三角形與其外接錐線的生成錐線性質探討
本研究源自三角形的重心及其外接圓所構作的線段比值的古老幾何性質，我們不但推廣原命題，還創造新命題：給定△ABC與其外接錐線Γ，令直線AG, BG, CG分別交Γ 於 A', B', C' 點，再取任意k值，探討P點集合的性質。 Γ3, k={P|AA'/PA' + BB'/PB' +CC'/PC'=k} (1)Γ3,k為二次曲線系，其橢圓、拋物線、雙曲線之形態不因k值而改變，而是被外接錐線Γ所決定。 (2)發現△ABC重心 G、Γ中心O、Γ3,k 中心O3,k 的共線性及比例常數。 (3)完整劃分 Γ3,k的非退化與退化型態，並發現只有Γ3,k 為橢圓時，k 值有跳躍現象。 (4) 發現錐線Γ上取相異六點而生成兩個錐線Γ3,k、Π3,k重合的充分條件。 最後，我們以「錐線 Γ 上取一點、兩點到多點」的線性組合手法，推廣多邊形與其外接錐線的生成錐線Γn,k之性質。
Reactivity of styrylmalonates as synthetic equivalents of Donor–acceptor cyclopropanes with aldehydes in the presence of BF3•Et2O
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.
A Novel Selection Process for the Conversion of Conventional Bacteria into Electrotrophs
The redox reactions of bacteria metabolism have been extrinsically studied. These mechanisms allow certain types of bacteria to be able to synthesize extremely valuable extracellular byproducts. Other types of bacteria are able to extract toxic metals from water by donating electrons directly to those aqueous metal ions, thus turning them into solid precipitates. However, the problem of these microorganisms is that their efficiency rates and production speeds are exceptionally low. This study focuses on the properties of electrotrophs, which are bacteria that can feed on pure electrons directly from an electrode (Rabaey et al 2010). Compared to normal organic-feeding bacteria, electrotrophs direct the majority of the electrons obtained to the production of metabolic byproducts (Nevin et al 2010). Therefore, when electrotrophs are employed in bioelectrochemical systems (BESs) their metabolic redox reaction efficiency rates are dramatically increased. This makes it possible to produce large quantities of valuable compounds such as hydrocarbons, plastics and medicine or efficiently remediating the environment (He et al 2016). Moreover, the usage of electricity as an energy source compared to conventional organic substrates is immensely cheaper (Rabaey et al 2010). However, not all bacteria are electrotrophs nor do all electrotrophs have favourable metabolic traits. Thus, there is a need for a novel procedure to turn conventional bacteria into electrotrophs which is a crucial step to making the BES an aggressive competitor in the sustainable energy industry.
Migration Data-Driven Mathematical Model for New City Growth
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.
Understanding the Modern Diagnoses of Protein C Deficiency "Pcd" with Unknown Gene Plays a Critical Role in the Inherited Thrombophilia
Protein C deficiency (PCD) is found in 1 out of 200 to 500 persons in the general global population which is also one of the common conditions of Inherited thrombophilia, it’s characterized by an increased tendency of blood to clot in human blood vessels. It is caused by several factors including mutations in the genes involved in thrombin binding, protein c activation and numerous clotting factors. This includes F5 (Factor 5 Leiden) gene on chromosome 1q24.2, F7 (Prothrombin) gene on chromosome 13q34, SERPINC1 (serpin peptidase inhibitor C) on chromosome 1q25.2, SERPIND1 (serpin peptidase inhibitor D) on chromosome 22q11.21, HRG (Histidine Rich Glycoprotein) on chromosome 3q27.3, PLAT (Plasminogen Activator) on chromosome 8q11.21 and THBD (Thrombomodulin) gene on chromosome 20p11.21. In the current study, a three Saudi families with inherited thrombophilia has been recruited to identify the underlying cause of this special condition. Whole exome sequencing, targeting all coding exons of the human genome, was performed using Illumina Nextera library preparation kits followed by paired-end sequencing on Illumina NextSeq500 instrument. Reads quality control was performed and reads were aligned to the reference genome using BWA software. Variants calling and annotation was performed using GATK. All known genes involved in causing inherited thrombophilia All known genes involved in causing PCD were excluded by whole exome sequencing. The genes that were previously reported to be involved in inherited thrombophilia were checked for any causative variant. No mutation has been identified in known genes. identifying a novel gene underlying PCD. The Result of this study will hopefully pave the way to better understanding the disease pathophysiology and help in developing DNA based diagnosis, carrier screening and somatic gene therapy.
SeedBot: Low-Cost Seeding Robot for Agricultural Applications
This paper presents a semi-autonomous seeding robot which is based on both electrical and mechanical platforms that perform advance agriculture process. SeedBot composed of four components: drilling mechanism, body of robot, seed container and paving mechanism. Other than those components the sensor system and the control system are also discussed. The aim of this study is designing and building a low-cost robotic system to automate and optimize process during farming especially for personal usage. This study demonstrates that semi-autonomous farming has crucial advantages over conventional farming. In addition to that, SeedBot provides safer, requires less manpower and precise farming than usual methods that we have so far.
Construction of an Emergency Portable Dynamo Mobile Phone Charging Station by Means of a Hand-Crank Gear Mechanism/ Solar Panels
The researchers aim to construct an emergency mobile phone charging station that runs on renewable energy and will serve as a cost-efficient alternative to more traditional power banks. Circuit components include a 20V / 6W solar panel supplemented by a hand-crank gear mechanism integrated with a 6V / 1A lead-acid battery, a usb output and an adjustable switch-mode power supply (SMPS) to convert excess voltage into current. Initial voltage and current outputs were measured under varying resistances. It was determined that the set-up satisfied the minimum voltage and current requirement for charging a mobile phone (5V / 1A). A subsequent phone charging test was executed using a Samsung Galaxy J2 (3.85V Li-ion battery 7.70W, Charge Voltage: 4.4V / 2000mAh) wherein it charged on an average of 0.277% per minute for the solar panel and an average of 0.263% per minute for the hand crank gear mechanism. A Mann-Whitney U statistical test was conducted to determine if the charging rate of the charging station had a significant difference from a commercially available power bank’s. The calculated UA: (4) from the test was below the lower limit and the UB: (217) was above the upper limit which indicated that there was a significant difference between the charging rates. While the efficiency was lower than the commercial power bank’s, it can still be used as an alternative charging method especially during emergencies and disasters.