Both mathematics and art consistently reflect the spirit of the age in which they arise. Consequently, the mathematics in China and in Korea during the Joseon Dynasty, in contrast to the deductive western mathematics,...Both mathematics and art consistently reflect the spirit of the age in which they arise. Consequently, the mathematics in China and in Korea during the Joseon Dynasty, in contrast to the deductive western mathematics, does not function on the basis of proving something deductively. Rather, the Chinese mathematics from this period was based upon making observations about problems by combining patterns with specific examples. In this paper, this author attempts to compare the differences in mathematics between the East and the West, and also to study the different perspectives in art between the East and the West, in order to identify the relationship between civilization, culture and the spirit of the age. This will explain the reason why the Western ＇One Point Perspective＇ had spread in China and the Chosen Dynasty, yet could not be permanently established in these countries.展开更多
Theater play that shows how textiles, make up, hair dyes and music players has changed along the last six decades, especially due to polymers. It is a play that has a historic, chemical and musical side that introduce...Theater play that shows how textiles, make up, hair dyes and music players has changed along the last six decades, especially due to polymers. It is a play that has a historic, chemical and musical side that introduces the use of ICT （information and communications technology）, such as Faeebook, Moodle platform, Web sites, E-mail, Word, Publisher, PowerPoint, Videos and Digital music. Results in the conduct of the students that participated： assertiveness, self-esteem, tolerance, cooperation, responsibility and teamwork, all of them significantly contributed a meaningful learning about the polymers.展开更多
Riemann problems for the compressible Euler system in two space dimensions are complicated and difficult,but a viable alternative remains missing.The author lists merits of one-dimensional Riemann problems and compare...Riemann problems for the compressible Euler system in two space dimensions are complicated and difficult,but a viable alternative remains missing.The author lists merits of one-dimensional Riemann problems and compares them with those for the current two-dimensional Riemann problems,to illustrate their worthiness.Two-dimensional Riemann problems are approached via the methodology promoted by Andy Majda in the spirits of modern applied mathematics;that is,simplified model is built via asymptotic analysis,numerical simulation and theoretical analysis.A simplified model called the pressure gradient system is derived from the full Euler system via an asymptotic process.State-of-the-art numerical methods in numerical simulations are used to discern small-scale structures of the solutions,e.g.,semi-hyperbolic patches.Analytical methods are used to establish the validity of the structure revealed in the numerical simulation.The entire process,used in many of Majda's programs,is shown here for the two-dimensional Riemann problems for the compressible Euler systems of conservation laws.展开更多
文摘Both mathematics and art consistently reflect the spirit of the age in which they arise. Consequently, the mathematics in China and in Korea during the Joseon Dynasty, in contrast to the deductive western mathematics, does not function on the basis of proving something deductively. Rather, the Chinese mathematics from this period was based upon making observations about problems by combining patterns with specific examples. In this paper, this author attempts to compare the differences in mathematics between the East and the West, and also to study the different perspectives in art between the East and the West, in order to identify the relationship between civilization, culture and the spirit of the age. This will explain the reason why the Western ＇One Point Perspective＇ had spread in China and the Chosen Dynasty, yet could not be permanently established in these countries.
文摘Theater play that shows how textiles, make up, hair dyes and music players has changed along the last six decades, especially due to polymers. It is a play that has a historic, chemical and musical side that introduces the use of ICT （information and communications technology）, such as Faeebook, Moodle platform, Web sites, E-mail, Word, Publisher, PowerPoint, Videos and Digital music. Results in the conduct of the students that participated： assertiveness, self-esteem, tolerance, cooperation, responsibility and teamwork, all of them significantly contributed a meaningful learning about the polymers.
基金supported partially by the National Science Foundation (No.DMS-0603859)
文摘Riemann problems for the compressible Euler system in two space dimensions are complicated and difficult,but a viable alternative remains missing.The author lists merits of one-dimensional Riemann problems and compares them with those for the current two-dimensional Riemann problems,to illustrate their worthiness.Two-dimensional Riemann problems are approached via the methodology promoted by Andy Majda in the spirits of modern applied mathematics;that is,simplified model is built via asymptotic analysis,numerical simulation and theoretical analysis.A simplified model called the pressure gradient system is derived from the full Euler system via an asymptotic process.State-of-the-art numerical methods in numerical simulations are used to discern small-scale structures of the solutions,e.g.,semi-hyperbolic patches.Analytical methods are used to establish the validity of the structure revealed in the numerical simulation.The entire process,used in many of Majda's programs,is shown here for the two-dimensional Riemann problems for the compressible Euler systems of conservation laws.
