Fluorine has a big influence on physical, chemical and biological properties of organic structures. Organofluorine compounds are widely used in modern medical chemistry to develop new drugs. Insertion of fluorine atom into organic molecules can improve their reactivity in biological systems, increase their metabolic stability, lipophilicity and permeability through membranes. As a consequence, in recent years, the percentage of drugs containing one or more fluorine atoms has increased rapidly up to 40%. The fluoroallylic fragment is also able to change properties of bioactive molecules. Its introduction into such structures as inhibitors of histonedeacetylase, inhibitors of matrix metalloproteinase, asparagine, glutamine, etc. increases their biological activity and electronic properties. We propose a new method for the synthesis of functionalized fluoroalkenes, based on the generation of fluoroallyl nucleophiles from silyl- and boronyl-substituted fluorocyclopropanes and their further usage in the allylation of carbonyl compounds or their derivatives. Due to the fact that the cyclopropanation of alkenyl boronates is not possible under conditions of alkaline dehydrohalogenation of dibromofluoromethane, we have developed a new method for the preparation of silyl- and boronyl-substituted cyclopropanes, which consist of carbene cyclopropanation of multiple C=C bonds by sodium dibromofluoroacetate catalyzed by (IPr)AgCl. The new method is effective for the cyclopropanation of not only boronyl- and silyl-substituted olefins, but also for low-reactivity alkenes, such as monoalkyl substituted alkenes, allyl alcohol ethers and α,β-unsaturated carbonyl compounds. The conditions for isomerization of silyl- and boronyl-substituted fluorohalocyclopropanes in the presence of catalytic amounts of copper (I) bromide in acetonitrile was selected. It was shown that the regioselectivity of the process is determined by the thermodynamic control. Thus, the formation of fluorovinylsilanes or fluorovinylboranes in the isomerization of α-silyl- or α-boronyl-gem-bromofluorophenylcyclopropanes and fluoroallylsilanes upon isomerization of β-silyl-gem-bromofluorophenylcyclopropanes was observed. Thus, new types of fluorinated reagents were obtained that are not previously described in the literature (...)

Monte Carlo methods are non-parametric algorithms that use random numbers and theorems of probability theory to approximate values that are not random. The purpose of my research was to approximate the surface of different geographical areas that can be easily approximated to polygons (e.g. lakes, glaciers, deserts) with Monte Carlo simulations starting from either Cartesian coordinates or pictures. Computer science would not exist without math, and this research project showed me the importance of a deep understanding of probability theory in the world of simulations and, more generally, the importance of developing new theorems and algorithms. The results of my research could be developed in different ways: it would be interesting to produce software that allows one to approximate areas from pictures taken from a smartphone; as well, the theorem I found has to be proven, and also Monte Carlo methods as a means of random number generation can always be improved. There are still many possibilities.

本研究主要以一連串地震分析，來討論台灣地區地震能量釋放的型態。首先求出地震活動參數，接著再繪製地震規模的年發生率，最後推算台灣地區地震能量釋放時前餘震與主震所占之比重。在地震參數上，發現地震活動度較高的月份中，在該月都發生了芮氏規模六級以上的大地震，因其餘震發生的頻率較小震頻繁，因此造成其a 值較大。另外本研究發現，在大地震來臨之前，地震A 值會升高，應可視為其A 值升高之因是由於前震的關係。在地震規模年發生率方面，繪製出圖表，最後發現台灣地區地震仍以小震多，另外大地震則有一定週期。在研究最後，了解台灣地區地震常數之後，本研究更以ESRI 的GIS 軟體ArcView9.0 版輸出台灣地震目錄，並從中了解台灣的震測儀器發展。This research presents a series of earthquake analyses to discuss earthquake’s energy release type. First, we evaluated earthquake’s constant and charted the percentage of earthquake measurement every year. Finally, count the after-shocks and the major earthquake measuring 6.0 and above on the ML happening in Taiwan area. Because the after-shock frequency is more than light earthquakes, as a result it causes the“a” enumeration is large. According to the percentage of earthquake measurement happening frequency every year, we illustrate a chart. Finally we find that in Taiwan area mirror earth-quakes account for a large percentage and major earthquakes happened regularly. When we realize the constant of earthquake, the study folds a variety of layers by using ArcView 9.0 edition of GIS (Geography Information System) of ESRI , knowing the earthquake in Taiwan.

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.

本研究目的在發展以水活性值作為食品水分含量和水溶液濃度估算之快速量測工具。對檢體之多點30℃水活性與水含量作圖，結合四階多項式數學模式模擬等溫吸濕曲線方程式(Moisture Sorption Isotherms)。以水活性實測值內插換算，獲取食品水分含量。對檢體之多點水活性與濃度作圖，結合多項式數學模式模擬水活性濃度曲線方程式。以水活性實測值內插換算，獲取水溶液濃度。結果顯示，隨機收集的食品檢體實測值與以模擬曲線內插而得之水分含量值偏差多不超過3%，實測值落點皆分布於模擬曲線附近，表示以此擬合曲線推算含水率確實可行。同時，水活性濃度模擬曲線準確度佳，不只適用於稀薄溶液，大範圍濃度均適用。

1 Purpose of the Research Nanocrystal thin films exhibit many useful properties, including electrochromicity and superconductivity. When synthesised via Molecular Beam Epitaxy (MBE), selection of substrate, specifically knowledge of crystal orientation, is critical. Reflection High Energy Electron Diffraction (RHEED) is an in situ crystal characterisation method highly compatible with MBE. This study explores a new method of RHEED analysis to determine crystal orientation. 2 Procedure/Theoretical Framework RHEED characterization is the incidence of a beam of high-energy electrons at a low angle with respect to the sample surface. Electrons diffract, and interfere to form patterns on the detector. Traditionally, studies of RHEED analyse one static image as a representation of the surface structure, or observations of RHEED patterns over time. The approach to RHEED analysis in this study exploits changes in RHEED patterns given a rotating substrate. Having specific rotational symmetries along different axes, crystal structures can be differentiated by determining rotational symmetry through RHEED. Electrons scatter upon incidence with crystal planes within the crystal to form Kikuchi lines on the RHEED detector (Fig. 2). The orientation of crystal with respect to incident electron beam affects the Kikuchi line patterns. If the crystal is rotated, crystal planes change orientation, and electrons would diffract from crystal planes in different directions. As such, as the crystal is rotated, the Kikuchi lines move. When the degree of rotation of the crystal corresponds to the rotational symmetry of the crystal (Fig. 1), the Kikuchi lines return to their original position. As crystals with different crystal plane orientations exhibit different orders of symmetries, analyzing the Kikuchi line patterns of the crystal at different degrees of rotation can reveal the rotational symmetry and consequently crystal plane orientation of a crystal. 3 Data/Experimental Testing In order to assess the practical viability of the proposed method, experiments were conducted on SrTiO3 (001), (110), and (111). SrTiO3 exists as a typical perovskite structure (Fig. 3), often used in the synthesis of superconductors via MBE. 3.1 Methodology RHEED images of each sample were taken at 0◦, 60◦, 90◦ and 180◦. Curves were fit to each Kikuchi line observed in the image (Fig. 4). These Kikuchi line approximations are compared by superimposing the curves traced and qualitatively assessing the degree of similarity between the Kikuchi lines of 2 images, to verify the order of symmetry and crystal orientation of the crystal. In the images of the superimposed Kikuchi lines illustrated in Fig. 5, there is similarity between the Kikuchi lines when only when the sample has been rotated by an angle corresponding its degree of symmetry. 4 Conclusions This study offers a method to determine the crystal orientation of thin film through determining the degree of rotational symmetry of the sample, by observation of Kikuchi lines in the RHEED pattern as the sample is rotated. Experimental data was analyzed qualitatively to verify the viability of this theoretical method in practice. This method could be extended to analyze the symmetry of other crystal structures. As it does not require information on the machine settings or usage of complex functions to produce a reliable output, this method is fast and straightforward, opening doors to more streamlined RHEED analysis.

本研究主要探討傾角對面轉變的影響與面轉變的原因。當柱體由肥皂水中拉起時，泡膜圖形可分為中央膜平行與垂直底面的形式，兩種形式因高的變化而互相轉換的過程稱為面轉變。三到六角柱傾角越大，面轉變時的高越大，反之亦然；六角柱可以面轉變，且在40°到45°之間有臨界角度存在。本研究以力與能量的角度解釋面轉變．泡膜藉由改變面積以達到最低的能量、維持穩定狀態，因此本研究計算、比較不同形式的泡膜面積，以解釋面轉變。我們同時發現三角錐與四角錐都不會發生面轉換；三角錐的實驗值多大於理論值，四角錐的實驗值則多小於理論值。

For a unique marine bird, so magnificent and accessible to the public, the Australasian Gannet (Morus serrator) colony found at Cape Kidnappers, 紐西蘭, significantly lacks research. Knowledge of gannet behaviour and how humans could best sustain a relationship with them remains unstudied. M. serrator are colonial monogamous breeders and produce a single chick each breeding season (Ismar, S.M.H. 2013). With the same mate over breeding seasons, pairs work cooperatively sharing the energy input into a single chick. Such parental care leads to highly territorial behaviour (McMeekan, C. P. & Wodzicki, K. A. 1946). This suggests more dominant gannets would claim larger territories to have a greater distance between nests of other birds, to increase the survival of their offspring. With a land-based colony this means the gannets are at risk from land and airborne predators, suggesting more dominant birds will claim territories in the central area as it offers greater safety from predator pressures (Minias, P. 2014). It was hypothesised that birds in the centre will have a greater distance between their nests and have a smaller height compared to those around the periphery of the Plateau Colony. The distances between nests and the heights of nests were recorded in the centre and around the periphery of the colony to determine if there was a correlation between the variables. It was found that centre nests had a greater distance between them and were of a smaller nest height when compared to those around the periphery. Anthropogenic influences from tourism and conservation has the potential to change the evolutionary trajectory of managed populations. This colony is protected by predator control programs. Altering this significant selection pressure has the potential to change the nesting behaviour of this species. Monitoring annual nesting distribution patterns and colony numbers over time, may enable informed development of more sustainable ecotourism and protection of the colony. This investigation provides baseline data to support further research on this colony.

Backpropagation neural networks were used to forecast daily rainfall with minimal error for Metro Manila in order to have an inexpensive way of accurately predicting weather. Calamities brought on by heavy rainfall have caused great economic, infrastructure and human loses. Neural networks have the ability to discern complex patterns in noisy data; this makes it a viable method for weather forecasting. Daily precipitation, humidity, rain indication, sea level pressure, temperature and maximum sustained wind speed for January 2000 to December 2010 were acquired from the Philippine Atmospheric Geophysical and Astrological Services Administration. The neural network made use of Python 2.7.2 and the backpropagation program by Neil Schemenauer (python.org). It considered different neural network architectures with a total of 2844 data sets for training and 708 data sets for testing. Each neural network’s accuracy was measured with a graph of the actual and predicted values, correlation coefficient, and root mean square error. It was observed that the neural network with architecture 5-8-1 yielded the most accurate results as it had the highest correlation coefficient of 0.48599 and smallest root mean square error of 14.84. It was also observed that the trends of the predicted values followed that of the target values. This suggests that it is possible to create a neural network with a moderate correlation given daily weather data. It is recommended that further researches make use of hourly data instead of daily data for more accurate results. Other variables, which might affect rainfall, not in this study should also be considered. This research could aid in the anticipation of calamities and the decision making involved in shipping, fishing and aviation industries.

Photochromism (from Greek φωζ photo “light” and χρωμα chroma “colour”) is determined as reversible transformation between two chemical species, induced by action of light [1]. Herewith, initial form and photoinduced isomer have different physical and chemical properties. The phenomenon is attractive for the design of hi-tech materials, including optical memory elements and molecular switches. Diarylethenes is the most promising class of organic photochromic compounds due to outstanding thermal stability of both isomers and high photostability [2]. The size of so-called ethene bridge significantly affects the photochromic reaction. The photochromic diarylethenes with 4-, 5-, and 6-membered cyclic ethene bridge are known, but there is no example with 3-membered bridge. In this study we report a new approach towards dithienylacetylenes 3 that include the synthesis of diarylcyclopropenones 2 via Friedel-Crafts alkylation of heterocyclic compounds 1 with tetrachlorocyclopropene and following UV-irradiation. It was found that the diarylethenes 2 do not display photochromic properties, but they undergo quantitative photoelimination of carbon monoxide upon UV-irradiation resulting in dithienylacetylene 3. Thus, we have proposed a new synthetic two-step approach to dithienylacetylenes 3 [3], which could be useful synthons in synthesis of photochromic diarylethenes with various ethene bridges.

尿酸氧化酶參與嘌呤代謝機制，然人類尿酸氧化酶基因已退化，易使過量尿酸沉積於關節造成痛風，因此微生物源尿酸氧化酶具極高研發價值。 本研究針對微生物源酵素進行基因體探勘，篩選出抗輻射奇異球菌(Deinococcus radiodurans)及耐熱雙球桿菌(Thermobispora bispora)源尿酸氧化酶基因，取得尿酸氧化酶重組蛋白質進行酵素活性測定、熱穩定分析、蛋白質結構解析、酵素對金屬離子耐受性分析與尿酸檢測應用。抗輻射奇異球菌源酵素於30℃催化速率較過去報導之酵素佳，而耐熱雙球桿菌源酵素於70℃催化效率與熱穩定性仍佳。解析耐熱雙球桿菌源酵素結構發現羧基端具特異性構型，推測與熱穩定性有關。本研究的兩種尿酸氧化酶，可分別作為降解尿酸的速效及緩解型藥物，並開發成快速檢測尿酸的簡易方法。

本作品為環球數學城市競賽的考題之推廣（ International Mathematics Tournament of the Towns, Senior A-Level Paper, Fall 2009, No. 7 ），然而此題目本身比較接近Scientific American （ Feb 1979 ）中 Martin Gardner 的文章 The Rotating Table 所提出的問題。 而此問題的多邊形版已被數學家解決(Ted Lewis & Stephen Willard, 1980, The Rotating Table,Mathematics Magazine, 53,Page 174-175.)。然而此份作品採用簡潔的初等數學歸納法證明了原本的多邊形情形，且專注於探討條件改變為m=n-1時的多邊形情形。 m=n-1時的情形是前人所沒有做出結果的，且m=n-1的情形遠遠比m=n 的情況來得複雜多變，其中估計上下界所使用的許多組合技巧相當特別。然而其中當n為3 和5的倍數時有比較特殊的情況，這一個部分僅能給出目前得出的k值上界。而其他情況則能夠找出所有的k值。