本文是利用整數分拆及排容原理研究以1x2 矩形鋪mxn 矩形的排法邏輯及總排法數，並進一步探討下列兩種情況：雙邊不含缺陷線及至少有一缺陷線的排法數。\r Based on the Apart of Number and the Inclusion- Exclution principle, this research intends to analyze the logic and final result of permutation by laying an 1x2 rectangle over an mxn rectangle. From the analysis, this study will go further to explore the possible permutation in the following two situations : when there is no fault line on both sides and when at least one fault line exists.\r

The purpose of my project was to determine which activity improved academic performance the most: 10 minutes of exercise, 10 minutes of Brain Gym (cross-lateral movements), or a combination of 5 minutes exercise and 5 minutes Brain Gym. This project was conducted to find which activity would be a better learning aid in grade 4 students. There were many steps to conducting this study. First, I located teachers and classes, willing to allow the testing and determined days and times to test. Next, I created consent forms to explain the project and had permission forms from the students and their parents signed. Then I prepared 15 math and reading tests at students’ grade level. There were two tests for 15 days- labeled Before Test and After Test. When I administered the tests for the classes doing the activities, I made sure the tests were given by the classroom teacher, which kept the students motivated. Tests were given every day for 5 days. The Before Test was given at 1:00 pm. Then at 1:30 pm students did 10 minutes of the planned activity for that week. Immediately after the activity, students were given the After Test. This was done every day and was repeated for Exercise, Brain Gym, and Combination week. The control class was designed to determine if doing the test for a second time in a day improved the student’s performance. The Before Test was given at 1:00 pm and then at 1:30 pm. When the Before Tests were completed, the students continued with their daily work for 10 minutes. Then at 1:40 pm students were given the After Test. This was repeated for Exercise, Brain Gym, and Combination week. Students were given 10 minutes to complete the scheduled activity that week; either Exercises, Brain Gym or a combination of the two. During the week of Exercise, Jumping jacks, Skipping, Stride jumps, Burpies, Twisties and Jogging on the spot were completed in the 10 minutes provided. During the Brain Gym week, there were 26 Brain Gym movements. The lists of movements were rotated each day; so all movements were performed. The test results of this study were intriguing. (Bar=Standard Deviation) I concluded that 10 minutes of exercise was the better brain booster. Exercise improved academic performance by 9.8%. Brain Gym improved academic performance by 0.2% and the combination activities increased test scores by an average of 3.2%. The control class test scores decreased on average by 1.0% indicating that writing the tests twice in a day, did not improve students’ test scores. Exercising for 10 minutes improved student’s math scores by 11.0% and reading scores by 6.9%. Brain Gym math test scores decreased by 1.4%, and increased in reading by 1.8%. In the combination of the two, the math test scores decreased by 1.0%, reading test scores increased by 7.4%. Overall, the most effective and reliable brain booster was 10 minutes of mild aerobic exercise alone.

At present Malaysia is the largest exporter of palm oil in the international market. In the process of extraction of palm oil from oil palm fruit, biomass materials such as palm empty fruit bunch (EFB) and palm pressed fibre (PPF) are generated as waste products. Natural fibres reinforced cement-based materials have gain increasing application in residential housing components. One of the natural fibres considered is oil palm empty fruit bunches (EFB) fibres which offer advantages such as availability, renewability, low cost and the established technology to extract the fibres. This study investigates the properties of cement board incorporated with large amount of oil palm EFB fibres Among the tests conducted was compressive strength, density, water absorption and thickness swelling tests. It was found that high EFB fibres content lead to lower strength and higher absorption . The results also indicate that high EFB fibres contents reduced the self-weight of the blocks and the resulting blocks can be classified as lightweight cement blocks suitable to be used as lightweight walling materials. Our research is to study the production of cement board using Empty fruit bunch(EFB)These board were made from empty fruit bunch, cement and water. Two chemical are added is aluminium sulphate and sodium silicate. Cement : EFB mixture by weight was 2.5:1, 2.75:1 and 3.0:1 used to produces a cement board.

Characterization of telescope lenses using physical optics and selection of the optimal physical parameters of a reflecting telescope’s optical units were done to improve the design, cost-efficiency, and quality of the 64-cm telescope (named Oof) housed at the National Institute of Physics. Characterization has been done through numerical modeling of the point spread function (PSF) in Python. The PSF code was based on the method of getting wave vectors by Richards and Wolf. The optimal PSF was established to be the PSF of a large monolithic mirror. The PSF of a single optical lens was compared to its counterpart segmented lenses. Through the comparison of maximum intensity, the normalized mean square error (NMSE) and the Linfoot’s criteria of correlation quality, fidelity, and relative structural content, the study has produced results which proved that highly segmented optical components produce results with less quality compared to less-segmented optical components. It was found that as the segmentation increases, the maximum intensity decreases. Higher values of maximum intensity denote higher light gathering power. The normalized mean square error of the set-ups having one to seven layers had values greater than zero but less than one. This denotes that the PSF of those set-ups are near the PSF of the optimal set-up. Higher values of correlation quality, fidelity, and relative structural content denote higher correlation, higher signal to noise ratio, higher closeness of correspondence between the optimal set-up and the segmented set-up. The number and the size of the optical components of the segmented mirror were manipulated in order to achieve a negligible difference between that of the optimal PSF and the PSF of a segmented mirror. The equivalent single lens radius in terms of maximum intensity of the current set-up of the telescope was determined to be 234.25 mm. If the optimal PSF is achieved, the physical parameters of the optical components generated may be applied to the optical components of the 64-cm telescope. The design that resulted from the study could be used in the future construction of a wide-aperture telescope, which could aid in the acquisition of knowledge about heavenly bodies.

1. 將 cos nθ以cosθ 形式依高次降羃排列展開，觀察各項係數，找尋其變化規律，進一步求得各項係數的一般項公式。2. 將 sin nθ以sinθ 形式依低次升羃排列展開，觀察各項係數之變化規律，進一步求得各項係數的一般項公式。3. 找出cos nθ 與cos(n-1)θ，cos(n+1)θ 之間的關係式。4. 找出sin nθ 與sin(n-1)θ，sin(n+1)θ 之間的關係式。5. 利用cos nθ 的係數間的遞迴關係，找出其相對應的特徵方程式。

編號1~mn 的mn 個物件已隨機置入m× n 階的矩陣中，另外有一行m 個空格的暫存區供物件暫存用。我們探討將這mn 個物件移至目標區並按照1,2,…, mn 的次序排列，所需的移動步數；每一步的移動中，只能移動每一行最頂層的物件到其他行(含暫存區)的最頂層或目標區。在這篇報告中，我們給出了一個適用於n ? m ?1時的移動方法，此方法在一般的情形下，所需的移動次數未必是最少；但是在最不利於移動的情形下，我們證明此方法所需的移動步數為最少。There are mn objects, numbered from 1 to mn, put on an m× n matrix randomly, and there is another column with m blank spaces for temporary storage purpose during moving. In each step of moving, we can only move the top object from one column to the top of another column or to the target pile. The total steps needed to move these mn objects to the target pile in increasing order from the bottom to the top is studied in this article. A general method for solving this problem when n ? m ?1 is given, and we prove that it provides an optimal solution in the worst cases. However, it may not always provide the minimal steps in all cases.

蝴蝶定理（Butterfly theorem）是在一個圓形中，設M為圓內弦PQ的中點，過M作弦AB和CD。設AD和BC各相交PQ於點X和Y，則M是XY的中點。 在此份研究中，我們探討正方形邊上兩個動點、正方形內一個定點以及邊上動點與內點的連線，延伸交四邊的另外兩點，所構成的「蝴蝶形狀」的「蝴蝶線」。主要利用兩個動點在邊上的位置，以及內點在正方形內的位置，尋找上述條件與蝴蝶線的關係。由於邊上四個點的分布對於蝴蝶線有很大的影響，所以又依照四點分布位置進行分段討論。另外，我們也尋找正方形內接蝴蝶形的特殊性質。

在數位化的今日，由於網際網路的技術蓬勃發展，網際網路變得更容易使用及具高度的親和性，使得網際網路的使用逐年成長。隨著越來越多人依賴網路進行交易，也衍生了層出不窮的網路詐騙問題。其中，網路釣魚就是一項著名的詐騙技術：詐騙者透過偽裝成知名企業的網站，藉此騙取使用者的個人私密資料。在本研究中，我們提出了一套植基於彩色視覺密碼學原理的網站驗證機制，使用者可以透過此機制，直接利用人類視覺的方式來驗證所連上的網站是否有問題，並在此機制之下，設計出另一套管理使用者密碼的方式，進而方便使用者不必費心的去記憶密碼。 Recently, as networks technology flourishes, Internet becomes easier and friendlier to use, and makes the usage of Internet grow up year after year. With more and more people relying on online transactions, it leads to endless network fraud issues. Among them, phishing is a well-known fraud technology to disguise the famous business website to get user’s private information by cheating. Therefore, in this study, an effective scheme based on color visual cryptography is proposed to test and verify the website. Through the proposed mechanism, users can check whether there is a problem website by using human vision directly. Furthermore, the proposed scheme also provides another way to manage user’s password effectively.

本實驗是利用二氧化矽分子篩保護奈米銀的方法，有別於市面上奈米銀產品大都以有機溶劑浸泡，且保護劑均是採取界面活性劑，該項產品浸在純水中除了不會改變溶液性質外，又能以分子篩特性讓奈米銀漸進式釋放而達到長效性效果。 針對棉衫吸附奈米銀實驗非常成功，經過十次以上洗滌且放置時間長達一個月以上，對於抗菌效果也有長效性的功能，為本次實驗重大突破。 The experiment is to use SiO2 molecular sieve protected nano Ag method , different from nano Ag popular product which is organic solvent-soak, and the protectant are all surfactant. This product will not change solvent’s proterty in pure water , beside , molecular sieve generally release nano Ag and achieve long-term effect . The experiment for cotton clothes adsorptive nano Ag is very successful , and achieve long-term effect in antibacterial property , that is the most significant .

This project was inspired by a tournament call the International Young Physicist’ Tournament (IYPT). The problem could be broken into two aims: ‘Investigate the forces that cause a ball to levitate in a titled airstream’ and ‘optimize the system for the maximum angle of tilt that results in a supported ball’. The first stage of the investigation was research and learning. Two fluid mechanics courses online were used to build a basic of knowledge of the subject. Next a force diagram was created to model the forces acting on the ball. The diagram identified a force called the lift force that must be acting on the ball to be supported. There were three contending theories that could explain the lift force: The Bernoulli theory, the Coanda theory and the Magnus theory. A practical investigation was then instigated to differentiate between these three theories. Since the Magnus theory is only applicable if the ball is spinning in the airstream, this theory was isolated by changing the center of mass of the ball but keep everything else constant (this allowed control of how much the ball spun in the airstream). Changing the center of mass didn’t impact on the maximum angle of tilt at all, proving that the spinning of the ball isn’t producing a significant amount of lift, and therefore the Magnus theory couldn’t be a cause for lift. Because further testing couldn’t isolate the Coanda and Bernoulli theories, a solution was developed to explain why the two remaining theories might co-exist. Further testing methods have been designed to investigate this possibility in more depth. To meet the second aim of this project, an investigation was launched to see how parameters affected the maximum angle that the ball could be supported at. The parameters investigated were: Ball radius, ball mass, ball surface, air speed and airstream diameter. A lot of time was spent creating a reliable experimental method. The method could be used to support a ball in an air stream, slowly tilt the air stream, and then measure the angle of tilt the moment that the ball fell out. After experimentation, a table was created to describe how the listed parameters affect the maximum angle of tilt that a ball can be supported at. Explanations were proposed for why each parameter affected this angle. Future experiments have been devised to build a deeper understanding of the effects of a wider range of parameters.

快門，捕捉最原始的感動；科技，創造最完美的呈現。當攝影遇上科學，成就了本研究的主題──高階電腦數位影像之研發。在我的研究過程中困難重重，從外景攝影、後製研究、影像創作到本研究撰寫完工，一切由我個人獨力進行，經歷了多次失敗，仍堅持的完成這重大的研究突破。 相信多數人會使用相機，但是對數位攝影這領域卻不甚了解，更別談藝術與科學的結合。因此希望本科展研究將會成為未來科技數位電腦的主軸，強調科技、即時、便利、環保、生活及教育的科學推廣，以實用並超越新世紀的數位領域，讓所有電腦愛好者，都可以輕鬆的應用此高階的數位暗房後製。讓電腦科技不只是零與一的組合，而是心靈與世界的互動！ ;Camera shutter captures the most original affection; technology creates the most perfect display. High-level digital image—when photography meets technology—is the theme of this research. However, in the process of the research, I have encountered many problems—from outdoor scene shot, production research, image creation to report writing—I did them individually and had undergone many failures, but I still insisted on finishing this big research breakthrough. I believe that many people can use the camera, but didn’t understand anything about the field of digital photography, let alone the combination of art and technology. I hope this technology development research would become the main perch of digital technology in the future—emphasizing technology ,instantaneous,convenience,environmentalprotection, livelihood, and popularize technology education—to use and go beyond the new age of digital field and to make computer lovers apply high-level darkroom production easily. Making computer technology not just combinations of zeros and ones, but the interaction between life and the world.

本研究係使⽤快速傅⽴葉轉換對⾦屬圓板撞擊產⽣的⾳頻進⾏分析，並搭配⾃製的運算叢集，來實現使材料辨識系統。本研究為分析⾦屬圓版與其相關之物理量對⾳頻的影響，吾⼈透過 Journal of Sounds and Vibrations 中的⼀篇 “The Influence Of Poisson’s Ratio On The Natural Frequencies Of Free Circular Plates”之公式，配合⼤量實驗做為數據轉換的基礎，找出⾦屬的Ψ值，如鋁為0.15762、鐵為0.28921、銅為0.36213，最後將之整合，並提出以機器學習的⽅式優化材料辨識系統，⼤⼤提⾼本研究之未來發展性。