設Γ為一平面曲線而 P 為一定點 ， 自 P 向γ所有的切線作對稱點，則所有對稱點所成的圖形Γ1 稱為曲線Γ對定點 P 的切線對稱作圖 ， Γ1 對定點 P 的切線對稱作圖 Γ2 稱為曲線Γ對定點P的2-th 切線對稱作圖 ， Γ2對定點 P的切線對稱作圖 Γ3稱為曲線Γ對定點 P的 3-th切線對稱作圖 ，…… 。以下是本文主要的結果：結論 A：當Γ為一圓形而 P 為圓上一點時 ， 計算其 nth 切線對稱作圖 的方程式。結論 B：當Γ為任意平滑的參數曲線而 P 為任意一點時 ， Γ的切線對稱作圖的切線 性質。結論 C：當Γ為任意平滑的參數曲線而 P 為(0，0)時， 計算其 nth 切線對稱作圖 的方程式。英文摘要：Given a plane curve Γand a fixed point P ,the locus of the reflection of P about the tangent to the curveΓis called the reflection to tangent line of Γwith respect to P.We denote Γ1 as the reflection to tangent line of Γwith respect to P, Γ2 as the reflection to tangent line of Γ1 with respect to P , Γ3 as the reflection to tangent line of Γ2 with respect to P ,and so on , we call Γn the n-th reflection to tangent line of Γwith respect to P. If Γ is a circle, and P is a point on the circle, we got the parametric equation of the nth reflection to tangent line of Γ with respect to P. And, for any parametric plane curve Γ; we got the method to draw the tangent of the reflection to tangent line of Γ.

前人研究發現聖嬰南方震盪(El Niño–Southern Oscillation, ENSO)和淘氣精靈(Elves)兩者間有顯著關係，顯示淘氣精靈的變化受太平洋上ENSO影響，因此我們想探討淘氣精靈與印度洋震盪(Indian Ocean Dipole, IOD)間是否也存在相似的關聯性。一般以DMI(Dipole Mode Index)代表IOD的發生情形，研究中我們挑出2005年6月2015年11月IOD正負事件時的海溫、雨量、閃電及淘氣精靈進行比較。研究結果顯示淘氣精靈在印度洋上也有震盪的現象，且其趨勢與海溫相同，再將其與雨量變化做比較後，我們推論IOD造成的海溫變化影響了大氣，進一步影響淘氣精靈的發生。

Microalgae-fungi biofuel has significantly less CO2 emissions than fossil fuels, making it much more environmentally friendly. As well, unlike traditional biofuel, microalgae-fungi does not require large masses of agricultural land for production. Thus, microalgae-fungi is an optimal option for biofuel production. This is a cost-effective renewable energy source that can be used in place of regular gas in cars and other means of transportation. By determining the most effective fungi for biofuel production, the threat of the impending environmental damage from pollution can be diminished. This novel experiment determines which fungi: Aspergillus niger, Rhizopus stolonifer or Saccharomyces cerevisiae, is the most effective bioflocculant in the microalgae-fungi co-pelletization process for biofuel production. We hypothesize that when paired with the microalgae Chlorella vulgaris, Rhizopus stolonifer will be the most effective. It has a high lipid content which could enhance the overall production of biofuel. Furthermore, its negative charge will aid with attracting and neutralizing the C. vulgaris colloidal particles resulting in an easier and more efficient removal of microalgae particles. Through the process of bioflocculation, pelletization, esterification and transesterification, the most effective fungi paired with C. vulgaris was determined. This experiment was carried out thoroughly and precisely resulting in a cost-effective solution for the world's current pollution crisis.

The synthesis of RNA using DNA (transcription) can be regulated by special proteins - transcription factors (TF) by binding to specific DNA regions - binding sites (BSTF). The purpose of the project is building a phylogenetic tree of orthologous groups of the each studying TF subfamilies, compare it with the tree of the corresponding BSTF motifs belonging to one orthologous group, find some common parts.

Cancer is the second leading cause of death today[1], accounting for nearly 1 in 6 deaths worldwide. Despite this, diagnosis and treatment models for cancer are limited and as such, new methods to identify and treat susceptible patients are required urgently. HLAF- adjacent transcript 10 (FAT10) is an oncogene that is strongly implicated in the development of inflammation-associated cancers[2]. Previous research on this highly polymorphic gene has identified 2 haplotypes – the reference haplotype, which is found in both cancer patients and healthy individuals, as well as an additional haplotype that is occurs at higher frequency in cancer patients and is associated with higher odds of cancer. In this study, it was hypothesised that the cancer-associated FAT10 haplotype can better promote tumorigenicity and could thereby serve as a useful biomarker for cancer. Here, we functionally characterize the 2 FAT10 haplotypes to understand how they influence some of the hallmarks of cancer. The cancer-exclusive haplotype was observed to enhance hallmarks of cancer, namely uncontrolled cell growth, resisting cell death and anchorage-independent growth as compared to the reference haplotype. Moreover, we uncovered the differential gene expression patterns induced by each haplotype. Molecules involved in cell adhesion and proliferation, as well as transcription were upregulated by the cancer-associated haplotype and hence could have contributed to the increased tumourigenic potential of the cancer haplotype.

Nowadays Electric energy is the most useful in the world because we use it every day for lightening, work, entertainment ext … but electric energy also can be expensive and it will pollute the air plus we all know that the air pollution is getting worse. Our world consumes a huge amount of electric energy . Also we know that the homelessness is getting higher all around the globe and it reached a high percentage. The high price and the sudden cut of the electric energy and with it the air pollution makes a big problem. That’s why we created this project named TURN ON which is a friend of the environment and a friend of the humans. Our product will help us to produce and create strong, clean and renewable energy plus it will help the homeless to have free food and free transport tickets. After doing a lot of researches we found that our new method of producing energy gives a great electric energy and limit pollution. The kinetic energy is produced using rotations. That’s why we used the rotations of motorbikes, bicycles, cars wheels and turn that mechanical energy (wm) into electrical energy (we) that we can easily use in our daily life plus we can help homeless by giving them food widgets… in exchange with the electrical energy that they produced while using bicycles…After performing several tests and taking notes, we are able to conclude that our apparatus is indeed efficient as it is able to convert the rotation into electronic energy that we can store and use in emergencies to solve this big problem and in the same time to limit air pollution with using bicycles and reducing hunger regarding homeless. This machine should be easy to implement, cheap, does not depend on any other parameters such as the wind. Any rotation in any place can be a source of Electrical Energy. To facilitate the use of this new device, A START UP will be launched to rent electric bikes for “free”, distribute free food, snacks, tickets to homeless regarding to the energy production.

福島核災的發生，更凸顯能源的重要性；又因近年來廢熱總量不斷提升與全球能源需求量增加，本研究利用熱電晶片冷端與熱端的溫度差產生電的特性，將環境廢熱回收成為可用的電能。 本研究設計之可撓性熱電晶片成功改良傳統熱電晶片的兩點缺點；其一 : 傳統的硬式平板狀晶片無法配合不同環境空間而改變其外型，其二 : 硬式晶片的表面為陶瓷片，較易摔破導致晶片毀損，本研究之可撓性熱電晶片改良以往熱電晶片的陶瓷基板材料，改用具有可撓性的FCCL材料作為基板，因此可完整吸收表面彎曲物體的能源並將熱能轉換成電能。本研究之可撓式熱電晶片成功大幅降低熱電晶片之成本，有利於未來大量生產，成功應用人體體溫發電，同時也可利用Peltier效應，作為醫療用冷敷或熱敷之器材。

I built a robot that is able to improve safety in mines. The robot takes a series of sensor readings, do 3D mapping to compare deteriorating physical conditions in time, detect CO and CH4 levels and record video footage. All of this information is then sent back to the user. The project aims to build a robot that could decrease the amount of casualties in mines due to gas or instability. A strict engineering process, which comprised researching different features on a robot, was followed. A prototype robot was built, tested and improvements made. Some of the challenges faced, while building the prototype robot, included manoeuvrability over any type of terrain, even rough and rocky terrain. Choosing the correct driving mechanism (wheels, tracks, suspension and steering) also proved to be a very important feature that had to be kept in mind. The sensors used included, a temperature, humidity, carbon monoxide gas, as well as a methane gas sensor. A Gyro, Accelerometer and compass for easier navigation were also used. Two cameras which included a front camera for navigation and 3D mapping as well as a back camera for navigation were installed. The robot was tested over various terrains, it was able to retrieve sensor data and all of the engineering goals were reached. After the robot was built it was tested on various terrains. The robot achieved all of the engineering goals. The sensors was able to give readings, the robot 3D mapped an area and was also able to manoeuvre over rough terrain.

我們這個作品是先由在長方形中切割出正方形的研究著手，先研究出在平面中，在一個邊長為任意正整數的長方形中，如何找到在其中切割出正方形，但正方形的邊長為最大，而且正方形的個數為最少的方法和規則。 緊接著，我們更進一步想研究這個問題在長方體中的研究：在長方體三邊長a、b、c（a、b、c均為正整數）中，如何在其中切割出正立方體，每次切割出邊長為最大的正立方體，而且正方體的個數為最少的方法和規則。 This study began with investigation of how to segment squares from a rectangle. We studied from a rectangle, with random positive integer sides, trying to figure out the methods and regulations to segments squares with the longest side length but the fewest number of squares within. Moreover, we took further step to examine a cuboid. We found out the methods and regulations to segment cubes with longest side length but fewest number of cubes from a cuboid with sides a, b, and c(a ,b ,c are positive integers).

本文記載台灣產安蛛科(Anapidae)微安蛛屬(Enielkenie)之未知種(Enielkenie sp.)。目前全世界的微安蛛屬記錄僅1屬1種，模式標本為原產高雄扇平之蟎微安蛛(Enielkenie acaroides Ono, 2006)。我們在新北市八里區利用柏氏漏斗對落葉層進行調查，發現未知種微安蛛，對雄雌標本進行描述、測量及繪圖。本種體型近似蟎微安蛛，但主要的差別為：腹部背面的筋點數目明顯多於蟎微安蛛、雄蛛觸肢腹面有一個向上突起，外雌器開口形狀，故本種可能為一未被描述的新種。人工飼養的情況下會結平面圓網，並在中央有一垂直絲，和Theridiosomatidae的網相似。

Antibacterial Properties of Mānuka Mānuka (Leptospermum scoparium) is a native 紐西蘭 plant that has long been used by indigenous Maori for its medicinal and therapeutic properties, yet is relatively unknown to science. Many of our native species may contain novel compounds with practical applications in our lives. Research indicates that mānuka has anti-microbial, anti-fungal, herbicidal, insecticidal and anti-bacterial properties, and suggests that compounds similar to Grandiflorone (ß-triketones) cause these effects. This project investigates the antibacterial properties of mānuka leaves, using the bacteria Photobacterium phosphoreum for biological testing. With the recent rise in multidrug-resistant bacteria, it is now more vital than ever to utilize traditional knowledge to inform research and development of innovative new antibiotics, antimicrobials and similar biologically important compounds.

Terpenoids are an irreplaceable class of natural products. The camphoryl group is an important moiety in the structure of chiral ligands for asymmetric synthesis catalysis or it can be used as an auxiliary group in asymmetric synthesis.[1] The usage of fenchone based molecules for asymmetric catalysis and synthesis is less common because of the difficulty of fenchone modifications due to steric hindrance. Camphor is a readily available starting molecule for the preparation of different compounds with biological activity. For example, camphor diimines demonstrate antiviral activity.[2] Fenchonyl amine-based molecules are potential therapeutic agents for the treatment of Alzheimer’s disease. Amines are a crucial class of organic compounds with multiple academic and industrial applications. There are a plethora of synthetic approaches towards amines synthesis and modifications, reductive amination being one of the most powerful and useful methods. However, the reductive amination of camphor and fenchone remains a challenge. A standard approach to reductive amination with amines other than ammonia and methylamine includes two steps: preparation of azomethines or Schiff bases in the presence of strong Lewis acids and their reduction with more or less conventional reducing agents. The synthesis of fenchonyl amines is even more challenging. There is no universal approach, and almost every manuscript reports some particular protocol different from others. In most cases, the first stage of this process requires quite harsh conditions. For example, the preparation of a Schiff base from camphor and 1-phenylethylamine requires 5-10 days of heating at 150°C.[3] Schiff bases of other primary amines could be prepared under similarly harsh conditions. Preparation of enamines is possible using titanium tetrachloride as a catalyst. The reduction also might be challenging. Sodium borohydride or sodium cyanoborohydride was described as suitable for this goal in several reports.[4] To the best of our knowledge, no papers describe any general approach for the direct reductive amination of camphor or fenchone. There is only one example of camphor direct reductive amination without an external hydrogen source using carbon monoxide as a reducing agent. This protocol is very efficient but its application is limited by the necessity of carbon monoxide and high-pressure equipment for the reaction setup.