The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson'...The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.展开更多
The purpose of this paper is to reconsider the utility representation problem of preferences,Sev-eral representation theorems are obtained on general choice spaces.Preferences having continuous utility functions are c...The purpose of this paper is to reconsider the utility representation problem of preferences,Sev-eral representation theorems are obtained on general choice spaces.Preferences having continuous utility functions are characterized by their continuities and countable satiation.It is showed that on a pairwise separable choice space,the sufficient and necessary condition for a preference to be represented by a contin-uous utility function is that the preference is continuous and countably satiable.For monotone prefer-ences,we obtain that any space has continuous utility representations.展开更多
文摘The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.
基金This work is supported by the natural science foundation.
文摘The purpose of this paper is to reconsider the utility representation problem of preferences,Sev-eral representation theorems are obtained on general choice spaces.Preferences having continuous utility functions are characterized by their continuities and countable satiation.It is showed that on a pairwise separable choice space,the sufficient and necessary condition for a preference to be represented by a contin-uous utility function is that the preference is continuous and countably satiable.For monotone prefer-ences,we obtain that any space has continuous utility representations.
