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The objective is to determine if Hsp70 is involved in the mechanism by which serum from burn rats induces apoptosis of cardiomyocytes. Cardiomyocytes in primary culture were assigned to the following groups: normal controls, normal rat serum, burn serum, burn serum plus empty vector control, and burn serum plus Hsp70transfection. Each group, except normal controls, was cultured with the corresponding serum for 2 hours. The empty vector controls and the Hsp70 groups were transfected, respectively, with the empty vector or pcDNA3.1-Hsp70recombinant plasmid 36 hours previously. Hsp70 protein levels were assessed by Western blot. Apoptotic cells were counted after Hoechst 33258 staining. Apoptosis of cardiomyocytes was also detected by the presence of “ladder” bands in agarose gels following electrophoresis of extracted DNA. Activation of caspase-3, -8, and -9 and Bid cleavage were assessed by Western blot. Hsp70 overexpression inhibited burn serum-induced apoptosis of cardiomyocytes; and burn serum-induced activation of caspases-3, -8, and -9; and Bid cleavage into tBid. Hsp70 inhibits burn serum-induced apoptosis by interfering with death receptor and mitochondrial pathways.

Motivated by the ideas of Kinoshita, we introduce the concept of minimal essential set of the coincident points for set-valued mappings, and we prove that there exists at least one minimal essential set and one essential component of the coincident points for set-valued mappings (satisfying some conditions).

In this paper, we study the stability of weakly efficient solution sets for optimization problems with set-valued maps. We introduce the concept of essential weakly efficient solutions and essential components of weakly efficient solution sets. We first show that most optimization problems with set-valued maps (in the sense of Baire category) are stable. Secondly, we obtain some sufficient conditions for the existence of one essential weakly efficient solution or one essential component of the weakly efficient solution set .

In this paper, we study the stability of the spectra of bounded linear operators B(X) in a Banach space X , and obtain that their spectra are stable on a dense residual subset of B(X) .

This paper proposes a formally stronger set-valued Caristi's fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland's variational principle and this set-valued Caristi's fixed point theorem. The results stated in this paper improve and strengthen the corresponding results in [4].

Motivated by the ideas of Kinoshita, we introduce the concept of minimal essential set of the coincident points for set-valued mappings, and we prove that there exists at least one minimal essential set and one essential component of the coincident points for set-valued mappings (satisfying some conditions).

In this paper, we study the stability of weakly efficient solution sets for optimization problems with set-valued maps. We introduce the concept of essential weakly efficient solutions and essential components of weakly efficient solution sets. We first show that most optimization problems with set-valued maps (in the sense of Baire category) are stable. Secondly, we obtain some sufficient conditions for the existence of one essential weakly efficient solution or one essential component of the weakly efficient solution set .

In this paper, we study the stability of the spectra of bounded linear operators B(X) in a Banach space X, and obtain that their spectra are stable on a dense residual subset of B(X).