In the framework of topological vector spaces, we give a characterization of strong Minkowski separation, introduced by Cheng, et al., in terms of convex body separation. From this, several results on strong Minkowski...In the framework of topological vector spaces, we give a characterization of strong Minkowski separation, introduced by Cheng, et al., in terms of convex body separation. From this, several results on strong Minkowski separation are deduced. Using the results, we prove a drop theorem involving weakly countably compact sets in locally convex spaces. Moreover, we introduce the notion of the co-drop property and show that every weakly countably compact set has the co-drop property. If the underlying locally convex space is quasi-complete, then a bounded weakly closed set has the co-drop property if and only if it is weakly countably compact.展开更多
In this article, we extend the cyclic antimonotonicity from scalar bifunctions to vector bifunctions. We find out a cyclically antimonotone vector bifunction can be regarded as a family of cyclically antimonotone scal...In this article, we extend the cyclic antimonotonicity from scalar bifunctions to vector bifunctions. We find out a cyclically antimonotone vector bifunction can be regarded as a family of cyclically antimonotone scalar bifunctions. Using a pre-order principle(see Qiu, 2014), we prove a new version of Ekeland variational principle(briefly, denoted by EVP), which is quite different from the previous ones, for the objective function consists of a family of scalar functions. From the new version, we deduce several vectorial EVPs for cyclically antimonotone equilibrium problems, which extend and improve the previous results. By developing the original method proposed by Castellani and Giuli, we deduce a number of existence results(no matter scalar-valued case,or vector-valued case), when the feasible set is a sequentially compact topological space or a countably compact topological space. Finally, we propose a general coercivity condition. Combining the general coercivity condition and the obtained existence results with compactness conditions, we obtain several existence results for equilibrium problems in noncompact settings.展开更多
It is well known that a supercritical single-type Bienayme-Galton-Watson process can be viewed as a decomposable branching process formed by two subtypes of particles: those having infinite line of descent and those w...It is well known that a supercritical single-type Bienayme-Galton-Watson process can be viewed as a decomposable branching process formed by two subtypes of particles: those having infinite line of descent and those who have finite number of descendants. In this paper we analyze such a decomposition for the linear-fractional Bienayme-Galton-Watson processes with countably many types. We find explicit expressions for the main characteristics of the reproduction laws for so-called skeleton and doomed particles.展开更多
Let R be an associative ring with identity. An R-module M is called an NCS module if l（M）∩y（M） = {0}, where l（M） and y（M） denote the set of all closed submodules and the set of all small submodules of M, resp...Let R be an associative ring with identity. An R-module M is called an NCS module if l（M）∩y（M） = {0}, where l（M） and y（M） denote the set of all closed submodules and the set of all small submodules of M, respectively. It is clear that the NCS condition is a generalization of the well-known CS condition. Properties of the NCS conditions of modules and rings are explored in this article. In the end, it is proved that a ring R is right ∑-CS if and only if R is right perfect and right countably ∑-NCS. Recall that a ring R is called right ∑-CS if every direct sum of copies of RR is a CS module. And a ring R is called right countably ∑-NCS if every direct sum of countable copies of RR is an NCS module.展开更多
In this article,we introduce and study the concept of countably generated dimension,which is a Krull-like dimension extension of the concept of DCC on countably generated submodules.We show that some of the basic resu...In this article,we introduce and study the concept of countably generated dimension,which is a Krull-like dimension extension of the concept of DCC on countably generated submodules.We show that some of the basic results of Krull dimension are true for countably generated dimension.It is shown that an jR-module M has Krull dimension if and only if it has countably generated dimension,and its Krull dimension and countably generated dimension coincide.展开更多
基金National Natural Science Foundation of China(10571035)
文摘In the framework of topological vector spaces, we give a characterization of strong Minkowski separation, introduced by Cheng, et al., in terms of convex body separation. From this, several results on strong Minkowski separation are deduced. Using the results, we prove a drop theorem involving weakly countably compact sets in locally convex spaces. Moreover, we introduce the notion of the co-drop property and show that every weakly countably compact set has the co-drop property. If the underlying locally convex space is quasi-complete, then a bounded weakly closed set has the co-drop property if and only if it is weakly countably compact.
基金supported by the National Natural Science Foundation of China(11471236,11561049)
文摘In this article, we extend the cyclic antimonotonicity from scalar bifunctions to vector bifunctions. We find out a cyclically antimonotone vector bifunction can be regarded as a family of cyclically antimonotone scalar bifunctions. Using a pre-order principle(see Qiu, 2014), we prove a new version of Ekeland variational principle(briefly, denoted by EVP), which is quite different from the previous ones, for the objective function consists of a family of scalar functions. From the new version, we deduce several vectorial EVPs for cyclically antimonotone equilibrium problems, which extend and improve the previous results. By developing the original method proposed by Castellani and Giuli, we deduce a number of existence results(no matter scalar-valued case,or vector-valued case), when the feasible set is a sequentially compact topological space or a countably compact topological space. Finally, we propose a general coercivity condition. Combining the general coercivity condition and the obtained existence results with compactness conditions, we obtain several existence results for equilibrium problems in noncompact settings.
文摘It is well known that a supercritical single-type Bienayme-Galton-Watson process can be viewed as a decomposable branching process formed by two subtypes of particles: those having infinite line of descent and those who have finite number of descendants. In this paper we analyze such a decomposition for the linear-fractional Bienayme-Galton-Watson processes with countably many types. We find explicit expressions for the main characteristics of the reproduction laws for so-called skeleton and doomed particles.
基金Acknowledgements The authors would like to thank Professor Dinh Van Huynh and Professor Sergio Lopez-Permouth for their nice suggestions. This work was supported by the Natural Science Foundation of Jiangsu Province （Nos. BK20130599, 20141327）, the National Natural Science Foundation of China （Grant No. 11371089）, and the Project-sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.
文摘Let R be an associative ring with identity. An R-module M is called an NCS module if l（M）∩y（M） = {0}, where l（M） and y（M） denote the set of all closed submodules and the set of all small submodules of M, respectively. It is clear that the NCS condition is a generalization of the well-known CS condition. Properties of the NCS conditions of modules and rings are explored in this article. In the end, it is proved that a ring R is right ∑-CS if and only if R is right perfect and right countably ∑-NCS. Recall that a ring R is called right ∑-CS if every direct sum of copies of RR is a CS module. And a ring R is called right countably ∑-NCS if every direct sum of countable copies of RR is an NCS module.
基金The author is grateful to the Research Council of Shahid Chamran University of Ahvaz for financial support(SCU.MM99.192).
文摘In this article,we introduce and study the concept of countably generated dimension,which is a Krull-like dimension extension of the concept of DCC on countably generated submodules.We show that some of the basic results of Krull dimension are true for countably generated dimension.It is shown that an jR-module M has Krull dimension if and only if it has countably generated dimension,and its Krull dimension and countably generated dimension coincide.
