‎In this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy‎, ‎{em Math‎. ‎Inequal‎. ‎Appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎Meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...

We describe the Minimal Model Program in the family of Q-Gorenstein projective horospherical varieties, by studying a family of polytopes defined from the moment polytope of a Cartier divisor of the variety we begin with. In particular, we generalize the results on MMP in toric varieties due to M. Reid, and we complete the results on MMP in spherical varieties due to M. Brion in the case of hor...

3 General results on summability and duality 4 3.1 Total algebras and duality . . . . . . . . . . . . . . . . . . . . . . 4 3.1.1 Series and infinite sums . . . . . . . . . . . . . . . . . . . 4 3.1.2 Summable families in Hom spaces. . . . . . . . . . . . . . 5 3.1.3 Substitutions . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Theorem of Cartier-Quillen-Milnor-Moore (analytic form) . ....

The study of free Baxter algebras was started by Rota and Cartier thirty years ago. We continue this study by applying two recent constructions of free Baxter algebras. We investigate the basic structure of a free Baxter algebra, and characterize in detail when a free Baxter algebra is a domain or a reduced algebra. We also describe the nilpotent radical of a free Baxter algebra when it is not ...

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We study the location and the size of the roots of Steiner polynomials of convex bodies in the Minkowski relative geometry. Based on a problem of Teissier on the intersection numbers of Cartier divisors of compact algebraic varieties it was conjectured that these roots have certain geometric properties related to the inand circumradius of the convex body. We show that the roots of 1-tangential ...

We introduce several definitions within the framework of vertex and conformal algebras which are analogous to some important concepts classical Lie theory. Most importantly, we define formal laws, correspond notion group law. prove suitable vertex/conformal versions a number results such as Milnor-Moore theorem, Cartier duality, equivalence between laws algebras.

We consider Lie algebroids over algebraic spaces (in short we call it as a-spaces) by considering the sheaf of Lie-Rinehart algebras. discuss about properties universal enveloping algebroid U(OX,L) a L an a-space (X,OX). This is done sheafification presheaf algebras for review extent to which structure (over special resembles bialgebras. In sequel present version Poincare-Birkhoff-Witt theorem ...