Vagueness of language has long been explored in the fields of philosophy and logic. Although Zadeh put forward fuzzy sets theory which was considered to be a decent quantitative instrument for the study of language va...Vagueness of language has long been explored in the fields of philosophy and logic. Although Zadeh put forward fuzzy sets theory which was considered to be a decent quantitative instrument for the study of language vagueness, the source of vagueness still remains a disputed issue. As the study of vagueness goes further, researchers attached more and more attention to the relation between language-cognition- reality, especially in the cognitive field. Thus we found that it would be more satisfied with the issue to construct a relation-model between five factors： reality, concept, human, language, and context. This model, which is different from the semantic triangle in explicating the factors, human and context, may help to explain the nature of vagueness and reclassify the language vagueness.展开更多
This paper is devoted to the investigation of the asymptotic behavior for a class of nonlinear parabolic partial functional differential equations. The boundedness and stability of the solutions are established by the...This paper is devoted to the investigation of the asymptotic behavior for a class of nonlinear parabolic partial functional differential equations. The boundedness and stability of the solutions are established by the upper-lower solution method. Some conditions are obtained by using the semigroup theory, the properties of nonnegative matrices and the techniques of inequalities to determine the asymptotically stable region of the equilibrium.展开更多
We study the global dynamics of a nonlocal population model with age structure in a bounded domain. We mainly concern with the case where the birth rate decreases as the mature population size become large. The analys...We study the global dynamics of a nonlocal population model with age structure in a bounded domain. We mainly concern with the case where the birth rate decreases as the mature population size become large. The analysis is rather subtle and it is inadequate to apply the powerful theory of monotone dynamical systems. By using the method of super-sub solutions, combined with the careful analysis of the kernel function in the nonlocal term, we prove nonexistence, existence and uniqueness of positive steady states of the model.Moreover, due to the mature individuals do not diffuse, the solution semiflow to the model is not compact. To overcome the difficulty of non-compactness in describing the global asymptotic stability of the unique positive steady state, we first establish an appropriate comparison principle. With the help of the comparison principle,we can employ the theory of dissipative systems to obtain the global asymptotic stability of the unique positive steady state. The main results are illustrated with the nonlocal Nicholson's blowflies equation and the nonlocal Mackey-Glass equation.展开更多
文摘Vagueness of language has long been explored in the fields of philosophy and logic. Although Zadeh put forward fuzzy sets theory which was considered to be a decent quantitative instrument for the study of language vagueness, the source of vagueness still remains a disputed issue. As the study of vagueness goes further, researchers attached more and more attention to the relation between language-cognition- reality, especially in the cognitive field. Thus we found that it would be more satisfied with the issue to construct a relation-model between five factors： reality, concept, human, language, and context. This model, which is different from the semantic triangle in explicating the factors, human and context, may help to explain the nature of vagueness and reclassify the language vagueness.
基金Supported by NNSFC(19971059)Education Burean of Sichuan Province(01LA43)
文摘This paper is devoted to the investigation of the asymptotic behavior for a class of nonlinear parabolic partial functional differential equations. The boundedness and stability of the solutions are established by the upper-lower solution method. Some conditions are obtained by using the semigroup theory, the properties of nonnegative matrices and the techniques of inequalities to determine the asymptotically stable region of the equilibrium.
基金supported by National Natural Science Foundation of China(Grant Nos.11031002 and 11371107)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20124410110001)
文摘We study the global dynamics of a nonlocal population model with age structure in a bounded domain. We mainly concern with the case where the birth rate decreases as the mature population size become large. The analysis is rather subtle and it is inadequate to apply the powerful theory of monotone dynamical systems. By using the method of super-sub solutions, combined with the careful analysis of the kernel function in the nonlocal term, we prove nonexistence, existence and uniqueness of positive steady states of the model.Moreover, due to the mature individuals do not diffuse, the solution semiflow to the model is not compact. To overcome the difficulty of non-compactness in describing the global asymptotic stability of the unique positive steady state, we first establish an appropriate comparison principle. With the help of the comparison principle,we can employ the theory of dissipative systems to obtain the global asymptotic stability of the unique positive steady state. The main results are illustrated with the nonlocal Nicholson's blowflies equation and the nonlocal Mackey-Glass equation.
