For a complete connected Riemannian manifold M let V∈C2(M) be such that μ(dx)=e−V(x)vol(dx) is probability measure on M. Taking μ as reference measure, we derive inequalities for measures linking relative entropy, Fisher information, Stein discrepancy and Wasserstein distance. These strengthen in particular the famous log-Sobolev transportation-cost inequality extend so-called Entropy/Stein-dis...

In this note we prove that the maximally defined operator associated with the Dirac-type differential expression M(Q) = i ( d dx Im −Q −Q − d dx Im ) , where Q represents a symmetric m × m matrix (i.e., Q(x) = Q(x) a.e.) with entries in L loc (R), is J -self-adjoint, where J is the antilinear conjugation defined by J = σ1C, σ1 = ( 0 Im Im 0 ) and C(a1, . . . , am, b1, . . . , bm) = (a1, . . . ,...

In this paper, we prove a Stolarsky type inequality for pseudo-integrals. More precisely, we show that: ∫ sup [0,1] f(x 1 a+b )dx ≥ ( ∫ sup [0,1] f(x 1 a )dx ) ̄ ( ∫ sup [0,1] f(x 1 b )dx ) , where a, b > 0, f : [0, 1] → [0, 1] is a continuous and strictly decreasing function ( strictly increasing function ) and μ is the sup-measure the same as Theorem 2.4. Also ̄ is represented by an increasing...

We determine the best constant K and extremals of the Opial-type inequality ∫ b a |yy ′| dx ≤ K(b − a) ∫ b a |y ′|2 dx where y is required to satisfy the boundary condition ∫ b a y dx = 0. The techniques employed differ from either those used recently by Denzler to solve this problem or originally to prove the classical inequality; but they also yield a new proof of that inequality.

In this article we give different sufficient conditions for inequality (∫ b a f(x)dx )β ≥ ∫ b a f(x)dx to hold.

BACKGROUND We critically evaluated the available evidence on genomic tests in breast cancer to define their prognostic ability and likelihood to determine treatment benefit. DESIGN Independent evaluation of six genomic tests [Oncotype Dx™, MammaPrint(®), Genomic Grade Index, PAM50 (ROR-S), Breast Cancer Index, and EndoPredict] was carried out by a panel of experts in three parameters: analyti...

Background: Innovation is a critical success factor of digital transformation (DX). Previous research has shown that open innovation (OI) can help companies accelerate DX and improve their business performance. Objective: This study develops conceptual OI framework to support (OIDX) provides an overview the dimensions. in this refers Open 2.0. Methods: We review previous on dimensions, identify...

Percutaneous skin prick tests (SPT) have been considered the preferred method for confirming IgE-mediated sensitization. This reliable and minimally invasive technique correlates with in vivo challenges, has good reproducibility, is easily quantified, and allows analyzing multiple allergens simultaneously. Potent extracts and a proficient tester improve its accuracy. Molecular-based allergy dia...

Exposure to glucocorticoids leads to numerous changes in various biological systems including the reproductive system. The aim of the present work was to find out whether dexamethasone (Dx) treatment of adult female rats would influence the histological and morphometric characteristics of the pituitary gonadotrophic cells (luteinizing--LH cells and follicle stimulating--FSH cells). One group of...