探討平面上n條直線，每兩條相交出一個交點，但不三線共點，並在每個交點上標上數字1至n-1，使任何一條直線上恰好出現1至n-1各一次。得到奇數條直線無法、偶數條直線可以。 推廣至三維空間，探討n個平面，每三個相交出一個交點，但不四面共點，發現到三維空間有兩種推廣方式： 一、在每個交點上標上數字，使每條直線上的數字都不重複 二、在每個交點上標上數字，使每個平面上的數字都不重複 在此兩種情況下，可見當有三個平面時皆可以。 探討第二種推廣後發現在六個平面時亦可以給出構造。而後又發現其等價於Baranyai's theorem故得到平面個數為三的倍數皆可以，再根據文獻構造出三維度空間9個平面的一種方法。

We were very curious about whether the aircraft will suffer lightning damages during flight, so we tried to search the answer on the internet. According to the searching results, we realized that during flight departure, passenger planes can suffer lightning damage. As a result, there will be lightning strike points, which needs immediate solutions for safety concerns. Besides, we found out that the exterior aircraft components, such as aircraft body, wings, tail, turbine engine and other areas, are vulnerable to corrosion, which also needs immediate solutions. Luckily, we came across a chance to chat with the engineer who works in the airport. Through that meeting, we knew that the maintenance of the aircraft is very important. However, the maintenance of the components depends on professional technicians, weather, the surrounding noise level, and other environmental effects. As a result, we think that it is initial for us to develop a device that can automatically complete the missions of aircraft maintenance. Below are two objectives that we need to complete: 1. Complete a non-destructive testing for aircraft damage, including corrosion and lightning strike points. Assessment areas include: Aircraft body, airplane wings, tail of the aircraft and the turbine engine 2. Engage in scanning results to analyze and predict for flight readiness. The collected results will proceed to the aviation company for inspection and maintenance. Based on these two objectives, we designed an automatic platform for aircraft maintenance. Below are four innovations of this platform: 1. we developed a method to replace the current stage based on the manual operation of the aircraft maintenance, the use of AGV (Automated guided vehicle) and the robotic arm combination. 2. Design a modular platform based on this method, including telescopic four-wheel independent rotating chassis and locking mechanism, scissors lifting mechanism, double sided synchronous belt forward detection telescopic mechanism, etc. The platform can shrink at the minimum height of A320, convenient access to the machine abdomen. 3. The positioning algorithm of the platform relative to the aircraft is proposed.

本實驗由透明壓克力管做盛水容器，上下密封後固定於震盪器上方使其垂直振動，水中的氣泡可能會下沉而非上浮。我們觀察水中的自製人工氣泡於不同因素下的下沉運動情形，並依觀察結果推測造成其下沉的因素，我們的理論所運用的變因有容器振動時的加速度、頻率、液體的黏滯係數、氣泡的形變量（不同材質），經過實驗後我們發現頻率並不會影響人工泡泡下沉的情形。我們將不同條件下，透過tracker程式追蹤其下沉的軌跡和時間的關係，再經由牛頓第二運動定律、阻力公式和簡諧運動結合推導出氣泡運動公式，再將此公式寫進Mathematica程式，並分別討論容器座標下的人工氣泡和實驗室座標下的人工氣泡，將所得到的理論值和實驗結果數據加以討論。

The purpose of this research is to prevent the desertification by using my original “agar sheets”. The dry regions, in other words, the desert has already occupied about forty percent of the surface of the earth (Figure 1). In addition, it is said that land of seven million hectares turn into desert every year. However, we can reproduce the green-bosomed earth by using appropriate means, because this desertification originated in excessive farming, excessive pasturing, and deforestation caused by human beings. I learned “Cape Erimo’s Green Construction Method”, which has succeeded in planting trees in the coast of Japan by using seaweed, and this method led me to use the agar to prevent the desertification, which is a familiar Japanese food made from seaweed. I think that it is possible to prevent the desertification of any conditioned lands by using my original “agar sheets.”

Quadcopters are incredible pieces of technology. Software on the flight controller is able to simultaneously stabilise the drone in three degrees of freedom, follow commands from the pilot and take pictures. 200 times per second the flight controller therefore measures the current position and RC signal, calculates a correction and sets the according engine speeds. This is a task that could never be done by a human being.

The purpose of this research is to prevent the desertification by using my original “agar sheets”. The dry regions, in other words, the desert has already occupied about forty percent of the surface of the earth (Figure 1). In addition, it is said that land of seven million hectares turn into desert every year. However, we can reproduce the green-bosomed earth by using appropriate means, because this desertification originated in excessive farming, excessive pasturing, and deforestation caused by human beings. I learned “Cape Erimo’s Green Construction Method”, which has succeeded in planting trees in the coast of Japan by using seaweed, and this method led me to use the agar to prevent the desertification, which is a familiar Japanese food made from seaweed. I think that it is possible to prevent the desertification of any conditioned lands by using my original “agar sheets.”

The growth of a city and the population movement has many correlations. However, the complex interaction causes difficulties in developing a mathematical model needed for analyzing the growth factor of a city and the movement factor of population. The model involving traditional equations cannot explain many phenomenon. The newly introduced data-science suggests possibilities to overcome these difficulties. Particularly, the abundant amount of accumulated data proposes a new solution for the problem we have. Throughout these steps, data-utilizing methodology, such as machine learning for artificial intelligence, are researched and developed with attention. In this research, data about accumulated for previous population movement and city growth are collected, and a mathematical science model based on data is developed to explain population movement and city growth by utilizing data analyzing methods such as machine learning. Especially, artificial neural network and stratified advance learning(deep learning) proves possibilities in solving many problems. This research aims to construct an artificial neural network appropriate for population movement and consequently use it in developing population movement model. Using this model, growth of many existing cities can be explained and furthermore, examining the population movement factor of a city and social factor necessary for city growth become possible. This model is expected to become the tool for resolving overpopulation and predicting and deciding factors needed for a new future city. In spite of decreasing population, it is still important to develop a model for population movement that well explains city growth and environment change.

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.

Plexiglas is a macromolecule (poly-methyl-methacrylate) obtained by polymerization of the Methyl Methacrylate. Cation exchanging resins have acidic groups such as COOH (carboxyl) and SO3H (sulfonic) which fix metallic cations dissolved in water releasing an equivalent of protons through the following reaction: 2 RCOOH + Me2+ (RCOO)2Me + 2 H+ Regeneration is made treating the exhausted resin with diluted hydrochloric acid (HCl) which moves the equilibrium to the left. The aim of our research is to re-use the discarded Plexiglas by transforming it into a cationic exchanging resin. Alkaline hydrolysis transforms the COOCH3 group into COO– group; the obtained group is then transformed into COOH group by means of a treatment with HCl. After the alkaline hydrolysis spectra of the solid show the characteristic band of the asymmetric stretching of the COO– (1610-1550) at 1567 (1st experiment) and at 1555 (2nd experiment). Instead after the acidic treatment the spectra of the solid show that this band has disappeared. On the contrary the characteristic band of the OH stretching of the COOH group (3300-2500) at 3228 (1st experiment) and at 3200 (2nd experiment) appears. The water hardness, due to Ca2+ and Mg2+ ions, is studied to verify the capability of the obtained resin to capture these cations. For this purpose, some mineral water is percolated through the micro-columns. There are three experimental evidences to validate the hypothesis: EDTA molecule (Ethylene Di-amino Tetra-Acetic acid, disodium salt) to estimate hardness is not required The pH of the percolated water through the column decreases from 8 of the mineral water without any treatment, to 6.3 after the treatment as expected The spectrum recorded in the visible range of the percolated mineral water through the column plus EBT (Eriochrome Black T) indicator is the same as the spectrum obtained using de-ionized water plus the same amount of EBT In conclusion, the study has provided evidence that it is possible to convert Plexiglas into cationic exchanging resin.

Gangrene is the death of tissue of certain parts of the body. In Indonesia, people who suffer from Diabetes will also often suffer from Gangrene, which usually affects a patient’s feet. The medication for it is not affordable for everybody. I have chosen the Horseshoe Crab, simply because it’s known widely in Indonesian and can be found easily. Also, due to the fact that, among all crustaceans, the Horseshoe Crab contains the highest levels of Chitin. By using the Chitin found in the shell of the Horseshoe Crab, I shall endeavor to heal the Gangrene of Diabetic Patients.

Donor–acceptor cyclopropanes (DACs), which can act as sources of 1,2- and 1,3-zwitterions in the presence of Lewis acids, are widely used in organic synthesis for the preparation of various carbo- and heterocyclic compounds, including natural compounds and their analogues. To date, many types of DACs reactivity have been identified. However, the chemistry of styrylmalonates (isomers of DACs, which can be easily generated from DACs) is almost undescribed and has a powerful synthetic potential. The use of styrylmalonates as synthetic equivalents of DACs allows us cardinally change the known reaction pathways of DACs. In this work, a new strategy for cascade assembly of substituted pyrenes based on the reactions of styrylmalonates with aldehydes in the presence of BF3•Et2O has been developed. Generation of formal 1,2-zwitterionic intermediates owing to complexation of dicarboxylate groups with BF3•Et2O is the driving force of the reaction discovered. This method makes it possible to assemble pyrenes or 5,6-dihydro-2H-pyran-2-ones in one synthetic stage from readily available starting compounds with high regio- and diastereoselectivity, and use these pyrenes in futher reactions. We’ve optimized conditions of the reaction and synthesized a number of various substituted pyrenes. Moreover, the reaction shows good results with various aromatic and heteroaromatic substituents. Pyrenes can be easily purified by crystallization. Every product was obtained selectively and determined by full set of physical-chemical methods, including X-ray analysis. 5,6-dihydro-2H-pyran-2-one skeleton is found in various natural compounds demonstrating a broad spectrum of biological activity, such as antiviral and antineoplastic.

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.