According to the bounded variation theory and the bounded distortion property of cookie-cutter-like （CCL） sets, the approximate self-similarity of cookie-cutter-like sets satisfying certain conditions is studied. Ba...According to the bounded variation theory and the bounded distortion property of cookie-cutter-like （CCL） sets, the approximate self-similarity of cookie-cutter-like sets satisfying certain conditions is studied. Based on the mean value theorem, it is proved that a class of special cookie-cutter-like sets is approximately self-similar. The results obtained in this paper extend the corresponding results that have already existed. K展开更多
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
An ideal I of a ring R is strongly separative provided that for all finitely generated projective R-modules A, B with A = AI and B = BI, if 2A ≌ A ＋ B, then A ≌ B. We prove in this paper that a regular ideal I of a...An ideal I of a ring R is strongly separative provided that for all finitely generated projective R-modules A, B with A = AI and B = BI, if 2A ≌ A ＋ B, then A ≌ B. We prove in this paper that a regular ideal I of a ring R is strongly separative if and only if each a E 1 ＋ I satisfying （1 - α）R ∝ r（a） is unit-regular, if and only if each a ∈ 1 ＋ I satisfying （1 - a2）R ∝ r（a2） is unit-regular, if and only if each a E 1 4- I satisfying R（1 - a）R = Rr（a） is unit-regular, if and only if each a ∈ 1 ＋ I satisfying R（1 -a^2）R = Rr（a^2） is unit-regular.展开更多
In this paper, the theorem of the alternative based on separation functions in ordered locally convex topological vector spaces has been established by using the concept on set valued mappings. The optimality con...In this paper, the theorem of the alternative based on separation functions in ordered locally convex topological vector spaces has been established by using the concept on set valued mappings. The optimality conditions in ref. for D convex function have been generalized to ordered locally convex topological vector space and the similarly optimality conditions for D subconvexlike functions, such as the necessary and sufficient conditions of nondominated solutions, the generalized saddle point theorems and the lagrange duality theorems, have been obtained.展开更多
Self-cancellation of modules having the finite exchange property is introduced. If a right R-module M has the finite exchange property, it is shown that M has selfcancellation if and only if EndR(M) is a strongly sepa...Self-cancellation of modules having the finite exchange property is introduced. If a right R-module M has the finite exchange property, it is shown that M has selfcancellation if and only if EndR(M) is a strongly separative ring. Using this result,some new characterizations of strong separativity are obtained.展开更多
基金Supported by the National Natural Science Foundation of China (50872100)
文摘According to the bounded variation theory and the bounded distortion property of cookie-cutter-like （CCL） sets, the approximate self-similarity of cookie-cutter-like sets satisfying certain conditions is studied. Based on the mean value theorem, it is proved that a class of special cookie-cutter-like sets is approximately self-similar. The results obtained in this paper extend the corresponding results that have already existed. K
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This research was supported by the Natural Science Foundation of Zhejiang Province （LY13A010019）, China.
文摘An ideal I of a ring R is strongly separative provided that for all finitely generated projective R-modules A, B with A = AI and B = BI, if 2A ≌ A ＋ B, then A ≌ B. We prove in this paper that a regular ideal I of a ring R is strongly separative if and only if each a E 1 ＋ I satisfying （1 - α）R ∝ r（a） is unit-regular, if and only if each a ∈ 1 ＋ I satisfying （1 - a2）R ∝ r（a2） is unit-regular, if and only if each a E 1 4- I satisfying R（1 - a）R = Rr（a） is unit-regular, if and only if each a ∈ 1 ＋ I satisfying R（1 -a^2）R = Rr（a^2） is unit-regular.
文摘In this paper, the theorem of the alternative based on separation functions in ordered locally convex topological vector spaces has been established by using the concept on set valued mappings. The optimality conditions in ref. for D convex function have been generalized to ordered locally convex topological vector space and the similarly optimality conditions for D subconvexlike functions, such as the necessary and sufficient conditions of nondominated solutions, the generalized saddle point theorems and the lagrange duality theorems, have been obtained.
文摘Self-cancellation of modules having the finite exchange property is introduced. If a right R-module M has the finite exchange property, it is shown that M has selfcancellation if and only if EndR(M) is a strongly separative ring. Using this result,some new characterizations of strong separativity are obtained.
