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。

在拋物線上置掛正三角形看似簡單，其實不然。本篇文章研究在二次函數的各種不同情況下，可做正三角形的分佈以及其個數。 1. 在一條拋物線上時，最多只能作正三角形。 4. 在三條對稱軸相等的拋物線和共頂點開口大小不同之拋物線上，本篇文章證明一定能找出正三角形落在它們之上。但由於最多有四個分界點，要解四次方乘組過於繁複，於是本篇文章對分界點作了一些估計，找出了分界點的極限值。 5. 本篇文章證明了對於給定的正n 邊形，存在一1 元n-1 次方程式可以通過它所有頂點。 Building a regular triangle on a parabolic curve looks easy . In fact , it doesn’t . This Article researches regular triangles distributions and its numbers in different conditions. 1. On one parabolic curve can only build regular triangles , squares and other regular polygons can’t be built. 4. For three parabolic curves which has same symmetrical axis or three concurrent parabolic curves, we prove that it can build at least one regular triangle on them .But because it can have at most 4 boundary points, to solve quartic equation is to complicated. So we do some estimation of boundary points, and find out some limits. 5. This Article prove that for given regular polygons , there exists a one dimension n-1 orders equation can pass all its apexes.

在1940 年代，Bouwkamp 提出一系列有關如何將矩形切割成若干個正方形的研究報告，但是如何找出正方形個數最少的方法仍是長久以來懸而未決的問題。在本研究報告中，首先引進「四角切割」的方法，並結合輾轉相除法的概念，來研究矩形的切割問題。我們的方法能大幅度降低正方形的個數，也適合做為此問題的上界函數。有關如何在長方體中切割出正立方體的組合，我們也將輾轉相除法的概念延伸到三維空間，進而建立所切割出最少個正立體數的一個上界模式。此外，藉由四角切割概念的延伸，我們也發現這個上界亦可再予修正。In 1940’s, Bouwkamp proposed the study of dissecting squares from rectangles. Among the study, the problem of the least number of dissected squares has been open for decades. In this project, we first propose a corner dissection method, associated with the famous Euclidean algorithm. By reducing nearly three fourths of the number dissected by the primitive Euclidian algorithm, our method indeed establish a suitable upper bound of the minimal number of dissected squares from the given rectangles Meanwhile, the Euclidean algorithm has also been considered to dissect the cubes from cuboids. We analyze the fundamental properties of the method and establish a prototype of upper bound function for the minimal number of dissected cubes. Moreover, the method of corner dissection has also been implemented for some cuboids, which also exhibits the acceptable improvement being a suitable upper bound.

「重複圖形」是本篇報告研究的問題，我們利用「方程式」建立一個尋找重複圖形，並証明其個數的方法。利用此方法得出下面的結論：1.會形成lap 2 的凸多邊形只有2 種，即三角形和四邊形。(1)「lap 2 三角形」只有1 種，即等腰直角三角形。(2)「lap 2 四邊形」只有1 種，即二邊之比為1： 且內角是45°、135°的平行四邊形。2.會形成lap 3 的凸多邊形只有2 種，即三角形和四邊形。(1)「lap 3 三角形」只有1 種，即內角為30°–60°–90°的直角三角形。3.其他的lap k 三角形：(1)任意內角為30°–60°–90°的直角三角形都是lap 3k²，其中k是正整數。(2)邊長比為1：m： 的直角三角形是lap (m²+1)k²三角形，其中m、k是正整數。 To find repeated figures, we construct a method to search them with the help of algebraic equations. Here we arrive at：1. There are only two kinds of lap 2 convex polygons, triangles and quadrilaterals. (1) The only lap 2 triangle is isogonal right-angled. (2) The only lap 2 quadrilateral is the one that contains angles 45°, 90° and two neighboring sides with the ratio 1: . 2. There are also two kinds of lap 3 convex polygons, triangles and quadrilaterals. (1) The only lap 3 triangle is the one with angles 30°, 60° and 90°. 3. Other kinds of lap k triangles are listed as following: (1) A triangle with angles 30o, 60°, 90° is a lap 3k², the k is a natural number. (2) A right-angled triangle whose ratio is 1 : m : is a lap (m2+1)k², the m and the k are natural numbers.

This project aims to explore the potential of inexpensive in-situ deposition of niobium nitride nanowires to improve electrical conductivity. Transition metal nitrides are well known for attributes such as superconductivity, high melting point, simple structure as well as excellent electrical and thermal conductivities. In particular, niobium nitride possesses exceptional hardness and high reflectivity, as well as being a stable field emitter, making it well suited to applications as a cold cathode material. Niobium nitrides are formed by the uptake of nitrogen by niobium. This is achieved by the exothermic formation of an interstitial solid solution of nitrogen atoms in the bcc lattice of the niobium. Existing research has established the possibility of preparing niobium nitride by heating niobium in nitrogen or ammonia over a range of temperatures, by heating niobium pentaoxide and carbon in the presence of nitrogen as well as by chemical vapor deposition of other niobium compounds, nitrogen or hydrogen. For the purpose of this study, a two-step process was used for synthesis. The benefits of a two-step process over direct ammonolysis are apparent, from the greater degree of freedom pertaining to parameter determination. Additionally, characterization of niobium pentaoxide nanowires synthesize under similar conditions is also made possible by terminating the reaction earlier. NbN nanowires were synthesized by annealing niobium pentaoxide nanowires at 850 oC for 2 hours. Subsequent characterization was done using Raman Spectroscopy, X-ray Diffraction (XRD) and Scanning Electron Microscopy (SEM). The presence of NbN nanowires via the conversion of Nb2O5 was ascertained by the absence of sharp peaks at 1000 cm-1 for Raman Spectroscopy and XRD plots. Field emission (FE) properties and electrical properties of NbN nanowires were then measured. NbN nanowires were found to have a high turn-on voltage, stable and relatively good field emission characteristics, demonstrating its potential as a cold cathode material. No current saturation was observed for an applied electric field of 0 to 6.0 V/ μm (5). This suggests a low degree of contact resistance for nanowires produced by this method of annealing, since the passage of electrons is not obstructed. Hence there will only be a small voltage drop between the SiO2 substrate and NbN nanowires. Samples containing NbN nanowires were dislodged by ultrasound to form an aqueous suspension of nanowires. A drop of suspension was dripped onto gold-finger substrates, and current-voltage (I-V) measurements of resultant nanowire bridges were taken. NbN nanowire bridges display Ohmic properties, in comparison with Nb2O5 nanowires that are semiconducting. Nanowire bridges obtained by heat-drying were denser and had better electrical properties than those obtained by evaporation to dryness. NbN nanowire bridges display Ohmic properties, in comparison with Nb2O5 nanowires that are semiconducting. Further work would include varying the cooling processes to observe any changes or deformation. Additionally, niobium nitride nanowires can be hybridized with carbon nanotubes (CNTs). A more in-depth comparison between niobium oxide and niobium nitride nanowires is also proposed, along with exploration of the nitrification of other transition metals.

Anthocyanin is a water soluble pigment that may appear in various colors such as red, blue, and purple according to the pH. Ube is a fruit in the Philippines that is 3rd of the most cultivated crops. Since Ube contains a lot of anthocyanin, it helps to make the anthocyanin solution. As Anthocyanin reacts to the oxygen quickly it is also used as air pollution indicator because it changes its color according to what substances they are attached to it. To check if the solution reacts to the pollution such as SO2 and NO. When those pollutions are made artificially, examining the intensity of the anthocyanin solution depending on different Mol of the pollutions was able. The power of penetration of lights though the UV-VIS spectrophotometer increases according to the number of molecules of SO2, and also NO. To examine the change of intensity of anthocyanin solution in actual atmosphere, the solutions were exposed outside for several hours. The power of penetration decreases when exposed to an actual atmosphere. The other substances and oxidation were the causes of the changed in color of the solution To facilitate the usage of anthocyanin solution efficiently, it should be preserved, so that the density of specific color will be preserved when used as real air pollution indicator. In order to check what kinds of chemicals can preserve the anthocyanin solution; different kinds of strong acids, strong base, salts, and metals were added to the solution. After getting the data, the characteristics of the chemical which preserved the anthocyanin were scrutinized, than compared to the density of pure anthocyanin solution. To use anthocyanin as air pollution indication as a solid, the Korean traditional paper and cloth were dyed using ube which contains lots of anthocyanin than checked the pixel of red, green, and blue color. Firstly, chose 6 different salts. And then filter and boiled the anthocyanin solution. And then put each different salt in each paper. After that, dried the paper and check the difference of pixel of each paper. As a result, Calcium hydroxide (CaOH2) has highest pixel point. So, using calcium hydroxide to dye clothes is useful and it’s also useful for the air pollution indicator through the experiment. Especially it reacts to Nox and Sox, according to this experiment, it can use for eco-friendly air pollution indicator.

We understood the definition and meaning of spider number by reading〝Wonders of Numbers〞. It interested us so much. So, we took further step to study the situation of extreme value when the gap sometimes lie on the line and sometimes on the circle or even on both. That is to say, we explored the relation between spider number and the gap when the spider number is maximum or minimum. New research for the application of spider number involves several directions. First, we design a new game called〝Stepping Land Mine〞with the rule of spider number. Give you a net with several hidden gaps, trying to find the right positions of gaps. Second is the further result for a different type of net about regular n-polygon. Third is a tactic for a net with destroying of the strategy points. In this situation, the gaps amount on the circle and on the line are fixed. At the same time, consider the situation of circles and lines designing the tactic of placing the gaps to attain the maximum of the destructive effect. 在本文中我們定義一個蜘蛛網上的蜘蛛數，若在蜘蛛網中加入缺口後，會影響蜘蛛數的大小。我們探討蜘蛛網上的缺口，該如何分配才能夠得到蜘蛛數的極值(最大值及最小值)。先觀察一直線和圓上缺口如何放置蜘蛛數有極值，再探討許多條直線及圓上的情況，進而推展至許多同心圓及通過圓心的許多條放射線的缺口，該如何放置，蜘蛛數才會有極值發生。

Starting from the problem in AMC competition of Australia, we try to find out the locus and its length when a point in a regular polygon rolls in a circle. The result is that the locus has a wonderful and regular cycle.Next, we discuss the regularity of the cycle when a regular polygon（n sides） rolls in another regular polygon. Furthermore,we discuss the the equation of the locus by changing the radius and the angle of rolling. we find out the argument function of the locus of a point inside when a a regular polygon（n sides）rolls in another regular polygon （m sides）： ， Aj is the summits of the regular polygon（m sides）, Bjcorresponds Aj when a point inside the regular polygon (n sides) rolls, ) And then, we do some moving simulation with some computer math software, such as Cabri Geometry、Mupad, etc. We discuss the regularity of the locus and its equation of a point inside when some special cycloids, like asteroids, cardioids, etc, roll in a certain condition. Moreover, with the result of research 2, we create the “plate＂ and apply for a patent on it. We hope to study math by playing games. 從澳洲AMC 競賽題出發，嘗試探討一正n 邊形中的一點在單位圓內滾動軌跡及其軌跡長度，發現該軌跡均會產生奇妙的循環規律。 接下來，推廣探討正n 邊形在其他正多邊形中滾動時循環的規律，並利用旋轉半徑及角度之間的變化深入探討其滾動軌跡方程式，發現正n 邊形繞正m 邊形滾動時其內部一點軌跡參數式為，其中， Aj 為 正m 邊形之各頂點、Bj 為正n 邊形中內部一點旋轉時對應 Aj 之點，。 進一步想嘗試使用數學電腦軟體如：Cabri Geometry、Mupad 等對以上研究去做一些動態模擬，並再探討一些特殊擺線如：星狀線、心臟線…等，在條件下相切滾動時，圖中某一點的軌跡規律性及其方程式。另外，應用研究二中的結果，創造出寓數學於遊戲的「圖形板」，並申請了新型專利。

搜尋太陽系外行星（extra-solar planet；exoplanet）是當今天文學家最重要的計畫之ㄧ；其中，當系外行星經過其主恆星碟面時，會造成光度略微下降，稱之為凌日現象（transit） 。本研究便是利用鹿林天文台SLT（Sne Little Telescope）望遠鏡來拍攝兩顆已知的系外行星HD 189733 b 和HD 209458 b在凌日時的影像。 我們得到約4000 張影像，再經過影像修正與資料分析後，我們作出凌日光變曲線圖、Bin圖及相位圖，並從中探討其特性。 經分析判斷後，HD 189733 看到一個剛開始發生和一個完整的凌日現象，分別由B濾鏡和 R 濾鏡所拍攝；而 HD 209458 則看到兩個剛開始發生，三個要結束的凌日現象，分別由B濾鏡、R 濾鏡和 Hα 濾鏡。 並由光變曲線，推得HD 189733 的基本參數，包括：行星半徑為 1.242個木星半徑、軌道傾角為88.94 度以及軌道半徑為 0.03115 天文單位。 Since 1995, more than 200 extra-solar planets have been found. Until today, astronomers still make efforts in searching extra-solar planets because it’s one of the most important projects in this century. During the crossing by the stellar disks (i.e., transits), the exoplanets will cause the brightness to decrease by a small amount. In the project, we have focused on the observations of two known transit exoplanets, HD 189733 b and HD 209458 b. The photometric observations were performed with the 40-cm SLT telescope on the Lulin Observatory. The results from the image procuring, data reduction and analysis are presented. We accrue and plot the light curve, bin and phase. We found out that HD 189733 has two transit ingresses with B, R band, and HD 209458 has two transit ingresses, two transit egresses with B, R, Hα band on phase. We figure out planetary parameters, RP is 1.242 RJ, inclination is 88.94° and orbital semi-major axis is 0.03115 AU by transit light curve.

Introduction The discovery of titania (TiO2) nanotubes suggests vast improvements over extant titania properties. Titania nanotubes are aligned in highly-ordered arrays with a large geometric surface area, making them the ideal material for many applications. However, the mechanism responsible for the growth rates of highly-ordered nanotubes with optimal adhesive properties is not fully explained or understood. Purpose of Research The aims of this project were threefold: to explore the effects of different anodizing parameters on the fabrication of titania nanotubes; to study the photocatalytic activity of the nanotubes; and to deposit gold nanoparticles into the nanotubes. Methodology Nanotube Fabrication: Titanium foil was subjected to potentiostatic anodization with the use of various fluorinebased electrolytes, anodization voltage and duration to compare the effects of different parameters. Scanning electron microscopy (SEM) was used to characterize the nanotube diameter and length of the anodized samples. Photo-electrochemica1 Water-splitting: A PEC cell was assembled using the nanotubes as the photoanode and the samples were anodically polarized in a 1M KOH electrolyte. A potentiostat was employed to control the applied bias and to measure the photocurrent response under light irradiation. Overall photoconversion efficiency (ηc) of the samples was then calculated. Catalyst Support: A gold precursor solution was prepared with HAuC14‧3H2O. Using a novel depositionprecipitation (DP) protocol, gold nanoparticles were deposited on the nanotubes. SEM was used to scan for traces of gold and their locations. Energy-Dispersive X-ray (EDX) spectroscopy was used to confirm the identity of the gold nanoparticles. Data and Discussion Nanotube Fabrication: Preliminary studies found the glycerol/water and glycerol/formamide combinations to be the most promising. In glycerol/water-based electrolytes, higher water content corresponded to a decrease in nanotube length while higher anodization voltage resulted in a significant increase in tube diameter and length. In glycerol/formamide-based electrolytes, higher water content corresponded to a decrease in nanotube diameter while higher fluorine concentration resulted in an increase in inter-tubular spacing. The effects of various fabrication parameters were better understood, contributing to greater control over array dimensions. Photo-electrochemical Water-splitting: A higher anodizaion voltage resulted in a significant improvement in photoconversion efficiency. However, this trend was reversed in chlorine-doped samples, where a longer anodization duration corresponded with better photoconversion efficiency. Doping was found to enhance the photoresponse of the samples, with 6.32 % photoconversion efficiency obtained, suggesting new strategies for light harvesting and a step closer towards commercially-viable solar energy. Catalyst Support: Gold nanoparticles (5-10 nm) were successfully deposited onto the titania nanotube samples. Based on current literature, this was the first successful attempt at depositing gold nanoparticles into titania nanotubes. An EDX spectrum confirmed the identity of the gold nanoparticles. Compared to current catalytic converters, the gold/titania nanotube structure offered a larger catalytic surface area for reactants and the ability to function at low temperatures. Conclusion: By understanding the effects of various parameters on titania nanotube fabrication, the anodization process can be optimized to enable more precise control over array dimensions. High photocatalytic efficiency has also been achieved. In addition, doping is found to improve the photoresponse of titania nanotubes. Gold nanoparticles have been deposited, to our knowledge for the first time, onto the surface and inner walls of titania nanotubes.

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.

Surfactants have a great effect on decreasing the surface tension in aqueous solution and thus they are important components in detergents. The present study aims to explore the cleaning mechanisms of the substances for greasy subjects such as bowls and clothes. The roles of various surfactants that have on the changes in the surface tension of aqueous solution in the presence and absence of additives such as tea and salt have been carefully studied by using a lab-made equipment. We carefully observed the changes in the oil droplets after pushing oil in a syringe to the aqueous\r solution containing surfactants and additives. With decreasing the surface tension of the aqueous solution, the size of the droplet becomes smaller. By using this simple lab-made equipment, we are able to determine the critical micelle concentration (CMC) of sodium dodecyl sulfate (SDS), with a result of 0.0079 M at 20 ℃. The result is in a good agreement with the literature (0.0077M). With decreasing temperature and adding salts such as sodium sulfate, the decreases in the surface tension have been confirmed by our simple experiments. This simple equipment also allows study of the effects of impure additives such as salt, tea, vinegar that have on the changes in the surface tension of aqueous solution containing commercial detergents. We have found that most of the additives have a great effect on reducing the surface tension of the aqueous solution. The present study results suggest that the simple experimental set-up is practical for measuring the CMC of surfactants and for exploring the effects of additives on changes in the cleaning ability of commercial detergents.界面活劑性可有效降低水溶液的表面張力，因此，他們是清潔劑的重要成份。該實驗主\r 要在探討各種物質的清潔機制。利用自製的實驗裝置，針對各種不同的界面活性劑在添加了鹽類或茶水後界面張力的改變量，作詳盡的探討。我們將含有不同濃度界面活性劑以及添加物的水溶液裝入容器中，在推擠針筒使其的油通過針頭並進入該溶液後，我們仔細的觀察紀錄油滴大小的改變。結果顯示界面張力的降低會使得油滴變小。藉這個自製的裝置，在20℃下，本實驗所測得的陰離子型界面活性劑-十二烷基硫酸鈉之臨界微胞濃度0.0079M。結果幾乎與過去的文獻0.0077M 值符合。該實驗同時也證實了降低溫度，添加了鹽類後，可有效的降低界面張力。此外，此實驗裝置也可以用來測量市面上販售的清潔劑在添加了不純的物質後，其界面張力的改變量。我們發現大多數的添加物都能有效降低界面張力。目前的實驗結果顯示，這項實驗裝置在測定臨界微胞上有很高的實用性，同時也可以探討不同的添加物對市面上販售的清潔劑之洗淨力的影響。