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A NOTE ON LINEAR COMBINATIONS OF AN IDEMPOTENT MATRIX AND A TRIPOTENT MATRIX
Yao, Hongmei,Sun, Yanling,Xu, Chuang,Bu, Changjiang The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5
Let $A_1$ and $A_2$ be nonzero complex idempotent and tripotent matrix, respectively. Denote a linear combination of the two matrices by A = $c_1A_1$ + $c_2A_2$, where $c_1,\;c_2$ are nonzero complex scalars. In this paper, under an assumption of $A_1A_2$ = $A_2A_1$, we characterize all situations in which the linear combination is tripotent. A statistical interpretation of this tripotent problem is also pointed out. Moreover, In [2], Baksalary characterized all situations in which the above linear combination is idem-potent by using the property of decomposition of a tripotent matrix, i.e. if $A_2$ is tripotent, then $A_2$ = $B_1-B_2$, where $B^2_i=B_i$, i = 1, 2 and $B_1B_2=B_2B_1=0$. While in this paper, by utilizing a method different from the one used by Baksalary in [2], we prove the theorem 1 in [2] again.
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A note on linear combinations of an idempotent matrix and a tripotent matrix
Hongmei Yao,Yanling Sun,CHUANG XU,CHANGJIANG BU 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
Let A1 and A2 be nonzero complex idempotent and tripotent matrix, respectively. Denote a linear combination of the two matrices by A = c1A1 + c2A2, where c1, c2 are nonzero complex scalars. In this paper, under an assumption of A1A2 = A2A1, we characterize all situations in which the linear combination is tripotent. A statistical interpretation of this tripotent problem is also pointed out. Moreover, In [2], Baksalary characterized all situations in which the above linear combination is idempotent by using the property of decomposition of a tripotent matrix, i.e. if A2 is tripotent, then A2 = B1 −B2, where B2 i = Bi, i = 1, 2 and B1B2 = B2B1 = 0. While in this paper, by utilizing a method different from the one used by Baksalary in [2], we prove the theorem 1 in [2] again. Let A1 and A2 be nonzero complex idempotent and tripotent matrix, respectively. Denote a linear combination of the two matrices by A = c1A1 + c2A2, where c1, c2 are nonzero complex scalars. In this paper, under an assumption of A1A2 = A2A1, we characterize all situations in which the linear combination is tripotent. A statistical interpretation of this tripotent problem is also pointed out. Moreover, In [2], Baksalary characterized all situations in which the above linear combination is idempotent by using the property of decomposition of a tripotent matrix, i.e. if A2 is tripotent, then A2 = B1 −B2, where B2 i = Bi, i = 1, 2 and B1B2 = B2B1 = 0. While in this paper, by utilizing a method different from the one used by Baksalary in [2], we prove the theorem 1 in [2] again.
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( Hongtao Liu ),( Seng Zhu ),( Yingying Sun ),( Na Li ),( Jingmin Gu ),( Changjiang Sun ),( Xin Feng ),( Wenyu Han ),( Jianxia Jiang ),( Liancheng Lei ) 한국미생물 · 생명공학회 2017 Journal of microbiology and biotechnology Vol.27 No.1
Meningitis caused by Streptococcus suis serotype 2 (S. suis 2) is a great threat to the pig industry and human health. Virulence factors associated with the pathogenesis of meningitis have yet to be clearly defined, even though many potential S. suis 2 virulence factors have been identified. This greatly hinders the progress of S. suis 2 meningitis pathogenesis research. In this study, a co-culture blood-brain barrier (BBB) model was established using primary porcine brain microvascular endothelial cells and astrocytes, and the whole genome library of S. suis 2 was constructed using phage display technology. Finally, a total of 14 potential virulence factors contributing to S. suis 2 adherence to and invasion of the BBB were selected by analyzing the interactions between the phage library and the co-culture model. Twelve of these factors have not been previously reported in meningitis-related research. The data provide valuable insight into the pathogenesis of S. suis 2 meningitis and potential targets for the development of drug therapies.
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Shuang Wang,Jingmin Gu,Meng Lv,Zhimin Guo,Guangmou Yan,Ling Yu,Chongtao Du,Xin Feng,Wenyu Han,Changjiang Sun,Liancheng Lei 한국미생물학회 2017 The journal of microbiology Vol.55 No.5
Bacteriophage endolysin is one of the most promising antibioticsubstitutes, but in Gram-negative bacteria, the outermembrane prevents the lysin from hydrolyzing peptidoglycansand blocks the development of lysin applications. Theprime strategy for new antibiotic substitutes is allowing lysinto access the peptidoglycan from outside of the bacteria byreformation of the lysin. In this study, the novel Escherichiacoli (E. coli) phage lyase lysep3, which lacks outside-in catalyticability, was fused with the N-terminal region of theBacillus amyloliquefaciens lysin including its cell wall bindingdomain D8 through the best manner of protein fusionbased on the predicted tertiary structure of lysep3-D8 to obtainan engineered lysin that can lyse bacteria from the outside. Our results showed that lysep3-D8 could lyse both Gramnegativeand Gram-positive bacteria, whereas lysep3 and D8have no impact on bacterial growth. The MIC of lysep3-D8on E. coli CVCC1418 is 60 μg/ml; lysep3-D8 can inhibit thegrowth of bacteria up to 12 h at this concentration. The bactericidalspectrum of lysep3-D8 is broad, as it can lyse of allof 14 E. coli strains, 3 P. aeruginosa strains, 1 Acinetobacterbaumannii strain, and 1 Streptococcus strain. Lysep3-D8 hassufficient bactericidal effects on the 14 E. coli strains testedat the concentration of 100 μg/ml. The cell wall binding domainof the engineered lysin can destroy the integrity of theouter membrane of bacteria, thus allowing the catalytic domainto reach its target, peptidoglycan, to lyse the bacteria. Lysep3-D8 can be used as a preservative in fodder to benefitthe health of animals. The method we used here proved to bea successful exploration of the reformation of phage lysin.
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