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The applications of additive map preserving idempotence ingeneralized inverse
Hongmei Yao,Zhaobin Fan,Jiapei Tang 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with n ≥ 3. We denote by Mn(R) the ring of all n×n matrices over R. Let <ζ(R)> be the additive subgroup of Mn(R) generated additively by all idempotent matrices. Let ξ = ζ(R)i or Mn(R). In this paper, by using an additive idempotence-preserving result obtained by Cao (see [4]), I characterize (i) the additive preservers of tripotence from ξ to Mm(R) when 2 and 3 are units of R; (ii) the additive preservers of inverses (respectively, Drazin inverses, group inverses, {1}-inverses, {2}-inverses, {1, 2}-inverses) from Mn(R) to Mm(R) when 2 and 3 are units of R. Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with n ≥ 3. We denote by Mn(R) the ring of all n×n matrices over R. Let <ζ(R)> be the additive subgroup of Mn(R) generated additively by all idempotent matrices. Let ξ = ζ(R)i or Mn(R). In this paper, by using an additive idempotence-preserving result obtained by Cao (see [4]), I characterize (i) the additive preservers of tripotence from ξ to Mm(R) when 2 and 3 are units of R; (ii) the additive preservers of inverses (respectively, Drazin inverses, group inverses, {1}-inverses, {2}-inverses, {1, 2}-inverses) from Mn(R) to Mm(R) when 2 and 3 are units of R.
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THE APPLICATIONS OF ADDITIVE MAP PRESERVING IDEMPOTENCE IN GENERALIZED INVERSE
Yao, Hongmei,Fan, Zhaobin,Tang, Jiapei Korean Society of Computational and Applied Mathem 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with $n\;{\geq}\;3$. We denote by $M_n(R)$ the ring of all $n{\times}n$ matrices over R. Let ($J_n(R)$) be the additive subgroup of $M_n(R)$ generated additively by all idempotent matrices. Let ($D=J_n(R)$) or $M_n(R)$. In this paper, by using an additive idem potence-preserving result obtained by Coo (see [4]), I characterize (i) the additive preservers of tripotence from D to $M_m(R)$ when 2 and 3 are units of R; (ii) the additive preservers of inverses (respectively, Drazin inverses, group inverses, {1}-inverses, {2}-inverses, {1, 2}-inverses) from $M_n(R)$ to $M_n(R)$ when 2 and 3 are units of R.
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Fuchuan Zhou,Hongmei Tang,Linfeng Wang,Ning Yan 대한토목학회 2022 KSCE JOURNAL OF CIVIL ENGINEERING Vol.26 No.10
After the road excavation of the hard and soft interlayered bedding slope in the mountainous region's valley area, the bedding slope often results in a catastrophic phenomenon, especially in the project's construction and operation where existed severe safety hazards. A geo-mechanical two-component model consisting of the slider and the underlying layer is proposed to analyze the rock block instability under the fissure water pressure, the shear deformation, and the compression deformation. The slider's complex stress field is derived by using elastic mechanics. The incremental energy equilibrium Equation is established based on the energy balance theory, and the generalized sliding force relative function of the slider and the generalized shear force relative function of the underlying soft rock are obtained. The deformation energy accumulation, transfer, and energy dissipation characteristics are analyzed. Put a rock slide in the bedding rock cutting slope happened at Jiaojiatan, Pengshui County, Chongqing municipality, China as a case. Results indicate that considering both the compression deformation and the shear deformation of the slider, the kinetic energy, the rapid launch speed of the projectile, the average projectile acceleration, and the failure stroke increase about 15.7 times, 4.0 times, 1.8 times, and 8.9 times respectively than that of only considering the shear deformation, and the dynamic disaster intensity is more severe and worthy of attention. The results that ignored the fissure water pressure and the compressive deformation energy coincide with the existing literature, which verifies the reasonable applied method in this paper. Considering the slider's different displacements and the height-length ratios, when the energy ratio function that represents the ratio of the incremental compression energy to the incremental shear energy concludes that when the range of the height-length ratio is between 0 to 0.95(flat and narrow sliders), the compression energy's contribution to the system’s elastic energy should be taken into consideration. The advantage of the energy balance method applied in the stability analysis of the bedding rock slope is that the potential unstable rock block's status can be predicted dynamically according to the variation of the underlying soft rock's deformation and that the elastic impact dynamic parameters can also be obtained compared with other instability analysis approach.
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Cao Zhengyan,Wu Peiyin,Gao Hongmei,Xia Ning,Jiang Ying,Tang Ning,Liu Guohua,Chen Zexiong 한국유전학회 2022 Genes & Genomics Vol.44 No.2
Background: Lonicera macranthoides is an important woody plant with high medicinal values widely cultivated in southern China. WRKY, one of the largest transcription factor families, participates in plant development, senescence, and stress responses. However, a comprehensive study of the WRKY family in L. macranthoides hasn't been reported previously. Objective: To establish an extensive overview of the WRKY family in L. macranthoides and identify senescence-responsive members of LmWRKYs. Methods: RNA-Seq and phylogenetic analysis were employed to identify the LmWRKYs and their evolutionary relationships. Quantitative real-time (qRT-PCR) and transgenic technology was utilized to investigate the roles of LmWRKYs in response to developmental-, cold-, and ethylene-induced senescence. Results: A total of 61 LmWRKY genes with a highly conserved motif WRKYGQK were identified. Phylogenetic analysis of LmWRKYs together with their orthologs from Arabidopsis classified them into three groups, with the number of 15, 39, and 7, respectively. 17 LmWRKYs were identified to be differentially expressed between young and aging leaves by RNA-Seq. Further qRT-PCR analysis showed 15 and 5 LmWRKY genes were significantly induced responding to tissue senescence in leaves and stems, respectively. What's more, five LmWRKYs, including LmWRKY4, LmWRKY5, LmWRKY6, LmWRKY11, and LmWRKY16 were dramatically upregulated under cold and ethylene treatment in both leaves and stems, indicating their involvements commonly in developmental- and stress-induced senescence. In addition, function analysis revealed LmWRKY16, a homolog of AtWRKY75, can accelerate plant senescence, as evidenced by leaf yellowing during reproductive growth in LmWRKY16-overexpressing tobaccos. Conclusion: The results lay the foundation for molecular characterization of LmWRKYs in plant senescence.
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