This paper discusses the solution of a group of two-order six elements rooted algebraic simultaneous equations set up by cosine law arising from the application example of subjectivity geometry[1]. By means of the imp...This paper discusses the solution of a group of two-order six elements rooted algebraic simultaneous equations set up by cosine law arising from the application example of subjectivity geometry[1]. By means of the implicit function theorem, this paper proves that there exists a unique real solution of those equations. Transforming this problem into an unconstrained nonlinear optimization problem, the solution can be found by known methods. 4 numerical example by descent method is given.展开更多
Constantine M. Dafermos has done extensive research at the interface of partial differential equations and continuum physics. He is a world leader in nonlinear hyperbolic conservation laws, where he introduced several...Constantine M. Dafermos has done extensive research at the interface of partial differential equations and continuum physics. He is a world leader in nonlinear hyperbolic conservation laws, where he introduced several fundamental methods in the subject including the methods of relative entropy, generalized characteristics, and wave-front tracking, as well as the entropy rate criterion for the selection of admissible wave fans. He has also made fundamental contributions on the mathematical theory of the equations of thermomechanics as it pertains in modeling and analysis of materials with memory, thermoelasticity, and thermoviscoelasticity. His work is distinctly characterized by an understanding of the fundamental issues of continuum physics and their role in developing new techniques of mathematical analysis.展开更多
基金Scientific Foundation of South China Unviersity of Technology
文摘This paper discusses the solution of a group of two-order six elements rooted algebraic simultaneous equations set up by cosine law arising from the application example of subjectivity geometry[1]. By means of the implicit function theorem, this paper proves that there exists a unique real solution of those equations. Transforming this problem into an unconstrained nonlinear optimization problem, the solution can be found by known methods. 4 numerical example by descent method is given.
文摘Constantine M. Dafermos has done extensive research at the interface of partial differential equations and continuum physics. He is a world leader in nonlinear hyperbolic conservation laws, where he introduced several fundamental methods in the subject including the methods of relative entropy, generalized characteristics, and wave-front tracking, as well as the entropy rate criterion for the selection of admissible wave fans. He has also made fundamental contributions on the mathematical theory of the equations of thermomechanics as it pertains in modeling and analysis of materials with memory, thermoelasticity, and thermoviscoelasticity. His work is distinctly characterized by an understanding of the fundamental issues of continuum physics and their role in developing new techniques of mathematical analysis.
