Abstract DREB1 of the AP2/ERF superfamily plays a key role in the regulation of plant response to low temperatures. In this study, a novel DREB1/CBF transcription factor, PnDREB1, was isolated from Iceland poppy (Papaver nudicaule), a plant adaptive to low temperature environments. It is homologous to the known DREB1s of Arabidopsis and other plant species. It also shares similar 3D structure, and conserved and functionally important motifs with DREB1s of Arabidopsis. The phylogenetic analysis indicated that the AP2 domain of PnDREB1 is similar to those of Glycine max, Medicago truncatula, and M. sativa. PnDREB1 is constitutively expressed in diverse tissues and is increased in roots. qPCR analyses indicated that PnDREB1 is significantly induced by freezing treatment as well as by abscissic acid. The expression levels induced by freezing treatment were higher in the variety with higher degree of freezing tolerance. These results suggested that PnDREB1 is a novel and functional DREB1 transcription factor involved in freezing response and possibly in other abiotic stresses. Furthermore, the freezing-induction could be suppressed by exogenous gibberellins acid, indicating that PnDREB1 might play some role in the GA signaling transduction pathway. This study provides a basis for better understanding the roles of DREB1 in adaption of Iceland poppy to low temperatures.

In this paper, we study the distribution on the eigenvalues of the preconditioned matrices that arise in solving two-by-two block non-Hermitian positive semidefinite linear systems by use of the accelerated Hermitian and skew-Hermitian splitting iteration methods. According to theoretical analysis, we prove that all eigenvalues of the preconditioned matrices are very clustered with any positive iteration parameters α and β; especially, when the iteration parameters α and β approximate to 1, all eigenvalues approach 1. We also prove that the real parts of all eigenvalues of the preconditioned matrices are positive, i.e., the preconditioned matrix is positive stable. Numerical experiments show the correctness and feasibility of the theoretical analysis. Mathematical subject classification: 65F10, 65N22, 65F50.