It is a classical inequality that the minimum of the ratio of the (weighted) arithmetic mean to the geometric mean of a set of positive variables is equal to one, and is attained at the center of the positivity cone. While there are numerous proofs of this fundamental homogeneous inequality, in the presence of an arbitrary subspace, and/or the replacement of the arithmetic mean with an arbitrar...

The phase structure of dense quark matter in the two color case has been investigated with nonzero baryon $${{\mu }_{{\text{B}}}}$$ , isospin }_{{\text{I}}}}$$ and chiral }_{{{\text{I5}}}}}$$ chemical potentials. It shown mean-field approximation that there exist three dualities, one them between phases spontaneous symmetry breaking condensation charged pions, found case. other dual symmetries ...

We consider convex programming problems in a canonical homogeneous format, a very general form of Karmarkar’s canonical linear programming problem. More specifically, by homogeneous programming we shall refer to the problem of testing if a homogeneous convex function has a nontrivial zero over a subspace and its intersection with a pointed convex cone. To this canonical problem, endowed with a ...