Related papers: Angles, triangle inequalities, correlation matrice…
We present some necessary and/or sufficient conditions for the positivity problem of three-term recurrence sequences. As applications we show the positivity of diagonal Taylor coefficients of some rational functions in a unified approach.…
A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent…
We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities.…
Despite the moduli space of triangles being three dimensional, we prove the existence of two triangles which are not isometric to each other for which the first, second and fourth Dirichlet eigenvalues coincide, establishing a numerical…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.
We consider mixed integer linear sets defined by two equations involving two integer variables and any number of non-negative continuous variables. The non-trivial valid inequalities of such sets can be classified into split, type 1, type…
In this paper, we establish several inequalities for different convex mappings that are connected with the Riemann-Liouville fractional integrals. Our results have some relationships with certain integral inequalities in the literature.
We study the effects on length spaces imposed by quadratic inequalities on the six distances between the points in every quadruple.
We establish a sharp inequality between the blocks of positive partitioned matrices and conjecture a triangle type inequality for contractions: Given three contactions A,B,C, we conjecture that the constant c=3/4 is sharp in the triangle…
A polynomial triangle is an array whose inputs are the coefficients in integral powers of a polynomial. Although polynomial coefficients have appeared in several works, there is no systematic treatise on this topic. In this paper we plan to…
In this paper, the versions of trigonometric functions of certain known inequalities for hyperbolic ones are proved, and then corresponding inequalities for means are presented.
To better understand the algebra $\mathcal{M}_n$ of all $n\times n$ complex matrices, we explore the class of accretive matrices. This class has received renowned attention in recent years due to its role in complementing those results…
Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in complex Hilbert spaces are given. Applications for complex-valued functions are provided as well.
We introduce a 3-dimensional categorical structure which we call intercategory. This is a kind of weak triple category with three kinds of arrows, three kinds of 2-dimensional cells and one kind of 3-dimensional cells. In one dimension, the…
We construct a converging geometric iterated function system on the moduli space of ordered triangles, for which the involved functions have geometric meanings and contain a non-contraction map under the natural metric.
The problems of continuation of a partially defined metric and a partially defined ultrametric were considered in (O. Dovgoshey, O. Martio and M. Vuorinen, Metrization of weighted graphs, Ann. Comb., 17:455--476, 2013) and (A. A. Dovgoshey…
We review some convexity inequalities for Hermitian matrices an add one more to the list.
The 3 X 3 CKM matrix defines six unitarity triangles in the complex plane, which will be carefully explored in the LHCb experiment and at the Super-B factory. We calculate the running effects of nine different inner angles and eighteen…