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.

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.

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.

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.

Production of Recombinant Human Papillomavirus Type 52 L1 Protein in Hansenula polymorpha Formed Virus-Like Particles

Liu, Cunbao,Yao, Yufeng,Yang, Xu,Bai, Hongmei,Huang, Weiwei,Xia, Ye,Ma, Yanbing The Korean Society for Microbiology and Biotechnol 2015 Journal of microbiology and biotechnology Vol.25 No.6

Human papillomavirus (HPV) type 52 is a high-risk HPV responsible for cervical cancer. HPV type 52 is common around the world and is the most common in some Asian regions. The available prophylactic HPV vaccines protect only from HPV types 16 and 18. Supplementing economical vaccines that target HPV type 52 may satisfactorily complement available prophylactic vaccines. A codon-adapted HPV 52 L1 gene was expressed in the methylotrophic yeast Hansenula polymorpha, which is used as an industrial platform for economical hepatitis B surface antigen particle production in China. We found that the recombinant proteins produced in this expression system could form virus-like particles (VLPs) with diameters of approximately 50 nm. This study suggests that the HPV 52 VLPs produced in this platform may satisfactorily complement available prophylactic vaccines in fighting against HPVs prevalent in Asia.

A Comparative Study on the Offshore Intensification of Supertyphoon Rammasun (2014) and Typhoon Rumbia (2013): the Role of Summer Monsoon

Zhixiang Xiao,Cai Yao,Xiaoli Luo,Hongmei Sun 한국기상학회 2021 Asia-Pacific Journal of Atmospheric Sciences Vol.57 No.3

The offshore intensificationmechanisms of Supertyphoon Rammasun (2014) and Typhoon Rumbia (2013) are analyzed and compared based on the best track typhoon data provided by the Shanghai Typhoon Institute of China Meteorological Administration (STI/CMA), ECMWF (CMA and JMA) objective (subjective) predicted typhoon track and intensity, and reanalysis data of the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR). Results show that the offshore sea surface temperature over 28 °C was conducive to the intensification of the two typhoons in the coastal area prior to their landfall in South China. Rammasun was embedded in an extremely active phase of a 10–20-day oscillation in the summer monsoon over the South China Sea and western North Pacific prior to its landfall. The low-level jet transported warm and moist air to the inner core of Rammasun and the deepening of the southwesterly monsoon flow up to 200 hPa reduced vertical wind shear, both favorable for the offshore rapid intensification of Rammasun. In 2013, the summer monsoon over the South China Sea and western North Pacific experienced quasi-20-day and quasi-10-day oscillations. The out of phase of the two oscillations resulted in relatively weak tropical and subtropical summer monsoon flow prior to the landfall of Rumbia. As a result, the low-level monsoon flow transported relatively less moist air into Rumbia, and the shallow monsoon flow was not conducive to the weakening of vertical wind shear, resulting in a less rapid offshore intensification of Rumbia than Rammasun.

Network Intrusion Detection Model based on Combination of Fisher Score and ELM Approach

Hong Mei,Wang Ju,Qi Yao Wu,Zhai Ning 보안공학연구지원센터 2016 International Journal of Security and Its Applicat Vol.10 No.11

The diversity and concealment of network attack lead to the difficulty of network intrusion detection, in order to further improve the detection accuracy and efficiency of network intrusion detection, this article proposes a novel model FS-ELM, which is based on the combination of Fisher Score (FS) for feature selection and ELM classifiers for network intrusion detection. In the proposed model, FS is used to conduct feature selection to select the most distinguished feature subsets, and then to get diverse training subsets, in terms of these subsets, ELM classifiers are trained. Finally the results are achieved. Experiment on KDD CUP 99 data set, by means of the experimental analysis and comparison with SVM, LS-SVM and KNN, the proposed model not only improves the detection accuracy, but also enhances detection efficiency, it proves that it is an effective model for network intrusion detection.