Let A∈C<sup>m×n</sup>,set eigenvalues of matrix A with |λ<sub>1</sub> （A）|≥|λ<sub>2</sub>（A）|≥…≥|λ<sub>n</sub>（A）|,write A≥0 if A is a positive semid...Let A∈C<sup>m×n</sup>,set eigenvalues of matrix A with |λ<sub>1</sub> （A）|≥|λ<sub>2</sub>（A）|≥…≥|λ<sub>n</sub>（A）|,write A≥0 if A is a positive semidefinite Hermitian matrix, and denote∧<sub>k</sub> （A）=diag （λ<sub>1</sub>（A）,…,λ<sub>k</sub>（A））,∧<sub>(</sub>（n-k）.（A）=diag (λ<sub>k+1</sub>（A）,…,λ<sub>n</sub>（A）)for any k=1, 2,...,n if A≥0. Denote all n order unitary matrices by U<sup>n×n</sup>.Problem of equalities to hold in eigenvalue inequalities for products of matrices展开更多
Polar microorganism resource development can be accomplished as long as its inherent characteristics,that is,biota quantity,diversity,and low temperature adaptability,as well as market demands and product feasibility,...Polar microorganism resource development can be accomplished as long as its inherent characteristics,that is,biota quantity,diversity,and low temperature adaptability,as well as market demands and product feasibility,are considered.*1 Characteristics of polar microorganisms Most importantly,the quantity and diversity of terrestrial and aquatic microorganisms in the polar regions is abundant(Abakumov and Mukhametova,2014),and species quantity and diversity in eutrophic polar areas can even become comparable to that in temperate climate regions(Hoovera and Pikutab,2010).This large,diverse polar region microbial biomass can become the basis for the development of novel resources.展开更多
基金Supported partly by National Natural Science Foundation of China
文摘Let A∈C<sup>m×n</sup>,set eigenvalues of matrix A with |λ<sub>1</sub> （A）|≥|λ<sub>2</sub>（A）|≥…≥|λ<sub>n</sub>（A）|,write A≥0 if A is a positive semidefinite Hermitian matrix, and denote∧<sub>k</sub> （A）=diag （λ<sub>1</sub>（A）,…,λ<sub>k</sub>（A））,∧<sub>(</sub>（n-k）.（A）=diag (λ<sub>k+1</sub>（A）,…,λ<sub>n</sub>（A）)for any k=1, 2,...,n if A≥0. Denote all n order unitary matrices by U<sup>n×n</sup>.Problem of equalities to hold in eigenvalue inequalities for products of matrices
文摘Polar microorganism resource development can be accomplished as long as its inherent characteristics,that is,biota quantity,diversity,and low temperature adaptability,as well as market demands and product feasibility,are considered.*1 Characteristics of polar microorganisms Most importantly,the quantity and diversity of terrestrial and aquatic microorganisms in the polar regions is abundant(Abakumov and Mukhametova,2014),and species quantity and diversity in eutrophic polar areas can even become comparable to that in temperate climate regions(Hoovera and Pikutab,2010).This large,diverse polar region microbial biomass can become the basis for the development of novel resources.
