The Experts below are selected from a list of 291 Experts worldwide ranked by ideXlab platform
Ravi A. Rao - One of the best experts on this subject based on the ideXlab platform.
-
The Quotient Unimodular Vector Group is Nilpotent
Leavitt Path Algebras and Classical K-Theory, 2020Co-Authors: Reema Khanna, Selby Jose, Sampat Sharma, Ravi A. RaoAbstract:Jose–Rao introduced and studied the Special Unimodular Vector Group \(\mathrm{SUm_r(R)}\) and \(\mathrm{EUm_r(R)}\), its Elementary Unimodular Vector subGroup. They proved that for \(r \ge 2\), \(\mathrm{EUm_r(R)}\) is a normal subGroup of \(\mathrm{SUm_r(R)}\). The Jose–Rao theorem says that the quotient Unimodular Vector Group, \(\mathrm{SUm_r(R)}/\mathrm{EUm_r(R)}\), for \(r \ge 2\), is a subGroup of the orthogonal quotient Group \(\mathrm{SO}_{2(r+1)}(R)/{\mathrm{EO}}_{2(r + 1)}(R)\). The latter Group is known to be nilpotent by the work of Hazrat–Vavilov, following methods of A. Bak; and so is the former. In this article we give a direct proof, following ideas of A. Bak, to show that the quotient Unimodular Vector Group is nilpotent of class \(\le d = \dim (R)\). We also use the Quillen–Suslin theory, inspired by A. Bak’s method, to prove that if \(R = A[X]\), with A a local ring, then the quotient Unimodular Vector Group is abelian.
-
A structure theorem for the elementary unimodular Vector Group
Transactions of the American Mathematical Society, 2005Co-Authors: Selby Jose, Ravi A. RaoAbstract:Given a pair of Vectors v,w ∈ R r+1 with = v · w T = 1, A. Suslin constructed a matrix S r (v,w) ∈ Sl 2 r(R). We study the subGroup SUm r (R) generated by these matrices, and its (elementary) subGroup EUm r (R) generated by the matrices S r (e 1 e, e 1 e T-1 ), for e ∈ E r+1 (R). The basic calculus for EUm r (R) is developed via a key lemma, and a fundamental property of Suslin matrices is derived.
Quan Zhou - One of the best experts on this subject based on the ideXlab platform.
-
Inhibitory effects of S100A4 gene silencing on alkali burn-induced corneal neovascularization: an in vivo study.
Molecular vision, 2017Co-Authors: Yu-lin Wang, Gui-ping Gao, Yuqin Wang, Zhi-you Peng, Quan ZhouAbstract:OBJECTIVE The purpose of this study is to explore the inhibitory effects of S100A4 gene silencing on alkali burn-induced corneal neovascularization (CNV) in rabbit models. METHODS Sixty-five rabbits were used to establish alkali-induced CNV models. After the operation, rabbits were given daily antibiotic eye drops and an eye ointment to prevent infection. The models were assigned to either an S100A4 siRNA or an empty Vector Group. Thirty rabbits were selected as the normal control Group. Quantitative real-time polymerase chain reaction (qRT-PCR) was performed to detect the mRNA expression of S100A4, vascular endothelial growth factor (VEGF), and tumor necrosis factor-α (TNF-α) in corneal tissues. Immunohistochemistry was used to detect the protein expression of VEGF in corneal tissues, and an enzyme-linked immunosorbent (ELISA) assay was used to detect the protein expression of VEGF and TNF-α in the aqueous humor. RESULTS The qRT-PCR results showed that S100A4 mRNA expression was lower in the S100A4 siRNA Group than in the empty Vector Group at 1, 3, 7, 14, and 28 days after an alkali burn. When compared with the empty Vector Group, the expression of VEGF and TNF-α mRNA was downregulated in the S100A4 siRNA Group. The immunohistochemistry results revealed that VEGF protein expression was downregulated in the S100A4 siRNA Group when compared to the empty Vector Group at 1, 3, 7, 14, and 28 days after an alkali burn. The ELISA results suggest that VEGF and TNF-α protein expression is downregulated in the S100A4 siRNA Group in comparison to the empty Vector Group at 1, 3, 7, 14, and 28 days after an alkali burn. CONCLUSIONS These findings indicate that S100A4 gene silencing can inhibit alkali burn-induced CNV in rabbits.
Qiang Hong-fu - One of the best experts on this subject based on the ideXlab platform.
-
Modified Differential Evolution Algorithm with Base Vector Group
Computer Engineering, 2012Co-Authors: Qiang Hong-fuAbstract:In base Vector randomly selection,the convergence speed of Differential Evolution(DE) algorithm is low.In order to solve this problem,a Modified DE(MDE) algorithm is proposed.Some good individuals are chosen to form the base Vector Group.Base Vector is chosen from the base Vector Group when mutation is operated.Test functions are used to prove the new algorithm.Results show that the modified algorithm can reduce the selecting range of base Vector and the iteration times for convergence.
Fu Li-zhi - One of the best experts on this subject based on the ideXlab platform.
-
The Compact Transformation Model in Vector Group Orthogonalization
Journal of Luohe Vocational and Technology College, 2009Co-Authors: Fu Li-zhiAbstract:Through proving Schmidt's orthogonalization equivalence law again based on modelization and programming,this paper presents the symmetries transformation model in Vector Group orthogonalization,which makes it possible to use computer to do program calculations.
Yu-lin Wang - One of the best experts on this subject based on the ideXlab platform.
-
Inhibitory effects of S100A4 gene silencing on alkali burn-induced corneal neovascularization: an in vivo study.
Molecular vision, 2017Co-Authors: Yu-lin Wang, Gui-ping Gao, Yuqin Wang, Zhi-you Peng, Quan ZhouAbstract:OBJECTIVE The purpose of this study is to explore the inhibitory effects of S100A4 gene silencing on alkali burn-induced corneal neovascularization (CNV) in rabbit models. METHODS Sixty-five rabbits were used to establish alkali-induced CNV models. After the operation, rabbits were given daily antibiotic eye drops and an eye ointment to prevent infection. The models were assigned to either an S100A4 siRNA or an empty Vector Group. Thirty rabbits were selected as the normal control Group. Quantitative real-time polymerase chain reaction (qRT-PCR) was performed to detect the mRNA expression of S100A4, vascular endothelial growth factor (VEGF), and tumor necrosis factor-α (TNF-α) in corneal tissues. Immunohistochemistry was used to detect the protein expression of VEGF in corneal tissues, and an enzyme-linked immunosorbent (ELISA) assay was used to detect the protein expression of VEGF and TNF-α in the aqueous humor. RESULTS The qRT-PCR results showed that S100A4 mRNA expression was lower in the S100A4 siRNA Group than in the empty Vector Group at 1, 3, 7, 14, and 28 days after an alkali burn. When compared with the empty Vector Group, the expression of VEGF and TNF-α mRNA was downregulated in the S100A4 siRNA Group. The immunohistochemistry results revealed that VEGF protein expression was downregulated in the S100A4 siRNA Group when compared to the empty Vector Group at 1, 3, 7, 14, and 28 days after an alkali burn. The ELISA results suggest that VEGF and TNF-α protein expression is downregulated in the S100A4 siRNA Group in comparison to the empty Vector Group at 1, 3, 7, 14, and 28 days after an alkali burn. CONCLUSIONS These findings indicate that S100A4 gene silencing can inhibit alkali burn-induced CNV in rabbits.
