Certain Types Of Meson Functional Equations With Parameters

In this paper,certain types of meson functional equations with parameters are main-ly studied.It includes the well-posedness of the equations.its parameter relationship and finite positive terms sum formulation,even explicit expression of its solution.As far as counting maps is concerned,Tutte created a new way,even laid the foun-dation of counting maps by proposing plane triangulations.Afterwards,many counting formulas of different types of maps had been calculated.Based on much progress in the field of counting maps,Professor Yanpei Liu developed and sorted out a series of functional equations from these counting formulas by combining the Blissard opera-tor.Especially about the condition of infinite parameters,he extended the functions to the space of infinite series from polynomials.introduced the definition of the meson functional,also systematically studied their qualitative theory and solving methods.It is much related to combinatorial enumerative theory,statistic mechanics and theoretical physics etc.This paper mainly provides certain types of meson functional equations with pa-rameters which include the generalizations of equations whose roots have been solved,and further research and generalization of equations whose solutions haven’t been solved so far.Although the solutions of these equations are meaningful for enumerative theo-ry, what this paper pay more attention to is how the solution extracted from the equation itself.In addition,it’s worth mentioning that this paper also shows the programming of a general equation solution,which not only verifies the results,but also lays the foundation for realizing effective and intelligent research in the future.In chapter 1, we review related concepts and the studies of meson functional equa-tions.In chapter 2, by adding relevant parameters to meson functional equations,we gen-eralize two types of meson functional equations,the well-posedness of the equation-s,relations among these parameters and finite positive term sum formulae and explicit expressions of solutions.In chapter 3,we do further research of Dongmei type meson functional equation-s,whose explicit expressions of solutions are provided by applying the matrix method.In addition,these meson equations with parameters are introduced whose solutions are s-tudied including the well-posedness of the equations,relations among parameters and finite positive term sum formulae as well as explicit formulae of solutions.In chapter 4,a program is provided to verify the results of the planting type of meson equations.