A GENERALIZATION OF REARRANGEMENT AND MATRIX PRODUCT INEQUALITIES

In this paper, some inequalities for sequence rearrangement and matrix product are established. The authors extend and improve some known results, and show that there are some errors in reference on inequalities for sequence rearrangement by examples.

Note on the Product Inequalities for Sequences of Multidimensional Integers

For multi-dimensional integer-valued sequence, a new proof of the upper-bound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characterize the Kondratiev space of random test function, in which space it is convenient to study random distribution,random partial differential equation and other problems.

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 higher grain production, the more social deprivation? A case study of Henan province in traditional agricultural areas of China

This paper examines the spatial-temporal dynamics of inequality from the perspective of social deprivation in the context of continuous growth of grain production using national census data from 2000 and 2010 for Henan province,China.Our analytical results show an overall level of social deprivation that is high and a widening social deprivation gap at the county level.The social deprivation shows great spatiotemporal heterogeneity,the higher deprived counties are mainly distributed in central and eastern Henan province,while counties with lower social deprivation are clustered in northwestern regions,formed a belt-shape spatial differential between the south(higher deprived counties clustered)and northwest(low deprived counties clustered)Henan in 2000,and changed toward a core-periphery semi annular spatial structure in 2010,the low deprived counties surrounded by high deprived counties.The social deprivation shows a"west low and east high"spatial pattern,similar to the grain production in Henan province.Socioeconomic development level was low in most counties in Yudong plain despite of keeping the continuous increase of grain production,meaning the higher grain output did not result in the more social development expected in Chinese traditional agricultural areas,and the regional disparity is expected to increase in the near future if development conditions are not changed,which could inspire more targeted rural governance options.

HOSVD-based LPV modeling and mixed robust H_2/H_∞ control design for air-breathing hypersonic vehicle

This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying（LPV） controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition（HOSVD） approach.The design of hypersonic flight control systems is highly challenging due to the enormous complexity of the vehicle dynamics and the presence of significant uncertainties.Motivated by recent results on both LPV control and tensor-product（TP） model transformation approach,the velocity and altitude tracking control problems for the air-breathing hypersonic vehicle is reduced to that of a state feedback stabilizing controller design for a polytopic LPV system with guaranteed performances.The controller implementation is converted into a convex optimization problem with parameterdependent linear matrix inequalities（LMIs） constraints,which is intuitively tractable using LMI control toolbox.Finally,numerical simulation results demonstrate the effectiveness of the proposed approach.

Some Inequalities for L_p-Dual Mixed Quermassintegrals

Wang and Zhang defined a type of Lp-dual mixed quermassintegrals based on the Lp-radial combinations and dual quermassintegrals of star bodies. In the article, the product inequalities for this Lp-dual mixed quermassintegrals are established. As the applications, we obtain the lower bounds of dual quermassintegrals product. Further, the Brunn-Minkowski type inequality and the cycle inequality for the Lp-dual mixed quermassintegrals are given.

Sharpness of some properties of weighted modulation spaces

We obtain some optimal properties on weighted modulation spaces. We find the necessary and sufficient conditions for product inequalities, convolution inequalities and embedding on weighted modulation spaces. Especially, we establish the analogue of the sharp Sobolev embedding theorem on weighted modulation spaces.