In this paper, we present an algorithm for embedding an m-sequential k-ary tree into its optimal hypercube with dilation at most 2 and prove its correctness.
In my former paper ＂A pre-order principle and set-valued Ekeland variational principle＂ （see [J. Math. Anal. Applo, 419, 904 937 （2014）]）, we established a general pre-order principle. From the pre-order princip...In my former paper ＂A pre-order principle and set-valued Ekeland variational principle＂ （see [J. Math. Anal. Applo, 419, 904 937 （2014）]）, we established a general pre-order principle. From the pre-order principle, we deduced most of the known set-valued Ekeland variational principles （denoted by EVPs） in set containing forms and their improvements. But the pre-order principle could not imply Khanh and Quy＇s EVP in [On generalized Ekeland＇s variational principle and equivalent formulations for set-valued mappings, J. Glob. Optim., 49, 381-396 （2011）], where the perturbation contains a weak T-function, a certain type of generalized distances. In this paper, we give a revised version of the pre-order principle. This revised version not only implies the original pre-order principle, but also can be applied to obtain the above Khanh and Quy＇s EVP. In particular, we give several new set-valued EVPs, where the perturbations contain convex subsets of the ordering cone and various types of generalized distances.展开更多
We give a general vectorial Ekeland＇s variational principle, where the objective function is defined on an F-type topological space and taking values in a pre-ordered real linear space. Being quite different from the...We give a general vectorial Ekeland＇s variational principle, where the objective function is defined on an F-type topological space and taking values in a pre-ordered real linear space. Being quite different from the previous versions of vectorial Ekeland＇s variational principle, the perturbation in our version is no longer only dependent on a fixed positive vector or a fixed family of positive vectors. It contains a family of set-valued functions taking values in the positive cone and a family of subadditive functions of topology generating quasi-metrics. Hence, the direction of the perturbation in the new version is a family of variable subsets which are dependent on the objective function values. The general version includes and improves a number of known versions of vectorial Ekeland＇s variational principle. From the general Ekeland＇s principle, we deduce the corresponding versions of Caristi-Kirk＇s fixed point theorem and Takahashi＇s nonconvex minimization theorem. Finally, we prove that all the three theorems are equivalent to each other.展开更多
We study properties of a relation in *-rings, called the core-EP (pre)order which was introduced by H. Wang on the set of all n × n complex matrices [Linear Algebra Appl., 2016, 508: 289-300] and has been recentl...We study properties of a relation in *-rings, called the core-EP (pre)order which was introduced by H. Wang on the set of all n × n complex matrices [Linear Algebra Appl., 2016, 508: 289-300] and has been recently generalized by Y. Gao, J. Chen, and Y. Ke to *-rings [Filomat, 2018, 32: 3073- 3085]. We present new characterizations of the core-EP order in *-rings with identity and introduce the notions of the dual core-EP decomposition and the dual core-EP order in *-rings.展开更多
We study a new binary relation defined on the set of rectangular complex matrices involving the weighted core-EP inverse and give its characterizations.This relation becomes a pre-order.Then,one-sided preorders associ...We study a new binary relation defined on the set of rectangular complex matrices involving the weighted core-EP inverse and give its characterizations.This relation becomes a pre-order.Then,one-sided preorders associated to the weighted core-EP inverse are given from two perspectives.Finally,we make a comparison for these two sets of one-sided weighted pre-orders.展开更多
文摘In this paper, we present an algorithm for embedding an m-sequential k-ary tree into its optimal hypercube with dilation at most 2 and prove its correctness.
基金Supported by National Natural Science Foundation of China(Grant Nos.11471236 and 11561049)
文摘In my former paper ＂A pre-order principle and set-valued Ekeland variational principle＂ （see [J. Math. Anal. Applo, 419, 904 937 （2014）]）, we established a general pre-order principle. From the pre-order principle, we deduced most of the known set-valued Ekeland variational principles （denoted by EVPs） in set containing forms and their improvements. But the pre-order principle could not imply Khanh and Quy＇s EVP in [On generalized Ekeland＇s variational principle and equivalent formulations for set-valued mappings, J. Glob. Optim., 49, 381-396 （2011）], where the perturbation contains a weak T-function, a certain type of generalized distances. In this paper, we give a revised version of the pre-order principle. This revised version not only implies the original pre-order principle, but also can be applied to obtain the above Khanh and Quy＇s EVP. In particular, we give several new set-valued EVPs, where the perturbations contain convex subsets of the ordering cone and various types of generalized distances.
基金Supported by National Natural Science Foundation of China(Grant Nos.10871141,11471236)
文摘We give a general vectorial Ekeland＇s variational principle, where the objective function is defined on an F-type topological space and taking values in a pre-ordered real linear space. Being quite different from the previous versions of vectorial Ekeland＇s variational principle, the perturbation in our version is no longer only dependent on a fixed positive vector or a fixed family of positive vectors. It contains a family of set-valued functions taking values in the positive cone and a family of subadditive functions of topology generating quasi-metrics. Hence, the direction of the perturbation in the new version is a family of variable subsets which are dependent on the objective function values. The general version includes and improves a number of known versions of vectorial Ekeland＇s variational principle. From the general Ekeland＇s principle, we deduce the corresponding versions of Caristi-Kirk＇s fixed point theorem and Takahashi＇s nonconvex minimization theorem. Finally, we prove that all the three theorems are equivalent to each other.
文摘We study properties of a relation in *-rings, called the core-EP (pre)order which was introduced by H. Wang on the set of all n × n complex matrices [Linear Algebra Appl., 2016, 508: 289-300] and has been recently generalized by Y. Gao, J. Chen, and Y. Ke to *-rings [Filomat, 2018, 32: 3073- 3085]. We present new characterizations of the core-EP order in *-rings with identity and introduce the notions of the dual core-EP decomposition and the dual core-EP order in *-rings.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11771076)sponsored by Shanghai Sailing Program(Grant No.20YF1433100).
文摘We study a new binary relation defined on the set of rectangular complex matrices involving the weighted core-EP inverse and give its characterizations.This relation becomes a pre-order.Then,one-sided preorders associated to the weighted core-EP inverse are given from two perspectives.Finally,we make a comparison for these two sets of one-sided weighted pre-orders.
