A proof is given that any λ _polynome over real quaternionic sfield can be factorized into produce of some linear factors.By the way,some properties and applications of this factorization in matrix theory are given.
Despite its utility in identifying patterns in celestial objects, the Hertzsprung-Russell diagram is not supported in dim or small stars;it struggles to provide insights into certain celestial objects such as brown dw...Despite its utility in identifying patterns in celestial objects, the Hertzsprung-Russell diagram is not supported in dim or small stars;it struggles to provide insights into certain celestial objects such as brown dwarfs [1]. The purpose of this experiment is to create an improved version of the diagram with a three-dimensional model that includes a third z-axis to accurately predict and chart the life cycles of all stars regardless of size. The values of the stars’ absolute magnitude and color indices were used to chart the surface gravity and metallicity, variables that were chosen due to their ease of collection and their likeliness to be within the range of values being assessed. To obtain the values for the model, data points from the database GAIA DR2 were utilized via the TAP protocol to query the SQL database. The data was transferred into a local CSV file to facilitate data manipulation. The data could be read and interpreted, as dim stars would likely have higher values of these variables, making it easier to include them in the diagram. The Pandas DataFrames tool on Python 3 was used to organize and manage the data efficiently. Matplotlib Graphs visualized the relationships between different stellar attributes by developing a linear regression line and an algorithm and creating scatter plots and sky maps to explore trends, hence designing three-dimensional diagrams. It was determined that the surface gravity diagram had a higher efficacy than metallicity due to their standard deviations of 0.4641441715272741 and 0.786577627976148, respectively.展开更多
文摘A proof is given that any λ _polynome over real quaternionic sfield can be factorized into produce of some linear factors.By the way,some properties and applications of this factorization in matrix theory are given.
文摘Despite its utility in identifying patterns in celestial objects, the Hertzsprung-Russell diagram is not supported in dim or small stars;it struggles to provide insights into certain celestial objects such as brown dwarfs [1]. The purpose of this experiment is to create an improved version of the diagram with a three-dimensional model that includes a third z-axis to accurately predict and chart the life cycles of all stars regardless of size. The values of the stars’ absolute magnitude and color indices were used to chart the surface gravity and metallicity, variables that were chosen due to their ease of collection and their likeliness to be within the range of values being assessed. To obtain the values for the model, data points from the database GAIA DR2 were utilized via the TAP protocol to query the SQL database. The data was transferred into a local CSV file to facilitate data manipulation. The data could be read and interpreted, as dim stars would likely have higher values of these variables, making it easier to include them in the diagram. The Pandas DataFrames tool on Python 3 was used to organize and manage the data efficiently. Matplotlib Graphs visualized the relationships between different stellar attributes by developing a linear regression line and an algorithm and creating scatter plots and sky maps to explore trends, hence designing three-dimensional diagrams. It was determined that the surface gravity diagram had a higher efficacy than metallicity due to their standard deviations of 0.4641441715272741 and 0.786577627976148, respectively.
