The sequence space bvp consisting of all sequences (xk) such that (xk -xk-1) belongs to the space gp has recently been introduced by Basar and Altay [Ukrainian Math. J., 55(1), 136-147(2003)]; where 1 ≤ p ≤ ...The sequence space bvp consisting of all sequences (xk) such that (xk -xk-1) belongs to the space gp has recently been introduced by Basar and Altay [Ukrainian Math. J., 55(1), 136-147(2003)]; where 1 ≤ p ≤ ∞. In the present paper, some results concerning with the continuous dual and f-dual, and the AD-property of the sequence space bvp have been given and the norm of the difference operator A acting on the sequence space bvp has been found. The fine spectrum with respect to the Goldberg's classification of the difference operator △ over the sequence space bvp has been determined, where 1≤p〈∞.展开更多
Water is a major limiting factor for food production and many countries fail to produce sufficient food for their population due to severe water scarcity (Jury and Vaux, 2005). Rice is the main staple food worldwide...Water is a major limiting factor for food production and many countries fail to produce sufficient food for their population due to severe water scarcity (Jury and Vaux, 2005). Rice is the main staple food worldwide. More than 50% of rice in the world is rain-fed and drought causes severe reduction in rice grain yield in rain-fed environments (Venuprasad et al., 2007; Zhang, 2007; Sandhu et al., 2014). Therefore, enhancing drought resistance (DR) of rice is important for food security. However, DR is a complex trait, which is controlled by a large number of loci with small effect and is also affected by different genetic background, genotype-by-environment interaction and other stresses such as heat (Hu and Xiong, 2014).展开更多
文摘The sequence space bvp consisting of all sequences (xk) such that (xk -xk-1) belongs to the space gp has recently been introduced by Basar and Altay [Ukrainian Math. J., 55(1), 136-147(2003)]; where 1 ≤ p ≤ ∞. In the present paper, some results concerning with the continuous dual and f-dual, and the AD-property of the sequence space bvp have been given and the norm of the difference operator A acting on the sequence space bvp has been found. The fine spectrum with respect to the Goldberg's classification of the difference operator △ over the sequence space bvp has been determined, where 1≤p〈∞.
基金supported by grants from the National Program for Basic Research of China(No.2012CB114305)the National Program on High Technology Development(No. 2012AA10A303)the Oversea Graduate Program from Ministry of Education to K.Songyikhangsuthor
文摘Water is a major limiting factor for food production and many countries fail to produce sufficient food for their population due to severe water scarcity (Jury and Vaux, 2005). Rice is the main staple food worldwide. More than 50% of rice in the world is rain-fed and drought causes severe reduction in rice grain yield in rain-fed environments (Venuprasad et al., 2007; Zhang, 2007; Sandhu et al., 2014). Therefore, enhancing drought resistance (DR) of rice is important for food security. However, DR is a complex trait, which is controlled by a large number of loci with small effect and is also affected by different genetic background, genotype-by-environment interaction and other stresses such as heat (Hu and Xiong, 2014).