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 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
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
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.
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.
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.
