesel. This is only partly true. Canada would have enough farmland, but only a fraction of that land is actually used to plant canola. By my calculations, Canada has enough canola to generate enough B20 for a year. This may seem like a drawback but realistically, a higher blend would be impractical due to the gelling factor. Also, if a B20 blend was used, land would be available to grow canola for other markets. If B100 was used, there would only be enough diesel for about three months consumption. By using all of the land for biodiesel feedstock, canola would become unavailable for other markets. If canola exports ceased, the countries that depend on our canola will be in a lot of trouble. Canada already produces a lot of canola and vegetable oil. Most of it goes to the fast food industry. The United States produces over three billion gallons of fryer oil yearly. This could provide Canada with a B50 blend for a year. Utilizing used vegetable oil in making biodiesel actually reduces emissions even more. This is accomplished by using a product that would normally go to waste and decompose, producing more carbon dioxide emissions. During this project, I have found that biodiesel is a practical alternative to petroleum diesel, if it is used in a blend. My experiment proves that biodiesel is a fuel alternative that could be implemented immediately, and one that does not require the research needed for other fuel alternatives such as hydrogen or electricity.

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.

Now a days cancer is one of the most important factor of death in the world so we decided to introduce people one of the easiest way of it’s prevention. However, the relation between green tea and cancer is not completely identified but the research shows that drinking green tea reduce the state of cancer. First we found some information about the green tea compounds then we investigated the cancer factors in different countries and stidied the experiments among 900 women showed that drinking tea reduce the state of ovary cancer. Green tea contains A, B, C, D vitamins & Fe, folic acid &also minerals such as Ca, K, Zn. This useful soft drink is a strong Anti?oxidant so prevent any kinds of cancer & blood clot. Therefore it reduce the state of heart attack. (Up to 31%) So it is not only prevention factor but also it can open a new way to cure different cancers.

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.

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.

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.

當世界各國正全力朝奈米科技發展，而奈米微粒對環境及人類健康影響與否未明朗之際，有關奈米微粒對人類健康影響之探討是刻不容緩之事。本研究的近程目標是合成金奈米粒子，遠程目標是擬探討金奈米粒子的生物毒性。此份研究主要是描述金奈米粒子的最大表面電漿吸收光譜特性及其最大吸收波長，而金奈米粒子的合成是利用四氯金酸( HAuCl4 )與還原劑—硼氫化鈉( NaBH4 )、聯胺水合物( N2H5OH )或檸檬酸鈉在陽離子界面活性劑的溶液( CH 3(CH2)15N+(CH3)3Br– ，溴化十六烷基三甲基銨，CTAB ) 當保護劑中，利用氧化還原方法直接生成金奈米粒子，並探討四氯金酸的濃度、還原劑的濃度、界面活性劑的濃度及反應溫度，對金奈米粒子生成之影響，另外也探討金奈米粒子的穩定性。有關金奈米粒子的光譜特性則利用UV/Vis 光譜儀測試。研究結果發現在相同的條件下，利用冰浴，以NaBH4 當還原劑所合成出的金奈米粒子之平均粒徑為11.70 nm ，而以N2H5OH 當還原劑所合成出的金奈米粒子之平均粒徑為20.25 nm， 有關金奈米粒子之結構及大小藉由穿透式電子顯微鏡( TEM ) 拍攝出的影像得以驗證。;This study mainly focused on the properties of the maximum surface plasmon absorption of gold nanoparticles and their wavelengths. The synthesis of gold nanoparticles made use of HAuCl4 aqueous solution and reducing agent, through the oxidation reduction method, with reductant, sodium borohydride ( NaBH4 ), hydrazine ( N2H5OH ) or sodium citrate solution in the presence of the cetytrimethylammonium bomide ( C19H42BrN,CTAB ) aqueous solution as protecting agent. The influence of concentration of HAuCl4, reductant, surfactant, and temperature on the synthesis of gold nanoparticles were explored. In addition, the stability of the gold nanoparticles was also explored. Measurements of spectral properties of gold nanoparticles were done by UV/Vis spectrometer.When NaBH4 was used as a reductant, the average diameter of gold nanoparticles was 11.70 nm. When N2H5OH was used as a reductant, the average diameter of the synthesized gold nanoparticles was 20.25 nm. The structures and sizes could be identified by the transmission of electron micrograph (TEM) images.

Lotus self-cleaning effect arises because the leaves have the superhydrophobic surfaces. When rain falls onto a lotus leaf, water beads up as a result of surface tension. The water drops promptly roll off the surface, taking every dirt with them. This phenomenon is called the lotus effect. With the aid of a light microscope and an Environmental Scanning Electron Microscope, we observe and describe the morphology of the leaves of Nelumbo nucifera in detail. We successfully observe the real interface between air, water droplets and the papillae of a lotus leaf, and find the evidence of a composite surface that is formed by epicuticular wax crystals and air. These observations improve our understanding of the two-level composite surfaces that are formed by micro-scale papillae, nano-scale epicuticular wax crystals and air. We try the method of using the critical angle of a static drop beginning to roll on inclined surface to evaluate the self-cleaning ability. We then find out that it may be a more precise criterion compared to using the static contact angle for the evaluation of the lotus effect. Literature review shows that the earlier investigation lacks the height(H) and interval(I) of the projections on the lotus leaf surface. A close relationship between the self-cleaning property and the H/I ratio is found. In this study, we present the experimental data of the height and interval of the projections on four different species of plant leaves that all have lotus effect, which may be of great help to technological applications. 蓮花效應是指蓮葉表面具有超疏水性與自我潔淨的能力，當雨水落在葉面，因為表面張力的作用形成水珠，水滴迅速滾離葉面，把灰塵一起帶走。本實驗以光學顯微鏡和環境式掃描式電子顯微鏡觀察蓮葉，詳細描述其表面形態，成功的發現空氣、水滴和蓮葉乳突真實的接觸界面以及表面蠟和空氣構成複合表面的證據。實驗結果可以使乳突、奈米表面臘質和空氣構成的雙層次複合表面更容易被了解。我們嘗試以水滴傾斜滾動臨界角來評估自潔能力強弱，實驗結果比傳統使用靜止接觸角更為準確。表面高度和間距的比值與蓮花效應有很大的關係，查閱文獻顯示蓮葉缺乏這些資料，本研究提出四種有自潔能力的葉子的實驗數據，這些數據應該對科技應用有很大的幫助。

The purpose of this project is to determine if it is possible to use Ascorbic Acid Sodium- Dependent Vitamin C Transporter Type II, SVCT2, as an effective and safe protein to attach to certain brain tumor treatments to bypass the Blood Brain Barrier (BBB). Stemming from this problem, a procedure was created to use in vitro engineering with the aid of a professor at the University of Calgary to combine SVCT2 and three specific tumor treatments; Imatinib Mesylate (STI-571), Temsirolimus (CCI-779), and Suberoylanilide Hydroxamic Acid (SAHA). Following this, a metabolic barrier had to be created to simulate the BBB. To do this, the use of three enzymes were mixed and held together using specific bonds. Finally, a special bio-tracer was placed within the barrier to detect any toxic effects that may be produced. Then two trials were made with each treatment on the barrier at 34°C, 37°C, and 39°C. Once this was done observations could be made. When the newly isolated SVCT2 attaches to the three cancer treatments, they would all be able to connect and form bonds with each other. Once the incubation period is over for the first trial at 34°C, 37°C and 39°C, several things would be observed within the data. When counting the number of cells that were able to get into the engineered metabolic barrier, it could be seen that there was a dramatic increase in the number of cells in the 37°C range. SVCT2 can be a powerful tool in combating cancer. Because of its specificity, it may prove to be more advantageous over the currently used drugs which may have unwanted toxic side effects on the CNS. In the near future, SVCT2 could have the potential to be adopted as a promising therapy against cancer and certain tumors. Furthermore, SVCT2 has the potential to be applied to many situations and can be modified to fit a number of situations that deal with getting past the Blood Brain Barrier. Initially, SVCT2 was only modified with three forms of treatment for Glioblastoma Multiforme, STI-571, CCI-779, and SAHA, however there are countless other treatments that have been developed, but that are not in use due to the BBB. This project was successful in determining an appropriate temperature of 37°C for the procedure to be used. The limitations of this experiment include the fact that this experiment was performed in vitro and so complexity among individuals cannot be analyzed. However, this is an early step for the future of SVCT2 as a treatment, and clinical trials to test SVCT2 in vivo may not be too far off.