相关论文: Norm inequalities related to the matrix geometric …

In the current note, we investigate the mathematical relations among the weighted arithmetic mean-geometric mean (AM-GM) inequality, the H\"{o}lder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical…

We assume that the forecast error follows a probability distribution which is symmetric and monotonically non-increasing on non-negative real numbers, and if there is a mismatch between observed and predicted value, then we suffer a loss.…

We will consider about some inequalities on operator means for more than three operators, for instance, ALM and BMP geometric means will be considered. Moreover, log-Euclidean and logarithmic means for several operators will be treated.

The simplex method in Linear Programming motivates several problems of asymptotic convex geometry. We discuss some conjectures and known results in two related directions -- computing the size of projections of high dimensional polytopes…

In this paper we offer a metric similar to graph edit distance which measures the distance between two (possibly infinite)weighted graphs with finite norm (we define the norm of a graph as the sum of absolute values of its edges). The main…

Well-known subadditivity results for positive operators (of Brown-Kosaki and Rotfeld/Ando-Zhan types) are extended to Hermitian and normal ones. Applications to Cartesian decomposition and block-matrices are given.

Let H be a positive semidefinite matrix partitioned into Hermitian blocks. Then, up to a direct sum operation, H is the average of matrices isometrically congruent to its partial trace. A few corollaries are given, related to important…

Matrix concentration inequalities give bounds for the spectral-norm deviation of a random matrix from its expected value. These results have a weak dimensional dependence that is sometimes, but not always, necessary. This paper identifies…

There are two natural metrics defined on an arbitrary convex cone: Thompson's part metric and Hilbert's projective metric. For both, we establish an inequality giving information about how far the metric is from being non-positively curved.

In this article we derive some polynomial inequalities for Mertens functions.

We describe the mathematical properties of pairwise comparisons matrices with coefficients in an arbitrary group. We provide a vocabulary adapted for the description of main algebraic properties of inconsistency maps, describe an example…

A geometrical interpretation of the $G$-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of…

This note presents a summary and review of various conditions and characterizations for matrix stability (in particular diagonal matrix stability) and matrix stabilizability.

In this paper, we introduce several geometric characterizations for strong minima of optimization problems. Applying these results to nuclear norm minimization problems allows us to obtain new necessary and sufficient quantitative…

Methods of determination of constants of the Standard Model are considered. The constants values obtained now are presented and experiments for improving some values are pointed out. A few possible generalized models are considered together…

We present a generalization of the notion of an algebra norm relevant to real finite-dimensional unital associative algebras. Among other things, this leads to a novel set of algebra isomorphism invariants, some of which are computationally…

We study one-dimensional integral inequalities, with quadratic integrands, on bounded domains. Conditions for these inequalities to hold are formulated in terms of function matrix inequalities which must hold in the domain of integration.…

Eve (2003), studied seven means from geometrical point of view. These means are \textit{Harmonic, Geometric, Arithmetic, Heronian, Contra-harmonic, Root-mean square and Centroidal mean}. Some of these means are particular cases of Gini's…

A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.

Certain new inequalities for the sums of factorials are presented.