PROBLEM OF EQUALITIES IN EIGENVALUE INEQUALITIES FOR PRODUCTS OF POSITIVE SEMIDEFINITE HERMITIAN MATRICES

Let A∈Cm×n,set eigenvalues of matrix A with |λ1 （A）|≥|λ2（A）|≥…≥|λn（A）|,write A≥0 if A is a positive semidefinite Hermitian matrix, and denote∧k （A）=diag （λ1（A）,…,λk（A））,∧(（n-k）.（A）=diag (λk+1（A）,…,λn（A）)for any k=1, 2,...,n if A≥0. Denote all n order unitary matrices by Un×n.Problem of equalities to hold in eigenvalue inequalities for products of matrices

The importance of product positioning and global branding for sustaining competitive advantage within the companies＇ global marketing strategy

In today＇s globally competitive world, because of the globalization, new business patterns and the changing nature of consumers, the companies feel the necessity to act strategic in the market and to reach up the target markets and sustain maximum customer satisfaction in order to compete and survive. In this context, within the study it is tried to define product positioning in international markets and global branding strategies conceptually and to focus on their contributions to the overall competitive advantage of the company. Initially, the study tries to present the association between product positioning and global branding approaches of the companies and sustaining competitive advantage. Justifications for the examination of the importance of companies＇ international product positioning and global branding orientations as a basis of creating competitive advantage were derived from the literature. It is suggested that the companies＇ product positioning and global branding orientations and sustaining competitive advantage are the important aspects in multinational management and international business areas. Therefore, the purpose of this study is to evaluate the impact of product positioning and global branding strategies of the companies with special references to various industries and global brands.

Some thoughts on the development of polar microbial resources

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.

Investigation of P T-symmetric Hamiltonian Systems from an Alternative Point of View

Two non-Hermitian PT-symmetric Hamiltonian systems are reconsidered by means of the algebraic method which was originally proposed for the pseudo-Hermitian Hamiltonian systems rather than for the PT-symmetric ones.Compared with the way converting a non-Hermitian Hamiltonian to its Hermitian counterpart,this method has the merit that keeps the Hilbert space of the non-Hermitian PT-symmetric Hamiltonian unchanged.In order to give the positive definite inner product for the PT-symmetric systems,a new operator V,instead of C,can be introduced.The operator V has the similar function to the operator C adopted normally in the PT-symmetric quantum mechanics,however,it can be constructed,as an advantage,directly in terms of Hamiltonians.The spectra of the two non-Hermitian PT-symmetric systems are obtained,which coincide with that given in literature,and in particular,the Hilbert spaces associated with positive definite inner products are worked out.