scholarly journals Schur convexity of mixed mean of n variables involving three parameters

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3663-3674
Author(s):  
Dong-Sheng Wang ◽  
Huan-Nan Shi ◽  
Chun-Ru Fu
Keyword(s):  
Lower Bound ◽  
Mixed Mean ◽  
Ky Fan ◽  
Schur Convexity ◽  
Harmonic Convexity

In this paper, we discuss the Schur convexity, the Schur geometric convexity and Schur harmonic convexity of the mixed mean of n variables involving three parameters. As an application, we have established some inequalities of the Ky Fan type related to the mixed mean of n variables, and the lower bound inequality of Gini mean for n variables is given.

Combo separability criteria and lower bound on concurrence

2021 ◽  
Author(s):  
Zangi Sultan ◽  
Jiansheng Wu ◽  
Cong-Feng Qiao
Keyword(s):  
Lower Bound ◽  
Correlation Matrix ◽  
Density Operator ◽  
Singular Values ◽  
Quantum Information Theory ◽  
Separability Criteria ◽  
The Given ◽  
Ky Fan ◽  
Natural Way ◽  
Extract Information

Abstract Detection and quantification of entanglement are extremely important in quantum information theory. We can extract information by using the spectrum or singular values of the density operator. The correlation matrix norm deals with the concept of quantum entanglement in a mathematically natural way. In this work, we use Ky Fan norm of the Bloch matrix to investigate the disentanglement of quantum states. Our separability criterion not only unifies some well-known criteria but also leads to a better lower bound on concurrence. We explain with an example how the entanglement of the given state is missed by existing criteria but can be detected by our criterion. The proposed lower bound on concurrence also has advantages over some investigated bounds.

scholarly journals Colorful Subhypergraphs in Kneser Hypergraphs

10.37236/3573 ◽  
2014 ◽  
Vol 21 (1) ◽  
Author(s):  
Frédéric Meunier
Keyword(s):  
Lower Bound ◽  
Chromatic Number ◽  
Bipartite Graphs ◽  
Uniform Hypergraph ◽  
Proper Coloring ◽  
Kneser Graph ◽  
Complete Bipartite Graphs ◽  
Definition Of ◽  
Ky Fan

Using a $\mathbb{Z}_q$-generalization of a theorem of Ky Fan, we extend to Kneser hypergraphs a theorem of Simonyi and Tardos that ensures the existence of multicolored complete bipartite graphs in any proper coloring of a Kneser graph. It allows to derive a lower bound for the local chromatic number of Kneser hypergraphs (using a natural definition of what can be the local chromatic number of a uniform hypergraph).

scholarly journals Schur-Convexity of a Class of Elementary Symmetric Composite Functions

2021 ◽  
Vol 66 (1) ◽  
pp. 1-19
Author(s):  
Huan-Nan Shi ◽  
◽  
Tao Zhang ◽  
Bo-Yan Xi ◽  
◽  
...  
Keyword(s):  
Convex Function ◽  
Symmetric Functions ◽  
Composite Function ◽  
Elementary Symmetric Functions ◽  
Composite Functions ◽  
Schur Convex ◽  
Harmonically Convex Function ◽  
Geometrically Convex Function ◽  
Schur Convexity ◽  
Harmonic Convexity

In this paper, using the properties of Schur-convex function, Schur-geometrically convex function and Schur-harmonically convex function, we provide much simpler proofs of the Schur-convexity, Schur-geometric convexity on and Schur-harmonic convexity on for a composite function of the elementary symmetric functions.

scholarly journals The generalized Heronian mean and its inequalities

2006 ◽  
pp. 60-75 ◽  
Author(s):  
Kaizhong Guan ◽  
Huantao Zhu
Keyword(s):  
Ky Fan ◽  
Schur Convexity ◽  
Heronian Mean

In this paper, a class of ratio inequalities for the generalized Heronian mean of two numbers are established. Some Ky Fan type inequalities are also proved. We define the generalized Heronian mean in n variables, whose properties, including Schur-convexity, are investigated.

scholarly journals Schur-convexity for a mean of two variables with three parameters

Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6643-6651
Author(s):  
Chun-Ru Fu ◽  
Dongsheng Wang ◽  
Huan-Nan Shi
Keyword(s):  
Mean Value ◽  
Mean Value Inequalities ◽  
Schur Convexity ◽  
Harmonic Convexity

Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a mean of two variables with three parameters are investigated, and some mean value inequalities of two variables are established.

scholarly journals Schur-Convexity for Elementary Symmetric Composite Functions and Their Inverse Problems and Applications

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2351
Author(s):  
Tao Zhang ◽  
Alatancang Chen ◽  
Huannan Shi ◽  
B. Saheya ◽  
Boyan Xi
Keyword(s):  
Inverse Problems ◽  
Composite Function ◽  
Dual Form ◽  
Composite Functions ◽  
Special Means ◽  
Schur Convexity ◽  
Harmonic Convexity ◽  
New Inequalities

This paper investigates the Schur-convexity, Schur-geometric convexity, and Schur-harmonic convexity for the elementary symmetric composite function and its dual form. The inverse problems are also considered. New inequalities on special means are established by using the theory of majorization.

The least distance between extremums and minimal period of solutions to autonomous vector differential equations

2019 ◽  
Vol 485 (2) ◽  
pp. 142-144
Author(s):  
A. A. Zevin
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Lipschitz Constant ◽  
Minimal Period ◽  
Arbitrary Vector ◽  
Vector Norm ◽  
Sharp Lower Bound

Solutions x(t) of the Lipschitz equation x = f(x) with an arbitrary vector norm are considered. It is proved that the sharp lower bound for the distances between successive extremums of xk(t) equals π/L where L is the Lipschitz constant. For non-constant periodic solutions, the lower bound for the periods is 2π/L. These estimates are achieved for norms that are invariant with respect to permutation of the indices.

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