A pointwise version of the Howard–Bezem notion of hereditary majorization is introduced which has various advantages, and its relation to the usual notion of majorization is discussed. This pointwise majorization of primitive recursive functionals (in the sense of Gödel’s T as well as Kleene/Feferman’s P̂R) is applied to systems of intuitionistic and classical arithmetic (H and Hc) in all finite...

Abstract Background and Aims Type 2 diabetes (T2D) is one of the prominent causes for chronic kidney disease (CKD) leading to end-stage renal failure. Traditionally, prevention retardation CKD was attempted with effective glycemic blood pressure control. In recent times sodium glucose co-transporter inhibitors (SGLT-2is), glucagon-like peptide 1 receptor agonists (GLP1-RA), non-steroidal minera...

In this paper we generalize (finite) block diagonal matrices to infinite dimensions and then by using row stochastic (as a special case), define the relation < bdr on c0, which is said majorization. We also obtain some important properties of Pbdr, set all bounded linear operators T : c0 ? c0; preserve Further, it obtained necessary conditions for operator be preserver majorization bdr. Also...

for $a,bin m_{nm},$ we say that $a$ is left matrix majorized (resp. left matrix submajorized) by $b$ and write $aprec_{ell}b$ (resp. $aprec_{ell s}b$), if $a=rb$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $r.$ moreover, we define the relation $sim_{ell s} $ on $m_{nm}$ as follows: $asim_{ell s} b$ if $aprec_{ell s} bprec_{ell s} a.$ this paper characterizes all linear p...

for vectors x, y ∈ rn, it is said that x is left matrix majorizedby y if for some row stochastic matrix r; x = ry. the relationx ∼` y, is defined as follows: x ∼` y if and only if x is leftmatrix majorized by y and y is left matrix majorized by x. alinear operator t : rp → rn is said to be a linear preserver ofa given relation ≺ if x ≺ y on rp implies that t x ≺ ty onrn. the linear preservers o...